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Biomedical subjects

M A Nowak

Publications and source records attributed to M A Nowak.

At least 55 records · Page 3Linked to original sources
PubMed1999

An error limit for the evolution of language.

On the evolutionary trajectory that led to human language there must have been a transition from a fairly limited to an essentially unlimited communication system. The structure of modern human languages reveals at least two steps that are required for such a transition: in all languages (i) a small number of phonemes are used to generate a large number of words; and (ii) a large number of words are used to a produce an unlimited number of sentences. The first (and simpler) step is the topic of the current paper. We study the evolution of communication in the presence of errors and show that this limits the number of objects (or concepts) that can be described by a simple communication system. The evolutionary optimum is achieved by using only a small number of signals to describe a few valuable concepts. Adding more signals does not increase the fitness of a language. This represents an error limit for the evolution of communication. We show that this error limit can be overcome by combining signals (phonemes) into words. The transition from an analogue to a digital system was a necessary step toward the evolution of human language.

Biological Evolution↗
PubMed1999

The continuous prisoner's dilemma: I. linear reactive strategies.

We present a general model for the Prisoner's Dilemma in which variable degrees of cooperation are possible, and payoffs are scaled accordingly. We describe a continuous strategy space, and divide this space into strategy families. We derive the payoff function for these families analytically, and study the evolutionary outcome when a wide range of strategies play against each other. Our results show that the initial degree of cooperation offered by a strategy is a decisive factor for evolutionary robustness: the most successful strategies in our model offer full cooperation as an initial move, but thereafter cooperate fully only if their opponent does the same. These strategies gradually raise the stakes when playing a strategy which is initially reticent to cooperate, but differ from the strategies predicted by other continuous models in that they are not only generous, but are also consistently optimistic and uncompromising.

Biological Evolution↗
PubMed1999

The continuous Prisoner's dilemma: II. Linear reactive strategies with noise.

We present a general model for the Continuous Prisoner's Dilemma and study the effect of errors. We find that cooperative strategies that can resist invasion by defectors are optimistic (make high initial offers), generous (always offer more cooperation than the partner did in the previous round) and uncompromising (offer full cooperation only if the partner does). A necessary condition for the emergence of cooperation in the continuous Prisoner's Dilemma with noise is b (1-p)>c, where b and c denote, respectively, the benefit and cost of cooperation, while p is the error rate. This relation can be reformulated as an error threshold: cooperation can only emerge if the probability of making a mistake is below a critical value. We note, however, that cooperation in the continuous Prisoner's Dilemma with noise does not seem to be evolutionarily stable: while it is possible to find cooperative strategies that resist invasion by defectors, such cooperators are generally invaded by more cooperative strategies which eventually yield to defectors. Thus, the long-term evolution of the continuous Prisoner's Dilemma is either characterized by unending cycles or by stable polymorphisms of cooperators and defectors.

Biological Evolution↗
PubMed1999

A simple relationship between viral load and survival time in HIV-1 infection.

Despite important recent insights into the short-term dynamics of HIV-1 infection, our understanding of the long-term pathogenesis of AIDS remains unclear. Using an approach that places rapid progressors, typical progressors, and nonprogressors on a single clinical spectrum of disease progression, we quantitate the previously reported relationship between viral load and survival time. We introduce the concept of viral constant, present evidence that this quantity is conserved across patients, and explore the immunopathological implications of this finding. We conclude with a quantitative approach for assessing the benefits of a given regime of antiviral therapy.

Acquired Immunodeficiency Syndrome↗
PubMed1999

The evolutionary language game.

We explore how evolutionary game dynamics have to be modified to accomodate a mathematical framework for the evolution of language. In particular, we are interested in the evolution of vocabulary, that is associations between signals and objects. We assume that successful communication contributes to biological fitness: individuals who communicate well leave more offspring. Children inherit from their parents a strategy for language learning (a language acquisition device). We consider three mechanisms whereby language is passed from one generation to the next: (i) parental learning: children learn the language of their parents; (ii) role model learning: children learn the language of individuals with a high payoff; and (iii) random learning: children learn the language of randomly chosen individuals. We show that parental and role model learning outperform random learning. Then we introduce mistakes in language learning and study how this process changes language over time. Mistakes increase the overall efficacy of parental and role model learning: in a world with errors evolutionary adaptation is more efficient. Our model also provides a simple explanation why homonomy is common while synonymy is rare.

Biological Evolution↗
PubMed1999

The evolution of language.

The emergence of language was a defining moment in the evolution of modern humans. It was an innovation that changed radically the character of human society. Here, we provide an approach to language evolution based on evolutionary game theory. We explore the ways in which protolanguages can evolve in a nonlinguistic society and how specific signals can become associated with specific objects. We assume that early in the evolution of language, errors in signaling and perception would be common. We model the probability of misunderstanding a signal and show that this limits the number of objects that can be described by a protolanguage. This "error limit" is not overcome by employing more sounds but by combining a small set of more easily distinguishable sounds into words. The process of "word formation" enables a language to encode an essentially unlimited number of objects. Next, we analyze how words can be combined into sentences and specify the conditions for the evolution of very simple grammatical rules. We argue that grammar originated as a simplified rule system that evolved by natural selection to reduce mistakes in communication. Our theory provides a systematic approach for thinking about the origin and evolution of human language.

Biological Evolution↗
PubMed1999

Dynamics of immune escape in HIV infection.

The dynamics between pathogens and the immune system involve complicated interactions of many different components and this makes the use of mathematical models necessary to provide a correct interpretation of empirical results as well as to generate new insights and hypotheses. We demonstrate this approach by discussing mathematical models describing the dynamics between HIV and the immune response. Specifically, we show that viral evolution towards increased antigenic diversity may be the driving force underlying HIV disease progression and the reason for the eventual breakdown of the immune system upon development of AIDS. Such insights have important implications for designing efficient treatment regimes for HIV-infected patients.

Acquired Immunodeficiency Syndrome↗
PubMed1999

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.

Antiviral Agents↗
PubMed1999

Genetic control and dynamics of the cellular immune response to the human T-cell leukaemia virus, HTLV-I.

About 1% of people infected with the human T-cell leukaemia virus, type 1 (HTLV-I) develop a disabling chronic inflammatory disease of the central nervous system known as HTLV-I-associated myelopathy/tropical spastic paraparesis (HAM/TSP). Patients with HAM/TSP have a vigorous immune response to HTLV-I, and it has been widely suggested that this immune response, particularly the HTLV-I-specific cytotoxic T-lymphocyte (CTL) response, causes the tissue damage that is seen in HAM/TSP. In this paper we summarize recent evidence that a strong CTL response to HTLV-I does in fact protect against HAM/TSP by reducing the proviral load of HTLV-I. We conclude that HTLV-I is persistently replicating at a high level, despite the relative constancy of its genome sequence. These results imply that antiretroviral drugs could reduce the risk of HAM/TSP by reducing the viral load, and that an effective anti-HTLV-I vaccine should elicit a strong CTL response to the virus. The dynamic nature of the infection also has implications for the epidemiology and the evolution of HTLV-I.

Human T-lymphotropic virus 1↗
PubMed1999

HLA alleles determine human T-lymphotropic virus-I (HTLV-I) proviral load and the risk of HTLV-I-associated myelopathy.

The risk of disease associated with persistent virus infections such as HIV-I, hepatitis B and C, and human T-lymphotropic virus-I (HTLV-I) is strongly determined by the virus load. However, it is not known whether a persistent class I HLA-restricted antiviral cytotoxic T lymphocyte (CTL) response reduces viral load and is therefore beneficial or causes tissue damage and contributes to disease pathogenesis. HTLV-I-associated myelopathy (HAM/TSP) patients have a high virus load compared with asymptomatic HTLV-I carriers. We hypothesized that HLA alleles control HTLV-I provirus load and thus influence susceptibility to HAM/TSP. Here we show that, after infection with HTLV-I, the class I allele HLA-A*02 halves the odds of HAM/TSP (P < 0.0001), preventing 28% of potential cases of HAM/TSP. Furthermore, HLA-A*02(+) healthy HTLV-I carriers have a proviral load one-third that (P = 0.014) of HLA-A*02(-) HTLV-I carriers. An association of HLA-DRB1*0101 with disease susceptibility also was identified, which doubled the odds of HAM/TSP in the absence of the protective effect of HLA-A*02. These data have implications for other persistent virus infections in which virus load is associated with prognosis and imply that an efficient antiviral CTL response can reduce virus load and so prevent disease in persistent virus infections.

Alleles↗
PubMed1999

Quantifying the kinetic parameters of prion replication.

The mechanism of protein-only prion replication is controversial. A detailed mathematical model of prion replication by nucleated polymerisation is developed, and its parameters are estimated from published data. PrP-res decay is around two orders of magnitude slower than PrP-sen decay, a plausible ratio of two parameters estimated from very different experiments. By varying the polymer breakage rate, we reveal that systems of short polymers grow the fastest. Drugs which break polymers could therefore accelerate disease progression. Growth in PrP-res seems slower than growth in infectious titre. This can be explained either by a novel hypothesis concerning inoculum clearance from a newly infected brain, or by the faster growth of compartments containing smaller polymers. The existence of compartments can also explain why prion growth sometimes reaches a plateau. Published kinetic data are all compatible with our mathematical model, so the nucleated polymerisation hypothesis cannot be ruled out on dynamic grounds.

Animals↗
PubMed1999

Dynamics of macrophage and T cell infection by HIV.

We analyse mathematical models comparing the in vivo dynamics of macrophage- and T cell infection by HIV. Experiments suggest that HIV can only replicate in activated T cells whereas cell activation may not be required for successful replication in macrophages. These assumptions lead to fundamentally different conditions required to establish a persistent infection in the two cell types. While persistent replication in macrophages is achieved if the basic reproductive ratio of the virus, R0, exceeds unity, the establishment of T cell infection may depend on a complex balance between host and viral parameters as well as initial conditions. More specifically, the replication rate of HIV needs to lie above a threshold level and the immune responsiveness of the host below a certain threshold for persistent T cell infection to be possible. In addition, initial virus load has to be intermediate and the initial abundance of CTLs low. Mathematical models predict that macrophage infection may be essential for the successful establishment of HIV in the primary phase of the infection. Acting as a reservoir, they allow the virus to evolve towards increased replication kinetics as well as away from immune recognition, thus paving the way for the rise of exclusively T cell tropic strains using the CXCR4-coreceptor.

CD4-Positive T-Lymphocytes↗
PubMed1999

Evolutionary preservation of redundant duplicated genes.

Gene duplication events produce both perfect and imperfect copies of genes. Perfect copies are said to be functionally redundant when knockout of one gene produces no 'scoreable', phenotypic effects. Preserving identical, duplicate copies of genes is problematic as all copies are prone to accumulate neutral mutations as pseudogenes, or more rarely, evolve into new genes with novel functions. We summarise theoretical treatments for the invasion and subsequent evolutionary modification of functionally redundant genes. We then consider the preservation of functionally identical copies of a gene over evolutionary time. We present several models for conserving redundancy: asymmetric mutation, asymmetric efficacy, pleiotropy, developmental buffering, allelic competition and regulatory asymmetries. In all cases, some form of symmetry breaking is required to maintain functional redundancy indefinitely.

Animals↗
PubMed1999

The dynamics of HTLV-I and the CTL response.

Dominik Wodarz and colleagues describe a mathematical model for the in vivo dynamics of human T-cell leukaemia virus type 1 (HTLV-I) infection and the virus-specific cytotoxic T lymphocyte response. They show that a high rate of viral replication is consistent with the relative sequence invariance of HTLV-I and might be necessary to maintain a persistent infection.

Antiviral Agents↗