arXiv subjects

Emmanuel Tannenbaum

Publications and source records attributed to Emmanuel Tannenbaum.

28 records · Page 2Linked to original sources

arXiv2005

Selective advantage for multicellular replicative strategies: A two-cell example

This paper develops a quasispecies model where cells can adopt a two-cell survival strategy. Within this strategy, pairs of cells join together, at which point one of the cells sacrifices its own replicative ability for the sake of the other cell. We develop a simplified model for the evolutionary dynamics of this process, allowing us to solve for the steady-state using standard approaches from quasispecies theory. We find that our model exhibits two distinct regimes of behavior: At low concentrations of limiting resource, the two-cell strategy outcompetes the single-cell survival strategy, while at high concentrations of limiting resource, the single-cell survival strategy dominates. Associated with the two solution regimes of our model is a localization to delocalization transition over the portion of the genome coding for the multicell strategy, analogous to the error catastrophe in standard quasispecies models. The existence of such a transition indicates that multicellularity can emerge because natural selection does not act on specific cells, but rather on replicative strategies. Within this framework, individual cells become the means by which replicative strategies are propagated. Such a framework is therefore consistent with the concept that natural selection does not act on individuals, but rather on populations.

q-bio.PE↗

arXiv2005

An RNA-centered view of eukaryotic cells

Emerging evidence suggests that the introns and intergenic sequences of the genomes of higher eukaryotes (the ``junk'' DNA) codes for a vast, RNA-based, genetic regulatory network. It is believed that this network is responsible for the variety and complexity of terrestrial life. We conjecture that this regulatory network is more properly viewed as an RNA ``community'', composed of a rich and largely unexplored biochemical web of RNA interactions. Viewed as an RNA-community, we hypothesize that the RNA regulatory network of higher eukaryotes can re-wire itself, and employ various and evolvable mutational strategies in response to external pressures. Thus, we argue that much evolutionary change is due to intracellular, RNA-mediated learning processes. Successful strategies and pathways are then recorded (hard-wired) into the DNA genome via reverse transcriptase. We present evidence which is consistent with this viewpoint, and make specific predictions which could be used to test the utility of our framework. If essentially correct, the RNA-community view of eukaryotic cells could reconcile measured point mutation and gene duplication rates with actual rates of evolutionary change. Futhermore, the RNA-community view of eukaryotic cells suggests that agent-based modeling techniques, used in mathematical economics, game theory, and neuroscience, will likely be as useful in understanding the functioning of eukaryotic cells as the pathway-based approaches of systems biology. We conclude this paper by arguing that a sufficient amount of biological knowledge has been accumulated to initiate a systematic program of experimental and computational studies of the origins and macroevolution of terrestrial life.

q-bio.MN↗

arXiv2004

Evolutionary dynamics of adult stem cells: Comparison of random and immortal strand segregation mechanisms

This paper develops a point-mutation model describing the evolutionary dynamics of a population of adult stem cells. Such a model may prove useful for quantitative studies of tissue aging and the emergence of cancer. We consider two modes of chromosome segregation: (1) Random segregation, where the daughter chromosomes of a given parent chromosome segregate randomly into the stem cell and its differentiating sister cell. (2) ``Immortal DNA strand'' co-segregation, for which the stem cell retains the daughter chromosomes with the oldest parent strands. Immortal strand co-segregation is a mechanism, originally proposed by Cairns (J. Cairns, {\it Nature} {\bf 255}, 197 (1975)), by which stem cells preserve the integrity of their genomes. For random segregation, we develop an ordered strand pair formulation of the dynamics, analogous to the ordered strand pair formalism developed for quasispecies dynamics involving semiconservative replication with imperfect lesion repair (in this context, lesion repair is taken to mean repair of postreplication base-pair mismatches). Interestingly, a similar formulation is possible with immortal strand co-segregation, despite the fact that this segregation mechanism is age-dependent. From our model we are able to mathematically show that, when lesion repair is imperfect, then immortal strand co-segregation leads to better preservation of the stem cell lineage than random chromosome segregation. Furthermore, our model allows us to estimate the optimal lesion repair efficiency for preserving an adult stem cell population for a given period of time. For human stem cells, we obtain that mispaired bases still present after replication and cell division should be left untouched, to avoid potentially fixing a mutation in both DNA strands.

q-bio.TO↗

arXiv2004

Semiconservative replication in the quasispecies model II: Generalization to arbitrary lesion repair probabilities

This paper extends the semiconservative quasispecies equations to account for arbitrary post-replication lesion repair efficiency. Such an extension could be an important tool for understanding processes such as cancer development and stem cell growth. Starting from the quasispecies dynamics over the space of genomes, we derive an equivalent dynamics over the space of ordered sequence pairs. From this set of equations, we are able to derive the infinite sequence length form of the dynamics for a class of ``master-genome''-based fitness landscapes. We use these equations to solve for a ``generalized'' single-fitness-peak landscape, where the master genome can sustain a maximum number of lesions and remain viable. The central pattern that emerges from our studies is that imperfect lesion repair often leads to increased mutational robustness over semiconservative replication with completely efficient lesion repair. The reason for this is that imperfect lesion repair breaks some of the correlation between the parent and daughter strands, thereby preventing replication errors from destroying the information in the original genome. The result is a delayed error catastrophe over that expected from the original semiconservative quasispecies model. In particular, we show that when only of the strands is necessary for conferring viability, then, when lesion repair is turned off, a semiconservatively replicating system becomes an effectively conservatively replicating one.

q-bio.PE↗

arXiv2004

Imperfect DNA Repair and the Error Catastrophe

In this Letter, we extend the semiconservative quasispecies equations to incorporate imperfect DNA lesion repair. We study the equilibrium behavior of this model in the limit of infinite sequence length and population size, using a single-fitness-peak landscape for which the master genome can sustain a finite number of lesions and remain viable. We provide a full analytical treatment of the problem, providing a general mathematical framework as well as the full solution for a particular class of fitness landscapes. Stochastic simulations using finite sequence lengths and populations agree well with the analytical results. Applications to biological systems are briefly discussed.

q-bio.BM↗

arXiv2004

Solution of the Quasispecies Model for an Arbitrary Gene Network

In this paper, we study the equilibrium behavior of Eigen's quasispecies equations for an arbitrary gene network. We consider a genome consisting of $ N $ genes, so that each gene sequence $ σ$ may be written as $ σ= σ_1 σ_2 ... σ_N $. We assume a single fitness peak (SFP) model for each gene, so that gene $ i $ has some ``master'' sequence $ σ_{i, 0} $ for which it is functioning. The fitness landscape is then determined by which genes in the genome are functioning, and which are not. The equilibrium behavior of this model may be solved in the limit of infinite sequence length. The central result is that, instead of a single error catastrophe, the model exhibits a series of localization to delocalization transitions, which we term an ``error cascade.'' As the mutation rate is increased, the selective advantage for maintaining functional copies of certain genes in the network disappears, and the population distribution delocalizes over the corresponding sequence spaces. The network goes through a series of such transitions, as more and more genes become inactivated, until eventually delocalization occurs over the entire genome space, resulting in a final error catastrophe. This model provides a criterion for determining the conditions under which certain genes in a genome will lose functionality due to genetic drift. It also provides insight into the response of gene networks to mutagens. In particular, it suggests an approach for determining the relative importance of various genes to the fitness of an organism, in a more accurate manner than the standard ``deletion set'' method. The results in this paper also have implications for mutational robustness and what C.O. Wilke termed ``survival of the flattest.''

q-bio.GN↗

arXiv2003

Semiconservative Replication in the Quasispecies Model

This paper extends Eigen's quasispecies equations to account for the semiconservative nature of DNA replication. We solve the equations in the limit of infinite sequence length for the simplest case of a static, sharply peaked fitness landscape. We show that the error catastrophe occurs when $ μ$, the product of sequence length and per base pair mismatch probability, exceeds $ 2 \ln \frac{2}{1 + 1/k} $, where $ k > 1 $ is the first order growth rate constant of the viable ``master'' sequence (with all other sequences having a first-order growth rate constant of $ 1 $). This is in contrast to the result of $ \ln k $ for conservative replication. In particular, as $ k \to \infty $, the error catastrophe is never reached for conservative replication, while for semiconservative replication the critical $ μ$ approaches $ 2 \ln 2 $. Semiconservative replication is therefore considerably less robust than conservative replication to the effect of replication errors. We also show that the mean equilibrium fitness of a semiconservatively replicating system is given by $ k (2 e^{-μ/2} - 1) $ below the error catastrophe, in contrast to the standard result of $ k e^{-μ} $ for conservative replication (derived by Kimura and Maruyama in 1966).

cond-mat↗

arXiv2003

The Error and Repair Catastrophes: A Two-Dimensional Phase Diagram in the Quasispecies Model

This paper develops a two gene, single fitness peak model for determining the equilibrium distribution of genotypes in a unicellular population which is capable of genetic damage repair. The first gene, denoted by $ σ_{via} $, yields a viable organism with first order growth rate constant $ k > 1 $ if it is equal to some target ``master'' sequence $ σ_{via, 0} $. The second gene, denoted by $ σ_{rep} $, yields an organism capable of genetic repair if it is equal to some target ``master'' sequence $ σ_{rep, 0} $. This model is analytically solvable in the limit of infinite sequence length, and gives an equilibrium distribution which depends on $ μ\equiv L\eps $, the product of sequence length and per base pair replication error probability, and $ \eps_r $, the probability of repair failure per base pair. The equilibrium distribution is shown to exist in one of three possible ``phases.'' In the first phase, the population is localized about the viability and repairing master sequences. As $ \eps_r $ exceeds the fraction of deleterious mutations, the population undergoes a ``repair'' catastrophe, in which the equilibrium distribution is still localized about the viability master sequence, but is spread ergodically over the sequence subspace defined by the repair gene. Below the repair catastrophe, the distribution undergoes the error catastrophe when $ μ$ exceeds $ \ln k/\eps_r $, while above the repair catastrophe, the distribution undergoes the error catastrophe when $ μ$ exceeds $ \ln k/f_{del} $, where $ f_{del} $ denotes the fraction of deleterious mutations.

cond-mat.stat-mech↗

arXiv2003

Equilibrium Distribution of Mutators in the Single Fitness Peak Model

This paper develops an analytically tractable model for determining the equilibrium distribution of mismatch repair deficient strains in unicellular populations. The approach is based on the single fitness peak (SFP) model, which has been used in Eigen's quasispecies equations in order to understand various aspects of evolutionary dynamics. As with the quasispecies model, our model for mutator-nonmutator equilibrium undergoes a phase transition in the limit of infinite sequence length. This "repair catastrophe" occurs at a critical repair error probability of $ ε_r = L_{via}/L $, where $ L_{via} $ denotes the length of the genome controlling viability, while $ L $ denotes the overall length of the genome. The repair catastrophe therefore occurs when the repair error probability exceeds the fraction of deleterious mutations. Our model also gives a quantitative estimate for the equilibrium fraction of mutators in {\it Escherichia coli}.

cond-mat.stat-mech↗

arXiv2001

A PDE-Based Approach to Classical Phase-Space Deformations

This paper presents a PDE-based approach to finding an optimal canonical basis with which to represent a nearly integrable Hamiltonian. The idea behind the method is to continuously deform the initial canonical basis in such a way that the dependence of the Hamiltonian on the canonical position of the final basis is minimized. The final basis incorporates as much of the classical dynamics as possible into an integrable Hamiltonian, leaving a much smaller non-integrable component than in the initial representation. With this approach it is also possible to construct the semiclassical wavefunctions corresponding to the final canonical basis. This optimized basis is potentially useful in quantum calculations, both as a way to minimize the required size of basis sets, and as a way to provide physical insight by isolating those effects resulting from integrable dynamics.

nlin.CD↗