Biomedical subjects

Rhonald C Lua

Publications and source records attributed to Rhonald C Lua.

4 recordsLinked to original sources

PubMed2006

Statistics of knots, geometry of conformations, and evolution of proteins.

Like shoelaces, the backbones of proteins may get entangled and form knots. However, only a few knots in native proteins have been identified so far. To more quantitatively assess the rarity of knots in proteins, we make an explicit comparison between the knotting probabilities in native proteins and in random compact loops. We identify knots in proteins statistically, applying the mathematics of knot invariants to the loops obtained by complementing the protein backbone with an ensemble of random closures, and assigning a certain knot type to a given protein if and only if this knot dominates the closure statistics (which tells us that the knot is determined by the protein and not by a particular method of closure). We also examine the local fractal or geometrical properties of proteins via computational measurements of the end-to-end distance and the degree of interpenetration of its subchains. Although we did identify some rather complex knots, we show that native conformations of proteins have statistically fewer knots than random compact loops, and that the local geometrical properties, such as the crumpled character of the conformations at a certain range of scales, are consistent with the rarity of knots. From these, we may conclude that the known "protein universe" (set of native conformations) avoids knots. However, the precise reason for this is unknown--for instance, if knots were removed by evolution due to their unfavorable effect on protein folding or function or due to some other unidentified property of protein evolution.

Evolution, Molecular↗

PubMed2005

First passage times and asymmetry of DNA translocation.

Motivated by experiments in which single-stranded DNA with a short hairpin loop at one end undergoes unforced diffusion through a narrow pore, we study the first passage times for a particle, executing one-dimensional Brownian motion in an asymmetric sawtooth potential, to exit one of the boundaries. We consider the first passage times for the case of classical diffusion, characterized by a mean-square displacement of the form <(Delta(x))2> approximately t, and for the case of anomalous diffusion or subdiffusion, characterized by a mean-square displacement of the form <(Delta(x))2> approximately t(gamma) with 0<gamma<1. In the context of classical diffusion, we obtain an expression for the mean first passage time and show that this quantity changes when the direction of the sawtooth is reversed or, equivalently, when the reflecting and absorbing boundaries are exchanged. We discuss at which numbers of "teeth" N (or number of DNA nucleotides) and at which heights of the sawtooth potential this difference becomes significant. For large N, it is well known that the mean first passage time scales as N2. In the context of subdiffusion, the mean first passage time does not exist. Therefore, we obtain instead the distribution of first passage times in the limit of long times. We show that the prefactor in the power relation for this distribution is simply the expression for the mean first passage time in classical diffusion. We also describe a hypothetical experiment to calculate the average of the first passage times for a fraction of passage events that each end within some time t*. We show that this average first passage time scales as N2/gamma in subdiffusion.

Cell Membrane↗

PubMed2005

Practical applicability of the Jarzynski relation in statistical mechanics: a pedagogical example.

We suggest and discuss a simple model of an ideal gas under the piston to gain an insight into the workings of the Jarzynski identity connecting the average exponential of the work over the nonequilibrium trajectories with the equilibrium free energy. We show that the identity is valid for our system, due to the very rapid molecules belonging to the tail of the Maxwell distribution. For the most interesting extreme, when the system volume is large, while the piston is moving with great speed (compared to thermal velocity) for a very short time, the necessary number of independent experimental runs to obtain a reasonable approximation for the free energy from averaging the nonequilibrium work grows exponentially with the system size.

Journal Article↗

PubMed2004

Topologically driven swelling of a polymer loop.

Numerical studies of the average size of trivially knotted polymer loops with no excluded volume were undertaken. Topology was identified by Alexander and Vassiliev degree 2 invariants. Probability of a trivial knot, average gyration radius, and probability density distributions as functions of gyration radius were generated for loops of up to N = 3,000 segments. Gyration radii of trivially knotted loops were found to follow a power law similar to that of self-avoiding walks consistent with earlier theoretical predictions.

Journal Article↗