Greg Lakatos

Clustered bottlenecks in mRNA translation and protein synthesis

Using a model based on the totally asymmetric exclusion process, we investigate the effects of slow codons along messenger RNA. Ribosome density profiles near neighboring clusters of slow codons interact, enhancing suppression of ribosome throughput when such bottlenecks are closely spaced. Increasing the slow codon cluster size beyond approximately 3-4 codons does not significantly reduce the ribosome current. Our results are verified by both extensive Monte Carlo simulations and numerical calculation, and provide a biologically motivated explanation for the experimentally observed clustering of low-usage codons.

Totally asymmetric exclusion processes with particles of arbitrary size

The steady-state currents and densities of a one-dimensional totally asymmetric exclusion process (TASEP) with particles that occlude an integer number (d) of lattice sites are computed using various mean-field approximations and Monte Carlo simulations. TASEPs featuring particles of arbitrary size are relevant for modelling systems such as mRNA translation, vesicle locomotion along microtubules and protein sliding along DNA. We conjecture that the nonequilibrium steady-state properties separate into low-density, high-density, and maximal current phases similar to those of the standard (d = 1) TASEP. A simple mean-field approximation for steady-state particle currents and densities is found to be inaccurate. However, we find local equilibrium particle distributions derived from a discrete Tonks gas partition function yield apparently exact currents within the maximal current phase. For the boundary-limited phases, the equilibrium Tonks gas distribution cannot be used to predict currents, phase boundaries, or the order of the phase transitions. However, we employ a refined mean-field approach to find apparently exact expressions for the steady-state currents, boundary densities, and phase diagrams of the d ≥ 1 TASEP. Extensive Monte Carlo simulations are performed to support our analytic, mean-field results.

First passage times of driven DNA hairpin unzipping

We model the dynamics of voltage-driven transport of DNA hairpins through transmembrane channels. A two-dimensional stochastic model of the DNA translocation process is fit to the measurements of Mathé, who pulled self-hybridized DNA hairpins through lipid-embedded alpha-hemolysin channels. As the channel was too narrow to accommodate hybridized DNA, dehybridization of the hairpin became the rate-limiting step of the transport process. We show that the mean first passage time versus voltage curve for the escape of the DNA from the transmembrane channel can be divided into two regions: (1) a low-voltage region where the DNA slides out of the pore in reverse and without undergoing significant dehybridization, and (2) a region where the DNA dehybridizes under the influence of the applied voltage and translocates across the membrane.

Hydrodynamic mean-field solutions of 1D exclusion processes with spatially varying hopping rates

We analyse the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean-field limit. The mean-field equations for particle densities are written in terms of Ricatti equations with the steady-state current J as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents J are found self-consistently. We find a number of cases where analytic solutions can be found exactly or approximated. Results for J from asymptotic analyses for slowly varying hopping rates agree extremely well with those from extensive Monte Carlo simulations, suggesting that mean-field currents asymptotically approach the exact currents in the hydrodynamic limit, as the hopping rates vary slowly over the lattice. If the forward hopping rate is greater than or less than the backward hopping rate throughout the entire chain, the three standard steady-state phases are preserved. Our analysis reveals the sensitivity of the current to the relative phase between the forward and backward hopping rate functions.

Structure and adsorption of water in nonuniform cylindrical nanopores.

Grand canonical Monte Carlo simulations are used to examine the adsorption and structure of water in the interior of cylindrical nanopores in which the axial symmetry is broken either by varying the radius as a function of position along the pore axis or by introducing regions where the characteristic strength of the water-nanopore interaction is reduced. Using the extended simple point charge (SPC∕E) model for water, nanopores with a uniform radius of 6.0 Å are found to fill with water at chemical potentials approximately 0.5 kJ∕mol higher than the chemical potential of the saturated vapor. The water in these filled pores exists in either a weakly structured fluidlike state or a highly structured uniformly polarized state composed of a series of stacked water clusters with pentagonal cross sections. This highly structured state can be disrupted by creating hydrophobic regions on the surface of the nanopore, and the degree of disruption can be systematically controlled by adjusting the size of the hydrophobic regions. In particular, hydrophobic banded regions with lengths larger than 9.2 Å result in a complete loss of structure and the formation of a liquid-vapor coexistence in the tube interior. Similarly, the introduction of spatial variation in the nanopore radius can produce two condensation transitions at distinct points along the filling isotherm.