Effect of Interactions on Molecular Fluxes and Fluctuations in the Transport Across Membrane Channels

Transport of molecules across membrane channels is investigated theoretically using exactly solvable one-dimensional discrete-state stochastic models. An interaction between molecules and membrane pores is modeled via a set of binding sites with different energies. It is shown that the interaction potential strongly influences the particle currents as well as fluctuations in the number of translocated molecules. For small concentration gradients the attractive sites lead to largest currents and fluctuations, while the repulsive interactions yield the largest fluxes and dispersions for large concentration gradients. Interaction energies that lead to maximal currents and maximal fluctuations are the same only for locally symmetric potentials, while they differ for the locally asymmetric potentials. The conditions for the most optimal translocation transport with maximal current and minimal dispersion are discussed. It is argued that in this case the interaction strength is independent of local symmetry of the potential of mean forces. In addition, the effect of the global asymmetry of the interaction potential is investigated, and it is shown that it also strongly affects the particle translocation dynamics. These phenomena can be explained by analyzing the details of the particle entering and leaving the binding sites in the channel.Comment: submitted to J. Chem. Phy

Effect of Inhomogeneity in Translocation of Polymers through Nanopores

The motion of polymers with inhomogeneous structure through nanopores is discussed theoretically. Specifically, we consider the translocation dynamics of polymers consisting of double-stranded and single-stranded blocks. Since only the single-stranded chain can go through the nanopore the double-stranded segment has to unzip before the translocation. Utilizing a simple analytical model, translocation times are calculated explicitly for different polymer orientations, i.e., when the single-stranded block enters the pore first and when the double-stranded segment is a leading one. The dependence of the translocation dynamics on external fields, energy of interaction in the double-stranded segment, size of the polymer and the fraction of double-stranded monomers is analyzed. It is found that the order of entrance into the pore has a significant effect on the translocation dynamics. The theoretical results are discussed using free-energy landscape arguments.Comment: 12 pages, 5 figures, submitted to J. Chem. Phy

Recent advances in experimental techniques to probe fast excited-state dynamics in biological molecules in the gas phase : dynamics in nucleotides, amino acids and beyond

In many chemical reactions, an activation barrier must be overcome before a chemical transformation can occur. As such, understanding the behaviour of molecules in energetically excited states is critical to understanding the chemical changes that these molecules undergo. Among the most prominent reactions for mankind to understand are chemical changes that occur in our own biological molecules. A notable example is the focus towards understanding the interaction of DNA with ultraviolet radiation and the subsequent chemical changes. However, the interaction of radiation with large biological structures is highly complex, and thus the photochemistry of these systems as a whole is poorly understood. Studying the gas-phase spectroscopy and ultrafast dynamics of the building blocks of these more complex biomolecules offers the tantalizing prospect of providing a scientifically intuitive bottom-up approach, beginning with the study of the subunits of large polymeric biomolecules and monitoring the evolution in photochemistry as the complexity of the molecules is increased. While highly attractive, one of the main challenges of this approach is in transferring large, and in many cases, thermally labile molecules into vacuum. This review discusses the recent advances in cutting-edge experimental methodologies, emerging as excellent candidates for progressing this bottom-up approach

Numerical simulation of conformational variability in biopolymer translocation through wide nanopores

Numerical results on the translocation of long biopolymers through mid-sized and wide pores are presented. The simulations are based on a novel methodology which couples molecular motion to a mesoscopic fluid solvent. Thousands of events of long polymers (up to 8000 monomers) are monitored as they pass through nanopores. Comparison between the different pore sizes shows that wide pores can host a larger number of multiple biopolymer segments, as compared to smaller pores. The simulations provide clear evidence of folding quantization in the translocation process as the biopolymers undertake multi-folded configurations, characterized by a well-defined integer number of folds. Accordingly, the translocation time is no longer represented by a single-exponent power law dependence on the length, as it is the case for single-file translocation through narrow pores. The folding quantization increases with the biopolymer length, while the rate of translocated beads at each time step is linearly correlated to the number of resident beads in the pore. Finally, analysis of the statistics over the translocation work unravels the importance of the hydrodynamic interactions in the process.Comment: 10 pages, 6 figures, to appear in J. Stat. (2009

Models of dynamic extraction of lipid tethers from cell membranes

When a ligand that is bound to an integral membrane receptor is pulled, the membrane and the underlying cytoskeleton can deform before either the membrane delaminates from the cytoskeleton or the ligand detaches from the receptor. If the membrane delaminates from the cytoskeleton, it may be further extruded and form a membrane tether. We develop a phenomenological model for this processes by assuming that deformations obey Hooke's law up to a critical force at which the cell membrane locally detaches from the cytoskeleton and a membrane tether forms. We compute the probability of tether formation and show that they can be extruded only within an intermediate range of force loading rates and pulling velocities. The mean tether length that arises at the moment of ligand detachment is computed as are the force loading rates and pulling velocities that yield the longest tethers.Comment: 16 pages, 7 figure

A novel method for measuring the bending rigidity of model lipid membranes by simulating tethers

The tensile force along a cylindrical lipid bilayer tube is proportional to the membrane's bending modulus and inversely proportional to the tube radius. We show that this relation, which is experimentally exploited to measure bending rigidities, can be applied with even greater ease in computer simulations. Using a coarse-grained bilayer model we efficiently obtain bending rigidities that compare very well with complementary measurements based on an analysis of thermal undulation modes. We furthermore illustrate that no deviations from simple quadratic continuum theory occur up to a radius of curvature comparable to the bilayer thickness.Comment: 7 pages, 5 figures, 1 tabl

Protein search for multiple targets on DNA

Protein-DNA interactions are crucial for all biological processes. One of the most important fundamental aspects of these interactions is the process of protein searching and recognizing specific binding sites on DNA. A large number of experimental and theoretical investigations have been devoted to uncovering the molecular description of these phenomena, but many aspects of the mechanisms of protein search for the targets on DNA remain not well understood. One of the most intriguing problems is the role of multiple targets in protein search dynamics. Using a recently developed theoretical framework we analyze this question in detail. Our method is based on a discrete-state stochastic approach that takes into account most relevant physical-chemical processes and leads to fully analytical description of all dynamic properties. Specifically, systems with two and three targets have been explicitly investigated. It is found that multiple targets in most cases accelerate the search in comparison with a single target situation. However, the acceleration is not always proportional to the number of targets. Surprisingly, there are even situations when it takes longer to find one of the multiple targets in comparison with the single target. It depends on the spatial position of the targets, distances between them, average scanning lengths of protein molecules on DNA, and the total DNA lengths. Physical-chemical explanations of observed results are presented. Our predictions are compared with experimental observations as well as with results from a continuum theory for the protein search. Extensive Monte Carlo computer simulations fully support our theoretical calculations

First-principles GW calculations for DNA and RNA nucleobases

On the basis of first-principles GW calculations, we study the quasiparticle properties of the guanine, adenine, cytosine, thymine, and uracil DNA and RNA nucleobases. Beyond standard G0W0 calculations, starting from Kohn-Sham eigenstates obtained with (semi)local functionals, a simple self-consistency on the eigenvalues allows to obtain vertical ionization energies and electron affinities within an average 0.11 eV and 0.18 eV error respectively as compared to state-of-the-art coupled-cluster and multi-configurational perturbative quantum chemistry approaches. Further, GW calculations predict the correct \pi -character of the highest occupied state, thanks to several level crossings between density functional and GW calculations. Our study is based on a recent gaussian-basis implementation of GW with explicit treatment of dynamical screening through contour deformation techniques.Comment: 5 pages, 3 figure

Transport of Molecular Motor Dimers in Burnt-Bridge Models

Dynamics of molecular motor dimers, consisting of rigidly bound particles that move along two parallel lattices and interact with underlying molecular tracks, is investigated theoretically by analyzing discrete-state stochastic continuous-time burnt-bridge models. In these models the motion of molecular motors is viewed as a random walk along the lattices with periodically distributed weak links (bridges). When the particle crosses the weak link it can be destroyed with a probability $p$, driving the molecular motor motion in one direction. Dynamic properties and effective generated forces of dimer molecular motors are calculated exactly as a function of a concentration of bridges $c$ and burning probability $p$ and compared with properties of the monomer motors. It is found that the ratio of the velocities of the dimer and the monomer can never exceed 2, while the dispersions of the dimer and the monomer are not very different. The relative effective generated force of the dimer (as compared to the monomer) also cannot be larger than 2 for most sets of parameters. However, a very large force can be produced by the dimer in the special case of $c=1/2$ for non-zero shift between the lattices. Our calculations do not show the significant increase in the force generated by collagenase motor proteins in real biological systems as predicted by previous computational studies. The observed behavior of dimer molecular motors is discussed by considering in detail the particle dynamics near burnt bridges.Comment: 21 pages and 11 figure

Sequence Heterogeneity Accelerates Protein Search for Targets on DNA

The process of protein search for specific binding sites on DNA is fundamentally important since it marks the beginning of all major biological processes. We present a theoretical investigation that probes the role of DNA sequence symmetry, heterogeneity and chemical composition in the protein search dynamics. Using a discrete-state stochastic approach with a first-passage events analysis, which takes into account the most relevant physical-chemical processes, a full analytical description of the search dynamics is obtained. It is found that, contrary to existing views, the protein search is generally faster on DNA with more heterogeneous sequences. In addition, the search dynamics might be affected by the chemical composition near the target site. The physical origins of these phenomena are discussed. Our results suggest that biological processes might be effectively regulated by modifying chemical composition, symmetry and heterogeneity of a genome.Comment: 10 pages, 5 figure