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PubMed1996

Electronic energy levels and hopping conductivity of an entire molecule of hagfish insulin.

The quantum-chemical calculation of an entire molecule of hagfish insulin was done by the ENFC method in which the matrix elements were calculated at the ab initio level using a minimal basis set with simulation of the aqueous solution environment. The ac conductivity for hagfish insulin was also calculated at the ab initio level by random walk theory. All the results were compared with those of pig insulin. It is shown that the reduction of HOMOs and LUMOs localized on the active sites of hagfish insulin agrees with the decrease in the biological reactivity of the insulin. The analysis of primary hopping events showed that a different sequence could influence the biological activity of insulin through the distribution of the hopping centers and the quantities of the hopping frequencies. The curve of the frequency versus ac conductivity of hagfish insulin shows that the different amino acid sequences of proteins influence the hopping conductivity. However, the electronic properties of native proteins are dominated by the three-dimensional conformations. Finally, the electronic mechanism of trans-membrane signal transforms by insulin and its receptor, which had been proposed by Ye and Ladik, was clearly described.

Amino Acid Sequence↗
PubMed1991

Some geometrical considerations on membrane insertion by exocytosis.

A two-dimensional random walk model is used to describe constitutive exocytic transport. Specifically, the possibility of attaining selective vesicle insertion by purely geometrical effects is studied. The distribution of vesicle insertion on the membrane and the average time of translocation are determined as a function of Golgi apparatus size and position, cell morphology and size, walk bias due to cytoplasmic streaming or differential movement on microtubules, and steric effects caused by other organelles. The simulations suggest that significant selectivity in targeting can result from adequate Golgi positioning, in accordance with the hypothesis of Golgi reorientation by the microtubular network (Singer and Kupfer, 1986, Annu. Rev. Cell Biol. 2, 337-365). The selectivity in targeting also depends on the cellular morphology. Segregation of vesicle insertion can be obtained in the transport to the cellular front end and lateral membrane surfaces of a quadrilateral cell, thus suggesting a geometrical component in the exocytic transport in polarized cells.

Animals↗
PubMed1994

Simulations of pulsed field gradient spin-echo measurements in porous media.

Under ideal conditions, in an isotropic homogeneous system, pulsed field gradient spin-echo (PFGSE) experiments measure the probability P(R,t), that a diffusing water molecule will travel a root mean square distance, R, in a time interval of length t. We will show that random walk simulations on model porous media provide valuable insight to the sensitivity of this measurement to (1) complex pore geometries and (2) enhanced relaxation at the pore-grain interface.

Computer Simulation↗
PubMed2006

The mechanism of proton transfer between adjacent sites on the molecular surface.

The surface of a protein, or a membrane, is spotted with a multitude of proton binding sites, some of which are only few A apart. When a proton is released from one site, it propagates through the water by a random walk under the bias of the local electrostatic potential determined by the distribution of the charges on the protein. Eventually, the released protons are dispersed in the bulk, but during the first few nanoseconds after the dissociation, the protons can be trapped by encounter with nearby acceptor sites. While the study of this reaction on the surface of a protein suffers from experimental and theoretical difficulties, it can be investigated with simple model compounds like derivatives of fluorescein. In the present study, we evaluate the mechanism of proton transfer reactions that proceed, preferentially, inside the Coulomb cage of the dye molecules. Kinetic analysis of the measured dynamics reveals the role of the dimension of the Coulomb cage on the efficiency of the reaction and how the ordering of the water molecules by the dye affects the kinetic isotope effect.

Binding Sites↗
PubMed2005

Modeling directed ligand passage toward enzyme active site by a 'double cellular automata' model.

It is recently proposed that directed passage of ligand on the surface of enzymes may play an important role in the process of enzyme activity, as a result of decreasing the required steps of random walking of the ligand toward the active site. Here, we revisited the approach applied by others, where a cellular automaton is designed to simulate the behavior of a ligand molecule traveling toward the active site of an enzyme. Since a cellular automaton plane is topologically equivalent to a torus surface, we recommended the use of a 'double cellular automata' to model globular proteins. With the boundary conditions applied, our model is topologically identical to a sphere. It was shown that using this model, even fewer steps are needed for a molecule to attend the active site. This assumption can lead to more realistic results in the modeling of surfaces with spherical topology.

Algorithms↗
PubMed2005

Coil dimensions of the mussel adhesive protein Mefp-1.

To obtain a better understanding of factors controlling cross-linking rates of Mussel adhesive proteins, we study the conformation of the Mussel Adhesive Protein Mefp-1. The dimensions of Mefp-1 in solution are determined by dynamic light scattering. Under physiological conditions, the hydrodynamic radius RH of Mefp-1 is found to be 10.5+/-1.1 nm. Measured Mefp-1 dimensions are compared with theoretical dimensions of Mefp-1 in random coil conformations. We have strong indications that Mefp-1, under dilute and physiological conditions, has a self-avoiding random walk conformation with helix-like deca-peptide segments. With a number of segments of approximately 90, the segment length is found to be 2.7 nm.

Animals↗
PubMed2006

Microtubules as mechanical force sensors.

Microtubules are polymers of tubulin subunits (dimers) arranged on a hexagonal lattice. Each tubulin dimer comprises two monomers, the alpha-tubulin and beta-tubulin, and can be found in two states. In the first state a mobile negative charge is located into the alpha-tubulin monomer and in the second into the beta-tubulin monomer. Each tubulin dimer is modeled as an electrical dipole coupled to its neighbors by electrostatic forces. The location of the mobile charge in each dimer depends on the location of the charges in the dimer's neighborhood. Mechanical forces that act on the microtubule affect the distances between the dimers and alter the electrostatic potential. Changes in this potential affect the mobile negative charge location in each dimer and the charge distribution in the microtubule. The net effect is that mechanical forces affect the charge distribution in microtubules. We propose to exploit this effect and use microtubules as mechanical force sensors. We model each dimer as a two-state quantum system and, following the quantum computation paradigm, we use discrete quantum random walk on the hexagonal microtubule lattice to determine the charge distribution. Different forces applied on the microtubule are modeled as different coin biases leading to different probability distributions of the quantum walker location, which are directly connected to different charge distributions. Simulation results show that there is a strong indication that microtubules can be used as mechanical force sensors and that they can also detect the force directions and magnitudes.

Biomechanical Phenomena↗
PubMed2004

The phylogeny of persistence in DNA.

We continue our study, Poland [Biophysical Chemistry 110 (2004) 59-2], of the distribution of C or G (C-G for short) in the DNA of select organisms, in particular, the tendency for C-G to cluster on all scales with respect to the number of bases considered. We previously found that if we counted the number of C-G bases in consecutive, nonoverlapping boxes containing a total of m bases, then the width of the distribution function describing how many C-G bases are in a box increases with respect to m dramatically relative to the width expected for a random distribution. The relative width of the C-G composition distribution function was found to vary accurately as a power law with respect to m, the size of the box, over a very wide range of m values. We express the power law in terms of a characteristic exponent gamma, that is, the relative widths of the distributions vary as m(gamma). The enhanced relative width of the distribution functions is a direct consequence of the tendency for boxes of similar composition to follow one another. This tendency represents persistence in composition from box to box and hence we refer to gamma as the persistence exponent. The occurrence of a power law means that the tendency for C-G to cluster is present on all scales of sequence length (box size) up to the total length of the chromosome which for bacteria is the entire genome. The persistence exponent gamma that characterizes the power law is thus an important parameter describing the distribution of C-G on all scales from individual base pairs up to the total length of the DNA sample considered. In the present paper, we determine the characteristic exponent gamma and the associated fractal dimension of DNA samples for a selection of species representing all of the major types of organism, that is, we explore the phylogeny of the exponent gamma. Here we treat six prokaryotes and six eukaryotes which, together with the species we have previously treated, brings the total number of species we have examined to 15. We find the power law form for the C-G distribution for all of the species treated and hence this behavior seems to be ubiquitous. The values of the characteristic exponent gamma that we find tend to cluster around the value gamma=0.20 with no obvious pattern with respect to phylogeny. The extreme values that we obtain are gamma=0.057 (yeast) and gamma=0.386 (human). We conclude by showing that the persistence of C-G clustering on the scale of the length of a chromosome is dramatically illustrated by interpreting the C-G distribution as a random walk.

Animals↗
PubMed2004

Lattice and non-lattice models of tumour angiogenesis.

In order to progress from the relatively harmless avascular state to the potentially lethal vascular state, solid tumours must induce the growth of new blood vessels from existing ones, a process called angiogenesis. The capillary growth centres around endothelial cells: there are several cell-based models of this process in the literature and these have reproduced some of the key microscopic features of capillary growth. The most common approach is to simulate the movement of leading endothelial cells on a regular lattice. Here, we apply a circular random walk model to the process of angiogenesis, and thus allow the cells to move independently of a lattice; the results display good agreement with empirical observations. We also run simulations of two lattice-based models in order to make a critical comparison of the different modelling approaches. Finally, non-lattice simulations are carried out in the context of a realistic model of tumour angiogenesis, and potential anti-angiogenic strategies are evaluated.

Angiogenesis Inhibitors↗
PubMed2005

Diffusion and home range parameters from rodent population measurements in Panama.

Simple random walk considerations are used to interpret rodent population data collected in Hantavirus-related investigations in Panama regarding the short-tailed cane mouse, Zygodontomys brevicauda. The diffusion constant of mice is evaluated to be of the order of (and larger than) 200 meters squared per day. The investigation also shows that the rodent mean square displacement saturates in time, indicating the existence of a spatial scale which could, in principle, be the home range of the rodents. This home range is concluded to be of the order of 70 meters. Theoretical analysis is provided for interpreting animal movement data in terms of an interplay of the home ranges, the diffusion constant, and the size of the grid used to monitor the movement. The study gives impetus to a substantial modification of existing theory of the spread of the Hantavirus epidemic which has been based on simple diffusive motion of the rodents, and additionally emphasizes the importance for developing more accurate techniques for the measurement of rodent movement.

Animals↗
PubMed2004

Equivalence of the microscopic and macroscopic models of chromatography: stochastic-dispersive versus lumped kinetic model.

The microscopic model of chromatography is a stochastic model that consists of two fundamental processes: (i) the random migration of the molecules in the mobile phase, and (ii) the random adsorption-desorption of molecules on the stationary phase contained in a chromatographic column. The diffusion and drift of the molecules in the mobile phase is described with a simple one-dimensional random walk. The adsorption-desorption process is modeled by a Poisson process that assumes exponential sojourn times of the molecules in both the mobile and the stationary phases. The microscopic, or molecular model of chromatography studied here turns out to be identical to the macroscopic lumped kinetic model of chromatography, whose solution is well known in chromatography. A complete equivalence of the two models is established via the identical expressions they provide for the band profiles.

Chromatography↗
PubMed2006

Tuning to natural stimulus dynamics in primary auditory cortex.

The amplitude and pitch fluctuations of natural soundscapes often exhibit "1/f spectra", which means that large, abrupt changes in pitch or loudness occur proportionally less frequently in nature than gentle, gradual fluctuations. Furthermore, human listeners reportedly prefer 1/f distributed random melodies to melodies with faster (1/f0) or slower (1/f2) dynamics. One might therefore suspect that neurons in the central auditory system may be tuned to 1/f dynamics, particularly given that recent reports provide evidence for tuning to 1/f dynamics in primary visual cortex. To test whether neurons in primary auditory cortex (A1) are tuned to 1/f dynamics, we recorded responses to random tone complexes in which the fundamental frequency and the envelope were determined by statistically independent "1/f(gamma) random walks," with gamma set to values between 0.5 and 4. Many A1 neurons showed clear evidence of tuning and responded with higher firing rates to stimuli with gamma between 1 and 1.5. Response patterns elicited by 1/f(gamma) stimuli were more reproducible for values of gamma close to 1. These findings indicate that auditory cortex is indeed tuned to the 1/f dynamics commonly found in the statistical distributions of natural soundscapes.

Acoustic Stimulation↗
PubMed2005

A local coupling model and compass parameter for eukaryotic chemotaxis.

Chemotaxis is a cellular sensing mechanism that guides immune cells to sites of infection and leads fibroblasts to sites of injury. Here, we show in migrating primary dendritic cells and fibroblasts that the leading edge is not a uniform signaling entity, but instead consists of independent coupling units in which transient activation of PI3-kinase links to local lamellipod extension and small discrete turns in the direction of migration. These findings led to a model in which global cell polarization is independent from the chemotaxis mechanism. In this model, chemotaxis does not require spatial integration but is instead a stochastic process in which each receptor binding event within the leading edge triggers a local lamellipod extension and a small turn in the direction of migration. We show that this model and a derived "compass parameter" are sufficient to simulate the observed random migration, biased random walk, and persistent chemotactic behaviors of eukaryotic cells.

Animals↗
PubMed2005

Evolution of host specificity in fleas: is it directional and irreversible?

Evolutionary trends in the evolution of host specificity have been the focus of much discussion but little rigorous empirical testing. On the one hand, specialization is often presumed to lead irreversibly into evolutionary dead ends and little diversification; this would mean that generalists might evolve into specialists, but not vice versa. On the other hand, low host specificity may limit the risk of extinction and provide more immediate fitness benefits to parasites, such that selection may favour evolution toward a generalist strategy. Here, we test for directionality in the evolution of host specificity using a large data set and phylogenetic information on 297 species of fleas parasitic on small mammals. The analyses determined whether host specificity, measured both as the number of host species exploited and their taxonomic diversity, was related to clade rank of the flea species, or the number of branching events between an extant species and the root of the phylogenetic tree (i.e., the total path length from the root of the tree to the species). Based on regression analyses, we found positive relationships between the number of host species used and clade rank across all 297 species, as well as within one (Hystrichopsyllidae) of four large families and one of seven large genera investigated separately; in addition, we found a positive relationship between the taxonomic diversity of host species used and clade rank in another of the seven genera. These results suggest a slight evolutionary trend of decreasing host specificity. Using a much more conservative likelihood ratio test, however, a random walk, or null model, of evolution could not be discarded in favour of the directional trends in all cases mentioned above. Still, these results suggest that host specificity may have tended to decrease in many flea lineages, a process that could have been driven by the benefits of exploiting a wide range of host species.

Adaptation, Biological↗
PubMed2004

Population-based prediction of trauma volumes at a Level 1 trauma centre.

OBJECTIVE: With an ageing US population, the demographics of traumatic injuries are being significantly altered. Census projections predict that the number of Americans over age 65 will double in the next 20 years. We used stochastic methods to forecast trauma admissions in order to predict the effects of such demographic changes at our trauma centre. METHODS: Age- and sex-related rates of traumatic admission were determined using population statistics and trauma registry data from 1994 to 1999. These rates were then projected from 2000 to 2025 based on both the Lee-Carter and random walk with drift methods. Stochastic population projections were made and paired with the projected trauma rates, allowing estimation of total trauma volume. RESULTS: Trauma rates were predicted to increase for most age groups. Trauma admissions are predicted to increase 57% by 2024. By 2019, 50% of trauma admissions will be 60 or older. CONCLUSIONS: Our trauma volume is expected to increase 57% by 2024, an increase of 2% per year. More of this volume will consist of elderly patients, potentially requiring increased health-care resources.

Adolescent↗
PubMed2005

Nuclear magnetic resonance diffusion with surface relaxation in porous media.

Nuclear magnetic resonance (NMR) diffusion simulations with surface relaxation were performed numerically in unconsolidated and consolidated porous media by a random walk technique. Two uniform and nonuniform models of surface relaxation were proposed and compared. The apparent diffusion coefficient and extinction function were determined and studied in the fast, slow and intermediate diffusion regimes of relaxation. According to theoretical predictions, it was observed that the extinction function does not depend on surface relaxivity parameter rho 2 in the slow diffusion regime. The apparent diffusion coefficients are independent of rho 2 in the fast diffusion regime and tend to be superposed onto a single curve in the slow one. The evolution of the apparent diffusion coefficients is gathered by a reduced representation in the fast diffusion regime.

Journal Article↗
PubMed2004

Three-dimensional diffusion of non-sorbing species in porous sandstone: computer simulation based on X-ray microtomography using synchrotron radiation.

The diffusion pathways of porous sandstone were examined by a three-dimensional (3-D) imaging technique based on X-ray computed tomography (CT) using the SPring-8 (Super Photon ring-8 GeV, Hyogo, Japan) synchrotron radiation facility. The analysis was undertaken to develop better understanding of the diffusion pathways in natural rock as a key factor in clarifying the detailed mechanism of the diffusion of radionuclides and water molecules through the pore spaces of natural barriers in underground nuclear waste disposal facilities. A cylindrical sample (diameter 4 mm, length 6 mm) of sandstone (porosity 0.14) was imaged to obtain a 3-D image set of 450(3) voxels=2.62(3) mm(3). Through cluster-labeling analysis of the 3-D image set, it was revealed that 89% of the pore space forms a single large pore-cluster responsible for macroscopic diffusive transport, while only 11% of the pore space is made up of isolated pores that are not involved in long-range diffusive transport. Computer simulations of the 3-D diffusion of non-sorbing random walkers in the largest pore cluster were performed to calculate the surface-to-volume ratio of the pore, tortuosity (diffusion coefficient in free space divided by that in porous rock). The results showed that (i) the simulated surface-to-volume ratio is about 60% of the results obtained by conventional pulsed-field-gradient proton nuclear magnetic resonance (NMR) laboratory experiments and (ii) the simulated tortuosity is five to seven times larger than the results of laboratory diffusion experiments using non-sorbing I(-) and Br(-). These discrepancies are probably attributed to the intrinsic sample heterogeneity and limited spatial resolution of the CT system. The permeability was also estimated based on the NMR diffusometry theory using the results of the random walk simulations via the Kozeny-Carman equation. The estimated permeability involved an error of about 20% compared with the permeability measured by the conventional method, suggesting that the diffusometry-based NMR well logging with gradient coils is applicable to the in-situ permeability measurement of strata. The present study demonstrated that X-ray CT using synchrotron radiation is a powerful tool for obtaining 3-D pore structure images without the beam-hardening artifacts inevitable in conventional CT using X-ray tubes.

Absorption↗
PubMed2004

Generalized-ensemble algorithms: enhanced sampling techniques for Monte Carlo and molecular dynamics simulations.

In complex systems with many degrees of freedom such as spin glass and biomolecular systems, conventional simulations in canonical ensemble suffer from the quasi-ergodicity problem. A simulation in generalized ensemble performs a random walk in potential energy space and overcomes this difficulty. From only one simulation run, one can obtain canonical ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article we review the generalized ensemble algorithms. Three well-known methods, namely, multicanonical algorithm (MUCA), simulated tempering (ST), and replica-exchange method (REM), are described first. Both Monte Carlo (MC) and molecular dynamics (MD) versions of the algorithms are given. We then present five new generalized-ensemble algorithms which are extensions of the above methods.

Algorithms↗