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 $\epsilon_r = L_{via}/L$, 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 {\it Escherichia coli}.Comment: 4 pages, 2 figures (included as separate PS files

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 $\tau$. 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.Comment: 4 pages, 3 figure

Host-Parasite Co-evolution and Optimal Mutation Rates for Semi-conservative Quasispecies

In this paper, we extend a model of host-parasite co-evolution to incorporate the semi-conservative nature of DNA replication for both the host and the parasite. We find that the optimal mutation rate for the semi-conservative and conservative hosts converge for realistic genome lengths, thus maintaining the admirable agreement between theory and experiment found previously for the conservative model and justifying the conservative approximation in some cases. We demonstrate that, while the optimal mutation rate for a conservative and semi-conservative parasite interacting with a given immune system is similar to that of a conservative parasite, the properties away from this optimum differ significantly. We suspect that this difference, coupled with the requirement that a parasite optimize survival in a range of viable hosts, may help explain why semi-conservative viruses are known to have significantly lower mutation rates than their conservative counterparts

A Selective Advantage for Conservative Viruses

In this letter we study the full semi-conservative treatment of a model for the co-evolution of a virus and an adaptive immune system. Regions of viability are calculated for both conservatively and semi-conservatively replicating viruses interacting with a realistic semi-conservatively replicating immune system. The conservative virus is found to have a selective advantage in the form of an ability to survive in regions with a wider range of mutation rates than its semi-conservative counterpart. This may help explain the existence of a rich range of viruses with conservatively replicating genomes, a trait which is found nowhere else in nature.Comment: 4 pages, 2 figure

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.Comment: 9 pages, 3 figure

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 $\sigma$ may be written as $\sigma = \sigma_1 \sigma_2 ... \sigma_N$. We assume a single fitness peak (SFP) 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.''Comment: 29 pages, 5 figures, to be submitted to Physical Review

Sustainable Photopolymers in 3D Printing:A Review on Biobased, Biodegradable, and Recyclable Alternatives

The global market for 3D printing materials has grown exponentially in the last decade. Today, photopolymers claim almost half of the material sales worldwide. The lack of sustainable resins, applicable in vat photopolymerization that can compete with commercial materials, however, limits the widespread adoption of this technology. The development of “green” alternatives is of great importance in order to reduce the environmental impact of additive manufacturing. This paper reviews the recent evolutions in the field of sustainable photopolymers for 3D printing. It highlights the synthesis and application of biobased resin components, such as photocurable monomers and oligomers, as well as reinforcing agents derived from natural resources. In addition, the design of biologically degradable and recyclable thermoset products in vat photopolymerization is discussed. Together, those strategies will promote the accurate and waste-free production of a new generation of 3D materials for a sustainable plastics economy in the near future

The mid-depth circulation of the Nordic Seas derived from profiling float observations

Article published in Tellus Series A-Dynamic meterology and oceanography, 62 (4): 516-529 AUG 2010The trajectories of 61 profiling Argo floats deployed at mid-depth in the Nordic Seas—the Greenland, Lofoten and Norwegian Basins and the Iceland Plateau—between 2001 and 2009 are analysed to determine the pattern, strength and variability of the regional circulation. The mid-depth circulation is strongly coupled with the structure of the bottom topography of the four major basins and of the Nordic Seas as a whole. It is cyclonic, both on the large-scale and on the basin scale, with weak flow (<1 cm s−1) in the interior of the basins and somewhat stronger flow (up to 5 cm s−1) at their rims. Only few floats moved from one basin to another, indicating that the internal recirculation within the basins is by far dominating the larger-scale exchanges. The seasonal variability of the mid-depth flow ranges from less than 1 cm s−1 over the Iceland Plateau to more than 4 cm s−1 in the Greenland Basin. These velocities translate into internal gyre transports of up to 15 ± 10 × 106 m3 s−1, several times the overall exchange between the Nordic Seas and the subpolar North Atlantic. The seasonal variability of the Greenland Basin and the Norwegian Basin can be adequately modelled using the barotropic vorticity equation, with the wind and bottom friction as the only forcing mechanisms. For the Lofoten Basin and the Iceland Plateau less than 50% of the variance can be explained by the wind

The Importance of DNA Repair in Tumor Suppression

The transition from a normal to cancerous cell requires a number of highly specific mutations that affect cell cycle regulation, apoptosis, differentiation, and many other cell functions. One hallmark of cancerous genomes is genomic instability, with mutation rates far greater than those of normal cells. In microsatellite instability (MIN tumors), these are often caused by damage to mismatch repair genes, allowing further mutation of the genome and tumor progression. These mutation rates may lie near the error catastrophe found in the quasispecies model of adaptive RNA genomes, suggesting that further increasing mutation rates will destroy cancerous genomes. However, recent results have demonstrated that DNA genomes exhibit an error threshold at mutation rates far lower than their conservative counterparts. Furthermore, while the maximum viable mutation rate in conservative systems increases indefinitely with increasing master sequence fitness, the semiconservative threshold plateaus at a relatively low value. This implies a paradox, wherein inaccessible mutation rates are found in viable tumor cells. In this paper, we address this paradox, demonstrating an isomorphism between the conservatively replicating (RNA) quasispecies model and the semiconservative (DNA) model with post-methylation DNA repair mechanisms impaired. Thus, as DNA repair becomes inactivated, the maximum viable mutation rate increases smoothly to that of a conservatively replicating system on a transformed landscape, with an upper bound that is dependent on replication rates. We postulate that inactivation of post-methylation repair mechanisms are fundamental to the progression of a tumor cell and hence these mechanisms act as a method for prevention and destruction of cancerous genomes.Comment: 7 pages, 5 figures; Approximation replaced with exact calculation; Minor error corrected; Minor changes to model syste

Irreversible thermodynamics of open chemical networks I: Emergent cycles and broken conservation laws

In this and a companion paper we outline a general framework for the thermodynamic description of open chemical reaction networks, with special regard to metabolic networks regulating cellular physiology and biochemical functions. We first introduce closed networks "in a box", whose thermodynamics is subjected to strict physical constraints: the mass-action law, elementarity of processes, and detailed balance. We further digress on the role of solvents and on the seemingly unacknowledged property of network independence of free energy landscapes. We then open the system by assuming that the concentrations of certain substrate species (the chemostats) are fixed, whether because promptly regulated by the environment via contact with reservoirs, or because nearly constant in a time window. As a result, the system is driven out of equilibrium. A rich algebraic and topological structure ensues in the network of internal species: Emergent irreversible cycles are associated to nonvanishing affinities, whose symmetries are dictated by the breakage of conservation laws. These central results are resumed in the relation $a + b = s^Y$ between the number of fundamental affinities $a$, that of broken conservation laws $b$ and the number of chemostats $s^Y$. We decompose the steady state entropy production rate in terms of fundamental fluxes and affinities in the spirit of Schnakenberg's theory of network thermodynamics, paving the way for the forthcoming treatment of the linear regime, of efficiency and tight coupling, of free energy transduction and of thermodynamic constraints for network reconstruction.Comment: 18 page