Optimization of brownian search strategies

What are the simplest search strategies that lead an animal to a particular target, what are their limitations, and what changes can be made to develop more effective strategies? To answer these question a class of search strategies was examined that require an animal to have only a minimal capacity for spatial orientation; the effectiveness of such strategies in solving the following basic search problem was determined. The animal begins its search at a distance r _o (starting distance) from a spatially fixed target. It detects the target when it has approached it to within a certain distance a (the detection radius). The analysed class of search strategies has the following characteristics: C1. The animal uses the same search strategy in all regions it enters. Therefore it needs no information as to the actual location of the target. C2. Its search strategy is constant in time. The animal has only to detect whether it has reached the target or not. C3. Once the animal has chosen a direction, it continues in that direction for a certain distance. This is the only way in which the preceding parts of the search affect the animal's decision as to the direction in which it will search next. In the long term the animal's movement directions are independent, with no preference for any particular direction. Despite their extreme simplicity in application these “Brownian” search strategies are remarkably successful (Fig. 1). Indeed, if the search is continued long enough the target is certain to be found. The success of the search depends in part on the search duration (Fig. 2) or the search-path length S, the starting distance and the detection radius. On the other hand, an animal can have a decisive influence on its degree of success simply by adjusting the frequency with which it changes its walking direction to match its sensory abilities. That is, a not-too-short Brownian search (S?r _o) is most successful when the searching animal, between the points at which it changes direction, walks approximately straight for a distance equal to the detection radius (Figs. 3 and 4). A further increase in search effectiveness is possible only by turning to another class of search strategies. These, however, demand that the animal either have more information about the position of its target at the beginning of the search or be able to organize its search behavior even over fairly long periods of time.     

Divide and conquer? Persistence of infectious agents in spatial metapopulations of hosts

Persistence of an infectious agent in a population is an important issue in epidemiology. It is assumed that spatially fragmenting a population of hosts increases the probability of persistence of an infectious agent and that movement of hosts between the patches is vital for that. The influence of migration on persistence is however often studied in mean-field models, whereas in reality the actual distance travelled can be limited and influence the movement dynamics. We use a stochastic model, where within- and between-patch dynamics are coupled and movement is modelled explicitly, to show that explicit consideration of movement distance makes the relation between persistence of infectious agents and the metapopulation structure of its hosts less straightforward than previously thought. We show that the probability of persistence is largest at an intermediate movement distance of the host and that spatially fragmenting a population of hosts is not necessarily beneficial for persistence.     

A simulation study of the dynamics of a driven filament in an Aristotelian fluid

We describe a method, based on techniques used in molecular dynamics, for simulating the inertialess dynamics of an elastic filament immersed in a fluid. The model is used to study the "one-armed swimmer". That is, a flexible appendage externally perturbed at one extremity. For small-amplitude motion our simulations confirm theoretical predictions that, for a filament of given length and stiffness, there is a driving frequency that is optimal for both speed and efficiency. However, we find that to calculate absolute values of the swimming speed we need to slightly modify existing theoretical approaches. For the more relevant case of large-amplitude motion we find that while the basic picture remains the same, the dependence of the swimming speed on both frequency and amplitude is substantially modified. For large-amplitudes we show that the one-armed swimmer is comparatively neither inefficient nor slow. This begs the question, why are there little or no one-armed swimmers in nature?     

On the relative importance of marker heterozygosity and intermarker distance in gene mapping.

Molecular biologists are often confronted with the problem of whether they should try to generate large numbers of very closely linked markers of low heterozygosity or smaller numbers of less closely linked markers of high heterozygosity. In other words, What is more important for gene mapping, high marker heterozygosity or dense marker spacing? We investigated that problem by analytically computing the expected lod score per meiosis in which the new locus is informative and phase known. We also looked at the length of the 1-unit-of-lod-score support interval for the expected lod score from 100 such meioses. We found that while both quantities have an influence on the number of meioses needed to find linkage, the length of the support interval is almost entirely dependent on the intermarker distance, for heterozygosities between 20 and 100%. However, the probability of any given meiosis being phase known and the ability to develop an accurate map of the markers are functions of marker heterozygosity, further complicating the issue.     

Length of mucin-like domains enhances cell-Ebola virus adhesion by increasing binding probability

The Ebola virus (EBOV) hijacks normal physiological processes by apoptotic mimicry to be taken up by the cell it infects. The initial adhesion of the virus to the cell is based on the interaction between T cell immunoglobulin and mucin domain protein, TIM, on the cell surface and phosphatidylserine (PS) on the viral outer surface. Therefore, it is important to understand the interaction between EBOV and PS and TIM, with selective blocking of the interaction as a potential therapy. Recent experimental studies have shown that for TIM-dependent EBOV entry, a mucin-like domain with a length of at least 120 amino acids is required, possibly because of the increase of area of the PS-coated surface sampled. We examine this hypothesis by modeling the process of TIM-PS adhesion using a coarse-grained molecular model. We find that the strength of individual bound PS-TIM pairs is essentially independent of TIM length. TIMs with longer mucin-like domains collectively have higher average binding strengths because of an increase in the probability of binding between EBOV and TIM proteins. Similarly, we find that for larger persistence length (less flexible), the average binding force decreases, again because of a reduction in the probability of binding.     

A mathematical model of population dynamics for Batesian mimicry system

We analyse a mathematical model of the population dynamics among a mimic, a corresponding model, and their common predator populations. Predator changes its search-and-attack probability by forming and losing its search image. It cannot distinguish the mimic from the model. Once a predator eats a model individual, it comes to omit both the model and the mimic species from its diet menu. If a predator eats a mimic individual, it comes to increase the search-and-attack probability for both model and mimic. The predator may lose the repulsive/attractive search image with a probability per day. By analysing our model, we can derive the mathematical condition for the persistence of model and mimic populations, and then get the result that the condition for the persistence of model population does not depend on the mimic population size, while the condition for the persistence of mimic population does depend the predator's memory of search image.     

A mathematical model of population dynamics for Batesian mimicry system

We analyse a mathematical model of the population dynamics among a mimic, a corresponding model, and their common predator populations. Predator changes its search-and-attack probability by forming and losing its search image. It cannot distinguish the mimic from the model. Once a predator eats a model individual, it comes to omit both the model and the mimic species from its diet menu. If a predator eats a mimic individual, it comes to increase the search-and-attack probability for both model and mimic. The predator may lose the repulsive/attractive search image with a probability per day. By analysing our model, we can derive the mathematical condition for the persistence of model and mimic populations, and then get the result that the condition for the persistence of model population does not depend on the mimic population size, while the condition for the persistence of mimic population does depend the predator's memory of search image.     

<Emphasis Type="Italic">Scoredist</Emphasis>: A simple and robust protein sequence distance estimator

Background  

Distance-based methods are popular for reconstructing evolutionary trees thanks to their speed and generality. A number of methods exist for estimating distances from sequence alignments, which often involves some sort of correction for multiple substitutions. The problem is to accurately estimate the number of true substitutions given an observed alignment. So far, the most accurate protein distance estimators have looked for the optimal matrix in a series of transition probability matrices, e.g. the Dayhoff series. The evolutionary distance between two aligned sequences is here estimated as the evolutionary distance of the optimal matrix. The optimal matrix can be found either by an iterative search for the Maximum Likelihood matrix, or by integration to find the Expected Distance. As a consequence, these methods are more complex to implement and computationally heavier than correction-based methods. Another problem is that the result may vary substantially depending on the evolutionary model used for the matrices. An ideal distance estimator should produce consistent and accurate distances independent of the evolutionary model used.     

A novel algorithm for finding interspersed repeat regions

The analysis of repeats in the DNA sequences is an important subject in bioinformatics. In this paper, we propose a novel projection-assemble algorithm to find unknown interspersed repeats in DNA sequences. The algorithm employs random projection algorithm to obtain a candidate fragment set, and exhaustive search algorithm to search each pair of fragments from the candidate fragment set to find potential linkage, and then assemble them together. The complexity of our projection-assemble algorithm is nearly linear to the length of the genome sequence, and its memory usage is limited by the hardware. We tested our algorithm with both simulated data and real biology data, and the results show that our projection-assemble algorithm is efficient. By means of this algorithm, we found an un-labeled repeat region that occurs five times in Escherichia coil genome, with its length more than 5,000 bp, and a mismatch probability less than 4%.     

Random walk with persistence and external bias

The partial differential equation of the random walk problem with persistence of direction and external bias is derived. By persistence of direction or internal bias we mean that the probability a particle will travel in a given direction need not be the same for all directions, but depends solely upon the particle's previous direction of motion. The external bias arises from an anisotropy of the medium or an external force on the particle. The problem is treated by considering that the net displacement of a particle arises from two factors, namely, that neither the probability of the particle traveling in any direction after turning nor the distance the particle travels in a given direction need be the same for all directions. A modified Fokker-Planck equation is first obtained using the assumptions that the particles have a distribution of travel times and speeds and that the average time of travel between turns need not be zero. The fional equation incopporating the assumption of a persistence of direction and an external bias is then derived. Applications to the study of diffusion and to long-chain polymers are then made. This work was done while the author was Public Health Service Research Fellow of The National Institute of Mental Health, Federal Security Agency.     

Technical improvements in the computational target search for antisense oligonucleotides

A number of theoretical and experimental approaches to design biologically active antisense oligonucleotides (AS-ON) have proven their usefulness. This includes systematic computational strategies that are based on the understanding of antisense mechanisms. Here, we investigate in detail the relationship between computational parameters of the local target search for the theoretical design of AS-ON and the hit rate, that is, the biologic efficacy of AS-ON in cell culture. The computational design of AS-ON studied in this work is based on an established algorithm to predict structurally favorable local target sites along a given target RNA against which AS-ON are directed. Briefly, a sequence segment of a certain length (window) is used to predict a group of lowest-energy RNA secondary structures. Subsequently, this window is shifted along the target sequence by a certain step width. To date, those technical parameters of the systematic structural target analysis have been chosen arbitrarily. Here, we investigate their role for the successful design of AS-ON and suggest an optimized computer-based protocol for the selection of favorable local target sequences and, hence, an improved design of active AS-ON. Further, this study provides systematic insights into the structure- function relationship of AS-ON.     

Fluorescent quantification of size and lamellarity of membrane nanotubes

Membrane nanotubes, ubiquitous in cellular systems, adopt a spectrum of curvatures and shapes that are dictated by their intrinsic physical characteristics as well as their interactions with the local cellular environment. A high bending flexibility is needed in the crowded cytoplasm where tubes often need to bend significantly in the axial direction at sub-micron length scales. We find the stiffness of spontaneously formed membrane nanotubes by measuring the persistence length of reconstituted membrane nanotubes freely suspended in solution and imaged by fluorescence microscopy. By quantifying the tube diameter we demonstrate for the first time that the persistence length scales linearly with radius. Although most tubes are uni-lamellar, the predicted linear scaling between tube radius and persistence length allows us to identify tubes that spontaneously form as multilamellar structures upon hydration. We provide the first experimental evidence that illumination of lipid fluorophores can have a profound effect on the lipid bilayer which we sensitively detect as a continuous change in the tube persistence length with time. The novel assay and methodology here presented has potential for quantification of the structural reinforcement of membrane tubes by scaffolding proteins.     

Human erythrocyte spectrin dimer intrinsic viscosity: temperature dependence and implications for the molecular basis of the erythrocyte membrane free energy

We have determined experimentally the temperature dependence of human erythrocyte spectrin dimer intrinsic viscosity at shear rates 8-12 s-1 using a Cartesian diver viscometer. We find that the intrinsic viscosity decreases from 43 +/- 3 ml/g at 4 degrees C to 34 +/- 3 ml/g when the temperature is increased to 38 degrees C. Our results show that spectrin dimers are flexible worm-like macromolecules with persistence length about 20 nm and that the mean square end-to-end distance for this worm-like macromolecules decreases when the temperature is increased. This implies that the spectrin dimer internal energy decreases when the end-to-end distance is increased and that the free energy increase associated with making the end-to-end distance longer than the equilibrium value for the free molecules is of entropic origin. The temperature dependence of the erythrocyte membrane shear modulus reported previously in the literature therefore appears mainly to be due to temperature dependent alterations in the membrane skeleton topology.     

Landscape structure shapes habitat finding ability in a butterfly

Land-use intensification and habitat fragmentation is predicted to impact on the search strategies animals use to find habitat. We compared the habitat finding ability between populations of the speckled wood butterfly (Pararge aegeria L.) from landscapes that differ in degree of habitat fragmentation. Naïve butterflies reared under standardized laboratory conditions but originating from either fragmented agricultural landscapes or more continuous forested landscapes were released in the field, at fixed distances from a target habitat patch, and their flight paths were recorded. Butterflies originating from fragmented agricultural landscapes were better able to find a woodlot habitat from a distance compared to conspecifics from continuous forested landscapes. To manipulate the access to olfactory information, a subset of individuals from both landscape types were included in an antennae removal experiment. This confirmed the longer perceptual range for butterflies from agricultural landscapes and indicated the significance of both visual and olfactory information for orientation towards habitat. Our results are consistent with selection for increased perceptual range in fragmented landscapes to reduce dispersal costs. An increased perceptual range will alter the functional connectivity and thereby the chances for population persistence for the same level of structural connectivity in a fragmented landscape.     

Polymer Uncrossing and Knotting in Protein Folding,and Their Role in Minimal Folding Pathways

We introduce a method for calculating the extent to which chain non-crossing is important in the most efficient, optimal trajectories or pathways for a protein to fold. This involves recording all unphysical crossing events of a ghost chain, and calculating the minimal uncrossing cost that would have been required to avoid such events. A depth-first tree search algorithm is applied to find minimal transformations to fold , , , and knotted proteins. In all cases, the extra uncrossing/non-crossing distance is a small fraction of the total distance travelled by a ghost chain. Different structural classes may be distinguished by the amount of extra uncrossing distance, and the effectiveness of such discrimination is compared with other order parameters. It was seen that non-crossing distance over chain length provided the best discrimination between structural and kinetic classes. The scaling of non-crossing distance with chain length implies an inevitable crossover to entanglement-dominated folding mechanisms for sufficiently long chains. We further quantify the minimal folding pathways by collecting the sequence of uncrossing moves, which generally involve leg, loop, and elbow-like uncrossing moves, and rendering the collection of these moves over the unfolded ensemble as a multiple-transformation “alignment”. The consensus minimal pathway is constructed and shown schematically for representative cases of an , , and knotted protein. An overlap parameter is defined between pathways; we find that proteins have minimal overlap indicating diverse folding pathways, knotted proteins are highly constrained to follow a dominant pathway, and proteins are somewhere in between. Thus we have shown how topological chain constraints can induce dominant pathway mechanisms in protein folding.