Kick-starting the ratchet: the fate of mutators in an asexual population

Muller's ratchet operates in asexual populations without intergenomic recombination. In this case, deleterious mutations will accumulate and population fitness will decline over time, possibly endangering the survival of the species. Mutator mutations, i.e., mutations that lead to an increased mutation rate, will play a special role for the behavior of the ratchet. First, they are part of the ratchet and can come to dominance through accumulation in the ratchet. Second, the fitness-loss rate of the ratchet is very sensitive to changes in the mutation rate and even a modest increase can easily set the ratchet in motion. In this article we simulate the interplay between fitness loss from Muller's ratchet and the evolution of the mutation rate from the fixation of mutator mutations. As long as the mutation rate is increased in sufficiently small steps, an accelerating ratchet and eventual extinction are inevitable. If this can be countered by antimutators, i.e., mutations that reduce the mutation rate, an equilibrium can be established for the mutation rate at some level that may allow survival. However, the presence of the ratchet amplifies fluctuations in the mutation rate and, even at equilibrium, these fluctuations can lead to dangerous bursts in the ratchet. We investigate the timescales of these processes and discuss the results with reference to the genome degradation of the aphid endosymbiont Buchnera aphidicola.     

Measurement of superhelix densities in buoyant dye/CsCl. The use of a standard other than native SV40 DNA.

The dye-induced separation between closed and open duplex DNAs in buoyant CsCl is determined primarily by the superhelix density of the closed DNA, provided that all other experimental variables (such as the solution density and dye concentration) are held constant. The extent of the buoyant separation may be used to estimate the superhelix density of an uncharacterized closed DNA, by comparison with the corresponding separation with native SV40 DNAs under identical conditions. We present here an extension of these quantitative relationships to permit the use of an arbitrarily selected closed duplex DNA of known superhelix density, with the accompanying open form, as a reference. The general result is that the ratio of buoyant separations for any two closed/open DNA pairs remains a linear function of the difference in superhelix densities between the closed DNAs. The value of the proportionality constant depends, however, upon the magnitude of the superhelix density of the closed DNA selected as reference.     

SMC complexes: Lifting the lid on loop extrusion

Loop extrusion has emerged as a prominent hypothesis for how SMC complexes shape chromosomes – single molecule in vitro observations have yielded fascinating images of this process. When not extruding loops, SMC complexes are known to topologically entrap one or more DNAs. Here, we review how structural insight into the SMC complex cohesin has led to a molecular framework for both activities: a Brownian ratchet motion, associated with topological DNA entry, might repeat itself to elicit loop extrusion. After contrasting alternative loop extrusion models, we explore whether topological loading or loop extrusion is more adept at explaining in vivo SMC complex function. SMC variants that experimentally separate topological loading from loop extrusion will in the future probe their respective contributions to chromosome biology.     

The Mtr4 ratchet helix and arch domain both function to promote RNA unwinding

Mtr4 is a conserved Ski2-like RNA helicase and a subunit of the TRAMP complex that activates exosome-mediated 3′-5′ turnover in nuclear RNA surveillance and processing pathways. Prominent features of the Mtr4 structure include a four-domain ring-like helicase core and a large arch domain that spans the core. The ‘ratchet helix’ is positioned to interact with RNA substrates as they move through the helicase. However, the contribution of the ratchet helix in Mtr4 activity is poorly understood. Here we show that strict conservation along the ratchet helix is particularly extensive for Ski2-like RNA helicases compared to related helicases. Mutation of residues along the ratchet helix alters in vitro activity in Mtr4 and TRAMP and causes slow growth phenotypes in vivo. We also identify a residue on the ratchet helix that influences Mtr4 affinity for polyadenylated substrates. Previous work indicated that deletion of the arch domain has minimal effect on Mtr4 unwinding activity. We now show that combining the arch deletion with ratchet helix mutations abolishes helicase activity and produces a lethal in vivo phenotype. These studies demonstrate that the ratchet helix modulates helicase activity and suggest that the arch domain plays a previously unrecognized role in unwinding substrates.     

Controlling the ratchet effect through the symmetries of the systems: application to molecular motors

We discuss a novel generic mechanism for controlling the ratchet effect through the breaking of relevant symmetries. We review previous works on ratchets where directed transport is induced by the breaking of standard temporal symmetries f(t)=-f(t+T/2) and f(t)=f(-t) (or f(t)=-f(-t)). We find that in seemingly unrelated systems the average velocity (or the current) of particles (or solitons) exhibits common features. We show that, as a consequence of Curie's symmetry principle, the average velocity (or the current) is related to the breaking of the symmetries of the system. This relationship allows us to control the transport in a systematic way. The qualitative agreement between the present analytical predictions and previous experimental, numerical, and theoretical results leads us to suggest that for the given breaking of the temporal symmetries there is an optimal wave form for a given time-periodic force. Also, we comment on how this mechanism can be applied to the case where a ratchet effect is induced by breaking of spatial symmetries. Finally, we conjecture that the ratchet potential underlying biological motor proteins might be optimized according to the breaking of the relevant symmetries.     

Cells as Active Particles in Asymmetric Potentials: Motility under External Gradients

Cell migration is a crucial event during development and in disease. Mechanical constraints and chemical gradients can contribute to the establishment of cell direction, but their respective roles remain poorly understood. Using a microfabricated topographical ratchet, we show that the nucleus dictates the direction of cell movement through mechanical guidance by its environment. We demonstrate that this direction can be tuned by combining the topographical ratchet with a biochemical gradient of fibronectin adhesion. We report competition and cooperation between the two external cues. We also quantitatively compare the measurements associated with the trajectory of a model that treats cells as fluctuating particles trapped in a periodic asymmetric potential. We show that the cell nucleus contributes to the strength of the trap, whereas cell protrusions guided by the adhesive gradients add a constant tunable bias to the direction of cell motion.     

Cells as Active Particles in Asymmetric Potentials: Motility under External Gradients

Cell migration is a crucial event during development and in disease. Mechanical constraints and chemical gradients can contribute to the establishment of cell direction, but their respective roles remain poorly understood. Using a microfabricated topographical ratchet, we show that the nucleus dictates the direction of cell movement through mechanical guidance by its environment. We demonstrate that this direction can be tuned by combining the topographical ratchet with a biochemical gradient of fibronectin adhesion. We report competition and cooperation between the two external cues. We also quantitatively compare the measurements associated with the trajectory of a model that treats cells as fluctuating particles trapped in a periodic asymmetric potential. We show that the cell nucleus contributes to the strength of the trap, whereas cell protrusions guided by the adhesive gradients add a constant tunable bias to the direction of cell motion.     

Temporal variation in selection accelerates mutational decay by Muller's ratchet

Asexual species accumulate deleterious mutations through an irreversible process known as Muller's ratchet. Attempts to quantify the rate of the ratchet have ignored the role of temporal environmental heterogeneity even though it is common in nature and has the potential to affect overall ratchet rate. Here we examine Muller's ratchet in the context of conditional neutrality (i.e., mutations that are deleterious in some environmental conditions but neutral in others) as well as more subtle changes in the strength (but not sign) of selection. We find that temporal variation increases the rate of the ratchet (mutation accumulation) and the rate of fitness decline over that of populations experiencing constant selection of equivalent average strength. Temporal autocorrelation magnifies the effects of temporal heterogeneity and can allow the ratchet to operate at large population sizes in which it would be halted under constant selection. Classic studies of Muller's ratchet show that the rate of fitness decline is maximized when selection is of a low but intermediate strength. This relationship changes quantitatively with all forms of temporal heterogeneity studied and changes qualitatively when there is temporal autocorrelation in selection. In particular, the rate of fitness decline can increase indefinitely with the strength of selection with some forms of temporal heterogeneity. Our finding that temporal autocorrelation in selection dramatically increases ratchet rate and rate of fitness decline may help to explain the paucity of asexual taxa.     

Seasonal Invasion Dynamics in a Spatially Heterogeneous River with Fluctuating Flows

A key problem in environmental flow assessment is the explicit linking of the flow regime with ecological dynamics. We present a hybrid modeling approach to couple hydrodynamic and biological processes, focusing on the combined impact of spatial heterogeneity and temporal variability on population dynamics. Studying periodically alternating pool-riffle rivers that are subjected to seasonally varying flows, we obtain an invasion ratchet mechanism. We analyze the ratchet process for a caricature model and a hybrid physical–biological model. The water depth and current are derived from a hydrodynamic equation for variable stream bed water flows and these quantities feed into a reaction-diffusion-advection model that governs population dynamics of a river species. We establish the existence of spreading speeds and the invasion ratchet phenomenon, using a mixture of mathematical approximations and numerical computations. Finally, we illustrate the invasion ratchet phenomenon in a spatially two-dimensional hydraulic simulation model of a meandering river structure. Our hybrid modeling approach strengthens the ecological component of stream hydraulics and allows us to gain a mechanistic understanding as to how flow patterns affect population survival.     

Residence time distribution in the chromatographic column: Applications in the separation engineering of DNA

Experimental and theoretical works were performed for the separation of large polyelectrolyte, such as DNA, in a column packed with gel particles under the influence of an electric field. Since DNA quickly orient in the field direction through the pores, this paper presents how intraparticle convection affects the residence time distribution of DNAs in the column. The concept is further illustrated with examples from solid-liquid systems, for example, from chromatography showing how the column efficiency is improved by the use of an electric field. Dimensionless transient mass balance equations were derived, taking into consideration both diffusion and electrophoretic convection. The separation criteria are theoretically studied using two different Peclet numbers in the fluid and solid phases. These criteria were experimentally verified using two different DNAs via electrophoretic mobility measurements, which showed how the separation position of the DNAs varies in the column in relation to the Peg/Pef values of an individual DNA. The residence time distribution was solved by an operator theory and the characteristic method to yield the column response.     

Ethidium DNA agarose gel electrophoresis: how it started

We started ethidium DNA agarose gel electrophoresis when our ultracentrifuge broke down and we needed an alternative method to check the quality of our mitochondrial DNA preparations. Agarose proved convenient for sizing DNA; ethidium in gel and buffer allowed visualization of DNA bands immediately after the run and improved the separation of the closed and open duplex forms of mitochondrial DNA circles. At smaller gel pore size mitochondrial DNA circles were excluded from the gel, whereas long linear DNAs were not. We concluded that the linear DNAs 'crawl like snakes head on through the gel'. This paper reviews some of the early experiments preceding the introduction of ethidium agarose gel electrophoresis.     

MULLER'S RATCHET AND THE ADVANTAGE OF SEX IN THE RNA VIRUS ϟ6

Population genetic models have shown that if genetic drift is strong and the rate of deleterious mutations is high, Muller's ratchet provides an advantage to sex. A previous study tested for the possibility that Muller's ratchet could work in RNA viruses, which are known to have very high mutation rates. Muller's ratchet was found to operate when lineages of the RNA bacteriophage φ6 were subjected to intensified genetic drift. The study did not determine, however, whether sex is advantageous to these viruses. We have examined whether sex can reverse the effects of Muller's ratchet by crossing nine φ6 lineages that were subjected to the ratchet in Chao's study. To determine whether there was a net advantage to sex, we analyzed the effect of crossing three lineages to all other lineages. Crossing increased significantly the fitness of two lineages, but it did not significantly affect the fitness of the third lineage. We argue that the minimal advantage of sex to these nine lineages is small, but positive. These results provide a possible scenario for the evolution of sex in an RNA phage like φ6.     

Force generation by actin polymerization II: the elastic ratchet and tethered filaments

The motion of many intracellular pathogens is driven by the polymerization of actin filaments. The propulsive force developed by the polymerization process is thought to arise from the thermal motions of the polymerizing filament tips. Recent experiments suggest that the nucleation of actin filaments involves a phase when the filaments are attached to the pathogen surface by a protein complex. Here we extend the "elastic ratchet model" of Mogilner and Oster to incorporate these new findings. We apply this "tethered ratchet" model to derive the force-velocity relation for Listeria and discuss relations of our theoretical predictions to experimental measurements. We also discuss "symmetry breaking" dynamics observed in ActA-coated bead experiments, and the implications of the model for lamellipodial protrusion in migrating cells.     

Loss of least-loaded class in asexual populations due to drift and epistasis

We consider the dynamics of a nonrecombining haploid population of finite size that accumulates deleterious mutations irreversibly. This ratchet-like process occurs at a finite speed in the absence of epistasis, but it has been suggested that synergistic epistasis can halt the ratchet. Using a diffusion theory, we find explicit analytical expressions for the typical time between successive clicks of the ratchet for both nonepistatic and epistatic fitness functions. Our calculations show that the interclick time is of a scaling form that in the absence of epistasis gives a speed that is determined by size of the least-loaded class and the selection coefficient. With synergistic interactions, the ratchet speed is found to approach zero rapidly for arbitrary epistasis. Our analytical results are in good agreement with the numerical simulations.     

Fluctuations of Fitness Distributions and the Rate of Muller's Ratchet

The accumulation of deleterious mutations is driven by rare fluctuations that lead to the loss of all mutation free individuals, a process known as Muller's ratchet. Even though Muller's ratchet is a paradigmatic process in population genetics, a quantitative understanding of its rate is still lacking. The difficulty lies in the nontrivial nature of fluctuations in the fitness distribution, which control the rate of extinction of the fittest genotype. We address this problem using the simple but classic model of mutation selection balance with deleterious mutations all having the same effect on fitness. We show analytically how fluctuations among the fittest individuals propagate to individuals of lower fitness and have dramatically amplified effects on the bulk of the population at a later time. If a reduction in the size of the fittest class reduces the mean fitness only after a delay, selection opposing this reduction is also delayed. This delayed restoring force speeds up Muller's ratchet. We show how the delayed response can be accounted for using a path-integral formulation of the stochastic dynamics and provide an expression for the rate of the ratchet that is accurate across a broad range of parameters.     

Fractionation of high molecular-weight duplex DNA molecules on dilute agarose gels

Fractionation of high molecular weight duplex DNAs was studied by electrophoresis on 0.05 to 1% agarose gels. Only the most diluted gels allowed the separation of T4 and T7 phages DNAs. The method makes use of progressive melting of the gel columns and may be applied to composite acrylamide agarose gels.     

Electrophoresis of long DNA molecules in linear polyacrylamide solutions

Electrophoresis of long DNA (T4 DNA; 166 kb, S. pombe chromosomal DNA; 3-6 Mb) in linear polyacrylamide solutions was investigated by fluorescence microscopy and capillary electrophoresis. In the past studies on electrophoresis of long DNA in a polymer solution, it was reported that DNA migrates in 'U-shape conformation'. We found that at higher polymer concentrations, the shape of the migrating DNA changes from U shape to linear shape ('I-shape conformation'). In the migration mode with the I-shape conformation, the DNA moves with almost constant velocity and constant shape. However, the migration velocity does depend on the DNA size, and it is possible to separate DNAs under this I-shape motion. Actually, Mb-sized DNAs are well separated within 5 min in the region for the I-shape motion by means of capillary electrophoresis with a DC field. Considering that it takes 20 h to separate Mb-sized DNAs by standard pulsed-field gel electrophoresis (PFGE), this results will be useful for the separation of giant DNAs.     

Small-world networks decrease the speed of Muller's ratchet

Muller's ratchet is an evolutionary process that has been implicated in the extinction of asexual species, the evolution of non-recombining genomes, such as the mitochondria, the degeneration of the Y chromosome, and the evolution of sex and recombination. Here we study the speed of Muller's ratchet in a spatially structured population which is subdivided into many small populations (demes) connected by migration, and distributed on a graph. We studied different types of networks: regular networks (similar to the stepping-stone model), small-world networks and completely random graphs. We show that at the onset of the small-world network - which is characterized by high local connectivity among the demes but low average path length - the speed of the ratchet starts to decrease dramatically. This result is independent of the number of demes considered, but is more pronounced the larger the network and the stronger the deleterious effect of mutations. Furthermore, although the ratchet slows down with increasing migration between demes, the observed decrease in speed is smaller in the stepping-stone model than in small-world networks. As migration rate increases, the structured populations approach, but never reach, the result in the corresponding panmictic population with the same number of individuals. Since small-world networks have been shown to describe well the real contact networks among people, we discuss our results in the light of the evolution of microbes and disease epidemics.