On the Physics of Size Selectivity

We demonstrate that two mechanisms used by biological ion channels to select particles by size are driven by entropy. With uncharged particles in an infinite cylinder, we show that a channel that attracts particles is small-particle selective and that a channel that repels water from the wall is large-particle selective. Comparing against extensive density-functional theory calculations of our model, we find that the main physics can be understood with surprisingly simple bulk models that neglect the confining geometry of the channel completely.Comment: 4 pages, 3 figures, Phys. Rev. Lett. (accepted

Voltage sensing in ion channels: Mesoscale simulations of biological devices

Electrical signaling via voltage-gated ion channels depends upon the function of a voltage sensor (VS), identified with the S1-S4 domain in voltage-gated K+ channels. Here we investigate some energetic aspects of the sliding-helix model of the VS using simulations based on VS charges, linear dielectrics and whole-body motion. Model electrostatics in voltage-clamped boundary conditions are solved using a boundary element method. The statistical mechanical consequences of the electrostatic configurational energy are computed to gain insight into the sliding-helix mechanism and to predict experimentally measured ensemble properties such as gating charge displaced by an applied voltage. Those consequences and ensemble properties are investigated for two alternate S4 configurations, \alpha- and 3(10)-helical. Both forms of VS are found to have an inherent electrostatic stability. Maximal charge displacement is limited by geometry, specifically the range of movement where S4 charges and counter-charges overlap in the region of weak dielectric. Charge displacement responds more steeply to voltage in the \alpha-helical than the 3(10)-helical sensor. This difference is due to differences on the order of 0.1 eV in the landscapes of electrostatic energy. As a step toward integrating these VS models into a full-channel model, we include a hypothetical external load in the Hamiltonian of the system and analyze the energetic in/output relation of the VS.Comment: arXiv admin note: substantial text overlap with arXiv:1112.299

Optimal Algorithms for Train Shunting and Relaxed List Update Problems

This paper considers a Train Shunting problem which occurs in cargo train organizations: We have a locomotive travelling along a track segment and a collection of n cars, where each car has a source and a target. Whenever the train passes the source of a car, it needs to be added to the train, and on the target, the respective car needs to be removed. Any such operation at the end of the train incurs low shunting cost, but adding or removing truly in the interior requires a more complex shunting operation and thus yields high cost. The objective is to schedule the adding and removal of cars as to minimize the total cost. This problem can also be seen as a relaxed version of the well-known List Update problem, which may be of independent interest. We derive polynomial time algorithms for Train Shunting by reducing this problem to finding independent sets in bipartite graphs. This allows us to treat several variants of the problem in a generic way. Specifically, we obtain an algorithm with running time O(n^{5/2}) for the uniform case, where all low costs and all high costs are identical, respectively. Furthermore, for the non-uniform case we have running time of O(n^3). Both versions translate to a symmetric variant, where it is also allowed to add and remove cars at the front of the train at low cost. In addition, we formulate a dynamic program with running time O(n^4), which exploits the special structure of the graph. Although the running time is worse, it allows us to solve many extensions, e.g., prize-collection, economies of scale, and dependencies between consecutive stations

Shortest Path with Alternatives for Uniform Arrival Times: Algorithms and Experiments

The Shortest Path with Alternatives (SPA) policy differs from classical shortest path routing in the following way: instead of providing an exact list of means of transportation to follow, this policy gives such a list for each stop, and the traveler is supposed to pick the first option from this list when waiting at some stop. First, we show that an optimal policy of this type can be computed in polynomial time for uniform arrival times under reasonable assumptions. A similar result was so far only known for Poisson arrival times, which are less realistic for frequency-based public transportation systems. Second, we experimentally evaluate such policies. In this context, our main finding is that SPA policies are surprisingly competitive compared to traditional shortest paths, and moreover yield a significant reduction of waiting times, and therefore improvement of user experience, compared to similar greedy approaches. Specifically, for roughly 25% of considered cases, we could decrease the expected waiting time by at least 20%. To run our experiments, we also describe a tool-chain to derive the necessary information from the popular GTFS-format, therefore allowing the application of SPA policies to a wide range of public transportation systems

Self-organized Models of Selectivity in Ca and Na Channels

A simple pillbox model with two adjustable parameters accounts for the selectivity of both DEEA Ca channels and DEKA Na channels in many ionic solutions of different composition and concentration. Only the side chains are different in the model of the Ca and Na channels. Parameters are the same for both channels in all solutions. 'Pauling' radii are used for ions. No information from crystal structures is used in the model. Side chains are grossly approximated as spheres. The predicted properties of the Na and Ca channels are very different. How can such a simple model give such powerful results when chemical intuition says that selectivity depends on the precise relation of ions and side chains? We use Monte Carlo simulations of this model that determine the most stable-lowest free energy-structure of the ions and side chains. Structure is the computed consequence of the forces in this model. The relationship of ions and side chains vary with ionic solution and are very different in simulations of the Na and Ca channels. Selectivity is a consequence of the 'induced fit' of side chains to ions and depends on the flexibility (entropy) of the side chains as well as their location. The model captures the relation of side chains and ions well enough to account for selectivity of both Na channels and Ca channels in the wide range of conditions measured in experiments. Evidently, the structures in the real Na and Ca channels responsible for selectivity are self-organized, at their free energy minimum. Oversimplified models are enough to account for selectivity if the models calculate the 'most stable' structure as it changes from solution to solution, and mutation to mutation.Comment: Version of http://www.ima.umn.edu/2008-2009/W12.8-12.08/abstracts.html, talk given at the Institute for Mathematics and its Applications, University of Minnesota, November 19, 2008. Abstract published in Biophysical Journal, Volume 96, Issue 3, 253

Membrane properties of Ranvier nodes from South American toads frogs (Bufo marinus ictericus and Leptodactylus ocellatus)

Estudaram-se propriedades eletrofisiológicas de membranas excitáveis em algusn anfíbios do Brasil. O presente trabalho refere-se aos resultados obtidos em nódulos de Ranvier de fibras motoras e sensoriais isoladas de Bufo marinus ictericus e Leptodactylus ocellatus. Empregou-se o método desenvolvido por Nonner (1969)

SRPT Is 1.86-competitive for Completion Time Scheduling

We consider the classical problem of scheduling preemptible jobs, that ar-rive over time, on identical parallel machines. The goal is to minimize the total completion time of the jobs. In standard scheduling notation of Graham et al. [5], this problem is denoted P | rj,pmtn | j cj. A pop-ular algorithm called SRPT, which always schedules the unfinished jobs with shortest remaining processing time, is known to be 2-competitive, see Phillips et al. [12, 13]. This is also the best known competitive ratio for any online algorithm. However, it is conjectured that the competitive ra-tio of SRPT is significantly less than 2. Even breaking the barrier of 2 is considered a significant step towards the final answer of this classical online problem. We improve on this open problem by showing that SRPT is 1.86-competitive. This result is obtained using the following method, which might be of general interest: We define two dependent random variables that sum up to the difference between the cost of an SRPT schedule and the cost of an optimal schedule. Then we bound the sum of the expected values of these random variables with respect to the cost of the optimal schedule, yielding the claimed competitiveness. Furthermore, we show a lower bound of 21/19 for SRPT, improving on the previously best known 12/11 due to Lu et al. [10]

On the validity of modeling concepts for the simulation of groundwater flow in lowland peat areas – case study at the Zegveld experimental field

The groundwater flow models currently used in the western part of The Netherlands and in other similar peaty areas are thought to be a too simplified representation of the hydrological reality. One of the reasons is that, due to the schematization of the subsoil, its heterogeneity cannot be represented adequately. Moreover, the applicability of Darcy's law in these types of soils has been questioned, but this law forms the basis of most groundwater flow models. <br><br> With the purpose of assessing the typical heterogeneity of the subsoil and to verify the applicability of Darcy's law, geo-hydrological fieldwork was completed at an experimental field within a research area in the western part of The Netherlands. The assessments were carried out for the so-called Complex Confining Layer (CCL), which is the Holocene peaty to clayey layer overlying Pleistocene sandy deposits. Borehole drilling through the CCL with a hand auger was completed and revealed the typical heterogeneous character of this layer, showing a dominance of muddy, humified peat which is alternated with fresher peat and clay. <br><br> Slug tests were carried out to study the applicability of Darcy's law, given that previous studies suggested its non-validity for humified peat soils due to a variable horizontal hydraulic conductivity <i>K</i><sub>h</sub> with head differences. For higher humification degrees, the experiments indeed suggested a variable <i>K</i><sub>h</sub>, but this appeared to be the result of the inappropriate use of steady-state formulae for transient experiments in peaty environments. The muddy peat sampled has a rather plastic nature, and the high compressibility of this material leads to transient behavior. However, using transient formulae, the slug tests conducted for different initial groundwater heads showed that there was hardly any evidence of a variation of the hydraulic conductivity with the applied head differences. Therefore, Darcy's law can be used for typical peat soils present in The Netherlands. <br><br> The heterogeneity of the subsoil and the apparent applicability of Darcy's law were taken into account for the detailed heterogeneous model that was prepared for the research area. A MODFLOW model consisting of 13 layers in which 4 layers represent the heterogeneous CCL was set up for an average year, assuming steady-state conditions; and for the winter of 2009 to 2010, adopting transient conditions. The transient model was extended to simulate for longer periods with the objective of visualizing the flow paths through the CCL. The results from these models were compared with a 10 layer model, whereby the CCL is represented by a single layer assuming homogeneity. From the comparison of the two model types, the conclusion could be drawn that a single layer schematization of the CCL produces flowpath patterns which are not the same but still quite similar to a 4 layer representation of the CCL. However, the single layer schematization results in a considerable underestimation of the flow velocity, and subsequently a longer travel time, through the CCL. Therefore, a single layer model of the CCL seems quite appropriate to represent the general flow behavior of the shallow groundwater system, but would be inappropriate for transport modeling through the CCL