Ard Louis

Abstract:

Genotype-phenotype (GP) maps specify how the random mutations that change genotypes generate variation by altering phenotypes, which, in turn, can trigger selection. Many GP maps share the following general properties: 1) The total number of genotypes N(G) is much larger than the number of selectable phenotypes; 2) Neutral exploration changes the variation that is accessible to the population; 3) The distribution of phenotype frequencies F(p)=N(p)/N(G), with N(p) the number of genotypes mapping onto phenotype p, is highly biased: the majority of genotypes map to only a small minority of the phenotypes. Here we explore how these properties affect the evolutionary dynamics of haploid Wright-Fisher models that are coupled to a random GP map or to a more complex RNA sequence to secondary structure map. For both maps the probability of a mutation leading to a phenotype p scales to first order as F(p), although for the RNA map there are further correlations as well. By using mean-field theory, supported by computer simulations, we show that the discovery time T(p) of a phenotype p similarly scales to first order as 1/F(p) for a wide range of population sizes and mutation rates in both the monomorphic and polymorphic regimes. These differences in the rate at which variation arises can vary over many orders of magnitude. Phenotypic variation with a larger F(p) is therefore be much more likely to arise than variation with a small F(p). We show, using the RNA model, that frequent phenotypes (with larger F(p)) can fix in a population even when alternative, but less frequent, phenotypes with much higher fitness are potentially accessible. In other words, if the fittest never 'arrive' on the timescales of evolutionary change, then they can't fix. We call this highly non-ergodic effect the 'arrival of the frequent'.

Abstract:

Dynamic DNA nanotechnology often uses toehold-mediated strand displacement for controlling reaction kinetics. Although the dependence of strand displacement kinetics on toehold length has been experimentally characterized and phenomenologically modeled, detailed biophysical understanding has remained elusive. Here, we study strand displacement at multiple levels of detail, using an intuitive model of a random walk on a 1D energy landscape, a secondary structure kinetics model with single base-pair steps and a coarse-grained molecular model that incorporates 3D geometric and steric effects. Further, we experimentally investigate the thermodynamics of three-way branch migration. Two factors explain the dependence of strand displacement kinetics on toehold length: (i) the physical process by which a single step of branch migration occurs is significantly slower than the fraying of a single base pair and (ii) initiating branch migration incurs a thermodynamic penalty, not captured by state-of-the-art nearest neighbor models of DNA, due to the additional overhang it engenders at the junction. Our findings are consistent with previously measured or inferred rates for hybridization, fraying and branch migration, and they provide a biophysical explanation of strand displacement kinetics. Our work paves the way for accurate modeling of strand displacement cascades, which would facilitate the simulation and construction of more complex molecular systems.

Abstract:

We experimentally study the viscous fingering instability in a fluid-fluid phase separated colloid-polymer mixture by means of laser scanning confocal microscopy and microfluidics. We focus on three aspects of the instability. (i) The interface between the two demixed phases has an ultralow surface tension, such that we can address the role of thermal interface fluctuations. (ii) We image the interface in three dimensions allowing us to study the interplay between interface curvature and flow. (iii) The displacing fluid wets all walls completely, in contrast to traditional viscous fingering experiments, in which the displaced fluid wets the walls. We also perform lattice Boltzmann simulations, which help to interpret the experimental observations. © 2013 The Royal Society of Chemistry.

Abstract:

Paramagnetic colloidal particles that are optically trapped in a linear array can form a zigzag pattern when an external magnetic field induces repulsive interparticle interactions. When the traps are abruptly turned off, the particles form a nonequilibrium expanding pattern with a zigzag symmetry, even when the strength of the magnetic interaction is weaker than that required to break the linear symmetry of the equilibrium state. We show that the transition to the equilibrium zigzag state is always potentially possible for purely harmonic traps. For anharmonic traps that have a finite height, the equilibrium zigzag state becomes unstable above a critical anharmonicity. A normal mode analysis of the equilibrium line configuration demonstrates that increasing the magnetic field leads to a hardening and softening of the spring constants in the longitudinal and transverse directions, respectively. The mode that first becomes unstable is the mode with the zigzag symmetry, which explains the symmetry of nonequilibrium patterns. Our analytically tractable models help to give further insight into the way that the interplay of such factors as the length of the chain, hydrodynamic interactions, thermal fluctuations affect the formation and evolution of the experimentally observed nonequilibrium patterns.