arXiv subjects

Emmanuel Tannenbaum

Publications and source records attributed to Emmanuel Tannenbaum.

At least 19 recordsLinked to original sources

arXiv2009

Second-Order Catalytic Quasispecies Yields First-Order Phase Transition

The quasispecies model describes processes related to the origin of life and viral evolutionary dynamics. We discuss how the error catastrophe that reflects the transition from localized to delocalized quasispecies population is affected by catalytic replication of different reaction orders. Specifically, we find that 2nd order mechanisms lead to 1st order discontinuous phase transitions in the viable population fraction, and conclude that the "higher" the interaction the "lower" the transition. We discuss potential implications for understanding the replication of highly mutating RNA viruses.

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arXiv2009

Semiconservative quasispecies equations for polysomic genomes: The general case

This paper develops a formulation of the quasispecies equations appropriate for polysomic, semiconservatively replicating genomes. This paper is an extension of previous work on the subject, which considered the case of haploid genomes. Here, we develop a more general formulation of the quasispecies equations that is applicable to diploid and even polyploid genomes. Interestingly, with an appropriate classification of population fractions, we obtain a system of equations that is formally identical to the haploid case. As with the work for haploid genomes, we consider both random and immortal DNA strand chromosome segregation mechanisms. However, in contrast to the haploid case, we have found that an analytical solution for the mean fitness is considerably more difficult to obtain for the polyploid case. Accordingly, whereas for the haploid case we obtained expressions for the mean fitness for the case of an analogue of the single-fitness-peak landscape for arbitrary lesion repair probabilities (thereby allowing for non-complementary genomes), here we solve for the mean fitness for the restricted case of perfect lesion repair.

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arXiv2009

Diploidy and the selective advantage for sexual reproduction in unicellular organisms

This paper develops mathematical models describing the evolutionary dynamics of both asexually and sexually reproducing populations of diploid unicellular organisms. We consider two forms of genome organization. In one case, we assume that the genome consists of two multi-gene chromosomes, while in the second case we assume that each gene defines a separate chromosome. If the organism has $ l $ homologous pairs that lack a functional copy of the given gene, then the fitness of the organism is $ κ_l $. The $ κ_l $ are assumed to be monotonically decreasing, so that $ κ_0 = 1 > κ_1 > κ_2 > ... > κ_{\infty} = 0 $. For nearly all of the reproduction strategies we consider, we find, in the limit of large $ N $, that the mean fitness at mutation-selection balance is $ \max\{2 e^{-μ} - 1, 0\} $, where $ N $ is the number of genes in the haploid set of the genome, $ ε$ is the probability that a given DNA template strand of a given gene produces a mutated daughter during replication, and $ μ= N ε$. The only exception is the sexual reproduction pathway for the multi-chromosomed genome. Assuming a multiplicative fitness landscape where $ κ_l = α^{l} $ for $ α\in (0, 1) $, this strategy is found to have a mean fitness that exceeds the mean fitness of all of the other strategies. Furthermore, while the other reproduction strategies experience a total loss of viability due to the steady accumulation of deleterious mutations once $ μ$ exceeds $ \ln 2 $, no such transition occurs in the sexual pathway. The results of this paper demonstrate a selective advantage for sexual reproduction with fewer and much less restrictive assumptions than previous work.

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arXiv2009

The influence of horizontal gene transfer on the mean fitness of unicellular populations in static environments

This paper develops a mathematical model describing the influence that conjugation-mediated Horizontal Gene Transfer (HGT) has on the mutation-selection balance in an asexually reproducing population of unicellular, prokaryotic organisms. It is assumed that mutation-selection balance is reached in the presence of a fixed background concentration of antibiotic, to which the population must become resistant in order to survive. We analyze the behavior of the model in the limit of low and high antibiotic-induced first-order death rate constants, and find that the highest mean fitness is obtained at low rates of bacterial conjugation. As the rate of conjugation crosses a threshold, the mean fitness decreases to a minimum, and then rises asymptotically to a limiting value as the rate of conjugation becomes infinitely large. However, this limiting value is smaller than the mean fitness obtained in the limit of low conjugation rate. This dependence of the mean fitness on the conjugation rate is fairly small for the parameter ranges we have considered, and disappears as the first-order death rate constant due to the presence of antibiotic approaches zero. For large values of the antibiotic death rate constant, we have obtained an analytical solution for the behavior of the mean fitness that agrees well with the results of simulations. The results of this paper suggest that conjugation-mediated HGT has a slightly deleterious effect on the mean fitness of a population at mutation-selection balance. Therefore, we argue that HGT confers a selective advantage by allowing for faster adaptation to a new or changing environment. The results of this paper are consistent with the observation that HGT can be promoted by environmental stresses on a population.

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arXiv2008

A Dual Role for Sex?

The two classic theories for the existence of sexual replication are that sex purges deleterious mutations from a population, and that sex allows a population to adapt more rapidly to changing environments. These two theories have often been presented as opposing explanations for the existence of sex. Here, we develop and analyze evolutionary models based on the asexual and sexual replication pathways in Saccharomyces cerevisiae (Baker's yeast), and show that sexual replication can both purge deleterious mutations in a static environment, as well as lead to faster adaptation in a dynamic environment. This implies that sex can serve a dual role, which is in sharp contrast to previous theories.

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arXiv2008

The effect of the SOS response on the mean fitness of unicellular populations: A quasispecies approach

This paper develops a quasispecies model that incorporates the SOS response. We consider a unicellular, asexually replicating population of organisms, whose genomes consist of a single, double-stranded DNA molecule, i.e. one chromosome. We assume that repair of post-replication mismatched base-pairs occurs with probability $ λ$, and that the SOS response is triggered when the total number of mismatched base-pairs exceeds $ l_S $. We further assume that the per-mismatch SOS elimination rate is characterized by a first-order rate constant $ κ_{SOS} $. For a single fitness peak landscape where the master genome can sustain up to $ l $ mismatches and remain viable, this model is analytically solvable in the limit of infinite sequence length. The results, which are confirmed by stochastic simulations, indicate that the SOS response does indeed confer a fitness advantage to a population, provided that it is only activated when DNA damage is so extensive that a cell will die if it does not attempt to repair its DNA.

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arXiv2008

The Effect of Mutators on Adaptability in Time-Varying Fitness Landscapes

This Letter studies the quasispecies dynamics of a population capable of genetic repair evolving on a time-dependent fitness landscape. We develop a model that considers an asexual population of single-stranded, conservatively replicating genomes, whose only source of genetic variation is due to copying errors during replication. We consider a time-dependent, single-fitness-peak landscape where the master sequence changes by a single point mutation every time $ τ$. We are able to analytically solve for the evolutionary dynamics of the population in the point-mutation limit. In particular, our model provides an analytical expression for the fraction of mutators in the dynamic fitness landscape that agrees well with results from stochastic simulations.

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arXiv2007

A comparison of sexual and asexual replication strategies in a simplified model based on the yeast life cycle

This paper develops simplified mathematical models describing the mutation-selection balance for the asexual and sexual replication pathways in {\it Saccharomyces cerevisiae}. We assume diploid genomes consisting of two chromosomes, and we assume that each chromosome is functional if and only if its base sequence is identical to some master sequence. The growth and replication of the yeast cells is modeled as a first-order process, with first-order growth rate constants that are determined by whether a given genome consists of zero, one, or two functional chromosomes. In the asexual pathway, we assume that a given diploid cell divides into two diploids. In the sexual pathway, we assume that a given diploid cell divides into two diploids, each of which then divide into two haploids. The resulting four haploids enter a haploid pool, where they grow and replicate until they meet another haploid with which to fuse. When the cost for sex is low, we find that the selective mating strategy leads to the highest mean fitness of the population, when compared to all of the other strategies. We also show that, at low to intermediate replication fidelities, sexual replication with random mating has a higher mean fitness than asexual replication, as long as the cost for sex is low. This is consistent with previous work suggesting that sexual replication is advantageous at high population densities, low replication rates, and intermediate replication fidelities. The results of this paper also suggest that {\it S. cerevisiae} switches from asexual to sexual replication when stressed, because stressful growth conditions provide an opportunity for the yeast to clear out deleterious mutations from their genomes.

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arXiv2007

Selective advantage for sexual reproduction with random haploid fusion

This paper develops a simplified set of models describing asexual and sexual replication in unicel- lular diploid organisms. The models assume organisms whose genomes consist of two chromosomes, where each chromosome is assumed to be functional if it is equal to some master sequence $ σ_0 $, and non-functional otherwise. The first-order growth rate constant, or fitness, of an organism, is determined by whether it has zero, one, or two functional chromosomes in its genome. For a population replicating asexually, a given cell replicates both of its chromosomes, and splits its genetic material evenly between the two cells. For a population replicating sexually, a given cell first divides into two haploids, which enter a haploid pool, fuse into diploids, and then divide via the normal mitotic process. Haploid fusion is modeled as a second-order rate process. When the cost for sex is small, as measured by the ratio of the characteristic haploid fusion time to the characteristic growth time, we find that sexual replication with random haploid fusion leads to a greater mean fitness for the population than a purely asexual strategy. However, independently of the cost for sex, we find that sexual replication with a selective mating strategy leads to a higher mean fitness than the random mating strategy. This result is based on the assumption that a selective mating strategy does not have any additional time or energy costs over the random mating strategy, an assumption that is discussed in the paper. The results of this paper are consistent with previous studies suggesting that sex is favored at intermediate mutation rates, for slowly replicating organisms, and at high population densities.

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arXiv2007

A comparison of three replication strategies in complex multicellular organisms: Asexual replication, sexual replication with identical gametes, and sexual replication with distinct sperm and egg gametes

This paper studies the mutation-selection balance in three simplified replication models. The first model considers a population of organisms replicating via the production of asexual spores. The second model considers a sexually replicating population that produces identical gametes. The third model considers a sexually replicating population that produces distinct sperm and egg gametes. All models assume diploid organisms whose genomes consist of two chromosomes, each of which is taken to be functional if equal to some master sequence, and defective otherwise. In the asexual population, the asexual diploid spores develop directly into adult organisms. In the sexual populations, the haploid gametes enter a haploid pool, where they may fuse with other haploids. The resulting immature diploid organisms then proceed to develop into mature organisms. Based on an analysis of all three models, we find that, as organism size increases, a sexually replicating population can only outcompete an asexually replicating population if the adult organisms produce distinct sperm and egg gametes. A sexual replication strategy that is based on the production of large numbers of sperm cells to fertilize a small number of eggs is found to be necessary in order to maintain a sufficiently low cost for sex for the strategy to be selected for over a purely asexual strategy. We discuss the usefulness of this model in understanding the evolution and maintenance of sexual replication as the preferred replication strategy in complex, multicellular organisms.

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arXiv2007

Speculations on the emergence of self-awareness in big-brained organisms

This paper argues that self-awareness is a learned behavior that emerges in organisms whose brains have a sufficiently integrated, complex ability for associative learning and memory. Continual sensory input of information related to the organism causes the organism's brain to learn the physical characteristics of the organism, in the sense that neural pathways are produced that are reinforced by, and therefore recognize, various features associated with the organism. This results in the formation of a set of associations that may be termed an organismal self-image, which provides a mechanistic basis for the emergence of various behaviors that are associated with self-awareness, such as self-recognition. In humans, self-awareness includes additional behaviors such as recognition of self-awareness, the concept of I, and various existential and religious questions. This paper shows how associative memory and learning, combined with an organismal self-image and, in the case of humans, language, leads to the emergence of these various behaviors. This paper also discusses various tautologies that invariably emerge when discussing self-awareness, that ultimately prevent an unambiguous resolution to the various existential issues that arise. We continue with various speculations on manipulating self-awareness, and discuss how concepts from set and logic may provide a highly useful set of tools in computational neuroscience for understanding the emergence of higher cognitive functions in complex organisms. The existence of other types of awareness, and the role of mirror neurons in the emergence of self-awareness, are also briefly discussed.

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arXiv2007

Associative learning in biochemical networks

We develop a simple, chemostat-based model illustrating how a process analogous to associative learning can occur in a biochemical network. Associative learning is a form of learning whereby a system "learns" to associate two stimuli with one another. In our model, two types of replicating molecules, denoted A and B, are present in some initial concentration in the chemostat. Molecules A and B are stimulated to replicate by some growth factors, denoted GA and GB, respectively. It is also assumed that A and B can covalently link, and that the conjugated molecule can be stimulated by either the GA or GB growth factors (and can be degraded). We show that, if the chemostat is stimulated by both growth factors for a certain time, followed by a time gap during which the chemostat is not stimulated at all, and if the chemostat is then stimulated again by only one of the growth factors, then there will be a transient increase in the number of molecules activated by the other growth factor. Therefore, the chemostat bears the imprint of earlier, simultaneous stimulation with both growth factors, which is indicative of associative learning. It is interesting to note that the dynamics of our model is consistent with various aspects of Pavlov's original series of associative learning experiments in dogs. We discuss how associative learning can potentially be performed in vitro within RNA, DNA, or peptide networks. We also highlight how such a mechanism could potentially be involved in genomic evolution, and suggest bioinformatics studies that could be used to find evidence for associative learning processes at work inside living cells.

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arXiv2006

Asexual and sexual replication in sporulating organisms

This paper develops models describing asexual and sexual replication in sporulating organisms. Replication via sporulation is the replication strategy for all multicellular life, and may even be observed in unicellular life (such as with budding yeast). We consider diploid populations replicating via one of two possible sporulation mechanisms: (1) Asexual sporulation, whereby adult organisms produce single-celled diploid spores that grow into adults themselves. (2) Sexual sporulation, whereby adult organisms produce single-celled diploid spores that divide into haploid gametes. The haploid gametes enter a haploid "pool", where they may recombine with other haploids to form a diploid spore that then grows into an adult. We consider a haploid fusion rate given by second-order reaction kinetics. We work with a simplified model where the diploid genome consists of only two chromosomes, each of which may be rendered defective with a single point mutation of the wild-type. We find that the asexual strategy is favored when the rate of spore production is high compared to the characteristic growth rate from a spore to a reproducing adult. Conversely, the sexual strategy is favored when the rate of spore production is low compared to the characteristic growth rate from a spore to a reproducing adult. As the characteristic growth time increases, or as the population density increases, the critical ratio of spore production rate to organism growth rate at which the asexual strategy overtakes the sexual one is pushed to higher values. Therefore, the results of this model suggest that, for complex multicellular organisms, sexual replication is favored at high population densities, and low growth and sporulation rates.

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arXiv2006

Temporal differentiation and the optimization of system output

This paper develops a set of simplified dynamical models with which to explore the conditions under which temporal differentiation leads to optimized system output. By temporal differentiation, we mean a division of labor whereby different subtasks associated with performing a given task are done at different times. The idea is that, by focusing on one particular set of subtasks at a time, it is possible to increase the efficiency with which each subtask is performed, thereby allowing for faster completion of the overall task. For this paper, we consider a process whereby some resource is converted into some final product in a series of three agent-mediated steps. Temporal differentiation is incorporated by allowing the agents to oscillate between performing the first two steps and performing the last step. We find that temporal differentiation is favored when the number of agents is small, and when the process intermediates have a much longer lifetime than the original resource. Within the framework of biological systems, we argue that these results provide a possible evolutionary basis for the emergence of sleep, and also of distinct REM and non-REM sleep states. We also discuss our use of a three-step model. Briefly, in order for temporal differentiation to increase product output in a mean-field description of resource metabolism, it is necessary for temporal differentiation to have a nonlinear effect on individual process rates. For stochastic models, we argue that temporal differentiation can increase product output even in fundamentally linear systems.

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arXiv2006

When does division of labor lead to increased system output?

This paper develops a set of simplified dynamical models with which to explore the conditions under which division of labor leads to optimized system output, as measured by the rate of production of a given product. We consider two models: In the first model, we consider the flow of some resource into a compartment, and the conversion of this resource into some product. In the second model, we consider the resource-limited growth of autoreplicating systems. In this case, we divide the replication and metabolic tasks among different agents. The general features that emerge from our models is that division of labor is favored when the resource to agent ratio is at intermediate values, and when the time cost associated with transporting intermediate products is small compared to characteristic process times. We discuss the results of this paper in the context of simulations with digital life. We also argue that division of labor in the context of our replication model suggests an evolutionary basis for the emergence of the stem-cell-based tissue architecture in complex organisms.

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arXiv2006

Sleep as the solution to an optimization problem

This paper develops a highly simplified model with which to analyze the phenomenon of sleep. Motivated by Crick's suggestion that sleep is the brain's way of ``taking out the trash,'' a suggestion that is supported by emerging evidence, we consider the problem of the filling and emptying of a tank. At any given time, the tank may take in external resource, or fill, if resource is available at that time, or it may empty. The filling phases correspond to information input from the environment, or input of some material in general, while the emptying phases correspond to the processing of the resource. Given a resource-availablility profile over some time interval $ T $, we develop a canonical algorithm for determining the fill-empty profile that produces the maximum quantity of processed resource at the end of the time interval. From this algorithm, it readily follows that for a periodically oscillating resource-availability profile, the optimal fill-empty strategy is given by a fill period when resource is available, followed by an empty period when resource is not. This cycling behavior is analogous to the wake-sleep cycles in organismal life, where the generally nocturnal sleep phase is a period where the information collected from the day's activities may be processed. The sleep cycle is then a mechanism for the organism to process a maximal amount of information over a daily cycle. Our model can exhibit phenomena analogous to ``microsleeps,'' and other behavior associated with breakdown in sleep patterns.

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arXiv2005

A hypothesis on the selective advantage for sleep

In this note, we present a hypothesis for the emergence of the phenomenon of sleep in organisms with sufficiently developed central nervous systems. We argue that sleep emerges because individual neurons must periodically enter a resting state and perform various ``garbage collection'' activities. Because the proper functioning of the central nervous system is dependent on the interconnections amongst a large collection of individual neurons, it becomes optimal, from the standpoint of the organism, for these garbage collection activities to occur simultaneously. We present analogies with complex structures in modern economies to make our case, although we emphasize that our hypothesis is purely speculative at this time. Although the ``garbage collection'' hypothesis has been previously advanced, we believe that our speculation is useful because it illustrates the power of a general paradigm for understanding the emergence of collective behavior in agent-built systems.

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arXiv2005

Sexual replication in the quasispecies model

This paper develops a simplified model for sexual replication within the quasispecies formalism. We assume that the genomes of the replicating organisms are two-chromosomed and diploid, and that the fitness is determined by the number of chromosomes that are identical to a given master sequence. We also assume that there is a cost to sexual replication, given by a characteristic time $ τ_{seek} $ during which haploid cells seek out a mate with which to recombine. If the mating strategy is such that only viable haploids can mate, then when $ τ_{seek} = 0 $, it is possible to show that sexual replication will always outcompete asexual replication. However, as $ τ_{seek} $ increases, sexual replication only becomes advantageous at progressively higher mutation rates. Once the time cost for sex reaches a critical threshold, the selective advantage for sexual replication disappears entirely. The results of this paper suggest that sexual replication is not advantageous in small populations per se, but rather in populations with low replication rates. In this regime, the cost for sex is sufficiently low that the selective advantage obtained through recombination leads to the dominance of the strategy. In fact, at a given replication rate and for a fixed environment volume, sexual replication is selected for in high populations because of the reduced time spent finding a reproductive partner.

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