Search PubMed⌕ Search

Biomedical subjects

David A Kessler

Publications and source records attributed to David A Kessler.

At least 19 recordsLinked to original sources
PubMed2006

Fluctuation-induced instabilities in front propagation up a comoving reaction gradient in two dimensions.

We study two-dimensional (2D) fronts propagating up a comoving reaction rate gradient in finite number reaction-diffusion systems. We show that in a 2D rectangular channel, planar solutions to the deterministic mean-field equation are stable with respect to deviations from planarity. We argue that planar fronts in the corresponding stochastic system, on the other hand, are unstable if the channel width exceeds a critical value. Furthermore, the velocity of the stochastic fronts is shown to depend on the channel width in a simple and interesting way, in contrast to fronts in the deterministic mean-field equation. Thus fluctuations alter the behavior of these fronts in an essential way. These effects are shown to be partially captured by introducing a density cutoff in the reaction rate. Moreover, some of the predictions of the cutoff mean-field approach are shown to be in quantitative accord with the stochastic results.

Journal Article↗
PubMed2006

Directional sensing in eukaryotic chemotaxis: a balanced inactivation model.

Many eukaryotic cells, including Dictyostelium discoideum amoebae, fibroblasts, and neutrophils, are able to respond to chemoattractant gradients with high sensitivity. Recent studies have demonstrated that, after the introduction of a chemoattractant gradient, several chemotaxis pathway components exhibit a subcellular reorganization that cannot be described as a simple amplification of the external gradient. Instead, this reorganization has the characteristics of a switch, leading to a well defined front and back. Here, we propose a directional sensing mechanism in which two second messengers are produced at equal rates. The diffusion of one of them, coupled with an inactivation scheme, ensures a switch-like response to external gradients for a large range of gradient steepness and average concentration. Furthermore, our model is able to reverse the subcellular organization rapidly, and its response to multiple simultaneous chemoattractant sources is in good agreement with recent experimental results. Finally, we propose that the dynamics of a heterotrimeric G protein might allow for a specific biochemical realization of our model.

Animals↗
PubMed2006

Equation-free dynamic renormalization of a Kardar-Parisi-Zhang-type equation.

In the context of equation-free computation, we devise and implement a procedure for using short-time direct simulations of a Kardar-Parisi-Zhang-(KPZ-) type equation to calculate the self-similar solution for its ensemble averaged correlation function. The method involves "lifting" from candidate pair-correlation functions to consistent realization ensembles, short bursts of KPZ-type evolution, and appropriate rescaling of the resulting averaged pair correlation functions. Both the self-similar shapes and their similarity exponents are obtained at a computational cost significantly reduced to that required to reach saturation in such systems.

Journal Article↗
PubMed2006

Analytic approach to the evolutionary effects of genetic exchange.

We present an approximate analytic study of our previously introduced model of evolution including the effects of genetic exchange. This model is motivated by the process of bacterial transformation. We solve for the velocity, the rate of increase of fitness, as a function of the fixed population size, N. We find the velocity increases with ln N, eventually saturating at an N which depends on the strength of the recombination process. The analytical treatment is seen to agree well with direct numerical simulations of our model equations.

Journal Article↗
PubMed2005

Front propagation up a reaction rate gradient.

We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of motion of the front. We study the system via reaction-diffusion equations, using the expedient of a cutoff in the reaction rate below some critical density to capture the essential role of fluctuations in the system. For large density, the velocity is large, which allows for an approximate analytic treatment. We derive an analytic approximation for the dependence of the front velocity on bulk particle density, showing that the velocity indeed diverges in the infinite density limit. The form in which diffusion is implemented, namely nearest-neighbor hopping on a lattice, is seen to have an essential impact on the nature of the divergence.

Journal Article↗
PubMed2005

Equilibrium state of molecular breeding.

We investigate the equilibrium state of the model of Peng, et al. for molecular breeding. In the model, a population of DNA sequences is successively culled by removing the sequences with the lowest binding affinity to a particular target sequence. The remaining sequences are then amplified to restore the original population size, undergoing some degree of point-substitution of nucleotides in the process. Working in the infinite population size limit, we derive an equation for the equilibrium distribution of binding affinity, here modeled by the number of matches to the target sequence. The equation is then solved approximately in the limit of large sequence length, in the three regimes of strong, intermediate and weak selection. The approximate solutions are verified via comparison to exact numerical results.

Base Pair Mismatch↗
PubMed2005

Fluctuation-regularized front propagation dynamics in reaction-diffusion systems.

We introduce and study a new class of fronts in finite particle-number reaction-diffusion systems, corresponding to propagating up a reaction-rate gradient. We show that these systems have no traditional mean-field limit, as the nature of the long-time front solution in the stochastic process differs essentially from that obtained by solving the mean-field deterministic reaction-diffusion equations. Instead, one can incorporate some aspects of the fluctuations via introducing a density cutoff. Using this method, we derive analytic expressions for the front velocity dependence on bulk particle density and show self-consistently why this cutoff approach can get the correct leading-order physics.

Biological Evolution↗
PubMed2005

Recombination dramatically speeds up evolution of finite populations.

We study the role of recombination, in the form of bacterial transformation, in speeding up Darwinian evolution. This is done by adding a new process to a previously studied Markov model of evolution on a smooth fitness landscape; this new process allows alleles to be exchanged with those in the surrounding medium. Our results, both numerical and analytic, indicate that, for a wide range of intermediate population sizes, recombination dramatically speeds up the rate of evolutionary advance.

Bacteria↗
PubMed2004

Distribution functions for filaments under tension.

We develop a biased Monte Carlo simulation technique to measure the distribution functions of the extension and the end-to-end distance of fluctuating filaments stretched by external force. The method is applicable for arbitrary ratio of the persistence length to the contour length and for arbitrary forces, and also for the case of steric constraints, such as an external wall. The fundamental idea underlying the algorithm is to account explicitly for the length-scale dependence of the effective elastic moduli. We find that orientational fluctuations and wall effects produce non-Gaussian distributions for nearly rigid filaments in the small to intermediate force regime. The simulation results are tested against analytic expressions for the force-extension curves, both in the semiflexible and nearly stiff limits.

Journal Article↗
PubMed2004

Analytical study of the effect of recombination on evolution via DNA shuffling.

DNA shuffling is an evolutionary protocol wherein cycles of selection, recombination, mutation, and amplification are employed to evolve proteins and DNA sequences. Experiments have shown its superiority to traditional protocols which do not employ recombination. Motivated by DNA shuffling, we investigate a multilocus evolutionary model that incorporates selection, recombination, and point mutations. Due to simplicity of the model, for the case of an infinite population we can obtain a full analytical treatment of both its dynamical and equilibrium properties, and study the benefit of recombination explicitly and quantitatively. We also briefly discuss finite-population size corrections.

Animals↗
PubMed2003

Does the continuum theory of dynamic fracture work?

We investigate the validity of the linear elastic fracture mechanics approach to dynamic fracture. We first test the predictions in a lattice simulation, using a formula of Eshelby for the time-dependent stress intensity factor. Excellent agreement with the theory is found. We then use the same method to analyze the experiment of Sharon and Fineberg. The data here are not consistent with the theoretical expectation.

Journal Article↗
PubMed2003

Stretching instability of helical springs.

We show that when a gradually increasing tensile force is applied to the ends of a helical spring with sufficiently large ratios of radius to pitch and twist to bending rigidity, the end-to-end distance undergoes a sequence of discontinuous stretching transitions. Subsequent decrease of the force leads to steplike contraction, and hysteresis is observed. For finite helices, the number of these transitions increases with the number of helical turns but only one stretching and one contraction instability survive in the limit of an infinite helix. We calculate the critical line that separates the region of parameters in which the deformation is continuous from that in which stretching instabilities occur.

Cholesterol↗
PubMed2003

Lissajous singularities.

Coherent optical Lissajous states are easily created by nonlinear processes such as second-harmonic generation (SHG). Singular properties of such states are discussed and illustrated theoretically with non-phase-matched SHG of an ellipse field containing a C point.

Journal Article↗
PubMed2002

Mode-I fracture in a nonlinear lattice with viscoelastic forces.

We study mode-I fracture in a viscoelastic lattice model with a nonlinear force law, with a focus on the velocity and linear stability of the steady-state propagating solution. This study is a continuation both of the study of the piecewise-linear model in mode I, and the study of more general nonlinear force laws in mode-III fracture. At small driving, there is a strong dependency of the velocity curve on the dissipation and a strong sensitivity to the smoothness of the force law at large dissipation. At large driving we calculate, via a linear stability analysis, the critical velocity for the onset of instability as a function of the smoothness, the dissipation and the ratio of lattice spacing to critical extension. This critical velocity is seen to be very sensitive to these parameters. We confirm our calculations via direct numerical simulations of the initial value problem.

Journal Article↗