Biomedical subjects

Emmanuel Tannenbaum

Publications and source records attributed to Emmanuel Tannenbaum.

13 recordsLinked to original sources

PubMed2006

Extracting viability landscapes from mutagen-response experiments.

This paper outlines a novel approach for determining the importance of various genes to the viability of an organism. The basic idea is to treat a population of cells at various concentrations of mutagen, and determine which genes lose functionality due to genetic drift at the various mutagen concentrations. The more strongly a given collection of genes contributes to the fitness of an organism, the higher the mutation rate required to induce loss of functionality in those genes via genetic drift. We argue that mutagen-based methods, if reliably implementable, can elucidate correlations amongst genes, and determine which sets of genes correspond to redundant pathways in the cell. The data obtained from mutagen-based methods could also be used to organize the genes in a genome into hierarchies of increasing importance to the fitness of the cell. Thus, such methods could shed light on the evolutionary history of an organism.

Animals↗

PubMed2006

Selective advantage for sexual reproduction.

This paper develops a simplified model for sexual reproduction within the quasispecies formalism. The model assumes a diploid genome consisting of two chromosomes, where 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 reproduction, given by a characteristic time tau(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 tau(seek) = 0, it is possible to show that sexual reproduction will always out compete asexual reproduction. However, as tau(seek) increases, sexual reproduction only becomes advantageous at progressively higher mutation rates. Once the time cost for sex reaches a critical threshold, the selective advantage for sexual reproduction disappears entirely. The results of this paper suggest that sexual reproduction 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 reproduction is selected for in high populations because of the reduced time spent finding a reproductive partner.

Biological Evolution↗

PubMed2006

Semiconservative quasispecies equations for polysomic genomes: the haploid case.

This paper develops the semiconservative quasispecies equations for genomes consisting of an arbitrary number of chromosomes. We assume that the chromosomes are distinguishable, so that we are effectively considering haploid genomes. We derive the quasispecies equations under the assumption of arbitrary lesion repair efficiency, and consider the cases of both random and immortal strand chromosome segregation. We solve the model in the limit of infinite sequence length for the case of the static single fitness peak landscape, where the master genome has a first-order growth rate constant of k>1, and all other genomes have a first-order growth rate constant of 1. If we assume that each chromosome can tolerate an arbitrary number of lesions, so that only one master copy of the strands is necessary for a functional chromosome, then for random chromosome segregation we obtain an equilibrium mean fitness of [equation in text] below the error catastrophe, while for immortal strand co-segregation we obtain kappa (t=infinity)=k[e(-mu(1-lambda/2))+e(-mulambda/2)-1] (N denotes the number of chromosomes, lambda denotes the lesion repair efficiency, and mu is identical with epsilonL, where epsilon is the per base-pair mismatch probability, and L is the total genome length). It follows that immortal strand co-segregation leads to significantly better preservation of the master genome than random segregation when lesion repair is imperfect. Based on this result, we conjecture that certain classes of tumor cells exhibit immortal strand co-segregation.

Animals↗

PubMed2006

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. The single-cell survival strategy becomes disadvantageous at low concentrations of limiting resource because the energetic costs of maintaining reproductive and metabolic pathways approach, and may even exceed, the rate of energy production, leaving little excess energy for the purposes of replicating a new cell. However, if the rate of energy production exceeds the energetic costs of maintaining metabolic pathways, then the excess energy, if shared among several cells, can pay for the reproductive costs of a single cell, leaving energy to replicate a new cell. 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.

Animals↗

PubMed2006

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 theorems, 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.

Animals↗

PubMed2005

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 and (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 Nature (London) 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.

Adult↗

PubMed2004

Imperfect DNA lesion repair in the semiconservative quasispecies model: derivation of the Hamming class equations and solution of the single-fitness peak landscape.

This paper develops a Hamming class formalism for the semiconservative quasispecies equations with imperfect lesion repair, first presented and analytically solved in Y. Brumer and E.I. Shakhnovich (q-bio.GN/0403018, 2004). 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 fitness landscapes defined by a master genome. 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. We determine the mean equilibrium fitness and error threshold for this class of landscapes, and show that when lesion repair is imperfect, semiconservative replication displays characteristics from both conservative replication and semiconservative replication with perfect lesion repair. The work presented here provides a formulation of the model which greatly facilitates the analysis of a relatively broad class of fitness landscapes, and thus serves as a convenient springboard into biological applications of imperfect lesion repair.

Animals↗

PubMed2004

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 the full genome sequence sigma may be written as sigma= sigma1sigma2...sigmaN, where sigma(i) are sequences of individual genes. We assume a single fitness peak model for each gene, so that gene i has some "master" sequence sigma(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."

Animals↗

PubMed2004

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 micro, the product of sequence length and per base pair mismatch probability, exceeds 2 ln [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--> infinity, the error catastrophe is never reached for conservative replication, while for semiconservative replication the critical micro 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(-micro/2) -1 ) below the error catastrophe, in contrast to the standard result of k e(-micro) for conservative replication (derived by Kimura and Maruyama in 1966). From this result it is readily shown that semiconservative replication is necessary to account for the observation that, at sufficiently high mutagen concentrations, faster replicating cells will die more quickly than more slowly replicating cells. Thus, in contrast to Eigen's original model, the semiconservative quasispecies equations are able to provide a mathematical basis for explaining the efficacy of mutagens as chemotherapeutic agents.

Base Pair Mismatch↗

PubMed2004

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 sigma(via), yields a viable organism with first-order growth rate constant k>1 if it is equal to some target "master" sequence sigma(via,0). The second gene, denoted by sigma(rep), yields an organism capable of genetic repair if it is equal to some target "master" sequence sigma(rep,0). This model is analytically solvable in the limit of infinite sequence length, and gives an equilibrium distribution which depends on micro identical with Lepsilon, the product of sequence length and per base pair replication error probability, and epsilon(r), the probability of repair failure per base pair. The equilibrium distribution is shown to exist in one of the three possible "phases." In the first phase, the population is localized about the viability and repairing master sequences. As epsilon(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 micro exceeds ln k/epsilon(r), while above the repair catastrophe, the distribution undergoes the error catastrophe when micro exceeds ln k/f(del), where f(del) denotes the fraction of deleterious mutations.

Computer Simulation↗

PubMed2003

Automated identification of RNA conformational motifs: theory and application to the HM LSU 23S rRNA.

We develop novel methods for recognizing and cataloging conformational states of RNA, and for discovering statistical rules governing those states. We focus on the conformation of the large ribosomal subunit from Haloarcula marismortui. The two approaches described here involve torsion matching and binning. Torsion matching is a pattern-recognition code which finds structural repetitions. Binning is a classification technique based on distributional models of the data. In comparing the results of the two methods we have tested the hypothesis that the conformation of a very large complex RNA molecule can be described accurately by a limited number of discrete conformational states. We identify and eliminate extraneous and redundant information without losing accuracy. We conclude, as expected, that four of the torsion angles contain the overwhelming bulk of the structural information. That information is not significantly compromised by binning the continuous torsional information into a limited number of discrete values. The correspondence between torsion matching and binning is 99% (per residue). Binning, however, does have several advantages. In particular, we demonstrate that the conformation of a large complex RNA molecule can be represented by a small alphabet. In addition, the binning method lends itself to a natural graphical representation using trees.

Automation↗

PubMed2003

Equilibrium distribution of mutators in the single fitness peak model.

This Letter 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 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 catas-trophe" occurs at a critical repair error probability of epsilon(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 Escherichia coli.

Base Pair Mismatch↗

PubMed2002

Partial-differential-equation-based approach to classical phase-space deformations.

This paper presents a partial-differential-equation-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 nonintegrable component than in the initial representation. With this approach it is also possible to construct the semiclassical wave functions 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.

Journal Article↗