From Synaptic Interactions to Collective Dynamics in Random Neuronal Networks Models: Critical Role of Eigenvectors and Transient Behavior.

The study of neuronal interactions is at the center of several big collaborative neuroscience projects (including the Human Connectome Project, the Blue Brain Project, and the Brainome) that attempt to obtain a detailed map of the entire brain. Under certain constraints, mathematical theory can advance predictions of the expected neural dynamics based solely on the statistical properties of the synaptic interaction matrix. This work explores the application of free random variables to the study of large synaptic interaction matrices. Besides recovering in a straightforward way known results on eigenspectra in types of models of neural networks proposed by Rajan and Abbott (2006), we extend them to heavy-tailed distributions of interactions. More important, we analytically derive the behavior of eigenvector overlaps, which determine the stability of the spectra. We observe that on imposing the neuronal excitation/inhibition balance, despite the eigenvalues remaining unchanged, their stability dramatically decreases due to the strong nonorthogonality of associated eigenvectors. This leads us to the conclusion that understanding the temporal evolution of asymmetric neural networks requires considering the entangled dynamics of both eigenvectors and eigenvalues, which might bear consequences for learning and memory processes in these models. Considering the success of free random variables theory in a wide variety of disciplines, we hope that the results presented here foster the additional application of these ideas in the area of brain sciences.

Incidence of Circulating Antibodies Against Hemagglutinin of Influenza Viruses in the Epidemic Season 2013/2014 in Poland.

The aim of this study was to determine the level of antibodies against hemagglutinin of influenza viruses in the sera of people in different age groups in the epidemic season 2013/2014 in Poland. The level of anti-hemagglutinin antibodies was determined by hemagglutination inhibition test (HAI). A total number of 1,050 randomly selected sera was tested in seven age groups. The level of antibodies against influenza viruses was very low, which indicates that the people have not been vaccinated against influenza in the epidemic season 2013/2014. The value of protection rate against influenza in the Polish population is very low. These results are worrying, because complications of influenza may be harmful to health and even life-threatening to persons who are not vaccinated. Furthermore, these results confirm the circulation of three antigenically different influenza virus strains, two subtypes of influenza A virus--A/California/7/2009/(H1N1)pdm09 and A/Victoria/361/2011(H3N2)--and B/Massachusetts/2/2012.

Late escape from an immunodominant cytotoxic T-lymphocyte response associated with progression to AIDS.

The precise role played by HIV-specific cytotoxic T lymphocytes (CTL) in HIV infection remains controversial. Despite strong CTL responses being generated during the asymptomatic phase, the virus persists and AIDS ultimately develops. It has been argued that the virus is so variable, and the virus turnover so great that escape from CTL recognition would occur continually, but so far there is limited evidence for CTL escape. The opposing argument is that evidence for CTL escape is present but hard to find because multiple anti-HIV immune responses are acting simultaneously during the asymptomatic phase of infection. We describe six donors who make a strong CTL response to an immunodominant HLA-B27-restricted epitope. In the two donors who progressed to AIDS, CTL escape to fixation by the same mutation was observed, but only after 9-12 years of epitope stability. CTL escape may play an important role in the pathogenesis of HIV infection.

HIV-1 Vpr increases viral expression by manipulation of the cell cycle: a mechanism for selection of Vpr in vivo.

The human immunodeficiency virus type 1 (HIV-1) encodes a protein, called Vpr, that prevents proliferation of infected cells by arresting them in G2 of the cell cycle. This Vpr-mediated cell-cycle arrest is also conserved among highly divergent simian immunodeficiency viruses, suggesting an important role in the virus life cycle. However, it has been unclear how this could be a selective advantage for the virus. Here we provide evidence that expression of the viral genome is optimal in the G2 phase of the cell cycle, and that Vpr increases virus production by delaying cells at the point of the cell cycle where the long terminal repeat (LTR) is most active. Although Vpr is selected against when virus is adapted to tissue culture, we show that selection for Vpr function in vivo occurs in both humans and chimpanzees infected with HIV-1. These results suggest a novel mechanism for maximizing virus production in the face of rapid killing of infected target cells.

Potent suppression of HIV-1 replication in humans by T-20, a peptide inhibitor of gp41-mediated virus entry.

T-20, a synthetic peptide corresponding to a region of the transmembrane subunit of the HIV-1 envelope protein, blocks cell fusion and viral entry at concentrations of less than 2 ng/ml in vitro. We administered intravenous T-20 (monotherapy) for 14 days to sixteen HIV-infected adults in four dose groups (3, 10, 30 and 100 mg twice daily). There were significant, dose-related declines in plasma HIV RNA in all subjects who received higher dose levels. All four subjects receiving 100 mg twice daily had a decline in plasma HIV RNA to less than 500 copies/ml, by bDNA assay. A sensitive RT-PCR assay (detection threshold 40 copies/ml) demonstrated that, although undetectable levels were not achieved in the 14-day dosing period, there was a 1.96 log10 median decline in plasma HIV RNA in these subjects. This study provides proof-of-concept that viral entry can be successfully blocked in vivo. Short-term administration of T-20 seems safe and provides potent inhibition of HIV replication comparable to anti-retroviral regimens approved at present.

Constant mean viral copy number per infected cell in tissues regardless of high, low, or undetectable plasma HIV RNA.

Quantitative analysis of the relationship between virus expression and disease outcome has been critical for understanding HIV-1 pathogenesis. Yet the amount of viral RNA contained within an HIV-expressing cell and the relationship between the number of virus-producing cells and plasma virus load has not been established or reflected in models of viral dynamics. We report here a novel strategy for the coordinated analysis of virus expression in lymph node specimens. The results obtained for patients with a broad range of plasma viral loads before and after antiretroviral therapy reveal a constant mean viral (v)RNA copy number (3.6 log10 copies) per infected cell, regardless of plasma virus load or treatment status. In addition, there was a significant but nonlinear direct correlation between the frequency of vRNA+ lymph node cells and plasma vRNA. As predicted from this relationship, residual cells expressing this same mean copy number are detectable (frequency <2/10(6) cells) in tissues of treated patients who have plasma vRNA levels below the current detectable threshold (<50 copies/ml). These data suggest that fully replication-active cells are responsible for sustaining viremia after initiation of potent antiretroviral therapy and that plasma virus titers correlate, albeit in a nonlinear fashion, with the number of virus-expressing cells in lymphoid tissue.

Fairness versus reason in the ultimatum game.

In the Ultimatum Game, two players are offered a chance to win a certain sum of money. All they must do is divide it. The proposer suggests how to split the sum. The responder can accept or reject the deal. If the deal is rejected, neither player gets anything. The rational solution, suggested by game theory, is for the proposer to offer the smallest possible share and for the responder to accept it. If humans play the game, however, the most frequent outcome is a fair share. In this paper, we develop an evolutionary approach to the Ultimatum Game. We show that fairness will evolve if the proposer can obtain some information on what deals the responder has accepted in the past. Hence, the evolution of fairness, similarly to the evolution of cooperation, is linked to reputation.

Population dynamics of immune responses to persistent viruses.

Mathematical models, which are based on a firm understanding of biological interactions, can provide nonintuitive insights into the dynamics of host responses to infectious agents and can suggest new avenues for experimentation. Here, a simple mathematical approach is developed to explore the relation between antiviral immune responses, virus load, and virus diversity. The model results are compared to data on cytotoxic T cell responses and viral diversity in infections with the human T cell leukemia virus (HTLV-1) and the human immunodeficiency virus (HIV-1).

Evolution of universal grammar.

Universal grammar specifies the mechanism of language acquisition. It determines the range of grammatical hypothesis that children entertain during language learning and the procedure they use for evaluating input sentences. How universal grammar arose is a major challenge for evolutionary biology. We present a mathematical framework for the evolutionary dynamics of grammar learning. The central result is a coherence threshold, which specifies the condition for a universal grammar to induce coherent communication within a population. We study selection of grammars within the same universal grammar and competition between different universal grammars. We calculate the condition under which natural selection favors the emergence of rule-based, generative grammars that underlie complex language.

Antigenic diversity thresholds and the development of AIDS.

Longitudinal studies of patients infected with HIV-1 reveal a long and variable incubation period between infection and the development of AIDS. Data from a small number of infected patients show temporal changes in the number of genetically distinct strains of the virus throughout the incubation period, with a slow but steady rise in diversity during the progression to disease. A mathematical model of the dynamic interaction between viral diversity and the human immune system suggests the existence of an antigen diversity threshold, below which the immune system is able to regulate viral population growth but above which the virus population induces the collapse of the CD4+ lymphocyte population. The model suggests that antigenic diversity is the cause, not a consequence, of immunodeficiency disease. The model is compared with available data, and is used to assess how the timing of the application of chemotherapy or immunotherapy influences the rate of progress to disease.

Quantitation of HIV-1-specific cytotoxic T lymphocytes and plasma load of viral RNA.

Although cytotoxic T lymphocytes (CTLs) are thought to be involved in the control of human immunodeficiency virus-type 1 (HIV-1) infection, it has not been possible to demonstrate a direct relation between CTL activity and plasma RNA viral load. Human leukocyte antigen-peptide tetrameric complexes offer a specific means to directly quantitate circulating CTLs ex vivo. With the use of the tetrameric complexes, a significant inverse correlation was observed between HIV-specific CTL frequency and plasma RNA viral load. In contrast, no significant association was detected between the clearance rate of productively infected cells and frequency of HIV-specific CTLs. These data are consistent with a significant role for HIV-specific CTLs in the control of HIV infection and suggest a considerable cytopathic effect of the virus in vivo.

Adaptive evolution of highly mutable loci in pathogenic bacteria.

Bacteria have specific loci that are highly mutable. We argue that the coexistence within bacterial genomes of such 'contingency' genes with high mutation rates, and 'housekeeping' genes with low mutation rates, is the result of adaptive evolution, and facilitates the efficient exploration of phenotypic solutions to unpredictable aspects of the host environment while minimizing deleterious effects on fitness.

Evolutionary origins and maintenance of redundant gene expression during metazoan development.

Various levels of redundancy in developmental gene function appear common in complex metazoans. There might be no apparent phenotype at many, or even any, of a gene's specific expression sites in homozygous null mutant embryos. Here we ask what underlies the origin of such arrangements. The generation of families of genes by duplication has clearly been important. Additionally, however, selection might have driven molecularly unrelated genes, which encode proteins of similar physiological function, to become expressed during the same sets of developmental events (times and places), even though each such gene might initially have evolved in connection with just one of these events.

Evolutionary games on cycles with strong selection.

Evolutionary games on graphs describe how strategic interactions and population structure determine evolutionary success, quantified by the probability that a single mutant takes over a population. Graph structures, compared to the well-mixed case, can act as amplifiers or suppressors of selection by increasing or decreasing the fixation probability of a beneficial mutant. Properties of the associated mean fixation times can be more intricate, especially when selection is strong. The intuition is that fixation of a beneficial mutant happens fast in a dominance game, that fixation takes very long in a coexistence game, and that strong selection eliminates demographic noise. Here we show that these intuitions can be misleading in structured populations. We analyze mean fixation times on the cycle graph under strong frequency-dependent selection for two different microscopic evolutionary update rules (death-birth and birth-death). We establish exact analytical results for fixation times under strong selection and show that there are coexistence games in which fixation occurs in time polynomial in population size. Depending on the underlying game, we observe inherence of demographic noise even under strong selection if the process is driven by random death before selection for birth of an offspring (death-birth update). In contrast, if selection for an offspring occurs before random removal (birth-death update), then strong selection can remove demographic noise almost entirely.

Spatial evolution of tumors with successive driver mutations.

We study the influence of driver mutations on the spatial evolutionary dynamics of solid tumors. We start with a cancer clone that expands uniformly in three dimensions giving rise to a spherical shape. We assume that cell division occurs on the surface of the growing tumor. Each cell division has a chance to give rise to a mutation that activates an additional driver gene. The resulting clone has an enhanced growth rate, which generates a local ensemble of faster growing cells, thereby distorting the spherical shape of the tumor. We derive formulas for the abundance and diversity of additional driver mutations as function of time. Our model is semi-deterministic: the spatial growth of cancer clones is deterministic, while mutants arise stochastically.

Competition between zidovudine-sensitive and zidovudine-resistant strains of HIV.

OBJECTIVE: To investigate competitive interactions between zidovudine-sensitive and resistant strains of HIV within the context of host-parasite population dynamic interactions between CD4+ cells and HIV. DESIGN: A mathematical model of the population dynamics of CD4+ cells, sensitive HIV and resistant HIV is developed. METHODS: The model is analysed numerically and analytically and model predictions are compared with previously published data on population dynamics of HIV and CD4+ cells in patients receiving zidovudine. A threshold result describing the critical dose of zidovudine above which resistant HIV will out-compete sensitive HIV is derived, as are expressions describing the critical effective doses for the eradication of sensitive and resistant strains. Numerical simulations of the dynamics of the shift from the pre-treatment, equilibrium to the treatment equilibrium are presented and an analytic expression approximating the time taken until virus growth restarts is derived. RESULTS: It is shown that competition between strains of virus is the important factor determining which type of virus will eventually start to grow during the course of zidovudine treatment, but host-parasite interactions are the important determinant of when viral resurgence occurs. CONCLUSIONS: Although resistant strains are observed after prolonged treatment with zidovudine, this model suggests that it is the growing supply of uninfected CD4+ cells which causes the eventual upsurge in viral burden.

The frequency of resistant mutant virus before antiviral therapy.

OBJECTIVE: To calculate the expected prevalence of resistant HIV mutants before antiviral therapy. DESIGN: HIV replication generates virus mutants. The prevalence of these mutants is determined by mutation and selection/fitness. Some mutations will confer drug resistance and it is crucial for the success of antiviral drug therapy to determine whether these resistant viruses are present before the initiation of therapy. METHODS: A quasispecies equation was used to calculate the expected frequency of drug-resistant virus prior to therapy. RESULTS AND CONCLUSIONS: We show how the pretreatment frequency of resistant virus depends on the number of point mutations between wild-type and mutant virus, the selective disadvantage of the resistant mutant and the intermediate mutants, and the mutation rate.

The evolutionary dynamics of HIV-1 quasispecies and the development of immunodeficiency disease.

This paper presents a theory to explain the development of immunodeficiency disease after a long and variable incubation period of infection with HIV-1. Two assumptions are central to the theory: (1) mutation via reverse transcription during viral replication can generate viral strains resistant to neutralization by antibodies specific to earlier mutants in a particular host; (2) the virus can kill the CD4-positive lymphocytes that play a role in mounting an immunological attack directed at the virus. The theory is examined via the development of a mathematical model which reveals that an increasing number of antigenically distinct viral strains may overwhelm the immune system of the host. As the viral diversity increases beyond a certain level the immune system is unable to suppress the population growth of all the strains simultaneously. The intuitive explanation of this pattern of model behaviour lies in the assumption that each virus can kill CD4-positive lymphocytes that are specific to any of the viral strains, but each lymphocyte only directs immunological attack against a single viral strain.(ABSTRACT TRUNCATED AT 250 WORDS)

Evolution of virulence in a heterogeneous host population.

There is a large body of theoretical studies that investigate factors that affect the evolution of virulence, that is parasite-induced host mortality. In these studies the host population is assumed to be genetically homogeneous. However, many parasites have a broad range of host types they infect, and trade-offs between the parasite virulence in different host types may exist. The aim of this paper is to study the effect of host heterogeneity on the evolution of parasite virulence. By analyzing a simple model that describes the replication of different parasite strains in a population of two different host types, we determine the optimal level of virulence in both host types and find the conditions under which strains that specialize in one host type dominate the parasite population. Furthermore, we show that intrahost evolution of the parasite during an infection may lead to stable polymorphisms and could introduce evolutionary branching in the parasite population.

Coinfection and the evolution of parasite virulence.

Analyses of the selection pressures acting on parasite virulence are made more complicated when individual hosts can simultaneously harbour many different strains or genotypes of a parasite. Here we explore the evolutionary dynamics of host-parasite associations in which individual hosts can be coinfected with many different parasite strains. (We take coinfection to mean that each strain transmits at a rate unaffected by the presence of others in the same host.) This study thus represents the opposite extreme to our earlier work on superinfection in which there is a dominance hierarchy such that only the most virulent strain present in a host is transmitted. For highly diverse populations of parasite strains, we find that such coinfection leads to selection for strains whose virulence-levels lie in a relatively narrow band close to the maximum consistent with the parasite's basic preproductive ratio, R0, exceeding unity.