Myalgic Encephalomyelitis Chronic Fatigue at the National Institutes of Health

Introduction

I summarize in Table 1 the results of a single-center, exploratory, cross-sectional study of post-infectious Myalgic Encephalomyelitis (PI-ME/CFS) conducted by the National Institute of Health, from October 2016 to January 2022. All the details of the study are available at this address. I run, for each measure, a statistical test. The analysis was performed by a custom R script (see the last paragraph).

Results

After correction for multiple comparisons, the only statistically significant difference between patients and controls is the number of bacterial species in the stool sample, which is lower in patients than in healthy controls (LTK, measure 11). If we do not consider the correction for multiple comparisons, we find also a lower oxygen consumption at the anaerobic threshold during the cardiopulmonary exercise test (ATVO2rel, measure 1) and a reduced variability in heart rate over a 24-hour period (SDNNi, measure 9). Perhaps surprisingly, both the total power consumed by the individuals as measured by a metabolic chamber (TBEU, 3) and the oxygen consumption of peripheral blood mononuclear cells per unit of time (MEFA, 8), are the same in patients and controls.

Table 1. For the meaning of the labels in the Test column, see below. The second column is the number associated with the test on the Results page (here). Healthy controls are indicated with the letter A, ME/CFS patients with B. The number of participants is labeled with the letter n. The means are marked with the letter m and the standard errors with the letter s. The p values are calculated with the double-tailed Student’s T-test and the corrected p values (last column) are computed employing the Benjamini-Hochberg correction.

ATVO2rel [1]. The Relative Volume of Oxygen at the Anaerobic Threshold (ATVO2rel) was determined during a cardiopulmonary exercise test (CPET). ATVO2rel represents the volume of oxygen consumed when a participant reaches AT, adjusted for their weight during the CPET. Results compared Healthy Volunteer Participants to ME/CFS Participants. Unit of Measure: mL/kg/min.

RER [2]. The Respiratory Exchange Ratio (VCO2/VO2) was determined during a cardiopulmonary exercise test (CPET). VCO2/VO2 is calculated by measuring the volume of carbon dioxide and oxygen the participant breathes during CPET. When the volume of carbon dioxide exceeds that of oxygen, it reflects a change from aerobic metabolism to anaerobic metabolism. When a participant has a Respiratory Exchange Ratio (RER) during CPET that is equal to or greater than 1.1 it is considered a sufficient exercise effort. Results compared Healthy Volunteer Participants to ME/CFS Participants. Unit of measure: ratio without dimensions.

TBEU [3]. Total body energy use. The total amount of energy expended per unit of time as measured by whole-room indirect calorimetry. This method measures the amount of oxygen consumed and carbon dioxide produced which can be used to calculate the amount of energy produced by biological oxidation and is measured by kilocalories per day. Measures were taken from Healthy and ME/CFS participants. Unit of measure: kcal/day.

WBC [4]. A comparison of the White Blood Cell (WBC) Count, i.e., a measurement of the number of white blood cells in the blood, of the two populations, is reported. Low values can suggest immune deficiencies. High values can suggest infection or inflammation. Blood was collected from healthy and ME/CFS participants at baseline. Unit of measure: number of WBCs(K)/uL.

ESR [5]. A comparison of the results of the Erythrocyte Sedimentation Rate (ESR), i.e., a measure of how quickly red blood cells settle at the bottom of a test tube, in the two populations is reported. A faster-than-normal rate of settling suggests inflammation. Blood was collected from healthy and ME/CFS participants at baseline. Unit of measure: mm/h.

CRP [6]. A comparison of the results of C-Reactive Protein (CRP), i.e., a measurement of a protein that is made by the liver, in the two populations is reported. A higher level than normal suggests inflammation. Blood was collected from healthy and ME/CFS participants at baseline. Unit of measure: mg/L.

WBC_CSF [7]. A comparison of the White Blood cell Count in Cerebrospinal Fluid (WBC in CFS), i.e., a measurement of the number of white blood cells in the cerebrospinal fluid, in the two populations is reported. Higher levels than normal suggest inflammation or infection in the central nervous system. CSF was collected from healthy and ME/CFS participants at baseline. Unit of measure: number of WBCs(K)/uL.

MEFA [8]. Mitochondrial Extracellular Flux Assay. The oxygen consumption rate of peripheral blood mononuclear cells per unit of time when the cells are in their normal, unprovoked state of function measured in Basal (units) was measured in Healthy and ME/CFS participants at baseline. This is a standard measure of mitochondrial respiration that is responsible for providing energy to cells. Unit of measure: Pmol/min.

SDNNi [9]. Effect of Maximal Exertion on Autonomic Function as Measured by SDNNi in Healthy and ME/CFS Participants. Variability of the time between heartbeats can be used to measure alterations in autonomic function. The Standard Deviation of the Normal-to-Normal Intervals (SDNNi) is a measure of the amount of beat-to-beat variability between each normal heartbeat collected over a 24-hour period. These results compare the SDNNi in healthy and ME/CFS participants at baseline. Unit of Measure: ms.

LTK [11]. Stool samples were taken from Healthy and ME/CFS participants at baseline. The number of specific types of bacteria, using the Least Known Taxon (LTK) units, was measured with the Shotgun Metagenomic method. Unit of measure: LTK.

TOVA [12]. The TOVA is a measure of cognitive function that assesses attention and inhibitory control. The test is used to measure a number of variables involving the test taker’s response to either a visual or auditory stimulus measured during a “simple, yet boring, computer game”. These measurements are then compared to the measurements of a group of people without attention disorders who took the T.O.V.A. The range of values for the score, after normalization to the population, is -10 to +10, with a lower score representing a worse attention score. The test was administered to Healthy and ME/CFS participants at baseline. Unit of measure: score on a scale.

PASAT [12]. The PASAT is a measure of cognitive function that assesses auditory information processing speed and flexibility, as well as calculation ability. Single digits are presented every 3 seconds and the patient must add each new digit to the one immediately prior to it. The test score is the total number of correct trials out of a possible 60. The test was administered to Healthy and ME/CFS participants at baseline. Unit of measure: score on a scale.

Methods

I manually copied in a csv file the results of the measures (including the number of participants of each measure, the mean values, and their standard errors) taken from the results page of the NIH website (here). I then read the file with a custom R script (see below) that performs the Student’s T-test (double-tailed) for each comparison and corrects the p values with the Benjamini-Hochberg method. When the interquartile range (IQR) was reported, I derived the standard deviation (SD) according to the formula IQR = 1.35*SD. The analysis was performed considering only the means and the standard deviations because the actual distributions of the measures were not available.

Download the csv file with the results: Data.csv

The R script that performs the statistical analysis on Data.csv:

# file name: NIH_ME_CFS
#
# Reading the input
#
NIH_data<-read.csv("Data.csv",sep=";",header = T)
attach(NIH_data) 
len<-length(Test) # number of tests
#
p<-c() # p values for all the comparisons
options(digits=2) # number of digits
#
# Student's T-test
#
for (i in 1:len) {
  sp<-sqrt(((nA[i]-1)*sA[i]^2 + (nB[i]-1)*sB[i]^2)/(nA[i]+nB[i]-2)) 
  TS<-abs(mA[i]-mB[i])/(sp*sqrt(1/nA[i] + 1/nB[i])) 
  p[i]<-2*pt(-TS,df=nA[i]+nB[i]-2,lower.tail = TRUE, log.p = FALSE)   
}
#
# Correction
#
p_cor<-p.adjust(p, method = "hochberg")
#
# Writing the results
#
NIH_statistics<-data.frame(Test,Test_N,nA,nB,mA,mB,sA,sB,p,p_cor)

The current outbreak of Chikungunya in Paraguay

After a brief overview of the epidemiology and clinical picture of Chikungunya, I analyze the evolution of the current epidemic in Paraguay.

Introduction

An increase in the cases of Chikungunya (CHIKV) has been registered in Paraguay since October 2022 (40th epidemiological week), with most of the cases localized in the city of Asunción and in the neighboring department of Central (Ministerio de la Salud, CDC). While in the year 2015, a total of 4297 cases were reported in the departments of Asunción and Central, and in 2016 this number was 1239, as of the 3rd of March of 2023 the number of notified cases in these two departments is already about 9000. The magnitude of the current epidemic episode, in comparison with the previous ones, can be fully appreciated by looking at Figure 1, from the Alerta Epidemiológica N° 3/2023 (here).

Figure 1. Weekly cases of Chikungunya in Paraguay from 2015 to the 7th week of 2023, from the Alerta Epidemiológica N° 3/2023, Ministerio de la Salud, Paraguay (here).

Epidemiology of Chikungunya

CHIKV is a disease due to an RNA virus in the alphavirus genus (of the family Togaviridae), transmitted to humans by mosquitos of the genus Aedes. Homo sapiens is the principal reservoir of the pathogen. The disease is endemic in the tropical areas of Africa and Asia, it is characterized in the acute phase by high fever and polyarthralgia. The name comes from a Tanzanian language and it means “to walk bent over”, “to be contorted”, and it alludes to the abnormal gait of the victims, due to joint and muscle pain. In 2013 the disease appeared for the first time in the Caribbean sea (Saint Martin Island) and in the following years it spread in the Americas, from north to south (Yactayo S. et al. 2016).

Figure 2. Weekly cases of Chikungunya in the Dominican Republic from the 8th week of 2014 to the 39th. From Ministerio de Salud Pública, República Dominicana (Pimentel R et al. 2014).

We know from previous outbreaks outside the Americas that the percentage of the population that develops the disease during an epidemic episode (attack rate) goes from 10 to 75% and that those who become infected but are asymptomatic are between 17.5 and 27.8% (Ayu Mas S. et al. 2010). During the outbreak of 2014 in the Dominican Republic the attack rate in the main cities of the nation ranged from 40% to 81%; the epidemic episode lasted from the eighth epidemiological week to the 39th of 2014 (see Figure 2) (Pimentel R et al. 2014). After an epidemic episode in the Italian region of Emilia Romagna (summer of 2007), the attack rate was only 10.2% while the percentage of asymptomatic cases was 18% (Moro ML et al. 2010).

Clinical aspects of Chikungunya

The incubation period is typically 3–7 days (range 1–12 days). The most common clinical findings are acute onset of fever and polyarthralgia. Joint pains are usually bilateral, symmetric, and often severe and debilitating. Other symptoms can include headache, myalgia, arthritis, conjunctivitis, nausea, vomiting, or maculopapular rash. Clinical laboratory findings can include lymphopenia, thrombocytopenia, and elevated creatinine. Rare complications include uveitis, retinitis, myocarditis, hepatitis, nephritis, bullous skin lesions, hemorrhage, meningoencephalitis, myelitis, Guillain-Barré syndrome, and cranial nerve palsies. People at risk for more severe disease include neonates exposed intrapartum, older adults (e.g. age > 65 years), and people with underlying medical conditions (e.g., hypertension, diabetes, or cardiovascular disease). The whole paragraph has been taken from (CDC).

While some patients with the acute disease recover fully, severe and debilitating polyarthralgia may persist and become chronic (duration above 3 months to years). Chronic symptoms were reported in up to 64% of the individuals after one year from the acute phase (Ayu Mas S. et al. 2010). After 2.5 years after the epidemic episode that stroke the Island of Curaçao, in the Caribbean Sea in July 2014, of those who developed the acute phase of the disease only 43% fully recovered: 35% were still mildly affected and 22% were highly affected. Highly affected patients reported the highest prevalence of ongoing rheumatic and non-rheumatic/psychological symptoms, with an increased prevalence of arthralgia in the lower extremities, fatigue, and pain (Doran C et al. 2022). Six years after the epidemic episode of CHIKV of 2005-2006 in Reunion Island (Indian Ocean), a follow-up on 252 military employees (95% males, mean age 44 years) compared those who had CHIKV (81) to those who didn’t (171). CHIK+ patients complained of more frequent and intense joint pain than CHIK- (38% vs. 17% declared suffering at least once a week; 48% vs. 16% declared moderate to intense pain, p 0.0001). The frequency of nonrheumatic symptoms such as fatigue, headache, and depression, was markedly higher among CHIK+ subjects (Marimoutou C et al. 2015). In another follow-up study 18 months after the 2005-2006 outbreak of Reunion, it was found that among 362 adult subjects who had reported either rheumatic pain or fatigue at the onset of the infection, 23.9% developed a CFS-like illness while only 7.4% among initially asymptomatic peers did (p< 0.01) (Duvignaud A et al. 2018).

Figure 3. Weekly cases of Chikungunya in Paraguay from the 40th week of 2022 to the 8th of 2023. From Ministerio de Salud Pública, Paraguay (here).

Analysis of the current Chikungunya epidemic episode in Paraguay

I have considered the latest resumen epidemiologico semanal de arbovirosis (as of the 7th of March 2023) with the weekly reported cases of Chikungunya in the whole national territory (Figure 3). I have searched for a differential equation that could describe the evolution of the cumulative number of cases (f). I considered an exponential model, a logistic one, and a Gaussian model. The mathematical details of the analysis and the script that performs the calculations are reported in the following paragraph. The result of the analysis is reported in Figure 4. The best model (according to both the $R^2$ and the statistic test specified in Table 1) is the exponential one, followed by the Gaussian one. The Logistic model of growth does not fit well the data. The Gaussian model predicts that the maximum rate of growth will be reached by the mid of April. If we dismiss the first five weeks, focusing on the latest development of the epidemic, the Gaussian model is more optimistic (while the exponential one does not change much, Figure 5) but the statistical parameters indicate a worse fit (Table 2). In this case, the Gaussian model predicts that the maximum rate of growth has been reached by the mid of February.

Figure 4. Cumulative cases of Chikungunya in Paraguay from the 40th week of 2022 to the 8th of 2023. Experimental data from Ministerio de Salud Pública, Paraguay (here). The best model is the exponential one, followed by the Gaussian; the logistic model of growth is clearly not good. The statistical parameters of the regression models are reported in Table 1.

Figure 5. Cumulative cases of Chikungunya in Paraguay from the 45th week of 2022 to the 8th of 2023 (we skip the first five weeks). Experimental data from Ministerio de Salud Pública, Paraguay (here). The statistical parameters of the regression models are reported in Table 2.

Table 1. Statistical parameters for the regression models. The statistical test on the coefficients is the standard test used for the angular coefficient of the linear regression for the logistic and the exponential model (with $H_0:\beta_0=0$ ), while in the case of the Gaussian model, it is an F-test. We consider here the first available data point as the starting point for the regressions.

Table 2. As in Table 1, but in this case, we start from the fifth week available.

Further reading (Spanish)

Informe del Ministerio de Salud Publica de Paraguay, 3 marzo 2023 (R).

Comunicado de La Universidad Nacional de Asunción, 3 marzo 2023 (R).

Noticiero de ADN, 8 marzo 2023 (R).

Updates

I will add here the simulations based on the updates by the Ministerio de la Salud of Paraguay. I note that each time there is an update of the page containing the data (this one), not only there is the add of the data of a week, but there is also a substantial change in the cases for all the previous weeks (not sure why this is the case, I assume that notified case must then be verified, so the number will be adjusted over time).

Figure 5.b. Cumulative cases of Chikungunya in Paraguay from the 40th week of 2022 to the 8th of 2023. For the simulation, we use only the last 10 weeks available. Experimental data from Ministerio de Salud Pública, Paraguay (here). F-test: 1.85e-06 (logistic), 1.74e-08 (exponential), 4.312e-07 (gaussian). Update of 10th March 2023.

Figure 5.b.2. Weekly cases of Chikungunya in Paraguay from the 40th week of 2022 to the 8th of 2023. For the simulation, we use only the last 10 weeks available. Experimental data from Ministerio de Salud Pública, Paraguay (here). F-test: 1.85e-06 (logistic), 1.74e-08 (exponential), 4.312e-07 (gaussian). Update of 10th March 2023.

Mathematical notes

The logistic model of growth is described by the differential equation

(1) $\frac{df(t)}{dt}\,=\,f(t)\left(r-\frac{r}{k}f(t)\right)$

Its solution is given by

(2) $f(t)\,=\frac{k}{1+\left(\frac{k}{f_0}-1\right)}e^{-r\left(t-t_0\right)}$

We can transform eq.1 into a linear relationship by writing

(3) $\frac{\frac{df(t)}{dt}}{f(t)}\,=\,r\,-\,\frac{r}{k}f(t)$

We then define the response variable $Y\,=\,\frac{\frac{df(t)}{dt}}{f(t)}$ and the explanatory variable $X\,=\,f(t)$ and we perform a linear regression between them (Figure 6), which gives us the parameters

$\beta_0\,=\,r,\,\beta_1\,=\,\frac{r}{k}$

From these two relations, we can calculate r and k; by substituting them into eq. 2 we get the logistic curve of Figure 4 and Figure 5.

The exponential model of growth is described by the (1) for $k\rightarrow\infty$ and the solution is

(4) $e^{r\left(t\,-\,t_0\right)+\ln(f_0)}$

By taking the linear logarithm of both hands of the equation, we have a linear relationship and we can perform a linear regression.

The gaussian model cannot be reduced to a linear model, in general (only when the derivative is smaller than 1). But it can be reduced to a polynomial model of the second order. We consider the differential equation

(5) $\frac{df(t)}{dt}\,=\,Ke^{-\frac{1}{2}\left(\frac{t-\mu}{\sigma}\right)^2}$

whose solution is

(6) $f(t)\,=\,f(t_0)+\sigma K \sqrt{2\pi}\left[\Phi\left(\frac{t-\mu}{\sigma}\right)-\Phi\left(\frac{t_0-\mu}{\sigma}\right)\right]$

If we now take the natural logarithm of both hands of the equation, we get a linear relationship:

(7) $\ln\left(\frac{df(t)}{dt}\right)\,=\,-\frac{1}{2\sigma^2}t^2+\frac{\mu}{\sigma^2}t-\frac{\mu^2}{2\sigma^2}+\ln (K)$

We can now perform a polynomial regression and calculate the unknowns K, $\mu$ , $\sigma$ . Once we know them, we put them into eq. 6 and we have the red curves in Figure 4 and Figure 5. The R script used to perform the regressions and to plot all the figures is reported after the figures.

Figure 6. Linear regression for the logistic model. Starting from the first data point available.

Figure 7. Linear regression for the exponential model. Starting from the first data point available.

Figure 8. Polynomial regression for the gaussian model. Starting from the first data point available.

# file name: chikungunya
#
# Asunciòn, 5 marzo 2023
#
# read the data
#
mydata<-read.csv(file = "Notificaciones Chikungunya.csv", header = T, sep =";")
#
# we define the vector for the cumulative number of cases (updated every week)
#
f<-mydata$CHIKV_not_PY_cum # cases
len<-length(f)
fc<-8 # weeks of forecast
stl<-1 # starting week for logistic regression
ste<-1 # starting week for exponential regression
stg<-1 # starting week for gaussian regression
#
#---------------------------------------------------------
# Logistic growth
#---------------------------------------------------------
#
# we define X (explanatory) and Y (response)
#
st<-stl # starting week
X<-f[st:(len-1)]
n<-length(X)
Y<-c()
for (h in 1:n) {
  i<-st+h-1
  Y[h]<-f[i+1]-f[i]
  Y[h]<-Y[h]/f[i]
}
#
# linear regression
#
Lin_re<-lm(Y~X) 
coefficients<-coef(Lin_re)
B0<-coefficients[[1]]
B1<-coefficients[[2]]
#
# we calculate the residues
#
R<-0
for (i in 1:n) {
  R[i]<-Y[i]-B0-B1*X[i]
}
#
# plotting the linear regression and the residues
#
fitted<-predict(Lin_re) # it contains the line of the regression
#
plot(X, Y, xlab = "f", ylab = "f'/f", pch=21,bg="blue")
abline(lm(Y~X),lwd=1.5, col="black") 
for (i in 1:n) lines (c(X[i],X[i]),c(Y[i], fitted[i]), col="red", lwd=2.5)
grid (col="black",lty="dashed",lwd=1.0)
#
# We calculate and store the logistic curve
#
t<-c(1:(len+fc)) # weeks
r<-B0
k<--r/B1
f2<-c()
t2<-c()
for (h in 1:(n+fc)) {
  i<-st+h-1
  den<-1+(k/f[st]-1)*exp(-r*(t[i]-t[st]))
  f2[h]<-k/den
  t2[h]<-t[i]
}
#
#---------------------------------------------------------
# Exponential growth
#---------------------------------------------------------
#
st<-ste
X<-t[st:(len-1)]
n<-length(X)
Y<-c()
for (h in 1:n) {
  i<-st+h-1
  Y[h]<-log(f[i])
}
#
# linear regression
#
Exp_re<-lm(Y~X) 
coefficients<-coef(Exp_re)
B0<-coefficients[[1]]
B1<-coefficients[[2]]
#
# we calculate the residues
#
R<-0
for (i in 1:n) {
  R[i]<-Y[i]-B0-B1*X[i]
}
#
# plotting the linear regression and the residues
#
fitted<-predict(Exp_re) # it contains the line of the regression
#
plot(X, Y, xlab = "log(cases)", ylab = "weeks", pch=21,bg="blue")
abline(lm(Y~X),lwd=2.5, col="black") 
for (i in 1:n) lines (c(X[i],X[i]),c(Y[i], fitted[i]), col="red", lwd=2.5)
grid (col="black",lty="dashed", lwd=1.5)
#
# We calculate and store the exponential curve
#
t<-c(1:(len+fc)) # weeks
f3<-c()
t3<-c()
for (h in 1:(n+fc)) {
  i<-st+h-1
  f3[h]<-exp(B0+B1*t[i])
  t3[h]<-t[i]
}
#
#---------------------------------------------------------
# Gaussian growth
#---------------------------------------------------------
#
st<-stg # starting week
X<-t[st:(len-1)]
n<-length(X)
Y<-c()
for (h in 1:n) {
  i<-st+h-1
  Y[h]<-log(f[i+1]-f[i])
}
#
# polynomial regression of the second order
#
Gau_re<-lm(Y~X+I(X^2))
coefficients_P<-coef(Gau_re)
B0P<-coefficients_P[[1]]
B1P<-coefficients_P[[2]]
B2P<-coefficients_P[[3]]
#
# we calculate the residues
#
R<-0
for (i in 1:n) {
  R[i]<-Y[i]-B0-B1*X[i]
}
#
# We plot the regression
#
plot(X,Y,pch=21,col="black",bg="red",xlim=c(X[1],X[n]),ylim=c(Y[1],max(Y)),xlab="weeks",ylab="log(f')")
par(new=T)
plot(X,(X^2)*B2P+X*B1P+B0P,type="l",col="red",lty=6,lwd=2,xlim=c(X[1],X[n]),ylim=c(Y[1],max(Y)),xlab="",ylab="")
#
# We calculate and store the logistic curve
#
s<-sqrt(-1/(2*B2P))
mu<-(s^2)*B1P
lnK<-B0P+0.5*(mu/s)^2 
K<-exp(lnK)
t<-c(1:(len+fc)) # weeks
f4<-c()
t4<-c()
for (h in 1:(n+fc)) {
  i<-st+h-1
  mul<-pnorm((t[i]-mu)/s) - pnorm((t[st]-mu)/s)
  f4[h]<-f[st]+s*K*sqrt(2*pi)*mul
  t4[h]<-t[i]
}
#
# We plot the actual data and the logistic fit
#
plot(t[1:len],f,xlab="semanas",ylab="notificaciones",pch=21,bg="blue",xlim=c(1,t[len+fc]),
     ylim=c(0,2*f[len])) # experimental data
par(new=T)
plot(t2,f2,xlab="",ylab="",xlim=c(1,t[len+fc]),ylim=c(0,2*f[len]),type="l",lty=4,lwd=2,col="black") # fitted log
par(new=T)
plot(t3,f3,xlab="",ylab="",xlim=c(1,t[len+fc]),ylim=c(0,2*f[len]),type="l",lty=2,lwd=2,col="black") # fitted exp
par(new=T)
plot(t4,f4,xlab="",ylab="",xlim=c(1,t[len+fc]),ylim=c(0,2*f[len]),type="l",lty=2,lwd=2,col="red") # fitted exp
grid (col="black",lty=1, lwd=1)
abline(v=c(14,18.5,22.5,27),col="black",lty=4,lwd=1.5)
text(x=c(16,20.5,25),y=c(5000,5000,5000),labels = c("Jan","Feb","Mar"))
legend("topleft",legend=c("logistic","exponential","gaussian"),lty=c(2,2,2),col=c("black","black","red"),lwd=c(4,2,2))
summary(Lin_re)
summary(Exp_re)
summary(Gau_re)

Analysis of a summary statistics generated from the UK Biobank database: new potential risk loci for ME/CFS and not otherwise specified chronic asthenia

… the only thing that is arbitrary about the various orders of a set of terms is our attention, for the terms themselves have always all the orders of which they are capable.
Bertrand Russell, Introduction to Mathematical Philosophy

Full-text article

I present here an analysis of the summary statistics elaborated by Neale’s Lab from the raw data released by the UK Biobank, a large-scale biomedical database that includes genetic data on 500,000 UK citizens. I filtered out variants with a minor allele frequency below 0.05, I included only variants that reached a p value below 5⋅10^−7 (even though only p < 5⋅10^−8 was considered for definitive associations), and I filtered out variants with a p value for the Hardy-Weinberg equilibrium below 10^−6.

Females with self-reported Chronic Fatigue Syndrome are associated with a region of chromosome 13 with high linkage disequilibrium, from position 41353297 to 41404706 (on h19) which includes gene SLC25A15. After applying statistical methods of fine-mapping (approximation of the joint model and posterior inclusion probability, PIP), I found rs11147812 (13:41404706:T:C) as the possible causal variant within this region. This same variant is associated with the whole sample of patients (males + females) at 5⋅10^−8 < p < 5⋅10^−7. The relaxed cutoff for statistical significance of 5⋅10^−7 has been recently proposed as a way to increase the rate of true positives without a substantial increase in false positive associations, in studies with a sample of 130,000. Patients presented a reduced frequency of the alternative allele at position 13:41404706, and this is expected to reduce the expression of SLC25A15 in adipose tissue and other tissues. Gene SLC25A15 encodes mitochondrial ornithine transporter I which is involved in the transport of ornithine inside mitochondria.

Males with chronic asthenia not otherwise specified (ICD10: R53) showed an association with a region in high LD of chromosome 18 (18:55452281 to 18:55460845). The only variant from this region with p < 5⋅10^−8 is rs62092652 (18:55454761:G:A) and it is confirmed as the causal variant in this region by PIP calculation. The alternative allele at this position is associated with a reduced expression of gene ATP8B1 in the brain. Since the alternative allele is more frequent in patients than in controls (frequency of 0.3501 and 0.2422, respectively), we may expect to find a reduced expression of ATP8B1 in the brain of patients. ATP8B1 encodes a member of the P-type cation transport ATPase family, which transport phosphatidylserine and phosphatidylethanolamine from one side of a bilayer to another. These two molecules are both phospholipids found in biological membranes.

Genetic data from the UK Biobank were also used to test previously proposed associations between ME/CFS and variants on TNF: none of the proposed associations was confirmed.

No overlap of the genetic signal from self-reported CFS and R53 was found with the psychiatric traits: bipolar II and depression.

This document also includes an introduction to some of the methods currently employed in the study of GWAS summary statistics.

Full-text article

Tryptophan metabolites in the cerebrospinal fluid of ME/CFS patients

Abstract

I present here a comparison between the levels of tryptophan (Trp), kynurenine (Kyn), serotonin (Ser), Kyn/Trp, and Ser/Trp in cerebrospinal fluid of 44 ME/CFS patients vs 21 sedentary controls. Raw data were retrieved from (Baraniuk JN et al. 2021). Stratification by sex has been included in the analysis. No differences can be found between patients and controls.

Methods

Once downloaded the raw data of (Baraniuk JN et al. 2021), I searched for metabolites of tryptophan metabolism by using the keywords: try, kyn, ser, quinolinic, picolinic, anthranilic, xanthurenic, melatonin. I retrieved the data for tryptophan, kynurenine, and serotonin, and I used them to calculate the ratios kynurenine/tryptophan and serotonin/tryptophan, for each patient. I then organized the data in three csv files (see supplementary material), one including the whole sample, one including females only, and one with males only. For each of the five variables Trp, Kyn, Ser, Kyn/Trp, Ser/Trp a statistical test was performed by the R script displayed at the bottom of this page (supplementary material). For the sample including both sexes, I run both the Student’s t-test and the Wilcoxon test, while for the other two samples only the latter test was performed. I removed a female patient from the data because of her unusually high level of serotonin (0.202), but this does not change the conclusion of this analysis.

	ME/CFS (44)	Sedentary control (21)	t-test p value	Wilcoxon p value
Trp	2.55 (0.652)	2.42 (0.688)	0.47	0.60
Kyn	0.0234 (0.0271)	0.0154 (0.0200)	0.24	0.27
Ser	0.0110 (0.00597)	0.00805 (0.00356)	0.041	0.028
Kyn/Trp	0.00936 (0.0113)	0.00580 (0.00789)	0.200	0.27
Ser/Trp	0.00448 (0.00227)	0.00349 (0.00188)	0.087	0.037

Table 1. Comparison between the levels of tryptophan (Trp), kynurenine (Kyn), serotonin (Ser), Kyn/Trp, and Ser/Trp in cerebrospinal fluid of 44 ME/CFS patients and 21 controls. Both the two-tailed Student’s t-test and the Wilcoxon test were employed. No correction for multiple comparisons is applied. Levels are reported as: mean (standard deviation of the sample).

Results

Serotonin and Ser/Trp are significantly elevated in ME/CFS patients vs sedentary controls (p = 0.028 and 0.037, respectively), Table 1, Figure 1. But once we apply a correction for three independent variables, these differences are no more statistically significant. When we stratified by sex, none of the comparisons led to a statistically significant difference between patients and controls (Figure 2, Figure 3). The conclusion is that no difference can be found in the level of Trp, Kyn, Ser, Kyn/Trp, and Ser/Trp in cerebrospinal fluid of ME/CFS patients when compared to sedentary controls. One female patient presented a very elevated serotonin level (she was removed from the analysis), another female patient showed elevated kynurenine, one male with ME/CFS had elevated tryptophan, and another male patient showed elevated kynurenine. The larger number of patients compared to controls might explain the presence, in patients, of some extreme values of the parameters considered, when compared to controls.

**Figure 1.** Comparison between the levels of tryptophan (Trp), kynurenine (Kyn), serotonin (Ser), Kyn/Trp, and Ser/Trp in cerebrospinal fluid of 44 ME/CFS patients and 21 controls. For each variable, the median, the 1st, and the 3rd quartile are indicated.

**Figure 2.** Comparison between the levels of tryptophan (Trp), kynurenine (Kyn), serotonin (Ser), Kyn/Trp, and Ser/Trp in cerebrospinal fluid of 35 female ME/CFS patients and 11 female controls. For each variable, the median, the 1st, and the 3rd quartile are indicated. For each comparison, the p value from the Wilcoxon test is displayed.

**Figure 3.** Comparison between the levels of tryptophan (Trp), kynurenine (Kyn), serotonin (Ser), Kyn/Trp, and Ser/Trp in cerebrospinal fluid of 9 male ME/CFS patients and 10 male controls. For each variable, the median, the 1st, and the 3rd quartile are indicated. For each comparison, the p value from the Wilcoxon test is displayed.

Supplementary material

The following R script calculates Table 1 and plots Figures 1, 2, and 3. It reads the three csv files below (click to download), one with both sexes lumped together, one with males, and one with females, respectively.

Trp_met.csv

Trp_met_females.csv

Trp_met_males.csv

# file name: tryptophan_wilcox_both_sexes
#
samples<-read.csv("Trp_met.csv", sep=";", header = TRUE) # we read the data
attach(samples) # this allows us to refer to the labels as variables 
#
# we define the number of patients and controls
#
ncfs<-length(samples[Group=="cfs0",1])
nsc<-length(samples[Group=="sc0",1])
#
# we store the measures of each metabolite for patients
#
kyn_cfs<-Kyn[1:ncfs]
trp_cfs<-Trp[1:ncfs]
ser_cfs<-Ser[1:ncfs]
#
# we store the measures of each metabolite for controls
#
a<-ncfs+1
kyn_sc<-Kyn[a:length(Kyn)]
trp_sc<-Trp[a:length(Kyn)]
ser_sc<-Ser[a:length(Kyn)]
#
# we calculate the ratios kyn/trp and ser/trp for patients
#
kyn_trp_cfs<-kyn_cfs/trp_cfs
ser_trp_cfs<-ser_cfs/trp_cfs
#
# we calculate the ratios kyn/trp and ser/trp for controls
#
kyn_trp_sc<-kyn_sc/trp_sc
ser_trp_sc<-ser_sc/trp_sc
#
# we plot the data for each metabolite: box-plots with points
#
plot(factor(Group),Kyn,xlab="groups",ylab="Kynurenine")
points(factor(Group),Kyn,pch=21,bg="red")
plot(factor(Group),Trp,xlab="groups",ylab="Tryptophan")
points(factor(Group),Trp,pch=21,bg="red")
plot(factor(Group),Ser,xlab="groups",ylab="Serotonin")
points(factor(Group),Ser,pch=21,bg="red")
#
# we plot the data for the two ratios
#
plot(factor(Group),c(kyn_trp_cfs,kyn_trp_sc),xlab="groups",ylab="Kyn/Trp")
points(factor(Group),c(kyn_trp_cfs,kyn_trp_sc),pch=21,bg="red")
plot(factor(Group),c(ser_trp_cfs,ser_trp_sc),xlab="groups",ylab="Ser/Trp")
points(factor(Group),c(ser_trp_cfs,ser_trp_sc),pch=21,bg="red")
#
# we run the Wilcoxon test for each metabolite and ratio
#
wilcox.test(kyn_cfs,kyn_sc)
wilcox.test(trp_cfs,trp_sc)
wilcox.test(ser_cfs,ser_sc)
wilcox.test(kyn_trp_cfs,kyn_trp_sc)
wilcox.test(ser_trp_cfs,ser_trp_sc)

An update on the UK Biobank: fine-mapping

The man who does not make his own tools does not make his own sculpture.
Irving Stone, The Agony and The Ecstasy

An analysis of the UK Biobank database carried out by Neale’s Lab pointed out a significant correlation between a region of chromosome 13 and females with self-reported Chronic Fatigue Syndrome (see this blog post). This result was further analyzed in a subsequent paper in which it was suggested that the causal variant within this region may be rs7337312 (position 13:41353297:G:A on reference genome GRCh37, forward strand) (Dibble J. et al. 2020). It is included in a regulatory region of gene SLC25A15, which encodes mitochondrial ornithine transporter I, and the potential biological effects of this variant have been discussed in the aforementioned study. I made an attempt at my own discussion of this variant (here).

It is not unusual for a GWAS study to associate a trait with a long sequence of variants belonging to the same chromosome and in a close physical relationship one with the other, due to high linkage disequilibrium often present between variants close to one another (see this blog post). Several methods have been developed in the last years to further refine the association and find the variant that causes the disease and drives the association of its nearby SNPs. These methods are based on both purely mathematical considerations and on the analysis of the known consequences of the variants, and we refer to them by the evocative name of fine-mapping (Schaid DJ et al. 2018).

I tried to develop my own method and software for a purely mathematical approach to fine-mapping and I applied it to the region associated with ME/CFS in females, and I found variant rs11147812 (13:41404706:T:C on h19) as the most likely causal one. The detailed discussion of the method I followed and the scripts I wrote are available here for download. It might be noted that this variant belongs to a genetic entity (pseudogene TPTE2P5) that harbors variants that have been strongly associated with the following hematic parameters (see GWAS catalog).

The alternative allele of rs11147812 has been reported to increase (effect size > 0) the expression of gene SLC25A15 in fat (see this page) with a p value of $2.85\cdot10^{-20}$ . Since the alternative variant is less frequent in patients than in controls, the prediction is that we have a reduced expression of SLC25A15 in fat, in female CFS patients.

Diastolic blood pressure (reduction)	Evangelou E et al. 2018
Blood volume occupied by platelets (increase)	Astle WG et al. 2016
Basophil count (decrease)	Masahiro K et al. 2018

Table. Significant associations between traits and variants of TPTE2P5.

Note. The header image shows the convergence of the linear method used by my script for fine-mapping the region on chromosome 13. The detailed discussion of the method I followed and the scripts I wrote are available here for download.

An estimation of the proportion of asymptomatic Omicron infection

Abstract

In this document, I compare data from two COVID vaccine trials carried out in South Africa (the Ubuntu trial and the Sisonke sub-study). Both trials were conducted on unvaccinated subjects, asymptomatic at the time of enrollment. Among them, some were found positive to SARS-CoV-2, but while the variant was identified as Delta in the Sisonke sub-study, the Omicron variant was reported in asymptomatic subjects of the Ubuntu trial. By considering the proportion of SARS-CoV-2 positive subjects in these two populations, the average number of daily confirmed cases, and the percentage of unvaccinated South African citizens at the respective times of enrollment of the two trials, I calculated the proportion of asymptomatic infections for Omicron, as a function of the same parameter for the Delta variant. I found that if we accept a proportion of asymptomatic infections of 17% for Delta, then we conclude that about 60% of all Omicron cases are asymptomatic, in unvaccinated subjects. This points towards significantly lower pathogenicity for the Omicron variant when compared to the Delta variant.

Introduction

The B.1.1.529 (Omicron) SARS-CoV-2 variant was first identified in Botswana and South Africa and was classified by WHO as a variant of concern (VOC) on 26 November 2021 (WHO website). As of 15 December 2021, the Omicron variant had already spread in 77 countries (especially in the United Kingdom, South Africa, and the United States) (Thakur V, Ratho RK, 2021). Omicron is characterized by a large number of mutations and deletions that seem to give it increased antibody escape capacity and enhanced transmissibility (Miller NL et al 2021). Yet, if we look at the number of deaths in South Africa (R), we note that despite a rapid increase in confirmed cases (most Omicron), it doesn’t follow the usual consequent increase (with a phase shift of two weeks). This suggests that Omicron is less dangerous than Delta, also considering that previous infection with Delta does not seem to protect against infection with Omicron (Garret N et al 2021) and that only 30% of the population of South Africa received at least one dose of vaccine (R).

In what follows I present a quantitative method for the comparison between the effect of Omicron and Delta on unvaccinated subjects. In particular, I calculate the ratio between asymptomatic SARS-CoV-2+ subjects and total SARS-CoV-2+ subjects for Omicron ( $r_{o}$ ) as a function of the same ratio for Delta ( $r_{\delta}$ ). We consider only subjects who did not receive any dose of vaccination against SARS-CoV-2. By considering only unvaccinated subjects, we eliminate the confounding effect of vaccination on the pathogenicity of Omicron and Delta. The aforementioned ratio might be considered one of the possible indexes of disease severity, while we wait for further data, according to the following assumption: the higher the number of asymptomatic carriers of a virus divided by the total number of carriers, the lower the pathogenicity of the virus. The derivation of the function $r_{o}\,=\,r_{o}(r_{\delta})$ is described in the Methods section.

Results

The function $r_{o}\,=\,r_{o}(r_{\delta})$ is plotted in Figure 1. It indicates the proportion of Omicron asymptomatic infections as a function of the same proportion for Delta, in unvaccinated subjects. As you can see, the Omicron variant leads to a higher proportion of asymptomatic cases when compared to the Delta one. If we assume for Delta a value $r_{\delta}\,=\,0.17$ (Byambasuren O. et al. 2020), we have that $r_{o}\,\sim\,0.6.$ The diagram has been plotted for two different choices of the ratio $k_{o}/k_{\delta}$ (the meaning of this ratio is explained in the following paragraph), but as you can see, it doesn’t change much whether you consider one value or the other.

**Figure 1.** The ratio of asymptomatic SARS-CoV-2+ subjects and total SARS-CoV-2+ subjects for the Omicron variant expressed as a function of the same ratio for the Delta variant. All subjects are considered unvaccinated.

Methods

Let $N_{pos}$ be the number of unvaccinated individuals positive to SARS-CoV-2 at a given time and $r$ the ratio between the unvaccinated individuals who are positive but are asymptomatic and $N_{pos}$ . Then, the total number of the asymptomatic and unvaccinated carriers of the virus is $N_{pos} r$ . If $N_{tot}$ is the total number of unvaccinated individuals without symptoms in a certain geographical region, then the ratio between asymptomatic and unvaccinated carriers of the virus and asymptomatic and unvaccinated individuals (no matter their positivity to the virus) is $\frac{N_{pos}r}{N_{tot}}$ . We are interested in expressing $r$ in the case of the Omicron variant (let’s say $r_{o}$ ) as a function of the same parameter in the case of the Delta variant (let’s say $r_{\delta}$ ). The following table collects the symbols we have just introduced. In what follows we will add a pedix $o$ for the Omicron variant and a pedix $\delta$ when we refer to the Delta variant.

Between December 2 and December 17, 2021, a total of 330 asymptomatic subjects from South Africa were enrolled in a phase III clinical trial (Ubuntu trial, PACTR202105817814362) to assess the relative efficacy of the COVID-19 vaccine mRNA-1273 (MODERNA). This population is exclusively made up of individuals who had not been previously exposed to any COVID-19 vaccine. This population included persons living with HIV (PLWH) with a median age of 39 years (18-76). Among them, 230 individuals were tested for SARS-CoV-2 by RT-PCR and 31% (71 subjects) turned out to be positive. Among them, 56 samples were successfully subjected to further investigations: all had S gene dropout, suggestive of Omicron infection (Garret N et al 2021). It is worth mentioning that positivity to Omicron does not correlate with previous exposure to SARS-CoV-2, in this population: in other words, previous exposure to other SARS-CoV-2 variants does not protect against Omicron. Positivity to Omicron does not correlate with CD4+ cell count in PLWH either, so it seems that HIV does not interfere with $r$ , the value we are interested in. If we now consider that the average daily number of confirmed new cases in South Africa for the interval December 2-17 is 18745, we can write

$N_{pos-o}\,=\,18745K_{o}\,+\,r_{o}N_{pos-o}\,\Rightarrow\,N_{pos-o}\,=\,\frac{18745K_{o}}{1\,-\,r_{o}}$

where $K_{o}$ is a multiplicative constant that accounts for all the possible errors in the measure of the positive symptomatic cases and also for the fact that we are here considering only unvaccinated subjects, while data available for confirmed cases does not distinguish between vaccinated and unvaccinated. Moreover, the number refers to average daily new cases, while we are in fact considering the number of total positive cases, at that point in time; so $K_{o}$ is also a way to get the latter from the former (assuming linear proportionality). Therefore, we can write

$\frac{N_{pos}r_{o}}{N_{tot-o}}\,=\,0.31\,\Rightarrow\,\frac{r_{o}}{1\,-\,r_{o}}\frac{18745K_{o}}{N_{tot-o}}\,=\,0.31$

Another study carried out in South Africa between June and August 2021 during the Delta outbreak (Sisonke sub-study, NCT04838795) reported a percentage of asymptomatic carriers of 2.4% (39/1604) among unvaccinated subjects (Garret N et al 2021). The average number of daily reported cases, in this case, is 12181; hence we have

$\frac{r_{\delta}}{1\,-\,r_{\delta}}\frac{12181K_{\delta}}{N_{tot-\delta}}\,=\,0.024$

These last two equations give

$\frac{(1\,-\,r_{\delta})r_{o}}{(1\,-\,r_{o})r_{\delta}}\frac{18745}{12181}\frac{K_{o}N_{tot-\delta}}{K_{\delta}N_{tot-o}}\,=\,\frac{0.31}{0.024}\Rightarrow$

$\Rightarrow\frac{(1\,-\,r_{\delta})r_{o}}{(1\,-\,r_{o})r_{\delta}}1.54\frac{K_{o}N_{tot-\delta}}{K_{\delta}N_{tot-o}}\,=\,12.92\Rightarrow$

$\Rightarrow r_{o}\,=\,\frac{12.92}{1.54\frac{1\,-\,r_{\delta}}{r_{\delta}}\frac{K_{o}N_{tot-\delta}}{K_{\delta}N_{tot-o}}\,+\,12.92}$

We are here considering unvaccinated subjects, but while in the period December 2-17 (Omicron outbreak) the percentage of subjects who received at least one dose of vaccine was on average 30.65%, in the time frame June-August (Delta outbreak), the same percentage was only 10.65% (remember that in both cases we consider subjects from South Africa) (R). Then we must assume that $N_{tot-o}\,=\,0.69N_{tot}$ and $N_{tot-\delta}\,=\,0.89N_{tot}$ , therefore we have

$\frac{N_{tot-\delta}}{N_{tot-o}}\,=\,\frac{0.89N_{tot}}{0.69N_{tot}}\,=\,1.29$

This means that $r_{o}$ is given by

$r_{o}\,=\,\frac{12.92}{1.99\frac{1\,-\,r_{\delta}}{r_{\delta}}\frac{K_{o}}{K_{\delta}}\,+\,12.92}$

Note that we are here considering only unvaccinated subjects, while the number of reported cases includes both vaccinated and unvaccinated individuals. This means that $K_{o}$ can’t have the same value of $K_{\delta}$ . One possible choice is to assume

$\frac{K_{o}}{K_{\delta}}\,=\,\frac{k\cdot k_{o}}{k\cdot k_{\delta}}\,=\,\frac{k_{o}}{k_{\delta}}\,=\,\frac{100-30.65}{100-10.65}\,=\,0.78$

where we assumed that k is the error (underestimation) made in measuring positive cases, which is the same in both cases since it depends on the efficiency of the health care system, on the behavior of the population, and other factors that do not change; while $k_{\delta}$ and $k_{o}$ are directly proportional to the percentage of individuals who are unvaccinated and allow for the calculation of the number of positive individuals with no prior vaccination from the number of positive individuals (no matter the vaccination status). Another possible choice is to assume that the confirmed cases are mostly unvaccinated and in this case we would simply have

$\frac{K_{o}}{K_{\delta}}\,=\,1$

All that said, we can now express $r_{o}$ as a function of $r_{\delta}$ and we get the plot in Figure 1. The script in Octave used to plot the figure is the one that follows. The number of confirmed cases has been retrieved from this website, in particular from this CSV file: (download).

% file name = omicron
% date of creation = 2/01/2022
clear all
close all 
% the array of r_delta
steps = 100;
r_delta(1) = 0;                                                            
r_delta(steps) = 1;
inc = ( r_delta(100) - r_delta(1) )/(steps-1)
for i = 2:steps-1
  r_delta(i) = r_delta(i-1) + inc;
endfor  
% the array of r_omicron
for i=1:steps
  ratio_r = (1 - r_delta(i))/r_delta(i);
  ratio_k = 0.78;
  r_omicron (i) = 12.92/((1.99*ratio_r*ratio_k) + 12.92);
  ratio_k = 1.;
  r_omicron2 (i) = 12.92/((1.99*ratio_r*ratio_k) + 12.92);
endfor
% plotting
plot (r_delta, r_omicron, '-k', "linewidth", 1)
hold on
plot (r_delta, r_omicron2, '--k', "linewidth", 1)
ylabel('r_{o} = (asymptomatic AND positive)/positive (Omicron)','fontsize',15); 
xlabel('r_{\delta} = (asymptomatic AND positive)/positive (Delta)','fontsize',15);
axis equal;    
axis([0,r_delta(steps),0,r_omicron2(steps)])                             
grid on
grid minor
legend ('k_{0}/k_{\delta} = 0.78', 'k_{0}/k_{\delta}  = 1', 'location', "northwest", 'fontsize', 15);

Limitations

The main limitation of this method is the fact that the characteristics of the two populations considered (the one from the Ubuntu trial and the one from the Sisonke sub-study) were not taken into account, so we can’t say whether these two populations are comparable with respect to variables such as age, comorbidities, and previous SARS-CoV-2 infection. We don’t know how well these two populations represent the general population either.

Further comments and conclusions

From the present analysis, the Omicron variant shows a higher relative number of asymptomatic cases, when compared to the Delta variant, in unvaccinated subjects. This points towards lower pathogenicity for the new variant.

In Italy, as of 31 December 2021, the prevalence of Omicron was only 20% (R), so its effect on the number of deaths and hospital resource use has yet to be appreciated. At present, with Delta being the most prevalent variant in our country, the large majority of deaths and intensive care occupation is seen among unvaccinated subjects who are accepted in intensive care units 6.5 times more than vaccinated subjects (Figure 2) and die 5.2 times more frequently (Figure 3). If Omicron is really less dangerous than Delta for unvaccinated subjects, we will see a progressive convergence between the yellow curve and the blue one in both Figure 2 and Figure 3. The plots below will be updated as new data become available.

Figure 2. The number of subjects admitted to intensive care unit, in Italy, for 100,000 unvaccinated (yellow), vaccinated (blue), boosted (green) subjects. You can select a specific age range from the bar at the top of the plot.

The equations of this blog post were written using $\LaTeX$ (see this article)

A complete (preload) failure

Featured

Introduction

Some days ago, David Systrom offered an overview of his work on cardiopulmonary testing in ME/CFS during a virtual meeting hosted by the Massachusetts ME/CFS & FM Association and the Open Medicine Foundation. In this blog post, I present an introduction to the experimental setting used for Systrom’s work (paragraph 1), a brief presentation of his previous findings (paragraph 2), and an explanation of his more recent discoveries in his cohort of patients (paragraph 3). In paragraph 4 you’ll find a note on how to support his research.

1. Invasive Cardiopulmonary Exercise Testing

It is a test that allows for the determination of pulmonary, cardiac, and metabolic parameters in response to physical exertion of increasing workload. It is, mutatis mutandis, the human equivalent of an engine test stand. A stationary bike with a mechanical resistance that increases by 10 to 50 Watts for minute is usually employed for assessing the patient in a upright position, but a recumbent bike can also be used in some instances. Distinguishing between these two different settings might be of pivotal relevance in ME/CFS and POTS. I shall now briefly describe some of the measurements that can be collected during invasive cardiopulmonary exercise testing (iCPET) and their biological meaning. For a more accurate and in-depth account, please refer to (Maron BA et al. 2013), (Oldham WM et al. 2016). I have used these papers as the main reference for this paragraph, unless otherwise specified.

Gas exchange. A face mask collects the gasses exchanged by the patient during the experiment and allows for monitoring of both oxygen uptake per unit of time (named $VO_2$ ) and carbon dioxide output ( $VCO_2$ ), measured in mL/min. Gas exchange is particularly useful for the determination of the anaerobic threshold (AT), i.e. the point in time at which the diagram of $VCO_2$ in function of $VO_2$ displays an abrupt increase in its derivative: at this workload, the patient starts relying more on her anaerobic energy metabolism (glycolysis, for the most part) with a build-up of lactic acid in tissues and blood (see Figure 1).

**Figure 1.** Diagram of $VCO_2$ in function of $VO_2$ . The point in which there is a change in the derivative with respect to $VO_2$ is called “anaerobic threshold” (AT). AT is highlighted with a vertical line in this picture. This diagram is from an actual CPET of a patient.

**Figure 1.** Diagram of $VCO_2$ in function of $VO_2$ . The point in which there is a change in the derivative with respect to $VO_2$ is called “anaerobic threshold” (AT). AT is highlighted with a vertical line in this picture. This diagram is from an actual CPET of a patient.

Oxygen uptake for unit of time at AT (called $VO_2$ max) can be considered an integrated function of patient’s muscular, pulmonary, and cardiac efficiency during exercise. It is abnormal when its value is below 80% of what predicted according to patient’s age, sex, and height. Importantly, according to some studies there might be no difference in $VO_2$ max between ME/CFS patients and healthy controls, unless the exercise test is repeated a day after the first measure: in this case the value max $VO_2$ for patients is significantly lower than for controls (VanNess JM et al. 2007), (Snell CR and al. 2013).

Another measure derived from the assessing of gas exchange is minute ventilation (VE, measured in L/min) which represents the total volume of gas expired per minute. The link between VE and $VO_2$ is as follows:

$VO_2\;=\;VE\cdot(inspired\;VO_2\; -\; expired\;VO_2)$

Maximum voluntary ventilation (MVV) is the maximum volume of air that is voluntarily expired at rest. During incremental exercise, a healthy person should be able to maintain her VE at a value ∼0.7 MVV and it is assumed that if the ratio VE/MVV is above 0.7, then the patient has a pulmonary mechanical limit during exercise. If VE is normal, then an early AT suggests an inefficient transport of oxygen from the atmosphere to muscles, not due to pulmonary mechanics, thus linked to either pulmonary vascular abnormalities or muscular/mitochondrial abnormalities. It is suggested that an abnormally high derivative of the diagram of VE in function of $VCO_2$ and/or a high ratio VE/ $VCO_2$ at AT (these are measures of how efficiently the system gets rid of $CO_2$ ) are an indicator of poor pulmonary vascular function.

Respiratory exchange ratio (RER) is a measure of the effort that the patient puts into the exercise. It is measured as follows:

$RER=\frac{VCO_2}{VO_2}$

and an RER>1.05 indicates a sufficient level of effort. In this case the test can be considered valid.

Arterial catheters. A sensor is placed just outside the right ventricle (pulmonary artery, Figure 2) and another one is placed in the radial artery: they allow for measures of intracardiac hemodynamics and arterial blood gas data, respectively. By using this setting, it is possible to indirectly estimate cardiac output (Qt) by using Fick equation:

$Qt=\frac{VO_2}{arterial\;O_2 - venous\;O_2}$

where the $arterial\;O_2$ is measured by the radial artery catheter and the venous one is measured by the one in the pulmonary artery (ml/L). An estimation for an individual’s predicted maximum Qt (L/min) can be obtained by dividing her predicted $VO_2$ max by the normal maximum value of $arterial\;O_2 - venous\;O_2$ during exercise, which is 149 mL/L:

$predicted\; Qt\;max=\frac{predicted\; VO_{2}max}{149 \frac{mL}{L}}$

If during iCPET the measured Qt max is below 80% of the predicted maximum cardiac output (as measured above), associated with reduced $VO_2$ max, then a cardiac abnormality might be suspected. Stroke volume (SV), defined as the volume of blood ejected by the left ventricle per beat, can be obtained from the Qt according to the following equation:

$Qt=SV\cdot HR\;\xrightarrow\;SV\;=\;\frac{Qt}{HR}\;=\;\frac{\frac{VO_2}{arterial\; O_2 - venous\; O_2}}{HR}$

where HR stands for heart rate. One obvious measure from the pulmonary catheter is the mean pulmonary artery pressure (mPAP). The right atrial pressure (RAP) is the blood pressure at the level of the right atrium. Pulmonary capillary wedge pressure (PCWP) is an estimation for the left atrial pressure. It is obtained by the pulmonary catheter. The mean arterial pressure (MAP) is the pressure measured by the radial artery catheter and it is a proxy for the pressure in the left atrium. RAP, mPAP, and PCWP are measured by the pulmonary catheter (the line in red) which from the right atrium goes through the tricuspid valve, enters the right ventricle, and then goes along the initial part of the pulmonary artery (figure 2).

**Figure 2.** Right atrial pressure (RAP) is the pressure of the right atrium, mean pulmonary arterial pressure (mPAP) is the pressure of the right ventricle, pulmonary capillary wedge pressure (PCWP) is an estimation of the pressure of the left atrium. Mean arterial pressure gives a measure of the pressure of the left ventricle. RAP, mPAP, and PCWP are measured by the pulmonary catheter (the line in red) which from the right atrium goes through the tricuspid valve, enters the right ventricle, and then goes across the initial part of the pulmonary artery (R).

Derived parameters. As seen, Qt (cardiac output) is derived from actual direct measures collected by this experimental setting, by using a simple mathematical model (Fick equation). Another derived parameter is pulmonary vascular resistance (PVR) which is obtained using the particular solution of the Navier-Stokes equations (the dynamic equation for Newtonian fluids) that fits the geometry of a pipe with a circular section. This solution is called the Poiseuille flow, and it states that the difference in pressure between the extremities of a pipe with a circular cross-section A and a length L is given by

$\Delta\;P\;=\;\frac{8\pi\mu L}{A^2}Q$

where $\mu$ is a mechanical property of the fluid (called dynamic viscosity) and Q is the blood flow (Maccallini P. 2007). As the reader can recognize, this formula has a close resemblance with Ohm’s law, with P analogous to the electric potential, Q analogous to the current, and $\frac{8\pi\mu L}{A^2}$ analogous to the resistance. In the case of PVR, Q is given by Qt while $\Delta\;P\;=\;mPAP\;-\;PCWP$ . Then we have:

$PVR\;=\;80\frac{\;mPAP\;-\;PCWP}{Qt}$

where the numeric coefficient is due to the fact that PVR is usually measured in $\frac{dyne\cdot s}{cm^5}$ and 1 dyne is $10^5$ Newton while 1 mmHg is 1333 N/m².

2. Preload failure

A subset of patients with exercise intolerance presents with preload-dependent limitations to cardiac output. This phenotype is called preload failure (PLF) and is defined as follows: RAP max < 8 mmHg, Qt and $VO_2$ max <80% predicted, with normal mPAP (<25 mmHg) and normal PVR (<120 $\frac{dyne\cdot s}{cm^5}$ ) (Maron BA et al. 2013). This condition seems prevalent in ME/CFS and POTS. Some of these patients have a positive cutaneous biopsy for small-fiber polyneuropathy (SFPN), even though there seems to be no correlation between hemodynamic parameters and the severity of SFPN. Intolerance to exercise in PLF seems to improve after pyridostigmine administration, mainly through potentiation of oxygen extraction in the periphery. A possible explanation for PLF in non-SFPN patients might be a more proximal lesion in the autonomic nervous system (Urbina MF et al. 2018), (Joseph P. et al. 2019). In particular, 72% of PLF patients fits the IOM criteria for ME/CFS and 27% meets the criteria for POTS. Among ME/CFS patients, 44% has a positive skin biopsy for SFPN. One possible cause for damage to the nervous system (both in the periphery and centrally) might be TNF-related apoptosis-inducing ligand (TRAIL) which has been linked to fatigue after radiation therapy; TRAIL increases during iCPET among ME/CFS patients (see video below).

3. Latest updates from David Systrom

During the Massachusetts ME/CFS & FM Association and Open Medicine Foundation Fall 2020 Event on Zoom, David Systrom reported on the results of iCPET in a set of ME/CFS patients. The $VO_2$ max is lower in patients vs controls (figure 3, up). As mentioned before, $VO_2$ max is an index that includes contributions from cardiac performances, pulmonary efficiency, and oxygen extraction rate in the periphery. In other words, a low $VO_2$ max gives us no explanation on why it is low. This finding seems to be due to different reasons in different patients even though the common denominator among all ME/CFS patients of this cohort is a low pressure in the right atrium during upright exercise (low RAP, figure 3, left). But then, if we look at the slope of Qt in function of $VO_2$ (figure 3, right) we find three different phenotypes. Those with a high slope are defined “high flow” (in red in figure 3). Then we have a group with a normal flow (green) and a group with a low flow (blue). If we look then at the ability to extract oxygen by muscles (figure 3, below) expressed by the ratio

$\frac{arterial\;O_2 - venous\;O_2}{HB}$

we can see that the high flow patients reach the lowest score. In summary, all ME/CFS patients of this cohort present with poor $VO_2$ max and preload failure. A subgroup, the high flow phenotype, has poor oxygen extraction capacity at the level of skeletal muscles.

**Figure 3.** The results presented by David Systrom are here displayed around a schematic representation of the circulatory system. $VO_2$ is a global measure of the efficiency of the circulatory system. CO, which stands for cardiac output (indicated Qt in this blog post) is related to the output of the left half of the heart. RAP is the pressure of the right atrium. *By Paolo Maccallini.*

**Figure 3.** The results presented by David Systrom are here displayed around a schematic representation of the circulatory system. $VO_2$ is a global measure of the efficiency of the circulatory system. CO, which stands for cardiac output (indicated Qt in this blog post) is related to the output of the left half of the heart. RAP is the pressure of the right atrium. *By Paolo Maccallini.*

Now the problem is: what is the reason for the preload failure? And in the high flow phenotype, why the muscles can’t properly extract oxygen from blood? As mentioned, about 44% of ME/CFS patients in this cohort has SFPN but there is no correlation between the density of small-fibers in the skin biopsies and the hemodynamic parameters. Eleven patients with poor oxygen extraction (high flow) had their muscle biopsy tested for mitochondrial function (figure 4) and all but one presented a reduction in the activity of citrate synthase (fourth column): this is the enzyme that catalyzes the last/first step of Krebs cycle and it is considered a global biomarker for mitochondrial function. Some patients also have defects in one or more steps of the electron transport chain (fifth column) associated with genetic alterations (sixth column). Another problem in high flow patients might be a dysfunctional vasculature at the interface between the vascular system and skeletal muscles (but this might be true for the brain too), rather than poor mitochondrial function.

**Figure 4.** Eleven patients with high flow (poor oxygen extraction) underwent a muscle biopsy. Mitochondrial function has been assessed in these samples and all the patients but one presented a reduced activity for the enzyme citrate synthase (4th column). Defects in the oxygen transport chain and in the mitochondrial chromosome have also been documented in 4 of them (column 5th and column 6th).

The use of an acetylcholinesterase inhibitor (pyridostigmine) improved the ability to extract oxygen in the high flow group, without improving cardiac output, as measured with a CPET, after one year of continuous use of the drug. This might be due to better regulation of blood flow in the periphery. This paragraph is an overview of the following video:

4. Funding

The trial on the use of pyridostigmine in ME/CFS at the Brigham & Women’s Hospital by Dr. David Systrom is funded by the Open Medicine Foundation (R). This work is extremely important, as you have seen, both for developing diagnostic tools and for finding treatments for specific subgroups of patients. Please, consider a donation to the Open Medicine Foundation to speed up this research. See how to donate.

The equations of this blog post were written using $\LaTeX$ (see this article).

Lettera aperta all’Osservatorio Malattie Rare

Non sarebbe necessario scrivere una nota all’articolo pubblicato dall’Osservatorio Malattie Rare (O.ma.r.) sulla malattia di Lyme alcuni giorni fa [1], in cui si liquidano i possibili esiti cronici della patologia in parola come non esistenti o riconducibili ad altre patologie, “non ultime le patologie psichiatriche”. Non sarebbe necessario, ho scritto, perché coloro che si occupano professionalmente della malattia di Lyme, nonché i pazienti, sono consapevoli che in realtà le possibili sequele della infezione acuta da Borrelia burgdorferi sono ben documentate in letteratura e costituiscono un problema di enorme portata su cui si concentra oggi molta ricerca, spesso di alto profilo [2].

E allora perché questa preterizione? Perché un articolo divulgativo pubblicato da O.ma.r. ha notevole risonanza e – se incompleto o impreciso – rischia di alimentare false credenze tra i neofiti. L’articolo in questione è encomiabile nel divulgare nozioni preziose sulla fase acuta della malattia e nel mettere in guardia contro test e trattamenti non provati, ma è del tutto fuorviante nella parte dedicata alle sequele croniche (penultimo paragrafo).

La malattia di Lyme risponde alle attuali cure antibiotiche nel 90% dei casi. Questo significa che un decimo di coloro che ogni anno, in estate, contrae la malattia per il morso di un vettore (principalmente l’Ixodes ricinus in Europa) andrà incontro a una condizione cronica (cioè con durata superiore ai sei mesi) e debilitante, nota in seno alla comunità scientifica con il nome di post-treatment Lyme disease syndrome, PTLDS [3], [4]. Il nome scelto (che si potrebbe tradurre come Sindrome della malattia di Lyme dopo trattamento) sta a indicare che i pazienti sperimenteranno sintomi, nonostante i trattamenti della fase acuta.

La causa della PTLDS è al momento non nota. Alcuni studi supportano l’ipotesi che ci sia una disfunzione immunitaria in questi pazienti. Due studi hanno dimostrato la presenza di anticorpi contro il sistema nervoso centrale nella metà dei pazienti PTLDS [5], [6], solo per citare i più recenti. Per approfondimenti su questo argomento si legga qui e qui. La ricerca in questo campo continua [7].

Altri gruppi hanno dimostrato la persistenza del patogeno – dopo trattamento – sia nel modello animale della malattia di Lyme [8], [9], [10], che negli esseri umani [11], [12]. Presso la Columbia University è stata avviata una raccolta di tessuti provenienti da individui deceduti, che abbiano avuto una ben documentata infezione da Borrelia burgdorferi (link) proprio per indagare ulteriormente questo aspetto.

Numerosi sforzi e investimenti sono stati profusi recentemente nella ricerca di nuovi agenti antimicrobici per questa infezione, nella speranza di scongiurare le sequele croniche, da parte della Università di Stanford [13], [14], della Università Johns Hopkins [15], [16], [17], della Università Northeastern [18].

Nell’articolo di O.ma.r si legge che la sindrome in questione – chiamata impropriamente post-Lyme dall’autore – è caratterizzata da “sintomi soggettivi – e dunque non quantificabili – quali affaticabilità e difficoltà a concentrarsi”. A questo proposito è quasi superfluo ricordare che molti sintomi sono soggettivi, finché l’ingegneria non ci offre uno specifico strumento di misura: si pensi alla risonanza magnetica nella sclerosi multipla o all’elettroencefalogramma nella epilessia. In secondo luogo, questi sintomi sono solo in parte soggettivi, infatti i pazienti PTLDS presentano alterazioni quantificabili nel sistema immunitario [5], [6], nella espressione genica [19], nel metabolismo [20], etc.

Per quanto riguarda il riferimento all’ambito psichiatrico, vale la pena fare delle considerazioni. E’ senz’altro vero che le principali patologie psichiatriche (i disturbi dell’umore da un lato e le psicosi dall’altro) contemplano gli episodi infettivi come fattore di rischio [21], [22], tuttavia la PTLDS semplicemente non si sovrappone alle patologie psichiatriche, né nella presentazione clinica, né nella epidemiologia, per questo è una categoria nosografica a sé stante (vedi qui). Per fare un esempio concreto: negare l’evidenza, come sembra fare questo articolo, è una delle possibili manifestazioni della schizofrenia paranoide [23], ma né questo tipo di sintomi né altri sintomi patognomonici per malattie psichiatriche sono menzionati nella definizione di caso della PTLDS [4].

Paolo Maccallini

Riferimenti

Orzes, E. (2019, Nov. 7). Malattia di Lyme, attenzione alle false credenze. O.ma.r. (link)
Instutute of Medicine (2011, Apr. 20). Critical Needs and Gaps in Understanding Prevention, Amelioration, and Resolution of Lyme and Other Tick-Borne Diseases: The Short-Term and Long-Term Outcomes – Workshop Report. Cap. 7 (link).
Centers for Disease Control and Prevention. Post-Treatment Lyme Disease Syndrome. (link).
Aucott, J., Crowder, L., & Kortte, K. (2013). Development of a foundation for a case definition of post-treatment Lyme disease syndrome. Int J Infect Dis, 17(6), p. e443-e449. (link).
Chandra A, Wormser GP, Klempner MS, et al. Anti-neural antibody reactivity in patients with a history of Lyme borreliosis and persistent symptoms. Brain Behav Immun 2010;24:1018–24 (link).
Jacek E, Fallon BA, Chandra A, Crow MK, Wormser GP, Alaedini A. Increased IFNalpha activity and differential antibody response in patients with a history of Lyme disease and persistent cognitive deficits. J Neuroimmunol 2013;255:85–91 (link).
Maccallini, P; Bonin, S; Trevisan, G. Autoimmunity against a glycolytic enzyme as a possible cause for persistent symptoms in Lyme disease. Med Hypotheses. 2018 Jan. (link).
Hodzic E, Feng S, Holden K, Freet KJ, Barthold SW. Persistence of Borrelia burgdorferi following antibiotic treatment in mice. Antimicrob Agents Chemother. 2008 May; 52(5) (link).
Yrjänäinen H, Hytönen J, Hartiala P, Oksi J, Viljanen MK. Persistence of borrelial DNA in the joints of Borrelia burgdorferi-infected mice after ceftriaxone treatment. APMIS. 2010 Sep 1;118(9) (link).
Embers, M et al. Persistence of Borrelia burgdorferi in Rhesus Macaques following Antibiotic Treatment of Disseminated Infection. PLoS One. 2012; 7(1). (link).
Marques, A. et al. Xenodiagnosis to detect Borrelia burgdorferi infection: a first-in-human study. Clin Infect Dis. 2014 Apr; 58(7):937-45 (link).
Sapi, E. et al.The Long-Term Persistence of Borrelia burgdorferi Antigens and DNA in the Tissues of a Patient with Lyme Disease. Antibiotics 2019, 8(4), 183. (link).
Wagh D, Pothineni VR, Inayathullah M, Liu S, Kim KM, Rajadas J. Borreliacidal activity of Borrelia metal transporter A (BmtA) binding small molecules by manganese transport inhibition. Drug Des Devel Ther. 2015 Feb 11;9:805-16. (link).
Venkata Raveendra Pothineni et al. Identification of new drug candidates against Borrelia burgdorferi using high-throughput screening. Drug Des Devel Ther. 2016; 10: 1307–1322. (link).
Feng J, Wang T, Shi W, Zhang S, Sullivan D, Auwaerter PG, Zhang Y. Identification of novel activity against Borrelia burgdorferi persisters using an FDA approved drug library. Emerg Microbes Infect. 2014 Jul; 3 (7). (link).
Jie Feng, Megan Weitner, Wanliang Shi, Shuo Zhang, David Sullivan, and Ying Zhang. Identification of Additional Anti-Persister Activity against Borrelia burgdorferi from an FDA Drug Library. Antibiotics (Basel). 2015 Sep; 4(3): 397–410. (link).
Feng J, Auwaerter PG, Zhang Y. Drug combinations against Borrelia burgdorferi persisters in vitro: eradication achieved by using daptomycin, cefoperazone and doxycycline. PLoS One. 2015 Mar 25;10(3). (link).
Sharma B, Brown AV, Matluck NE, Hu LT, Lewis K. Borrelia burgdorferi, the Causative Agent of Lyme Disease, Forms Drug-Tolerant Persister Cells. Antimicrob Agents Chemother. 2015 Aug;59(8):4616-24. (link).
Jerome Bouquet et al. Longitudinal Transcriptome Analysis Reveals a Sustained Differential Gene Expression Signature in Patients Treated for Acute Lyme Disease. mBio. 2016 Jan-Feb; 7(1). (link).
Fallon BA et al. Regional cerebral blood flow and metabolic rate in persistent Lyme encephalopathy. Arch Gen Psychiatry. 2009 May;66(5):554-63. (link).
Benros ME et al. Autoimmune diseases and severe infections as risk factors for mood disorders: a nationwide study. JAMA Psychiatry. 2013 Aug;70(8): 812-20. (link).
Benros ME et al. Autoimmune diseases and severe infections as risk factors for schizophrenia: a 30-year population-based register study. Am J Psychiatry. 2011 Dec;168(12). (link).
Rajiv Tandon et al. Definition and description of schizophrenia in the DSM-5. Schizophrenia Research, Volume 150, Issue 1, October 2013, Pages 3-10. (link).

Mark Davis e il test immunitario universale

1. Introduzione

Queste sono solo alcune note raccolte dal discorso che Mark Davis ha pronunciato in occasione del Community Symposium tenutosi nell’agosto scorso (2017) a Stanford (video). Nei paragrafi 2, 3, 4 e 5 introdurrò alcune nozioni di base sui recettori delle cellule T (T cell receptors: TCR); il paragrafo 6, attraverso riferimenti al video già menzionato e a tre articoli pubblicati da Davis et al. nel corso degli ultimi quattro anni, descrive una nuova tecnologica sviluppata da Mark Davis e colleghi. Questi cenni preliminari dovrebbero auspicabilmente fornire i mezzi per comprendere a pieno la portata dei dati pilota presentati da Mark Davis a proposito dell’attività delle cellule T nella ME/CFS (paragrafo 7) e nella malattia di Lyme cronica (paragrafo 8), mostrando perché tale tecnologia prometta di divenire una sorta di test universale per qualsiasi tipo di infezione o patologia autoimmune, nota o sconosciuta.

2. Cellule T

I linfociti T sono una tipologia di leucociti (o globuli bianchi), vale a dire la componente cellulare del nostro sistema immunitario. La gran parte dei linfociti T in circolo è rappresentata da linfociti T helper (T helper cells: Th cells) e da linfociti T citotossici (cytotoxic T lymphocytes: CTL). Mentre la funzione dei linfociti T helper è quella di regolare l’attività degli altri leucociti attraverso la produzione di un’ampia gamma di trasmettitori chimici (le citochine, cytokines), le CTL sono coinvolte direttamente nella soppressione delle cellule ospiti infette. I linfociti T appartengono al ramo cosiddetto adattivo del sistema immunitario, assieme alle cellule B (le fabbriche di anticorpi), e, in quanto tali, il loro compito è quello di garantire una difesa specifica, su misura, contro gli agenti patogeni: per contrastare uno specifico agente patogeno, il nostro sistema immunitario può schierare in campo non solo anticorpi specifici ma anche specifici linfociti T (Th cells e CTL). Il ramo innato del sistema immunitario, invece, (nel quale rientrano le cellule natural killer, i macrofagi, le cellule dendritiche, i mastociti…) è in grado di fornire soltanto una difesa aspecifica, una prima linea di risposta immunitaria.

3. Recettori dei linfociti T

I linfociti T sono in grado di andare alla ricerca di specifici patogeni grazie a una molecola espressa sopra la propria superficie, chiamata recettore del linfocita T (TCR). Nella figura 1 si può vedere una schematica rappresentazione del TCR e del meccanismo in virtù del quale il linfocita T riconosce il proprio target. Gli antigenti (proteine) degli agenti patogeni vengono indicati ai linfociti T da altre cellule del nostro corpo: vengono esposte sopra molecole chiamate Complesso Maggiore di Istocompatibilità (MHC), che si trova espresso sulla membrana esterna. Se un dato antigene mostra compatibilità con il TCR di uno specifico linfocita T, tale linfocita T si attiva e comincia a proliferare (espansione clonale, clonal expansion). Le due catene principali (α and β) sono assemblate combinando la trascrizione di segmenti di gene, ognuno dei quali ha copie multiple, leggermente diverse fra loro: in altre parole, i TCR vengono assemblati a partire da peptidi scelti a caso da un insieme di diverse alternative possibili. Questo comporta un repertorio di 10^15 diversi possibili TCR (Mason DA 1998). Ogni linfocita T mostra un solo tipo di TCR.

4. Cellule T helper

Le cellule T helper sono programmate per riconoscere esclusivamente antigeni esposti dalle molecole MHC di seconda classe (II): questa classe di MHC viene espressa sulla membrana esterna di alcuni leucociti, principalmente le cellule dendritiche, le cellule B e i macrofagi (tutte assieme dette “cellule che presentano l’antigene”, antigen presenting cells: APC). Le molecole MHC II legano il TCR delle cellule T helper grazie al peptide CD4 (espresso unicamente dalle cellule T helper). L’antigene presentato dalle molecole MHC è un peptide lungo 13-17 amminoacidi (Rudensky, et al., 1991) (figura 2).

5. Linfociti T citotossici

I TCR espressi dai linfociti T citotossici (CTL) possono legare solo antigeni esposti dalle molecole MHC di prima classe (I), che si trovano nella membrana esterna di qualunque cellula del nostro corpo. La glicoproteina CD8 è la molecola che rende i TCR espressi dalle CTL specifici per il MHC I. Mentre gli antigeni esposti dalle APC appartengono a patogeni raccolti sul campo di battaglia di passate infezioni, i peptidi esposti dal MHC I di una specifica cellula appartengono a patogeni che hanno fatto ingresso nella cellula stessa, e pertanto costituiscono la prova di un’infezione intracellulare ancora in atto (figura 3). Nel momento in cui un CTL riconosce un antigene che combacia con il proprio TCR, il CTL iduce l’apoptosi (morte programmata) della cellula che mostra l’antigene. Gli antigeni esposti dal MHC I sono peptidi che vanno dagli 8 ai 10 amminoacidi (Stern, et al., 1994).

Figure 3. Una cellula infetta espone un antigene virale sul proprio MHC I. Il TCR di un CTL si lega a questo peptide ed invia un segnale interno diretto al suo proprio nucleo, il quale risponde attivando l’apoptosi (attraverso il rilascio di granzimi, ad esempio) della cellula infetta (disegno di Paolo Maccallini).6. Il test immunologico universale

Nel corso del suo discorso, Mark Davis illustra alcuni concetti base sul sistema immunitario, prima di passare a introdurre i nuovi, entusiasmanti dati riguardo alla ME/CFS e alla Lyme cronica (o post-treatment Lyme disease syndrome: PTLDS). Contestualmente, però, dedica alcuni minuti alla descrizione di un complesso nuovo test che teoricamente renderebbe possibile estrapolare tutte le informazioni contenute nel repertorio di TCR presenti – in un dato momento – nel sangue di un essere umano. Un test del genere – che chiamerei “test immunologico universale” – avrebbe la capacità di determinare se un paziente presenta un’infezione in corso (e, nel caso, indicare il patogeno coinvolto) oppure una malattia autoimmune (anche qui specificando la natura dell’autoantigene, ossia il tessuto attaccato dal sistema immunitario). A quanto mi è dato di comprendere, il test richiede tre passaggi, che elenco nelle sezioni seguenti.

6.1. Primo step: sequenziamento del TCR

Come già spiegato nel paragrafo 3, quando un linfocita T incontra un peptide a cui è compatibile, comincia a proliferare; pertanto, nel sangue di un paziente con infezione in corso (o con reazione contro il proprio organismo, cioè con reazione autoimmune) è possibile trovare molteplici copie di linfociti T che esprimono il medesimo TCR: a differenza dei controlli sani, nei quali circa il 10% delle CD8 totali è rappresentato da copie di pochi diverse linfociti T (figura 4, prima linea), nei pazienti affetti da Lyme incipiente – un esempio di infezione attiva – o sclerosi multipla (MS) – un esempio di malattia autoimmune – abbiamo una massiccia clonazione di alcune linee di CTL (figura 5, seconda e terza riga, rispettivamente). Il primo step del test immunologico universale starà allora nell’identificazione dell’esatta sequenza di TCR espressa dai linfociti T presenti nel sangue, come si legge in Han A et al. 2014, dove troviamo descritto il sistema per sequenziare i geni delle catene α e β di un dato linfocita T. Tale approccio permette di costruire grafici come quello in figura 4 e quindi permette di determinare se il paziente presenti in atto un’attività anomala dei linfociti T oppure no. Qualora si riscontri un fenomeno di espansione clonale, è legittimo ipotizzare che stia avendo luogo o un’infezione o una condizione autoimmune di qualche sorta.

Clonal expansion CD8 — **Figure 4.** Ogni cerchio rappresenta un paziente. Nella prima riga vediamo quattro controlli sani, che non presentano affatto espansione clonale delle cellule CD8 (come nel primo paziente da sinistra) oppure la presentano in maniera assai moderata (come indicato dalle porzioni in blu, bianco e grigio). Nella seconda riga troviamo invece quattro pazienti con malattia di Lyme attiva (fase incipiente) e possiamo ben notare come ciascuno di loro, nessuno escluso, presenti espansione clonale di solo tre diverse T cells (porzioni in rosso, blu e arancione). Nella terza riga, infine, abbiamo quattro pazienti affetti da MS, le cui cellule CD8 sono per maggior parte rappresentate da cloni di una selezione ristretta di T cells.
Fonte: slide proposte da Mark Davis durante il Community Symposium.

6.2. Secondo step: raggruppamento dei TCR

Mark Davis e colleghi hanno realizzato un software capace di identificare i TCR che condividono il medesimo antigene, sia in un singolo individuo che trasversalmente a un gruppo. L’algoritmo è stato denominato GLIPH (grouping of lymphocyte interaction by paratope hotspots) ed ha dato prova di poter raggruppare – per fare un esempio – i recettori dei linfociti T CD4 di 22 soggetti con infezione da M. tuberculosis latente in 16 gruppi distinti, ognuno dei quali comprende TCR provenienti da almeno tre individui (Glanville J et al. 2017). Cinque di questi gruppi sono riportati nella figura 5. L’idea sottostante è che TCR che appartengono allo stesso raggruppamento reagiscano allo stesso complesso peptide-MHC (pMHC).

**Figure 5.** Cinque gruppi di TCR provenienti da 22 diversi pazienti affetti da turbercolosi latente, raggruppati grazie al GLIPH. La prima colonna da sinistra riporta l’identificativo dei TCR; la seconda l’identificativo dei pazienti. Le CDR per le catene β e α si trovano, rispettivamente, sulla terza e sulla quinta colonna. Tratto da Glanville J et al. 2017.

6.3. Terzo step: ricerca degli epitopi

Come abbiamo visto, questa nuova tecnologia consente di rilevare se sia in atto un’espansione clonale di linfociti T sequenziando i TCR dal sangue periferico. Consente inoltre di raggruppare i TCR presenti in un singolo paziente o condivisi da più pazienti. Il passaggio successivo è quello di identificare a quale/i tipo/i di antigene ognuno di questi raggruppamenti reagisca. Infatti, se potessimo identificare degli antigeni comuni in un gruppo di pazienti dai sintomi comparabili nei quali si riscontri un’espansione clonale in atto e simili TCR, saremmo messi in grado di comprendere se il loro sistema immunitario stia attaccando un patogeno (e di identificare il patogeno) o se stia piuttosto attaccando un tessuto ospite e, qualora fosse questo il caso, di identificare il tessuto. Come già detto, il numero di possibili combinazioni per il materiale genetico dei TCR è calcolato attorno ai 10^15, ma il numero dei possibili epitopi di cellule Th è circa 20^15, che corrisponde a più di 10^19. Ciò implica che i TCR debbano essere in una qualche misura cross-reattivi se vogliono essere in grado di riconoscere tutti i possibili peptidi esposti dai MHC (Mason DA 1998). Il grado di tale cross-reattività e il meccanismo attraverso il quale viene ottenuta sono stati spiegati con esattezza da Mark Davis e colleghi in un recente articolo (Birnbaum ME et al. 2014), che ci fornisce il terzo step del test immunologico universale. Lo scopo di questa fase consiste nel prendere un dato TCR e trovare il repertorio dei suoi specifici antigeni (giova ripetere che, appunto, ogni TCR reagisce a più antigeni). Per comprendere come ciò sia possibile, guardiamo a uno degli esperimenti descritti nell’articolo più sopra citato. I ricercatori si sono concentrati su due TCR ben precisi (chiamati Ob.1A12 e Ob.2F3), clonati da un paziente con MS e noti per essere capaci di riconoscere i pepetidi 85-99 (figura 6) della proteina basica della mielina (MBP) esposti dall’ HLA-DR15. Hanno poi preparato un insieme di cellule di lievito che esprimono molecole HLA-DR15, ognuna caratterizzata da un diverso peptide formato da 14 amminoacidi, con amminoacidi fissi esclusivamente alle posizioni 1 e 4, dove il peptide è ancorato al MHC (figura 6, sinistra). Quando alla coltura di cellule di lievito che esprimono complessi pMHC vengono aggiunte copie di Ob.1A12, queste legano solo con alcune di quelle e, come è possibile vedere dalla parte destra della figura 6, per ciascuna posizione degli epitopi legati dal Ob.1A12 esiste un amminoacido con maggior tasso di probabilità: ad esempio, l’epitopo Ob.1A12 tipico presenta preferibilmente alanina (A) in posizione -4, istidina (H) in posizione -3, arginina (R) in posizione -2, e così via. Da notare che istidina (H) in posizione 2 e fenilanina (F) in posizione 3 sono amminoacidi obbligatori per un epitopo di Ob.1A12.

Ob. 1A12 — **Figure 6.** Sulla sinistra: il peptide 85-99 della proteina basica della mielina (*myelin basic protein*, MPB) è risaputo essere un epitopo per il TCR Ob.1A12. In posizione 1 e 4 possiede due residui che gli consentono di legare con la molecola MHC. In posizione -2, -1, 2, 3 3 5 troviamo invece i residui che legano con il TCR. La seconda riga rappresenta l’epitopo generico della libreria peptidica utilizzata per identificare il grado di cross-reattività tra tutti i possibili epitopi di Ob.1A12. A destra: la probabilità di ciascun amminoacido per ciascuna posizione è rappresentata da sfumature di viola. Come potete vedere, l’istidina (H) in posizione 2 e la fenilalanina (F) in posizione 3 sono amminoacidi obbligatori affinché un epitopo sia reattivo con Ob.1A12. Da (Birnbaum ME et al 2014).

La tabella sulla destra della figura 6 rappresenta, infatti, una tabella di sostituzione (substitution matrix) di dimensioni 14×20, uno strumento impiegato per scansionare il database dei peptidi in modo da trovare, tra tutti i peptidi conosciuti espressi da creature viventi, tutti i possibili epitopi specifici per Ob.1A12. Le matrici di sostituzione vengono solitamente utilizzate nel cosiddetto allineamento di peptidi (peptide alignment), una tecnica che punta all’identificazione di similitudini tra peptidi. Tali matrici sono basate su considerazioni di tipo evoluzionistico (Dayhoff, et al., 1978) o sullo studio delle regioni conservate delle proteine (Henikoff, et al., 1992). Ma la ricerca degli epitopi specifici di un dato TCR richiede (come abbiamo visto per Ob.1A12) una matrice di sostituzione costruita ad hoc per quel TCR: ogni TCR richiede la propria matrice di sostituzione, ottenuta incubando cellule T esprimenti quel TCR con una coltura di lieviti che espongono sui propri MHC una grande varietà di peptidi casuali, e analizzando poi i dati ricavati dall’esperimento. Quindi, un processo piuttosto complesso! Nel caso di Ob.1A12, questo processo ha portato a 2330 peptidi (incluso MBP), mentre la matrice di sostituzione specifica per Ob.2F3 ha trovato 4824 epitopi all’interno dell’intero database di peptidi. Questi peptidi includevano sia proteine non umane (batteriche, virali…) che peptidi umani. Per 33 di loro (26 non umani e 7 proteine umane), questo gruppo di ricercatori ha eseguito un test per verificare direttamente la previsione: 25/26 dei peptidi ambientali e 6/7 dei peptidi umani hanno indotto la proliferazione di cellule T che esprimono il TCR Ob.1A12 e/o il Ob.2F3, e questa è una prova della validità di questa analisi! Questi 33 peptidi sono riportati nella figura 7. Questo è l’ultimo passaggio del test immunitario universale, quello che dal TCR conduce agli epitopi. Come avete visto, un enorme insieme di diversi peptidi da diverse fonti reagisce con un singolo tipo di TCR; in altre parole, la cross-reattività è una proprietà intrinseca del TCR. Ciò significa anche che i test di trasformazione linfocitaria (LTT), ampiamente utilizzati in Europa per l’individuazione di infezioni da Borrelia burgdorferi e altri patogeni, comportano un rischio elevato di risultati falsi positivi e richiedono un processo di validazione sperimentale e teorica, attualmente mancante.

Crossreactive epitopes — **Figura 7.** Una serie di 33 peptidi che si suppongono essere epitopi specifici sia per Ob.1A12 che per Ob.2F3. Tratto da Birnbaum ME et al. 2014.

Siamo ora pronti ad apprezzare appieno i dati pilota che Mark Davis ha presentato al Symposium sull’espansione clonale delle cellule T CD8 nella ME/CFS e nella Lyme cronica.

7. “We have a hit!”

Mark Davis, insieme a Jacob Glanville e José Montoya, hanno sequenziato TCR dal sangue periferico di 50 pazienti ME/CFS e 49 controlli (primo passo del test immunitario universale, ricordate?), quindi li hanno raggruppati usando l’algoritmo GLIPH (secondo passo). Hanno trovato 28 cluster, ciascuno costituito da più di 2500 sequenze simili, e ogni cluster raccoglie sequenze multiple dallo stesso individuo e sequenze (che sono forse più importanti) da pazienti diversi (figura 8). Il cluster che ho cerchiato in rosso, ad esempio, è una raccolta di oltre 3000 TCR simili. La presenza di questi ampi cluster nei pazienti ME/CFS, rispetto ai controlli sani, rappresenta una prova indiretta di una risposta specifica delle cellule T a un trigger comune in questo gruppo di pazienti, che potrebbe essere un agente patogeno o un tessuto del corpo (o tutti e due).

Clustered TCR — **Figura 8.** Nella ME/CFS le sequenze di TCR ricavati da 50 pazienti formano 28 raggruppamenti che presentano più di 2500 sequenze simili – cosa che assolutamente non avviene nei controlli sani. Questo fa pensare ad una qualche risposta immunitaria ad un patogeno o ad un tessuto umano (o entrambi). Fonte: slide proposta da Mark Davis durante il Community Symposium.

Tra questi 50 pazienti ME/CFS, Davis e colleghi hanno selezionato 6 pazienti con geni HLA simili (figura 9, sinistra), 5 femmine tra loro, e hanno studiato i loro TCR più in profondità. Nella metà destra della figura 9, è possibile vedere per ciascun paziente il grado di espansione clonale delle CTL. Ricordate che nei controlli sani solo circa il 10% dei CTL è composto da cloni di alcune cellule (figura 4, prima riga), mentre qui vediamo che circa il 50% di tutti i CTL è composto da cloni. Quindi, una “marcata espansione clonale” delle cellule T CD8, come ha detto Davis.

ME subjects CD8 — **Figura 9**. A sinistra: sono stati selezionati 6 pazienti ME/CFS con HLA simili. Sulla prima colonna da sinistra sono stati riportati gli identificativi dei pazienti; la seconda colonna ci informa sull’età di ciascuno; la terza sul genere; la quarta avvisa di eventuali esposizione a citomegalovirus; la quinta riguarda i geni del MHC I. A destra: l’analisi dell’espansione clonale delle cellule T CD8 per ognuno dei pazienti. L’espansione clonale è marcata (circa al 50%), se comparata a quella dei controlli sani (circa al 10%).

Le sequenze delle catene α e β dei TCR di tre dei sei pazienti (pazienti L4-02, L4-10 e L3-20) sono riportate in figura 10 (ho verificato che effettivamente si tratta di catene α e β di TCR umani, inserendole in BLAST).

TCR epitope — **Figura 10.** Catene β (prima colonna) e rispettive catene α (quinta colonna) provenienti da tre pazienti ME/CFSchains (L4-02, L4-10, and L3-20, ultima colonna).

Quindi, abbiamo visto finora i primi due passaggi del test immunitario universale. E il terzo passo? Nel suo discorso, Mark Davis non ha presentato alcun particolare epitopo, ha solo mostrato una diapositiva con quella che probabilmente è la selezione degli epitopi dalla libreria discussa nel paragrafo 6.3 da parte di uno dei TCR riportati in figura 10. Questa selezione è riportato in figura 11, ma da quella foto non è possibile raccogliere alcuna informazione sull’identità di questi epitopi. Come probabilmente ricorderete dal paragrafo 6.3, l’analisi dei peptidi selezionati da un TCR nella libreria di peptidi consente l’identificazione di una matrice di sostituzione che può essere utilizzata per selezionare tutti i possibili epitopi di quel TCR specifico, dal database delle proteine. Quest’ultima fase cruciale deve essere ancora eseguita, o è già stata eseguita, ma Davis non ha comunicato i risultati preliminari durante il suo discorso. Recentemente sono state messe a disposizione nuove risorse dalla Open Medicine Foundation, affinché questa ricerca promettente possa essere ulteriormente perseguita (R). Lo scopo qui, come già detto, è di trovare l’antigene che innesca questa risposta delle cellule T. Come ha detto Mark Davis, potrebbe essere un antigene di un agente patogeno specifico (forse un patogeno comune che va e viene) che suscita una risposta immunitaria anomala che finisce per colpire alcuni tessuti ospiti (microglia, per esempio), portando così attivazione immunitaria che è stata recentemente segnalata da Mark Davis stesso e altri in ME/CFS (Montoya JG et al. 2017). L’idea di un patogeno comune che innesca una risposta immunitaria patologica non è nuova in medicina, e la febbre reumatica (RF) è un esempio di una tale malattia: la RF è una malattia autoimmune che attacca il cuore, il cervello e le articolazioni ed è generalmente innescata da uno streptococco che infetta la gola (Marijon E et al. 2012). L’altra possibilità è, naturalmente, quella di un’infezione in corso di qualche tipo, che deve ancora essere rilevata. Come detto (vedi par. 6.1), l’espansione clonale delle cellule T CD8 è presente sia nelle infezioni acute (come la malattia di Lyme) che nelle malattie autoimmuni (come la SM) (figura 4), quindi dobbiamo aspettare l’identificazione dell’antigene se vogliamo capire se l’attività del CTL è contro un agente patogeno e/o contro un tessuto del nostro corpo.

peptide library — **Figura 11.** Nella figura possiamo osservare la selezione, che avviene in più momenti, di una serie di peptidi da parte di un particolare TCR proveniente da un paziente ME/CFS. La selezione ha luogo tra una enorme quantità di peptidi esposti dall’ HLA-A2 (MHC I) espresso da cellule di lievito. Ad ogni passaggio il numero di possibili peptidi si riduce.

8. La Lyme cronica esiste

È stato probabilmente trascurato il fatto che nel suo discorso, Mark Davis ha riportato anche dati molto interessanti sulla sindrome della malattia di Lyme post-trattamento (PTLDS, nota anche come malattia di Lyme cronica). In particolare, ha trovato un’espansione clonale marcata nelle cellule T CD8 di 4 pazienti PTLDS (circa il 40% dei CTL totali) come riportato nella figura 12: si consideri che in questo caso le fette blu rappresentano cellule T uniche, mentre tutte le altre fette rappresentano cloni! Tutto ciò che è stato detto sull’espansione clonale CD8 nella ME/CFS si applica anche in questo caso: potrebbe essere la prova di un’infezione in corso – forse la stessa B. burgdorferi, come suggerito da diversi modelli animali (Embers ME et al. 2017), (Embers ME et al. 2012), (Hodzic E et al. 2008), (Yrjänäinen H et al. 2010) – o una coinfezione (un virus?). Oppure potrebbe essere l’espressione di una reazione autoimmune innescata dalla infezione iniziale. Questo deve ancora essere scoperto, eseguendo il test immunitario universale completo, ma ciò che è già chiaro dalla figura 12 è che la PTLDS è una condizione reale, con qualcosa di veramente anomalo nella risposta immunitaria: la Lyme cronica esiste.

PTLDS CD8 — **Figura 12.** Espansione clonale di cellule T CD8 in quattro pazienti affetti da Lyme cronica. L’espansione clonale, che indica l’attività delle cellule T contro un patogeno o un tessuto ospite, è assai marcata.

9. Conclusioni

Mark Davis e altri ricercatori hanno sviluppato un test complesso che è in grado di sequenziare i TCR dai pazienti, raggrupparli in gruppi di TCR che reagiscono agli stessi antigeni e scoprire gli antigeni che hanno attivato quella particolare risposta delle cellule T. Questo test è una sorta di test immunitario universale che è teoricamente in grado di riconoscere se una persona (o un gruppo di pazienti) presenta una risposta immunitaria contro un agente patogeno o contro uno dei loro stessi tessuti (o entrambe le cose). Questo approccio ha già fornito dati pilota su una attivazione anomala delle cellule T CD8 nei pazienti ME/CFS e nei pazienti PTLDS e, si spera, identificherà il trigger di questa risposta immunitaria nel prossimo futuro. Se la ME/CFS è causata da un’infezione attiva, da una malattia autoimmune o da entrambe le cose, il test immunologico universale potrebbe essere in grado di dircelo. Questa nuova tecnologia è per l’immunologia, ciò che il sequenziamento dell’intero genoma è per la genetica, o la metabolomica è per le malattie molecolari: non cerca un particolare agente patogeno o una particolare malattia autoimmune. No, cerca tutte le possibili infezioni e disturbi immunitari, anche quelli che devono ancora essere scoperti.

Why we can’t use LTTs, yet

A line of T cells (called Ob.2F3) expressing the same T cell receptor (TCR) from an MS patient was studied in 2014 and it was found to proliferate when incubated with 4824 different peptides. Thirty-three of them were further studied (see figure) and found to belong to both Homo sapiens and several different, unrelated microbes (Birnbaum ME et al. 2014). The taking home message here is that T cells are not specific to a single pathogen, they are highly cross-reactive, as it was already pointed out in this pivotal study: (Mason DA 1998). And this means that we can’t use lymphocyte transformation tests (LTTs) the way we do now.

I feel really frustrated when patients send me their LTTs and ask me to comment the results. I have to say that they have wasted their money and that these results are useless. I do hope that my blog can make a difference and stop this unfair commerce at the expenses of desperate folks.

Convegno nazionale sulla ME/CFS, Paolo Maccallini

Quello che segue è il mio intervento durante il convegno nazionale sulla ME/CFS tenutosi a Thiene, tappa italiana dell’End ME/CFS Worldwide Tour. L’intervento è molto denso e veloce, ho dovuto condensare 4 anni di ricerche in 30 minuti. Qualcuno ha notato che sembravo dopato. Lo ero, letteralmente: ero alla fine di un lungo trattamento cortisonico e avevo assunto modafinil per la circostanza. Altrimenti non sarei riuscito. Le slide usate per questo intervento, insieme ad altre che non ho avuto modo di far vedere al convegno, sono disponibili qui. Sotto il video c’è un sommario del contenuto dell’intervento, e il momento del video in cui i vari argomenti sono stati trattati. Ringrazio Giuseppe Pozza per aver realizzato il video.

Note biografiche, criteri diagnostici e disturbi cognitivi (00:50)
Intolleranza ortostatica (08:39)
Citochine (09:45)
Citotossicità delle NK (11:15)
Disfunzioni metaboliche (12:40)
Anomalie del sistema nervoso centrale (20:50)
Anomalie del microbioma (22:40)
Analisi genetica (24:20)
La mia ricerca su Lyme e autoanticorpi (27:50)
Anticorpi anti-muscarinici e anti-beta adrenergici nella M/CFS (32:20)
Studi a cui ho partecipato come paziente, conclusioni e ringraziamenti (34:53)

Riascoltando il mio intervento ho provato stupore nel constare, forse per la prima volta, come la mia mente sia sopravvissuta. Solo io posso sapere cosa ho passato, nessuno sa che per gli ultimi 17 anni sono stato incapace di pensare per più del 90% del tempo. E non intendo incapace di risolvere sistemi di equazioni differenziali; no, intendo incapace di sostenere una conversazione o di leggere un libro.

Nonostante sia stata così colpita dalla malattia, nonostante sia stata privata di stimoli, nostante la solitudine estrema, i farmaci inutili e il consumarsi dei lustri, è sopravvissuta. Questo organo di un chilo e mezzo scarso che mi contiene tutto, che ha perso così tanto, che ho dato per spacciato tante volte, è sopravvissuto. La vita vuole vivere e non si arrende.

Test a due livelli per la malattia di Lyme

Per ottimizzare i test sierologici in termini di sensibilità e specificità, si adotta in Europa, quanto negli Stati Uniti, un algoritmo a due livelli (vedi Figura 1). Il primo livello è costituito da un test ad alta sensibilità (il test ELISA); coloro che sono negativi a questo test vengono considerati sieronegativi, coloro che sono positivi accedono a un test di secondo livello altamente specifico (il western blot), il cui scopo è quello di minimizzare il numero di falsi positivi (Wilske B. et al. 2007).

two tiers.png — **Figura 1.** Algoritmo decisionale per il test a due livelli.

In Tabella 1 sono riportati i dati statistici relativi a un test a due livelli in cui il primo livello è rappresentato da un test ELISA con antigeni ottenuti da sonicato da cellula intera di Borrelia afzelii per le IgM, con aggiunta di VlsE ricombinate da B. afzelii, B. garinii e B. burgdorferi ss per le IgG; il secondo livello è invece costituito da un western blot i cui antigeni sono proteine estratte da B. burgdorferi ss (ceppo B31) e da Borrelia afzelii (ceppo PKo) con aggiunta di VlsE ricombinate da B burgdorferi ss (ceppo B31) (Branda JA. et al. 2013). Si può notare che con questa procedura si ha un 12% di falsi negativi nel gruppo neuroborreliosi e una percentuale di falsi positivi sempre minore del 2%.

doppio livello.png — **Tabella 1.** Sono riportati sensibilità, specificità, valore predittivo positivo (VPP) e valore predittivo negativo (VPN) per un western blot europeo. EM sta per eritema migrante, NB per neuroborreliosi, ACA per acrodermatite cronica atrofica. IgG e IgM sono considerate insieme. Da (Branda JA. et al. 2013) con modifiche.

A conclusione di questo paragrafo, si segnala che nel 2011 i CDC hanno modificato le loro raccomandazioni, includendo la possibilità dell’uso diretto di un immunoblot per le IgG, senza passare per il test di primo livello (R).

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Model	Test on the coefficients (p value)	$\bf R^2$
Logistic	0.0199	0.2661
Exponential	$<2\cdot 10^{-16}$	0.9934
Gaussian	$1.035\cdot 10^{-12}$	0.9611

Model	Test on the coefficients (p value)	$\bf R^2$
Logistic	0.03251	0.2868
Exponential	$7.278\cdot 10^{-15}$	0.9872
Gaussian	$5.475\cdot 10^{-9}$	0.9464

$N_{pos}$	The number of carriers of the virus who did not receive the vaccine.
$N_{tot}$	The number of asymptomatic individuals who did not receive the vaccine. Their positivity to the virus is not specified.
$r$	The ratio between the asymptomatic carriers of the virus who are unvaccinated and $N_{pos}$ .
$N_{pos}r$	The number of asymptomatic carriers of the virus who did not receive the vaccine.

paolo maccallini

and the race to solve ME/CFS and related diseases

Category: Medicine

Myalgic Encephalomyelitis Chronic Fatigue at the National Institutes of Health

The current outbreak of Chikungunya in Paraguay

Analysis of a summary statistics generated from the UK Biobank database: new potential risk loci for ME/CFS and not otherwise specified chronic asthenia

Tryptophan metabolites in the cerebrospinal fluid of ME/CFS patients

An update on the UK Biobank: fine-mapping

An estimation of the proportion of asymptomatic Omicron infection

A complete (preload) failure

Lettera aperta all’Osservatorio Malattie Rare

Mark Davis e il test immunitario universale

Why we can’t use LTTs, yet

Convegno nazionale sulla ME/CFS, Paolo Maccallini

Test a due livelli per la malattia di Lyme