Cooperative transport in nanochannels.

Channel transport of different species of particles is viewed usually only in terms of competition and selectivity. In this paper we show that transport of one species may be promoted by the presence of another and that both may even mutually cooperate. We investigate a discretized Markovian model of nanochannel transport via in-channel sites, allowing for the simultaneous transport of several different species of particles; interaction between transported particles is included via the condition of single occupancy on a channel site. By numerically solving the model exactly, particularly an analysis of situations of crowding in the channel is possible and we observe three situations: mutual cooperation, promotion of one species at the cost of the other, and mutual competition. The physical situation has a strong nonequilibrium character as Onsager's relations on coupled flows do not hold.

Zebrafish crypt neurons project to a single, identified mediodorsal glomerulus.

Crypt neurons are a third type of olfactory receptor neurons with a highly unusual "one cell type--one receptor" mode of expression, the same receptor being expressed by the entire population of crypt neurons. Attempts to identify the target region(s) of crypt neurons have been inconclusive so far. We report that TrkA-like immunoreactivity specifically labeled somata, axons, and terminals of zebrafish crypt neurons and reveal a single glomerulus, mdg2 of the dorsomedial group, as target glomerulus of crypt neurons. Injection of a fluorescent tracing dye into the mdg2 glomerulus retrogradely labeled mostly crypt neurons, as assessed by quantitative morphometry, whereas no crypt neurons were found after injections in neighboring glomeruli. Our data provide strong evidence that crypt neurons converge onto a single glomerulus, and thus form a labeled line consisting of a single sensory cell type, a single olfactory receptor and a single target glomerulus.

Ancestral amphibian v2rs are expressed in the main olfactory epithelium.

Mammalian olfactory receptor families are segregated into different olfactory organs, with type 2 vomeronasal receptor (v2r) genes expressed in a basal layer of the vomeronasal epithelium. In contrast, teleost fish v2r genes are intermingled with all other olfactory receptor genes in a single sensory surface. We report here that, strikingly different from both lineages, the v2r gene family of the amphibian Xenopus laevis is expressed in the main olfactory as well as the vomeronasal epithelium. Interestingly, late diverging v2r genes are expressed exclusively in the vomeronasal epithelium, whereas "ancestral" v2r genes, including the single member of v2r family C, are restricted to the main olfactory epithelium. Moreover, within the main olfactory epithelium, v2r genes are expressed in a basal zone, partially overlapping, but clearly distinct from an apical zone of olfactory marker protein and odorant receptor-expressing cells. These zones are also apparent in the spatial distribution of odor responses, enabling a tentative assignment of odor responses to olfactory receptor gene families. Responses to alcohols, aldehydes, and ketones show an apical localization, consistent with being mediated by odorant receptors, whereas amino acid responses overlap extensively with the basal v2r-expressing zone. The unique bimodal v2r expression pattern in main and accessory olfactory system of amphibians presents an excellent opportunity to study the transition of v2r gene expression during evolution of higher vertebrates.

Thermodynamics of competitive molecular channel transport: application to artificial nuclear pores.

In an analytical model channel transport is analyzed as a function of key parameters, determining efficiency and selectivity of particle transport in a competitive molecular environment. These key parameters are the concentration of particles, solvent-channel exchange dynamics, as well as particle-in-channel- and interparticle interaction. These parameters are explicitly related to translocation dynamics and channel occupation probability. Slowing down the exchange dynamics at the channel ends, or elevating the particle concentration reduces the in-channel binding strength necessary to maintain maximum transport. Optimized in-channel interaction may even shift from binding to repulsion. A simple equation gives the interrelation of access dynamics and concentration at this transition point. The model is readily transferred to competitive transport of different species, each of them having their individual in-channel affinity. Combinations of channel affinities are determined which differentially favor selectivity of certain species on the cost of others. Selectivity for a species increases if its in-channel binding enhances the species' translocation probability when compared to that of the other species. Selectivity increases particularly for a wide binding site, long channels, and fast access dynamics. Recent experiments on competitive transport of in-channel binding and inert molecules through artificial nuclear pores serve as a paradigm for our model. It explains qualitatively and quantitatively how binding molecules are favored for transport at the cost of the transport of inert molecules.

Microcanonical replica exchange molecular dynamics simulation of proteins.

We present microcanonical replica exchange molecular dynamics simulations as an alternative to canonical ones. Its advantage is the easily tunable high acceptance rate for replica exchange. We present the theory, comment on its actual implementation, and demonstrate its application for a common test case, the trp-cage protein.

Dynamics and efficiency of Brownian rotors.

Brownian rotors play an important role in biological systems and in future nanotechnological applications. However the mechanisms determining their dynamics, efficiency, and performance remain to be characterized. Here the F0 portion of the F-ATP synthase is considered as a paradigm of the Brownian rotor. In a generic analytical model we analyze the stochastic rotation of F0-like motors as a function of the driving free energy difference and of the free energy profile the rotor is subjected to. The latter is composed of the rotor interaction with its surroundings, of the free energy of chemical transitions, and of the workload. The dynamics and mechanical efficiency of the rotor depend on the magnitude of its stochastic motion driven by the free energy difference and its rectification on the reaction-diffusion path. We analyze which free energy profiles provide maximum flow and how their arrangement on the underlying reaction-diffusion path affects rectification and--by this--the efficiency.

Optimized explicit-solvent replica exchange molecular dynamics from scratch.

Replica exchange molecular dynamics (REMD) simulations have become an important tool to study proteins and other biological molecules in silico. However, such investigations require considerable, and often prohibitive, numerical effort when the molecules are simulated in explicit solvents. In this communication we show that in this case the cost can be minimized by choosing the number of replicas as N(opt) approximately 1+0.594 radical C ln(Tmax/Tmin), where C is the specific heat, and the temperatures distributed according to Ti(opt) approximately T min(Tmax/Tmin)(i-1)/(N-1).

Backbone and side-chain ordering in a small protein.

We investigate the relation between backbone and side-chain ordering in a small protein. For this purpose, we have performed multicanonical simulations of the villin headpiece subdomain HP-36, an often used toy model in protein studies. Concepts of circular statistics are introduced to analyze side-chain fluctuations. In contrast to earlier studies on homopolypeptides [Wei et al., J. Phys. Chem. B 111, 4244 (2007)], we do not find collective effects leading to a separate transition. Rather, side-chain ordering is spread over a wide temperature range. Our results indicate a thermal hierarchy of ordering events, with side-chain ordering appearing at temperatures below the helix-coil transition but above the folding transition. We conjecture that this thermal hierarchy reflects an underlying temporal order, and that side-chain ordering facilitates the search for the correct backbone topology.

Folding proteins by first-passage-times-optimized replica exchange.

Replica exchange simulations have become the method of choice in computational protein science, but they still often do not allow an efficient sampling of low-energy protein configurations. Here, we reconstruct replica flow in the temperature ladder from first passage times and use it for temperature optimization, thereby maximizing sampling. The method is applied in simulations of folding thermodynamics for a number of proteins starting from the pentapeptide Met-enkephalin, through the 36-residue HP-36, up to the 67-residue protein GS-alpha3W.

Network analysis of the state space of discrete dynamical systems.

We study networks representing the dynamics of elementary 1D cellular automata (CA) on finite lattices. We analyze scaling behaviors of both local and global network properties as a function of system size. The scaling of the largest node in-degree is obtained analytically for a variety of CA including rules 22, 54, and 110. We further define the path diversity as a global network measure. The coappearance of nontrivial scaling in both the hub size and the path diversity separates simple dynamics from the more complex behaviors typically found in Wolfram's class IV and some class III CA.

On the helix-coil transition in alanine based polypeptides in gas phase.

Using multicanonical simulations, the authors study the effect of charged end groups on helix formation in alanine based polypeptides. They confirm earlier reports that neutral polyalanine exhibits a pronounced helix-coil transition in gas phase simulations. Introducing a charged Lys+ at the C terminal stabilizes the alpha helix and leads to a higher transition temperature. On the other hand, adding the Lys+ at the N terminal inhibits helix formation. Instead, a more globular structure was found. These results are in agreement with recent experiments on alanine based polypeptides in gas phase. They indicate that present force fields describe accurately the intramolecular interactions in proteins.

Side-chain and backbone ordering in homopolymers.

In order to study the relation between backbone and side-chain ordering in proteins, we have performed multicanonical simulations of deka-peptide chains with various side groups. Glu(10), Gln(10), Asp(10), Asn(10), and Lys(10) were selected to cover a wide variety of possible interactions between the side chains of the monomers. All homopolymers undergo helix-coil transitions. We found that peptides with long side chains that are capable of hydrogen bonding, i.e., Glu(10), and Gln(10), exhibit a second transition at lower temperatures connected with side-chain ordering. This occurs in the gas phase as well as in solvent, although the character of the side-chain structure is different in each case. However, in polymers with short side chains capable of hydrogen bonding, i.e., Asp(10) and Asn(10), side-chain ordering takes place over a wide temperature range and exhibits no phase transition-like character. Moreover, non-backbone hydrogen bonds show enhanced formation and fluctuations already at the helix-coil transition temperature, indicating competition between side-chain and backbone hydrogen bond formation. Again, these results are qualitatively independent of the environment. Side-chain ordering in Lys(10), whose side groups are long and polar, also takes place over a wide temperature range and exhibits no phase transition-like character in both environments. Reasons for the observed chain length threshold and consequences from these results for protein folding are discussed.

Generalized ensemble and tempering simulations: a unified view.

From the underlying master equations we derive one-dimensional stochastic processes that describe generalized ensemble simulations as well as tempering (simulated and parallel) simulations. The representations obtained are either in the form of a one-dimensional Fokker-Planck equation or a hopping process on a one-dimensional chain. In particular, we discuss the conditions under which these representations are valid approximate Markovian descriptions of the random walk in order parameter or control parameter space. They allow a unified discussion of the stationary distribution on, as well as of the stationary flow across, each space. We demonstrate that optimizing the flow is equivalent to minimizing the first passage time for crossing the space and discuss the consequences of our results for optimizing simulations. Finally, we point out the limitations of these representations under conditions of broken ergodicity.

Optimizing replica exchange moves for molecular dynamics.

We sketch the statistical physics framework of the replica exchange technique when applied to molecular dynamics simulations. In particular, we draw attention to generalized move sets that allow a variety of optimizations as well as new applications of the method.

Dynamics and optimal number of replicas in parallel tempering simulations.

We study the dynamics of parallel tempering simulations, also known as the replica exchange technique, which has become the method of choice for simulation of proteins and other complex systems. Recent results for the optimal choice of the control parameter discretization allow a treatment independent of the system in question. By analyzing mean first passage times across the control parameter space, we find an expression for the optimal number of replicas in simulations covering a given temperature range. Our results suggest a particular protocol to optimize the number of replicas in actual simulations.

Side-chain and backbone ordering in a polypeptide.

We report results from multicanonical simulations of polyglutamic acid chains of length of ten residues. For this simple polypeptide we observe a decoupling of backbone and side-chain ordering in the folding process. While the details of the two transitions vary between the peptide in gas phase and in an implicit solvent, our results indicate that, independent of the specific surroundings, upon continuously lowering the temperature side-chain ordering occurs only after the backbone topology is completely formed.

Molecular transport through channels and pores: effects of in-channel interactions and blocking.

Facilitated translocation of molecules through channels and pores is of fundamental importance for transmembrane transport in biological systems. Several such systems have specific binding sites inside the channel, but a clear understanding of how the interaction between channel and molecules affects the flow is still missing. We present a generic analytical treatment of the problem that relates molecular flow to the first passage time across and the number of particles inside the channel. Both quantities depend in different ways on the channel properties. For the idealized case of noninteracting molecules, we find an increased flow whenever there is a binding site in the channel, despite an increased first passage time. In the more realistic case that molecules may block the channel, we find an increase of flow only up to a certain threshold value of the binding strength and a dependence on the sign of the concentration gradient, i.e., asymmetric transport. The optimal binding strength in that case is analyzed. In all cases the reason for transport facilitation is an increased occupation probability of a particle inside the channel that overcomes any increase in the first passage time because of binding.

Violating conformal invariance: two-dimensional clusters grafted to wedges, cones, and branch points of Riemann surfaces.

Lattice animals are one of the few critical models in statistical mechanics violating conformal invariance. We present here simulations of two-dimensional site animals on square and triangular lattices in nontrivial geometries. The simulations are done with the pruned-enriched Rosenbluth method (PERM) algorithm, which gives very precise estimates of the partition sum, yielding precise values for the entropic exponent theta (Z(N) approximately micro(N)N(-theta)). In particular, we studied animals grafted to the tips of wedges with a wide range of angles alpha, to the tips of cones (wedges with the sides glued together), and to branching points of Riemann surfaces. The latter can either have k sheets and no boundary, generalizing in this way cones to angles alpha>360 degrees, or can have boundaries, generalizing wedges. We find conformal invariance behavior, theta approximately 1/alpha , only for small angles (alpha << 2pi) , while theta approximately = const-alpha/2pi for alpha << 2pi. These scalings hold both for wedges and cones. A heuristic (nonconformal) argument for the behavior at large alpha is given, and comparison is made with critical percolation.

Stationary flow, first passage times, and macroscopic Fick's first diffusion law: application to flow enhancement by particle trapping.

A generalized macroscopic Fick's first diffusion law is derived which describes steady-state particle flow between two baths explicitly as a function of the concentration gradient, acting as the thermodynamic driving force, times a functional of the first passage time. The latter is shown to be the ratio of the number of particles trapped between the baths and the first passage time. Particle trapping is shown to be a powerful mechanism by which flow can be enhanced. This is analyzed for two examples: a potential and an entropy trap.