Sul versante dei test, si parla di test di stimolazione linfocitaria, sia utilizzando le cellule T che utilizzando i macrofagi. Questi test sono in fase di sviluppo e quelli già venduti ai pazienti (in Germania ad esempio) non sono in realtà al momento utilizzabili.
Sul lato dei sintomi cronici: le cause ipotizzate sono persistenza della infezione, alterazioni immunitarie, modifiche nell’encefalo, coinfezioni non identificate (e quindi non trattate).
Fallon enfatizza il fatto che la persistenza della infezione non è da considerare la sola causa dei sintomi cronici. Da quello che sento ogni giorno, i pazienti sono dogmatici su questo punto: i sintomi cronici sono il prodotto di una infezione cronica. Può anche essere, in alcuni casi, ma per ora non si sa e tutti i tentativi di cura dei sintomi cronici sono risultati fallimentari: non ci sono farmaci approvati per questi pazienti. I medici spesso sono dogmatici, perché il dogma richiede il minimo sforzo cognitivo; i pazienti non dovrebbero fare lo stesso errore.
In generale io sono d’accordo con quello che dice Fallon, perché è molto onesto. Del resto lui non ha nulla da vendere e il suo scopo è perseguire la verità, avendo anche un congiunto malato.
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Con l’arrivo della bella stagione, inizia la migrazione dei professionisti del settore sanitario alla volta dei convegni medici. Questa’anno vale la pena ricordare due appuntamenti nostrani, a ridosso l’uno dell’atro:
A lot of work has been done to attest the prevalence of glycolytic enzymes, and in particular of enolase, as autoantigens in autoimmune disorders. Antibodies to the isoform alpha (and to a lesser extent to the isoform gamma) of the enzyme enolase have been reported in a variety of immunological diseases (table 1), and yet the prevalence of these autoantibodies in ME/CFS has not been measured, so far, as has been recently pointed out (Sotzny F et al. 2018).
Anti-enolase Abs in ME/CFS
Recently a role for anti-gamma enolase Abs has been proposed in post-treatment Lyme disease syndrome: it has been postulated that sequence similitude between Borrelia own enolase and human enolase might be the cause of cross-reactive autoantibodies (Maccallini P et al. 2018). A similar pathogenic role for anti-enolase antibodies has been previously proposed in PANDAS (Dale, et al., 2006) and in rheumatoid arthritis (Lee JY et al 2015), with the putative triggering bacterial enolases belonging to Streptococcus pyogenes and to Porphyromonas gingivalis, respectively. Besides molecular mimicry, a pathological increase in glycolytic enzymes expression has been proposed as the cause for the rise of autoantibodies to these proteins (Chang X et Wei Chao 2011). Both these triggering events are theoretically possible in ME/CFS, given that this disease is initiated by an infectious event in many cases (Hickie I et al. 2006) and an increase in glycolysis has been described in peripheral white blood cells from ME/CFS patients (Lawson N et al. 2016). Although autoimmunity against enolase is present in many autoimmune diseases, it seems that different autoepitopes are involved in different diseases (see epitopes in red, in table 2). So if we found autoantibodies to enolase in ME/CFS, we could perhaps find a specific autoepitope useful for diagnostic purposes.
In what follows I will present a set of codes that I have written in Octave and in Fortran for the study of random variables that follow a gamma distribution. In another post, we will discuss the beta distribution.
2_The gamma distribution
A random variable is said to have a gamma distribution with parameters (α, λ) if its density is given by
with α, λ>0 and where Γ(α) is the gamma function, which is quite a pain in the lower back, as you will see. This random variable can be used to describe the probability that the duration of life of an entity (whether it is a mechanical component or a bacterium) depends on time. The gamma distribution allows to describe the following situations:
for α>1 the probability of failure of a mechanical component (or death of an organism) increases as the time passes by (increasing hazard rate);
for α=1 the probability of failure is constant (constant hazard rate);
for α<1 the failure is less likely as time passes by (decreasing hazard rate).
The hazard rate is the limit below:
where F_X(t) is the distribution function of the gamma distribution. I have not been able to find an analytic expression for the hazard rate of the gamma distribution, but I have been able to obtain it with the computer-aided calculation (see below). But in order to calculate F_X(t), we need to calculate the gamma function…
3_The gamma function
Γ(α) (the gamma function) is an integral function that cannot be calculated analytically:
It has to be calculated with numerical integration, but a problem is that Γ(α) is an indefinite integral. One way to face this problem is to stop the numerical integration when the addend is below a certain cut off (let’s say 0.0001). It is worth noting that an important feature of this function is that if you know its value in an interval such as [x, x+1], then you can derive Γ(α) for any other possible value of α. This is due to the recursive formula: Γ(α+1) = αΓ(α). That said, I have calculated Γ(α) in [1, 2] and then I have used these values to define Γ(α) in [0, 4] with the .exe file (written in Fortran) available here. Download it and put it in a folder. When you run it, it gives a .txt file with the values of Γ(α) in [0, 4] and two .mat files that can be used to build the plot of Γ(α) (see figure 1). Values of Γ(α) in [0, 2] are tabulated below, while those of you who like the very long list of numbers can find a huge table with values of the gamma function in [0, 4] at the end of this article.
4_The distribution function
The distribution function of the gamma density cannot be calculated analytically so, again, I had to make good use of my poor coding skills and I wrote a code in Octave (here, it uses the two .mat files generated by the code in Fortran mentioned above!) and one in Fortran (available here). In figure 2 (code in Octave) you can find the density and the distribution function for different values of α.
The code in Fortran, on the other hand, asks the user for the values of α and λ and gives a plot for the density and one for the distribution function. Moreover, it gives a .txt file with the values of the distribution function. Note that you can only place values for α that are below 25, otherwise you generate an overflow condition. I am not sure why you have overflow condition with a value of α that is below 34, but this is another story. Nevertheless, for those who are interested, Γ(n) = (n-1)! and the biggest factorial that can be handled by a computer in single precision mode (where 8 bits are used for the exponent) is 33!. So, we have a little mystery here… The reason why I have stuck with single precision is that DISLIN – the graphics library – seems to be unable to handle double precision numbers. If you are interested in the gamma function, the density and the distribution function for α = 20 and λ=2, then the code in Fortran gives for Γ(20) a value of 1.216451E+17 and the two plots in figure 3.
5_The hazard rate
As mentioned in paragraph 2, the hazard rate of the gamma distribution cannot be easily studied. I forgot to mention that it is relatively easy to prove that it is constant for α=1. But what happens for α>1 and for α<1? In order to answer, I have written a code (download) that plots it and it seems to be possible to say that the hazard rate increases for α>1 and decreases for α<1. This means that the gamma distribution is suitable for modeling each of the three kinds of patterns for the probability of failure as the time passes by. In figure 4 you find an example of the hazard rate for α<1 (left) and an example for α>1 (right).
A table for the gamma function in [0.01, 3.99] is reported below. In each column, the value of α is indicated on the left while the corresponding value for Γ(α) is indicated on the right.
A new study from Columbia University, Stony Brook University and the CDC – that has seen the collaboration of Brian Fallon and W. Ian Lipkin, among others – has proposed a new serological test for Lyme disease and coinfections (Babesia microti, Anaplasma phagocytophilum, Ehrlichia chaffeensis, Rickettsia ricketsii and some viruses that are not present in Europe) (Tokarz R et al. 2018). Current serologic analyses consist of a two-tiered algorithm: a measure of serum activity against a main immunogenic protein of B. burgdorferi (whether it is VlsE or its peptide C6) is followed by a western blot, where the immune response to a set of several full-length proteins is performed. This method lacks sensitivity for early Lyme disease (Aguero-Rosenfeld ME et al 2005) and – according to studies on the animal model of Lyme disease – it might miss some cases of disseminated infection too (Embers ME, 2012), (Nicholas A, 2017), (Embers ME 2017). So, there is common agreement that a better test is urgently needed.
The quest for immunogenic peptides in Lyme patients: the set of proteins
Most B cells epitopes on non-denaturated proteins (i.e. proteins that conserve their tertiary structure) are believed to be conformational (Morris, 2007) but it is also true that in the average B cell epitope, a linear stretch of 5 amino acids is reported (Kringelum, et al., 2013). This means that it is conceivable to search for new immunogenic peptides in Lyme disease with the following method: each protein from Borrelia, known to be immunogenic in humans, is divided in peptides with a fixed length, then each of these peptides is exposed to sera from patients. Those peptides that strongly bind sera from patients are eligible as immunogenic peptides useful for diagnostic purposes. This is exactly what has been done in this study, and this elaborate analysis has been performed not only for Borrelia burgdorferi but also for the other tick-borne pathogens already mentioned. In particular, the length of the peptides has been fixed to be 12, and contiguous peptides have an overlapping of 11 amino acids. The set of immunogenic proteins chosen for each pathogen are reported in table 1.
A new array of diagnostic peptides in Lyme disease
The analysis was conducted using sera from 66 Lyme patients (27 early Lyme, 19 with positive IgG western blot, 10 with acute neuroborreliosis). The end result is the set of peptides reported in table 2. There is also a set of peptides specific for neuroborreliosis (table 3).
Flagellin B: a new specific peptide for diagnostic purposes is born
It is widely recognized that reactivity of sera to Flagellin B (FlaB, p41) is common in healthy persons too (Chandra A et al. 2011). This is due to the fact that this protein is highly conserved among bacteria, so there is cross-reactivity and FlaB is almost without utility for diagnostic purposes. That said, one of the results of this study is that peptide 211-223 fro FlaB is highly immunogenic in patients and is also not-cross-reactive with flagellar proteins from other bacteria (I have checked using this peptide as query sequence in a BLAST search among bacteria, with a word of 3 and with standard settings: no match has been found). So we have a new specific peptide for diagnostic purposes. In figure 1 this epitope is reported in yellow, on the 3D structure of Flagellin B.
The strange case of VlsE and C6
Vmp-like sequence expressed (VlsE) is a major immunogenic protein of Borrelia burgodorferi, widely used for the first-tier test of Lyme disease (Aguero-Rosenfeld ME et al 2005). This protein goes through a process of variation during mammalian infection that involves six variable regions (VR1-VR6) and it has been postulated that this gene recombination of the locus that codes for VlsE is responsible – at least in part – for the ability of B. burgodorferi of evading the immune system (Zhang JR et al. 1997). Nevertheless, six regions of this protein are invariable (IR1-6) and these ones have been studied as possible peptides to use for diagnosis. One of them, peptide IR6 (also called C6), has been used as a diagnostic tool (Liang FT et al. 1999). In the present study, the peptide that pops up from the analysis is the same C6 (peptide 274-290 in table 1), while in neuroborreliosis there are two more peptides on VlsE that appear to be useful markers. I have reported these three peptides on the 3D structure of VlsE, the one experimentally determined in (Eicken C et al. 2002), see figure 2. It is worth noting now that peptide 274-290 (C6) is buried inside the protein, so it is difficult to understand how it could be a B cell epitope, since B cell epitope protrudes from the surface (Thornton, et al., 1986) and this is probably due to the fact that B cell receptors need to bind their specific antigen, in order for B cell to be activated. This is the very first time that I realize that C6 is not surface exposed. So, how could the immune system generate an antibody to a hidden peptide? I have to think about that.
OspC and the buried epitope
Another weird case is that of OspC, where one of the two main epitopes found in patients with neuroborreliosis is buried in the cytoplasmic membrane of Borrelia burgdorferi (figure 2, right). This is an uncommon case, I guess, for the same reason mentioned above: BCRs need surface exposure in order to bind their specific epitope. The other peptide (132-144) appears to be a classic surface exposed B cell epitope.