Statistical mechanics for biological applications: focusing on the immune system

The emergence in the last decades of a huge amount of data in many fields of biology triggered also an increase of the interest by quantitative disciplines for life sciences. Mathematics, physics and informatics have been providing quantitative models and advanced statistical tools in order to help the understanding of many biological problems. Statistical mechanics is a field that particularly contributed to quantitative biology because of its intrinsic predisposition in dealing with systems of many strongly interacting agents, noise, information processing and statistical inference. In this Thesis a collection of works at the interphase between statistical mechanics and biology is presented. In particular they are related to biological problems that can be mainly reconducted to the biology of the immune system. Beyond the unification key given by statistical mechanics of discrete systems and quantitative modeling and analysis of the immune system, the works presented here are quite diversified. The origin of this heterogeneity resides in the intent of using and learning many different techniques during the lapse of time needed for the preparation of the work reviewed in this Thesis. In fact the work presented in Chapter 3 mainly deals with statistical mechanics, networks theory and networks numerical simulations and analysis; Chapter 4 presents a mathematical physics oriented work; Chapter 5 and 6 deal with data analysis and in particular wth clinical data and amino acid sequences data sets, requiring the use of both analytical and numerical techniques. The Thesis is conceptually organized in two main parts. The first part (Chapters 1 and 2) is dedicated to the review of known results both in statistical mechanics and biology, while in the second part (Chapters 3, 4 and 6) the original works are presented together with briefs insights into the research fields in which they can be embedded. In particular, in Chapter 1 some of the most relevant models and techniques in statistical mechanics of mean field spin systems are reviewed, starting with the Ising model and then passing to the Sherrington-Kirkpatrik model for spin glasses and to the Hopfield model for attractors neural networks. The replica method is presented together with the stochastic stability method as a mathematically rigorous alternative to replicas. Chapter 2 is dedicated to a very schematic overview of the biology of the immune system. In Chapter 3, Section 3.1 is dedicated to the presentation of a mathematical phenomenological model for the study of the idiotypic network while Section 3.2 serves as a review of the statistical mechanics based models proposed by Elena 1 2 Introduction Agliari and Adriano Barra as toy models meant to underline the possible role of complex networks within the immune system. In Chapter 4 the mathematical model of an analogue neural network on a diluted graph is studied. It is shown how the problem can be mapped in a bipartite diluted spin glass. The model is rigorously solved at the replica symmetric level with the use of the stochastic stability technique and fluctuations analysis is used to study the spin glass transition of the system. A topological analysis of the network is also performed and different topological regimes are proven to emerge though the tuning of the model parameters. In Chapter 5 a model for the analysis of clinical records of testing sets of patients is presented. The model is based on a Markov chain over the space of clinical states. The machinery is applied to data concerning the insurgence of Tuberculosis and Non-Tuberculous Infections as side effects in patients treated with Tumor Necrosis Factor inhibitors. The analysis procedure is capable of capturing clinical details of the behaviors of different drugs. Lastly, Chapter 6 is dedicated to a statistical inference analysis on deep sequencing data of an antibodies repertoire with the purpose of studying the problem of antibodies affinity maturation. A partial antibodies repertoire from a HIV-1 infected donor presenting broadly neutralizing serum is used to infer a probability distribution in the space of sequences that is compared with neutralization power measurements and with the deposited crystallographic structure of a deeply matured antibody. The work is still in progress, but preliminary results are encouraging and are presented here

Statistical mechanics for biological applications: focusing on the immune system

The emergence in the last decades of a huge amount of data in many fields of biology triggered also an increase of the interest by quantitative disciplines for life sciences. Mathematics, physics and informatics have been providing quantitative models and advanced statistical tools in order to help the understanding of many biological problems. Statistical mechanics is a field that particularly contributed to quantitative biology because of its intrinsic predisposition in dealing with systems of many strongly interacting agents, noise, information processing and statistical inference. In this Thesis a collection of works at the interphase between statistical mechanics and biology is presented. In particular they are related to biological problems that can be mainly reconducted to the biology of the immune system. Beyond the unification key given by statistical mechanics of discrete systems and quantitative modeling and analysis of the immune system, the works presented here are quite diversified. The origin of this heterogeneity resides in the intent of using and learning many different techniques during the lapse of time needed for the preparation of the work reviewed in this Thesis. In fact the work presented in Chapter 3 mainly deals with statistical mechanics, networks theory and networks numerical simulations and analysis; Chapter 4 presents a mathematical physics oriented work; Chapter 5 and 6 deal with data analysis and in particular wth clinical data and amino acid sequences data sets, requiring the use of both analytical and numerical techniques. The Thesis is conceptually organized in two main parts. The first part (Chapters 1 and 2) is dedicated to the review of known results both in statistical mechanics and biology, while in the second part (Chapters 3, 4 and 6) the original works are presented together with briefs insights into the research fields in which they can be embedded. In particular, in Chapter 1 some of the most relevant models and techniques in statistical mechanics of mean field spin systems are reviewed, starting with the Ising model and then passing to the Sherrington-Kirkpatrik model for spin glasses and to the Hopfield model for attractors neural networks. The replica method is presented together with the stochastic stability method as a mathematically rigorous alternative to replicas. Chapter 2 is dedicated to a very schematic overview of the biology of the immune system. In Chapter 3, Section 3.1 is dedicated to the presentation of a mathematical phenomenological model for the study of the idiotypic network while Section 3.2 serves as a review of the statistical mechanics based models proposed by Elena 1 2 Introduction Agliari and Adriano Barra as toy models meant to underline the possible role of complex networks within the immune system. In Chapter 4 the mathematical model of an analogue neural network on a diluted graph is studied. It is shown how the problem can be mapped in a bipartite diluted spin glass. The model is rigorously solved at the replica symmetric level with the use of the stochastic stability technique and fluctuations analysis is used to study the spin glass transition of the system. A topological analysis of the network is also performed and different topological regimes are proven to emerge though the tuning of the model parameters. In Chapter 5 a model for the analysis of clinical records of testing sets of patients is presented. The model is based on a Markov chain over the space of clinical states. The machinery is applied to data concerning the insurgence of Tuberculosis and Non-Tuberculous Infections as side effects in patients treated with Tumor Necrosis Factor inhibitors. The analysis procedure is capable of capturing clinical details of the behaviors of different drugs. Lastly, Chapter 6 is dedicated to a statistical inference analysis on deep sequencing data of an antibodies repertoire with the purpose of studying the problem of antibodies affinity maturation. A partial antibodies repertoire from a HIV-1 infected donor presenting broadly neutralizing serum is used to infer a probability distribution in the space of sequences that is compared with neutralization power measurements and with the deposited crystallographic structure of a deeply matured antibody. The work is still in progress, but preliminary results are encouraging and are presented here

Organization and evolution of synthetic idiotypic networks

We introduce a class of weighted graphs whose properties are meant to mimic the topological features of idiotypic networks, namely the interaction networks involving the B-core of the immune system. Each node is endowed with a bit-string representing the idiotypic specificity of the corresponding B cell and a proper distance between any couple of bit-strings provides the coupling strength between the two nodes. We show that a biased distribution of the entries in bit-strings can yield fringes in the (weighted) degree distribution, small-worlds features, and scaling laws, in agreement with experimental findings. We also investigate the role of ageing, thought of as a progressive increase in the degree of bias in bit-strings, and we show that it can possibly induce mild percolation phenomena, which are investigated too.Comment: 13 page

<Notes> Production Techniques and Employment Creation in Underdeveloped Economies

The immune system has developed a number of distinct complex mechanisms to shape and control the antibody repertoire. One of these mechanisms, the affinity maturation process, works in an evolutionary-like fashion: after binding to a foreign molecule, the antibody-producing B-cells exhibit a high-frequency mutation rate in the genome region that codes for the antibody active site. Eventually, cells that produce antibodies with higher affinity for their cognate antigen are selected and clonally expanded. Here, we propose a new statistical approach based on maximum entropy modeling in which a scoring function related to the binding affinity of antibodies against a specific antigen is inferred from a sample of sequences of the immune repertoire of an individual. We use our inference strategy to infer a statistical model on a data set obtained by sequencing a fairly large portion of the immune repertoire of an HIV-1 infected patient. The Pearson correlation coefficient between our scoring function and the IC50 neutralization titer measured on 30 different antibodies of known sequence is as high as 0.77 (p-value 10-6), outperforming other sequence- and structure-based models

Sacral nerve stimulation allows for decreased antegrade continence enema use in children with severe constipation.

BackgroundSacral nerve stimulation (SNS) can be beneficial for children with constipation, but no studies have focused on children with constipation severe enough to require antegrade continence enemas (ACEs). Our objective was to evaluate the efficacy of SNS in children with constipation treated with ACE.MethodsUsing a prospective patient registry, we identified patients &lt;21years old who were receiving ACE prior to SNS placement. We compared ACE/laxative usage, PedsQL Gastrointestinal Symptom Scale (GSS), Fecal Incontinence Quality of Life Scale (FIQL), Fecal Incontinence Severity Index (FISI), and Vancouver Dysfunctional Elimination Syndrome Score (DES) at baseline and progressive follow-up time intervals.ResultsTwenty-two patients (55% male, median 12years) were included. Median ACE frequency decreased from 7 per week at baseline to 1 per week at 12months (p&lt;0.0001). Ten children (45%) had their cecostomy/appendicostomy closed. Laxative use, GSS, FIQL, and DES did not change. FISI improved over the first 12months with statistical significance reached only at 6months (p=0.02). Six (27%) children experienced complications after SNS that required further surgery.ConclusionsIn children with severe constipation dependent on ACE, SNS led to a steady decrease in ACE usage with nearly half of patients receiving cecostomy/appendicostomy closure within 2years.Level of evidenceIV

Analogue neural networks on correlated random graphs

We consider a generalization of the Hopfield model, where the entries of patterns are Gaussian and diluted. We focus on the high-storage regime and we investigate analytically the topological properties of the emergent network, as well as the thermodynamic properties of the model. We find that, by properly tuning the dilution in the pattern entries, the network can recover different topological regimes characterized by peculiar scalings of the average coordination number with respect to the system size. The structure is also shown to exhibit a large degree of cliquishness, even when very sparse. Moreover, we obtain explicitly the replica symmetric free energy and the self-consistency equations for the overlaps (order parameters of the theory), which turn out to be classical weighted sums of 'sub-overlaps' defined on all possible sub-graphs. Finally, a study of criticality is performed through a small-overlap expansion of the self-consistencies and through a whole fluctuation theory developed for their rescaled correlations: Both approaches show that the net effect of dilution in pattern entries is to rescale the critical noise level at which ergodicity breaks down.Comment: 34 pages, 3 figure

Application of a stochastic modeling to evaluate tuberculosis onset in patients treated with tumor necrosis factor inhibitors

In this manuscript we apply stochastic modeling to investigate the risk of reactivation of latent mycobacterial infections in patients undergoing treatment with tumor necrosis factor inhibitors. First, we review the perspective proposed by one of the authors in a previous work and which consists in predicting the occurrence of reactivation of latent tuberculosis infection or newly acquired tuberculosis during treatment; this is based on variational procedures on a simple set of parameters (e.g. rate of reactivation of a latent infection). Then, we develop a full analytical study of this approach through a Markov chain analysis and we find an exact solution for the temporal evolution of the number of cases of tuberculosis infection (re)activation. The analytical solution is compared with Monte Carlo simulations and with experimental data, showing overall excellent agreement. The generality of this theoretical framework allows to investigate also the case of non-tuberculous mycobacteria infections; in particular, we show that reactivation in that context plays a minor role. This may suggest that, while the screening for tuberculous is necessary prior to initiating biologics, when considering non-tuberculous mycobacteria only a watchful monitoring during the treatment is recommended. The framework outlined in this paper is quite general and could be extremely promising in further researches on drug-related adverse events.Comment: 26 pages, 7 figure

Prediction of Ab-gp120 binding sites classified as <i>binding</i> if the minimum distance between any atom of the residue and the antigen is less than 5Å, <i>proximal</i> if the distance is between 5Å and 10Å, <i>distant</i> if it is more than 10Å.

<p>Note that the PDB structure 3SE9 shows 17 <i>binding</i> residues in the VRC-PG04 heavy chain which is 225 residues long.</p