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Indo-European Network in Mathematics for Health and Disease

Final Report Summary - INDOEUROPEAN-MATHDS (Indo-European Network in Mathematics for Health and Disease)

The main aim of this proposal was to set up an Indo-European Research Network in Mathematics for Health and Disease, INDOEUROPEAN MATHDS, that has allowed the transfer of knowledge, research and training between partners. The Network involves physicists, mathematicians, statisticians, probabilists, biologists, immunologists and engineers. Other objectives of this proposal were:

1) To establish research collaborations between the experimental, clinical and theoretical partners of the Network to develop mathematical and computational models for health and disease;

2) To establish research collaborations between the different theoretical groups to discuss, compare, test and validate different modelling approaches;

3) To train a new generation of multi-disciplinary (experimental, clinical and theoretical) scientists both in ERA and in India, with the aim to exchange post-graduate students and research fellows, so that they benefit from the broader knowledge, skills and tools provided by the Network;

4) To enhance the international outreach dimension of the EU partners by delivering lectures and seminars at the UNM q-bio series of Summer Schools and Conferences, and the Spring Schools to be organised and hosted by the Indian partners;

5) To enhance the international dimension of research in India in the area of Mathematics for Health and Disease, by organising and hosting four training and research events (Spring Schools) in India; and

6) To enhance the international outreach dimension of the UNM q-bio series of Summer Schools and Conferences.

A final research objective of the Network was to develop, by means of the Research Staff Exchange Scheme, four long-term directions in Mathematics for Health and Disease. Given the clinical and experimental expertise of the Indian, EU and Australian partners, and the mathematical and computational expertise of the Indian, EU, USA and Canadian partners, we have

i) Developed mathematical and computational models of host-pathogen and virus dynamics, with a focus on pathogenic and molecular characterisation of viruses and bacteria, in order to understand if regulation of immune activation can be a potentially optimum way for disease management;

ii) Developed mathematical and computational models of immune cellular processes, such as differentiation and cellular fate, as well as ageing, validated by experimental data, with a focus on T cells;

iii) Developed stochastic mathematical models of receptor-mediated processes in health and disease, with a focus on the CCR5 receptor, VEGF receptor, T cell receptor and B cell receptor; and

iv) Developed statistical tools and methods to characterise the genomic fluidity of human pathogens, in order to understand microbial pathogen evolution and what constitutes the boundary between commensal and pathogenic organisms.

Selected results for each research theme are given below:

Host-pathogen and virus dynamics (Theme 1).

Partners 6 and 8 have developed mathematical and statistical approaches to improve our understanding of the pathogenic and molecular characterisation of viruses and bacteria. New collaborations have been developed and led to a joint publication that has involved modelling and statistical analysis of patients co-infected with HIV and HCV under HIV treatment.

Partner 3 has made use of computational and mathematical models to decipher how during the many cycles of replication between infection of a host and transmission to the next host, HIV-1 is under selection for escape from immune responses, and not transmission. They have found that when the rate of immune escape is comparable to what has been observed in patients, immune selection within hosts is dominant over selection for transmission.

Partner 14 has developed a new collaboration with Partner 1 to study the modulatory of new mathematical network models of host-pathogen interactions. Many networks are characterised by their modularity, that is, the network can be divided into several connected clusters (or ``communities''), with the connection density in each cluster being significantly higher than that for the entire network. In a recent publication, Sitabhra Sinha has explored the role of modularity in organising the collective dynamics of social networks. In collaboration with Partner 1, he aims to develop modular network of host-pathogen interactions in epidemiology.

Partner 8 has developed mathematical models of the effect of integrase inhibition in HIV-1 viral dynamics, as well the stochastic control of cell fate determination in HIV-1 infected cells using a direct solution of the chemical master equation.

Immune cellular processes and ageing (Theme 2).

Partner 4 has developed new mathematical models (making use of experimental data generated by partner 10) and a joint publication. In this collaboration the aim is to understand how T cells integrate alternative signal combinations and make decisions affecting immune response strength or tolerance. Their results imply that the T cell receptor (TCR) and co-stimulatory signals imprint an early, cell-intrinsic, division fate, whereby cells effectively count through generations before returning automatically to a quiescent state. This autonomous programme can be extended by cytokines. Signals from the TCR, co-stimulatory receptors, and cytokines add together using a linear division calculus, allowing the strength of a T cell response to be predicted from the sum of the underlying signal components. These data resolve a long-standing co-stimulation paradox and provide a quantitative paradigm for therapeutically manipulating immune response strength.

Partner 1 has developed mathematical models of the T cell repertoire that help understand how T cells make decisions based on T cell receptor (TCR) diversity and clonal sizes. In collaboration with Partner 2, they have published in the Journal of Theoretical Biology (2016) their work on how many TCR clones does the body maintain? Their results indicate that the history of a clonotype starts with release from the thymus, and ends with extinction. Competition and cross-reactivity are included in a natural way. The average number of cells per clonotype, in a human body, is only of order 10.

Partner 11 has been carrying out a number of experiments with CD4 T cells (activation). Cells were harvested at time points 1, 3, 12, 24 and 48 hours post-activation. The cells were stained for expression of early activation marker CD69 and late activation marker CD25 along with CD62L using 3-colour flow cytometry. Additionally, the cells were also stained with propidium iodide for performing cell cycling analysis. In collaboration with Partner 1, they have developed mathematical models of the experimental assay based on the hypothesis of the strength of signal.

Receptor-mediated processes in health and disease (Theme 3).

Partner 11 has developed a mathematical model of the role of CCR5 on target CD4+ T cells susceptible to infection by R5-tropic HIV-1. Their model employs a reaction network-based approach to describe protein interactions that precede viral entry coupled with the ternary complex model to quantify the allosteric interactions of the co-receptor antagonist and predicts the fraction of target cells fused. By fitting model predictions to published data of cell-cell fusion in the presence of the CCR5 antagonist vicriviroc, they estimated the threshold surface density of gp120-CCR5 complexes for cell-cell fusion.

Partner 1 has developed mathematical models to describe the interaction between the vascular endothelial growth factor A (VEGF-A) with the VEGFR-1 and VEGFR-2 receptors in human endothelial cells. This interaction plays a fundamental role in cancer development and angiogenesis. They have analysed the time scales for signal formation, when this signal is directly identified with the number of activated (or phosphorylated) receptor-ligand bound complexes in the system at any given time.

Partner 6, in collaboration with partner 3, has been working on a Bayesian approach to T cell receptor specificity. They have applied methods of Bayesian inference to quantify receptor specificity.

Genomic fluidity of human pathogens (Theme 4).

Partner 12 has worked on the bacteria Helicobacter pylori and its pathogenicity to understand the dynamics of host-pathogen interaction and genome evolution. Of particular relevance in this context is to consider the variation of Helicobacter pylori infection rates and disease outcomes among different populations. Their analysis of the virulence genes within the core genome, however, revealed a comparable pathogenic potential of all three strains. They have also identified four genes limited to strains of East-Asian lineage.

Partner 3 has been working o immuno-epidemiological modelling of HIV-1 to predict that high heritability of the set-point virus load takes place while selection for CTL escape dominates virulence evolution.

Partner 12 has studied the Escherichia coli sequence type 131 (ST131), a pandemic clone associated with multi-drug-resistant and extra-intestinal infections. They have analysed the genomic and functional attributes of the H30-Rx sub-clonal strains NA097 and NA114, belonging to the ST131 lineage. They have carried out whole-genome sequencing, comparative analysis, phenotypic virulence assays, and profiling of the antibacterial responses of THP1 cells infected with these sub-clones.

Partner 1 has developed an extensive research programme on the analysis of epidemic processes. For these processes, and through the analysis of the corresponding continuous-time Markov chain, they have been able to compute a number of quantities of interest: the length of the outbreak, the maximum number of individuals simultaneously infected during the outbreak, the total number of individuals suffering the disease during the outbreak, the probability of a given individual being infected during the outbreak, and the exact reproduction number of a given individual in this group. The meeting organised at IMSc has allowed the group to develop a collaboration with the Bayesian modelling group at LSHTM, led by Dr. Anton Camacho (LSHTM, London) and Dr. Sebastian Funk (LSHTM, London).