Emmanuel Tannenbaum

Signals and control aspects of optimal mass transport and the Boltzmann entropy

In this note we describe some properties of the Wasserstein-2 metric on the space of probability distributions. It turns out that the resulting geodesics lead to interesting connections with the Boltzmann entropy, the heat equations (both linear and nonlinear), and suggest possible Riemannian structures on density functions. In particular, we observe similarities and connections with other metrics originating in Information geometry and prediction theory.

RNA–Magnesium–Protein Interactions in Large Ribosomal Subunit

Some of the magnesium ions in the ribosome are coordinated by multiple rRNA phosphate groups. These magnesium ions link distal sequences of rRNA, primarily by incorporating phosphate groups into the first coordination shell. Less frequently, magnesium interacts with ribosomal proteins. Ribosomal protein L2 appears to be unique by forming specific magnesium-mediated interactions with rRNA. Using optimized models derived from X-ray structures, we subjected rRNA/magnesium/water/rProtein L2 assemblies to quantum mechanical analysis using the density functional theory and natural energy decomposition analysis. The combined results provide estimates of energies of formation of these assemblies, and allow us to decompose the energies of interaction. The results indicated that RNA immobilizes magnesium by multidentate chelation with phosphate, and that the magnesium ions in turn localize and polarize water molecules, increasing energies and specificities of interaction of these water molecules with L2 protein. Thus, magnesium plays subtle, yet important, roles in ribosomal assembly beyond neutralization of electrostatic repulsion and direct coordination of RNA functional groups.

The Influence of Horizontal Gene Transfer on the Mean Fitness of Unicellular Populations in Static Environments

Horizontal gene transfer (HGT) is believed to be a major source of genetic variation, particularly for prokaryotes. It is believed that horizontal gene transfer plays a major role in shaping bacterial genomes and is also believed to be responsible for the relatively rapid dissemination and acquisition of new, adaptive traits across bacterial strains. Despite the importance of horizontal gene transfer as a major source of genetic variation, the bulk of research on theoretical evolutionary dynamics and population genetics has focused on point mutations (sometimes coupled with gene duplication events) as the main engine of genomic change. Here, we seek to specifically model HGT processes in bacterial cells, by developing a mathematical model describing the influence that conjugation-mediated 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 to survive. We find that HGT has a nontrivial effect on the mean fitness of the population. However, one of the central results that emerge from our analysis is that, at mutation–selection balance, conjugation-mediated HGT has a slightly deleterious effect on the mean fitness of a population. Therefore, we conclude that HGT does not confer a selection advantage in static environments. Rather, its advantage must lie in its ability to promote faster adaptation in dynamic environments, an interpretation that is consistent with the observation that HGT can be promoted by environmental stresses on a population.

Effect of chromosomal instability on the mutation-selection balance in unicellular populations.

This paper develops a mathematical model describing the evolutionary dynamics of a unicellular, asexually replicating population exhibiting chromosomal instability. Chromosomal instability is a form of genetic instability characterized by the gain or loss of entire chromosomes during cell division. We assume that the cellular genome is divided into several homologous groups of chromosomes, and that a single functional chromosome per homologous group is required for the cell to have the wild-type fitness. If the fitness is unaffected by the total number of chromosomes in the cell, our model is analytically solvable, and yields a mean fitness at mutation-selection balance that is identical to the mean fitness when there is no chromosomal instability. If this assumption is relaxed and the total number of chromosomes in the cell is not allowed to increase without bound, then chromosomal instability leads to a reduction in mean fitness. The results of this paper provide a useful baseline that can inform both future theoretial and experimental studies of chromosomal instability.

A quasispecies approach to the evolution of sexual replication in unicellular organisms

This study develops a simplified model describing the evolutionary dynamics of a population composed of obligate sexually and asexually reproducing, unicellular organisms. The model assumes that the organisms have diploid genomes consisting of two chromosomes, and that the sexual organisms replicate by first dividing into haploid intermediates, which then combine with other haploids, followed by the normal mitotic division of the resulting diploid into two new daughter cells. We assume that the fitness landscape of the diploids is analogous to the single-fitness-peak approach often used in single-chromosome studies. That is, we assume a master chromosome that becomes defective with just one point mutation. The diploid fitness then depends on whether the genome has zero, one, or two copies of the master chromosome. We also assume that only pairs of haploids with a master chromosome are capable of combining so as to produce sexual diploid cells, and that this process is described by second-order kinetics. We find that, in a range of intermediate values of the replication fidelity, sexually reproducing cells can outcompete asexual ones, provided the initial abundance of sexual cells is above some threshold value. The range of values where sexual reproduction outcompetes asexual reproduction increases with decreasing replication rate and increasing population density. We critically evaluate a common approach, based on a group selection perspective, used to study the competition between populations and show its flaws in addressing the evolution of sex problem.

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 Saccharomyces cerevisiae, or Baker’s yeast. The simplified models are based on the single-fitness-peak approximation in quasispecies theory. 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. For the sake of generality, our model allows for mitotic recombination and asymmetric chromosome segregation. 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. In the sexual pathway, we consider two mating strategies: (1) a selective strategy, where only haploids with functional chromosomes can fuse with one another; (2) a random strategy, where haploids randomly fuse with one another. 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. When the cost for sex is low, sexual replication with random mating also has a higher mean fitness than asexual replication without mitotic recombination or asymmetric chromosome segregation. We also show that, at low replication fidelities, sexual replication with random mating has a higher mean fitness than asexual replication, as long as the cost for sex is low. If the fitness penalty for having a defective chromosome is sufficiently high and the cost for sex sufficiently low, then at low replication fidelities the random mating strategy has a mean fitness that is a factor of

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

\sqrt{2}

Effect of mutators on adaptability in time-varying fitness landscapes

larger than the asexual mean fitness. We argue that for yeast, the selective mating strategy is the one that is closer to reality, which if true suggests that sex may provide a selective advantage under considerably more relaxed conditions than previous research has indicated. The results of this paper also suggest that 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. That being said, our model does not contradict theories for the evolution of sex that argue that sex evolved because it allows a population to more easily adapt to changing conditions.