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).
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%.
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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The translation to Italian of this article is available here.
Parvovirus B19 is a single-stranded DNA virus with a tropism for precursors of Homo sapiens’ erythrocytes. It was discovered in 1975 (Cossart YE et al. 1975) and was associated with human disease in 1981 (Pattison JR. et al. 1981). Its genome consists of a linear single-stranded DNA with a length of 5.600 bases that includes the genes for the two capsid proteins VP1 and VP2 and for the non-structural protein NP1 (Trösemeier JH. et al. 2014). Its Linnaean classification is the one reported in the table below. Parvovirus B19 has a diameter of only 25 nm, and this explains its name: parvum is a Latin adjective that means small. In children, the acute infection is associated with erythema infectiosum (also known as Fifth disease). In immunocompetent adults, it can cause acute symmetric polyarthropathy, whereas in the immunocompromised host persistent B19 infection is manifested as pure red cell aplasia and chronic anaemia (Heegaard ED et Brown KE 2002). Parvovirus B19 spreads through respiratory secretions, such as saliva, sputum, or nasal mucus, when an infected person coughs or sneezes [R]. It is known to persist in peripheral white blood cells (Saal JG. et al. 1992).
Prolonged and chronic fatigue has been described during acute and convalescent parvovirus infection (Kerr JR et al. 2001) and it is associated with raised levels of TNF-α and INF-γ. A study followed 39 patients with acute Parvovirus B19 infection for an average of two years and reported that 5 (13%) of them developed CFS. Most of them had positive PCR and/or positive IgG in blood for B19. Deterioration in memory and concentration, post-exertional malaise, and myalgia were present in all of them. The prevalence of anti-VP1/2 IgG was about the same in patients and controls, while anti-NS1 IgG and DNA in serum where more prevalent in patients than in controls (Kerr JR. et al. 2002). In 2009 Fremont and colleagues searched for viral DNA in gut biopsies (from both the gastric antrum and the duodenum) and they found a higher prevalence in patients vs controls. And yet, patients with positive PCR for Parvovirus B19 DNA in biopsies had negative PCR in their blood (Frémont M. et al. 2009). Another study found a higher prevalence of anti-NS1 IgG in patients vs controls, whereas serum DNA, anti-VP1/2 IgG, anti-VP 1 IgM, anti-NS1 IgM were not different between patients and controls. Antibodies to NS1 were associated with arthralgia, among patients (Kerr JR. et al. 2010). Recently, another group confirmed a normal prevalence of anti-VP1/2 IgG in patients with an increase in anti-VP 1 IgM and serum DNA (Rasa S. et al. 2016).
1: biopsies from both the gastric antrum and the duodenum. 2: they used this kit. WBC, white blood cells.
I have found four cases of ME/CFS patients with confirmed active B19 infection (DNA in the blood) successfully treated with intravenous immunoglobulins, with rapid resolution of symptoms and clearance of the infection. In three cases the treatment was as follows: 400mg/kg/day for five days (Kerr JR. et al. 2003). In the remaining patient the posology is not reported (Jacobson SK. et al. 1997).
Acute Parvovirus infection can lead to ME/CFS in more than 10% of cases (Kerr JR et al. 2001), (Kerr JR. et al. 2002). This prevalence is in agreement with the percentage of those who develop ME/CFS after Giardia duodenalis (Mørch K et al. 2013), Epstein-Barr virus, Coxiella burnetii, and Ross River virus (Hickie I. et al. 2006) symptomatic and laboratory-confirmed infections (see also this post). This would suggest that different pathogens can trigger a common pathway that ultimately leads to ME/CFS. And yet, markers of active Parvovirus B19 infection are more common among ME/CFS patients than in healthy controls: this is the case of viral DNA in gastric mucosa (Frémont M. et al. 2009) and serum (Rasa S. et al. 2016), and of anti-VP 1 IgM (Rasa S. et al. 2016). Moreover, the synthesis of specific IgGs to NS1 is significantly more prevalent in patients vs controls, and this kind of antibodies has been documented to be more frequent in case of more severe and persistent course of B19 infection (von Poblotzki A. et al. 1995). Four cases of ME/CFS with active B19 infection were successfully treated with IVIG (Jacobson SK. et al. 1997), (Kerr JR. et al. 2003). At the same time, the seroprevalence of B19 with regards to VP 1/2 IgG is the same in patients and controls (Kerr JR. et al. 2002), (Kerr JR. et al. 2010), (Rasa S. et al. 2016) which means that the number of individuals that get the virus in their lifetime is the same in patients and controls.
Seroprevalence of Parvovirus B19 is the same in ME/CFS patients and controls, but active infection is more prevalent in cases versus controls. Moreover, patients are more likely to have IgGs to NS1, a marker of persistent course of B19 infection. IVIGs might be a therapeutic option in ME/CFS patients with active B19 infection.
IgM tests present a high rate of false positive results. This can lead to misdiagnosis, inappropriate treatments, and lack of treatment for the true aetiology (Landry ML. 2016). In the following table, I have collected several well-documented cases of IgM tests falsely positive for an infectious disease. In most of these studies, the cause of the false positive result was found to be either another acute infection or autoantibodies, including rheumatoid factor (RF), an IgM that binds to the Fc region of IgG. So it might be important to determine the exact origin of a false positive IgM test, in cases where a diagnosis is hard to find: it could be the clue that ultimately leads to the true aetiology.
List of abbreviations. CHF, congestive heart failure; CHIK virus, Chikungunya virus; CMV, cytomegalovirus; EBV, Epstein-Barr virus; HAV, hepatitis A virus; HDF, human diploid fibroblast cells; HEV, hepatitis E virus; HIV, human immunodeficiency virus; HHV-6, human herpesvirus type 6; HSV, herpes simplex virus; RF, rheumatoid factor; VZV, varicella-zoster virus; WNV, West Nile virus.
Cross-reactivity with other pathogens
One possible cause for false positive results is cross-reactivity between antigens that belong to different pathogens. A little-known example of this phenomenon comes from the research on ME/CFS: in the study that ultimately ruled out the involvement of XMR virus in the pathogenesis of ME/CFS, antibodies to that pathogen were found in about 6% of both cases and healthy controls, whereas the molecular testing turned out to be negative in all participants (Alter HJ. et al. 2012). So, sera reactivity to XMRV is likely due to a relatively common pathogen that has an antigen similar to another one belonging to XMRV.
In one case of false positive HSV IgM due to VZV infection, the serum/CSF IgM ratio as a function of time had the same profile for both the viruses, suggesting cross-reactivity (Kinno R. et al. 2015). Cross-reactivity between HSV IgM and VZV IgM seems quite common, with both false positive HSV samples due to reactivity to VZV and false positive VZV IgMs due to IgM against HSV (Ziegler T. et al. 1989).
Interestingly enough, although OspC is considered to be a highly specific antigen of B. burgdorferi, OspC IgM is often positive in patients with active EBV or CMV infections (Goossens HA. et al. 1998). If cross-reactivity was responsible for false positive OspC IgM in infectious mononucleosis, we would expect false positive IgM for EBV and CMV in early Lyme disease. And this is is exactly what has been found in two cases of acute Lyme disease, where falsely positive IgM to VCA has been documented (Pavletic A. Marques AR. 2017).
Latent infections reactivation
It has been described a rise of EBV VCA IgM titers in CMV primary infections. This is likely due to EBV reactivation in many cases. This can lead to a misdiagnosis of a primary EBV infection, instead of a primary CMV infection. This error can have serious consequences during immune suppression or pregnancy, when CMV infections are health-threatening (Aalto MS et al. 1998).
Rheumatoid factor interference
As mentioned in the introduction, rheumatoid factor (RF) is an autoantibody – mainly of the IgM subclass – that is found in most of the patients with rheumatoid arthritis (Hermann E. et al. 1986). It binds the constant region (Fc region) of human IgGs and thus can bind the enzyme-linked immunoglobulins often used in serologic assays, leading to falsely positive results (Pan J. et al. 2018).
Cross-reactivity with autoantigens
Another possible cause of falsely positive IgM tests to a pathogen is the presence of autoantibodies other than RF. Autoantibodies to fibroblast cells have been found to be the cause of a false positive IgM test for HSV and CMV (Ziegler T. et al. 1989). This kind of reactivity to self-antigens is probably non-specific of a particular autoimmune disease, and it has been found for instance in pretibial myxedema, Graves’ disease, and Hashimoto’s thyroiditis (Arnold K. et al. 1995).
The effect of prevalence on the rate of false positive results
The likelihood of a false positive result is inversely correlated with the prevalence of the pathogen in the specific population considered. In other words, the rarer the disease, the more likely a positive test for that disease is a false positive. This can be easily seen introducing the predictive positive value (PPV), which is the probability that a positive test is really a true positive (Lalkhem AG. et McCluskey A. 2008). PPV is given by
In the following figure, you can see how PPV increases as the prevalence increases. This diagram has been plotted considering a sensitivity of 67% and a specificity of 53%.
In the following four tables, I present a collection of integrals and integral functions that are of common use in Statistics. The values for the Beta function have been calculated by a code of mine that uses – as a recursive function – another code that I wrote for the calculation of the Gamma Function (see the related blog post). Below these tables, you find a representation of the Beta function, plotted by my code. I have demonstrated each one of these results and these calculations will be included in an upcoming book.
Many of my readers are probably aware of the attempts that are currently being made to mathematically simulate the energy metabolism of ME/CFS patients, integrating metabolic data with genetic data. In particular, dr. Robert Phair has developed a mathematical model of the main metabolic pathways involved in energy conversion, from energy stored in the chemical bonds of big molecules like glucose, fatty acids, and amino acids, to energy stored in adenosine triphosphate (ATP), ready to use. Phair, who is an engineer, determined the differential equations that rule this huge amount of chemical reactions and adapted them to the genetic profile found in ME/CFS patients. Genetic data are the result of the analysis of the exomes of more than 40 patients (I am among them). He found, in particular, that the enzyme ATP synthase (one step of the mitochondrial electron transport chain, called complex V) presents a damaging variant that is found in less than 30% of healthy controls while being detected in more than 60% of ME/CFS patients. He found other enzymes (I don’t know their exact number) of energy metabolism meeting these same criteria. Setting a reduced activity for these enzymes in his mathematical model, he found that, after particularly stressing events (such as infections), ME/CFS patients metabolism can fall into a low-energy state without being able to escape from it (this theory has been called the “metabolic trap hypothesis”) (R, R, R). Phair’s hypothesis is currently being experimentally tested and has not been published yet, but some years ago two physicists published an interesting mathematical model of energy metabolism during and after exercise, in ME/CFS patients compared to healthy controls (Lengert N. et Drossel B. 2015). In what follows I will describe this model and its predictions and we will also see how these differential equations look like.
Metabolic pathways that have been analyzed
The model by Lengert and Drossel extends two previously published systems of differential equations that describe the behaviour of glycolysis, Krebs cycle (hugely simplified as a single reaction!), mitochondrial electron transport chain (described in detail), creatine kinase system, and of conversion of adenosine diphosphate (ADP) in ATP, in skeletal muscles (Korzeniewski B. et Zoladz JA. 2001), (Korzeniewski B. et Liguzinski P. 2004). They added equations for lactate accumulation and efflux out of the cell, for de novo synthesis of inosine monophosphate (IMP) during recovery, for degradation of adenosine monophosphate (AMP) into IMP, for degradation of IMP to inosine and hypoxanthine. All the pathways involved are collected in figure 1. These reactions are described by 15 differential equations and the solution is a set of 15 functions of time that represent the concentration of the main metabolites involved (such as lactate, pyruvate, ATP etc). Let’s now take a closer look at one of these equations and at the general structure of the whole system of equations.
Figure 1. This is a schematic representation of the metabolic pathways described by the mathematical model developed by Lengert and Drossel. In detail: cytosolic synthesis and degradation of ADP, AMP and IMP (left), protein kinase pathway and glycolysis (centre), electron transport chain and TCA cycle (right). From Lengert N. et Drossel B. 2015.
Differential equations for chemical reactions
Let’s consider the equation used by the Authors for the reaction catalyzed by lactate dehydrogenase (the transformation of pyruvate into lactate, figure 2) where they also took into account the efflux of lactate from the cytosol. The differential equation is the following one:
where the three parameters are experimentally determined and their values are
The first one describes the activity of the enzyme lactate dehydrogenase: the higher this parameter is, the more active the enzyme is. The second one describes the inverse reaction (from lactate to pyruvate). The third one is a measure of how much lactate the cell is able to transport outside its membrane. You have probably recognized that the equation of lactate is a first-order ordinary differential one. We say “first-order” because in the equation there is only the first-order derivative of the function that we have to determine (lactate, in this case); “ordinary” refers to the fact that lactate is a function only of one variable (time, in this case). You can easily realize that an equation like that can be written as follows:
Suppose now that we had other two differential equations of this type, one for pyruvate and one for protons (the other two functions of time that are present in the equation):
We would have a system of three ordinary differential equations like this one
The initial values of the functions that we have to determine are collected in the last row: these are the values that they have at the beginning of the simulation (t=0). In this case, these values are the concentrations of lactate, pyruvate and protons in the cytosol, at rest. The three functions of time are called the solution to the system. This kind of system of equations is an example of a Cauchy’s problem, and we know from mathematical theory that not only it has a solution, but that this solution is unique. Moreover, whereas this solution can’t be always easily found with rigorous methods, it is quite easy to solve the problem with computational methods, like the Runge-Kutta method or the Heun’s method. All that said, the system of ordinary differential equations proposed by Lengert and Drossel for energy metabolism is just like this one, with the exception that it comprises 15 equations instead of three. So, the main difficulty in this kind of simulation is not the computational aspect but the determination of the parameters (like the enzymatic ones) and of the initial values, that have to be collected from the medical literature or have to be determined experimentally, if not already available. The other problem is how to design the equations: there are several ways to build a model for a chemical reaction or for any other biological process.
The mathematical model of ME/CFS
How do we adapt to ME/CFS patients a model of energy metabolism that has been set with parameters taken from experiments performed on healthy subjects? This is a very good question, and we have seen that Robert Phair had to use genetic data from ME/CFS patients on key enzymes of energy metabolism, in order to set his model. But this data was not available when Lengert and Drossel designed their equations. So what? They looked for studies about the capacity of oxidative phosphorylation in ME/CFS patients in comparison with healthy subjects, and they found that it had been measured with different experimental settings by various groups and that the common denominator was a reduction ranging from about 35% (Myhill S et al. 2009), (Booth, N et al 2012), (Argov Z. et al. 1997), (Lane RJ. et al. 1998) to about 20% (McCully KK. et al. 1996), (McCully KK. et al. 1999). So the idea of the Authors was to multiply the enzymatic parameter of each reaction belonging to the oxidative phosphorylation by a number ranging from 0.6 (severe ME/CFS) to 1.0 (healthy person). In particular, they used a value of 0.7 for ME/CFS, in their in silico experiments.
Predictions of the mathematical model
The mathematical model was used to perform in silico exercise tests with various length and intensities. What they found was that the time of recovery in the average ME/CFS patient was always greater if compared to a healthy person. The time of recovery is defined as the time that a cell needs to replenish its content of ATP (97% of the level in resting state) after exertion. In Figure 3 you see the results of the simulation for a very short (30 seconds) and very intense exercise. As you can see, in the case of a healthy cell (on the left) the recovery time is of about 600 minutes (10 hours) whereas a cell from a person with ME/CFS (on the right) requires more than 1500 minutes (25 hours) to recover.
Another interesting result of the simulation is an increase in AMP in patients vs control (figure 3, orange line). This is due to the compensatory use of the two metabolic pathways in figure 4: the reaction catalyzed by adenylate kinase, in which two molecules of ADP are used to produce a molecule of ATP and a molecule of AMP; and the reaction catalyzed by AMP deaminase, that degrades AMP to IMP (that is then converted to inosine and hypoxanthine). These two reactions are used by ME/CFS patients more than in healthy control, in order to increase the production of ATP outside mitochondria.
If we give a closer look at the concentrations of AMP and IMP in the 4 hours following the exertion (figure 5), we actually see an increased production of IMP (green line) and AMP (orange line) in skeletal muscles of ME/CFS patients (on the right) vs controls (left).
A further compensatory pathway used by patients (according to this model) is the production of ATP from ADP by the enzyme creatine kinase (figure 6). This is another way that we have on our cells to produce ATP in the cytosol without the help of mitochondria. In this model of ME/CFS, there is an increase in the use of this pathway, which leads to a decrease in cellular concentration of phosphocreatine and an increase in the cellular concentration of creatine (figure 7).
Comparison with available metabolic data
I am curious to see if data from the various metabolomic studies done after the publication of the model by Lengert and Drossel are in agreement with it. I will discuss this topic in another article because I still have to study this aspect. I would just point out that if we assumed true the high rate of IMP degradation proposed in this model, we would probably find a high level of hypoxanthine in the blood of patients, compared to controls, whereas this metabolite is decreased in patients, according to one study (Armstrong CW et al. 2015).
Comparison with the model by Phair
The metabolic model by Robert Phair will probably give a more accurate simulation of the energy metabolism of patients if compared with the system of ordinary differential equations that we have discussed in this article. And there are two reasons for that. The first one is that Phair has included equations also for fatty acid beta-oxidation, pentose phosphate pathway, and NAD synthesis from vitamin niacin. The other one is that, whereas the two German physicists reduced the velocities of all the enzymatic reactions that happen in mitochondria, Phair has genetic data for every enzyme involved in these reactions for a group of ME/CFS patients and thus he can determine and set the actual degree of activity for each enzyme. But there is a further level required in order to bring the mathematical simulation closer to the reality: gene expression. We know, for instance, that in ME/CFS patients there is a higher than normal expression of aconitase (an enzyme belonging to the TCA cycle) and of ATP synthase (Ciregia F et al 2016) and this should be taken into account in a simulation of ME/CFS patients energy metabolism. Note that ATP synthase is exactly the enzyme that Phair has found to be genetically damaged in patients, and this makes perfect sense: if an enzyme has reduced activity, its reaction can be speeded up by expressing more copies of the enzyme itself.
One could expect that, in a near future, genetic data and gene expression data from each of us will be used to set mathematical models for metabolic pathways, in order to build a personalized model of metabolism that might be used to define, study and correct human diseases in a personalized fashion. But we would need a writer of sci-fiction in order to tell this chapter of the future of medicine.
Con una versione più sofisticata (e invasiva) del consueto test cardiopolmonare con la cyclette, il dr. Systrom riporta che nella maggioranza dei pazienti ME/CFS la capacità delle vene delle gambe e dell’addome di contrarsi e spingere il sangue verso l’atrio destro è ridotta. Cioè la pressione del sangue all’imbocco dell’atrio destro – durante esercizio – è inadeguata. Altra anomalia è l’uso inadeguato di ossigeno da parte dei muscoli scheletrici. E questo difetto può essere dovuto a due cause: una disfunzione dei vasi e/o una disfunzione dei mitocondri. In altre parole, l’ossigeno non è utilizzato perché il sistema che lo trasporta non funziona e/o perché gli organelli che lo usano non riescono a svolgere la loro attività.
Poco meno della metà dei pazienti di Systrom presenta una biopsia cutanea positiva per la neuropatia delle piccole fibre, una patologia ben nota che si riscontra nel 40% dei pazienti con fibromialgia, nel 40% dei pazienti con POTS, e in varie altre patologie.
Systrom riporta risultati positivi con la piridostigmina, un inibitore dell’acetilcolinesterasi (l’enzima che degrada l’acetilcolina). Ha trattato 300 pazienti e il farmaco sembra funzionare per l’intolleranza all’esercizio.
La particolarità di questo test – rispetto al consueto test da sforzo con cyclette – è l’uso di un catetere nella arteria del polso destro e di un secondo catetere che raggiunge l’imbocco della arteria polmonare. I cateteri permettono di misurare la pressione del fluido e di prelevare sangue da utilizzare per misure dei gas in miscela e di altri parametri.
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One of my best drawings ever. I was about to undergo surgery to remove my thyroid (I had just discovered a tumor in my gland) and I was still mourning the recent loss of my brother when I made this drawing. I was disabled and I had already lost many years of my life, because of a disease without a name. I was completely alone. Everything was against me.
And yet, all that is left of that despair is this beautiful image.