Diffusion on a hypercubic lattice with pinning potential: exact results for the error-catastrophe problem in biological evolution

In the theoretical biology framework one fundamental problem is the so-called error catastrophe in Darwinian evolution models. We reexamine Eigen's fundamental equations by mapping them into a polymer depinning transition problem in a ``genotype'' space represented by a unitary hypercubic lattice. The exact solution of the model shows that error catastrophe arises as a direct consequence of the equations involved and confirms some previous qualitative results. The physically relevant consequence is that such equations are not adequate to properly describe evolution of complex life on the Earth.Comment: 10 pages in LaTeX. Figures are available from the authors. [email protected] (e-mail address

Coupled dynamics of sequence selection and compactification in mean-field hetero-polymers

We study a simple solvable model describing the genesis of monomer sequences for hetero-polymers (such as proteins), as the result of the equilibration of a slow stochastic genetic selection process which is assumed to be driven by the competing demands of functionality and reproducibility of the polymer's folded structure. Since reproducibility is defined in terms of properties of the folding process, one is led to the analysis of the coupled dynamics of (fast) polymer folding and (slow) genetic sequence selection. For the present mean-field model this analysis can be carried out using the finite-dimensional replica method, leading to exact results for (first- and second-order) transitions and to rich phase diagrams.Comment: 21 pages, 7 figure

Selection for Replicases in Protocells

PMCID: PMC3649988This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Constrained Nonlinear Model Predictive Control of an MMA Polymerization Process via Evolutionary Optimization

In this work, a nonlinear model predictive controller is developed for a batch polymerization process. The physical model of the process is parameterized along a desired trajectory resulting in a trajectory linearized piecewise model (a multiple linear model bank) and the parameters are identified for an experimental polymerization reactor. Then, a multiple model adaptive predictive controller is designed for thermal trajectory tracking of the MMA polymerization. The input control signal to the process is constrained by the maximum thermal power provided by the heaters. The constrained optimization in the model predictive controller is solved via genetic algorithms to minimize a DMC cost function in each sampling interval.Comment: 12 pages, 9 figures, 28 reference

Sequence selection in an autocatalytic binary polymer model

An autocatalytic pattern matching polymer system is studied as an abstract model for chemical ecosystem evolution. Highly ordered populations with particular sequence patterns appear spontaneously out of a vast number of possible states. The interplay between the selected microscopic sequence patterns and the macroscopic cooperative structures is examined. Stability, fluctuations, and evolutionary selection mechanisms are investigated for the involved self-organizing processes

Preliminary steps toward artificial protocell computation

Protocells are hypothesised as a transitional phase in the origin of life, prior to the evolution of fully functional prokaryotic cells. The work reported here is being done in the context of the PACE project, which is investigating the fabrication of artificial protocells de novo. We consider here the important open question of whether or how articifial protocells (if or when they are successfully fabricated) might be applied as “computing” devices—what sort of computing might they be suitable for, and how might they be “programmed”? We also present some preliminary analysis of a crude model of such “evolutionary protocell computation”