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PubMed1996

Boundary conditions for- single-ion diffusion.

We have constructed a theory for diffusion through the pore of a single-ion channel by taking a limit of a random walk around a cycle of states. Similar to Levitt's theory of single-ion diffusion, one obtains boundary conditions for the Nernst-Planck equation that guarantee that the pore is occupied by at most one ion. Two of the terms in the boundary conditions are identical to those given by Levitt. However, the construction gives rise to a third term not found in Levitt's theory. With this term, the channel spends exponentially distributed intervals in the empty state. Ion sample paths have been simulated to help visualize trajectories near the channel entrances, with and without the new term. We use the modified Levitt theory to fit several potential profiles to the conductance data of Russell et al. In particular, we have analyzed the profile for Na+ in gramicidin calculated by Roux and Karplus. The peak-to-peak amplitude of their result must be reduced to at most 35% of its original value to fit the data. But with this reduction, excellent fits are obtained.

Computer Simulation↗
PubMed1996

A perturbed two-level model for exciton trapping in small photosynthetic systems.

The study of exciton trapping in photosynthetic systems provides significant information about migration kinetics within the light harvesting antenna (LHA) and the reaction center (RC). We discuss two random walk models for systems with weakly coupled pigments, with a focus on the application to small systems (10-40 pigments/RC). Details of the exciton transfer to and from the RC are taken into consideration, as well as migration within the LHA and quenching in the RC. The first model is obtained by adapting earlier local trap models for application to small systems. The exciton lifetime is approximated by the sum of three contributions related to migration in the LHA, trapping by the RC, and quenching within the RC. The second model is more suitable for small systems and regards the finite rate of migration within the LHA as a perturbation of the simplified model, where the LHA and the RC are each represented by a single pigment level. In this approximation, the exciton lifetime is the sum of a migration component and a single nonlinear expression for the trapping and quenching of the excitons. Numerical simulations demonstrate that both models provide accurate estimates of the exciton lifetime in the intermediate range of 20-50 sites/RC. In combination, they cover the entire range of very small to very large photosynthetic systems. Although initially intended for regular LHA lattices, the models can also be applied to less regular systems. This becomes essential as more details of the structure of these systems become available. Analysis with these models indicates that the excited state decay in LH1 is limited by the average rate at which excitons transfer to the RC from neighboring sites in the LHA. By comparing this to the average rate of transfer within the LHA, various structural models that have been proposed for the LH1 core antenna are discussed.

Bacterial Proteins↗
PubMed1997

The effects of geometrical parameters on synaptic transmission: a Monte Carlo simulation study.

Monte Carlo simulations of transmitter diffusion and its interactions with postsynaptic receptors have been used to study properties of quantal responses at central synapses. Fast synaptic responses characteristic of those recorded at glycinergic junctions on the teleost Mauthner cell (time to peak approximately 0.3-0.4 ms and decay time constant approximately 3-6 ms) served as the initial reference, and smaller contacts with fewer postsynaptic receptors were also modeled. Consistent with experimental findings, diffusion, simulated using a random walk algorithm and assuming a diffusion coefficient of 0.5-1.0 x 10(-5) cm2 s(-1), was sufficiently fast to account for transmitter removal from the synaptic cleft. Transmitter-receptor interactions were modeled as a two-step binding process, with the double-bound state having opened and closed conformations. Addition of a third binding step only slightly decreased response amplitude but significantly slowed both its rising and decay phases. The model allowed us to assess the sources of response variability and the likelihood of postsynaptic saturation as functions of multiple kinetic and spatial parameters. The method of nonstationary fluctuation analysis, typically used to estimate the number of functional channels at a synapse and single channel current, proved unreliable, presumably because the receptors in the postsynaptic matrix are not uniformly exposed to the same profile of transmitter concentration. Thus, the time course of the probability of channel opening most likely varies among receptors. Finally, possible substrates for phenomena of synaptic plasticity, such as long-term potentiation, were explored, including the diameter of the contact zone, defined by the region of pre- and postsynaptic apposition, the number and distribution of the receptors, and the degree of vesicle filling. Surprisingly, response amplitude is quite sensitive to the size of the receptor-free annulus surrounding the receptor cluster, such that expansion of the contact zone could produce an appreciable increase in quantal size, normally attributed to either the presence of more receptors or the release of more transmitter molecules.

Algorithms↗
PubMed1997

Residence time calculation for chemotactic bacteria within porous media.

Local chemical gradients can have a significant impact on bacterial population distributions within subsurface environments by evoking chemotactic responses. These local gradients may be created by consumption of a slowly diffusing nutrient, generation of a local food source from cell lysis, or dissolution of nonaqueous phase liquids trapped within the interstices of a soil matrix. We used a random walk simulation algorithm to study the effect of a local microscopic gradient on the swimming behavior of bacteria in a porous medium. The model porous medium was constructed using molecular dynamics simulations applied to a fluid of equal-sized spheres. The chemoattractant gradient was approximated with spherical symmetry, and the parameters for the swimming behavior of soil bacterium Pseudomonas putida were based on literature values. Two different mechanisms for bacterial chemotaxis, one in which the bacteria responded to both positive and negative gradients, and the other in which they responded only to positive gradients, were compared. The results of the computer simulations showed that chemotaxis can increase migration through a porous medium in response to microscopic-scale gradients. The simulation results also suggested that a more significant role of chemotaxis may be to increase the residence time of the bacteria in the vicinity of an attractant source.

Biophysical Phenomena↗
PubMed1997

Inversely correlated cycles in speed and turning in an ameba: an oscillatory model of cell locomotion.

Previous biophysical models of ameboid crawling have described cell movement in terms of a persistent random walk. Speed and orientation were treated in the latter model as independent and temporally homogeneous stochastic processes. We show here that, at least in the case of Dictyostelium discoideum, both speed control and reorientation processes involve a deterministic, periodic component. We also show that the processes are synchronized and negatively correlated, as was suggested by earlier findings. That is, increased turning correlates with periods of slow movement. Therefore, previous models are inconsistent with the behavior of cells. Using a heuristic approach, we have developed a mathematical model that describes the statistical properties of the cell's velocity and movement of its centroid. Our observations and the model are consistent with the phenomenological description of ameboid motility as a cyclic process of pseudopod extension and retraction.

Amoeba↗
PubMed1999

Direct observation of one-dimensional diffusion and transcription by Escherichia coli RNA polymerase.

The dynamics of nonspecific and specific Escherichia coli RNA polymerase (RNAP)-DNA complexes have been directly observed using scanning force microscopy operating in buffer. To this end, imaging conditions had to be found in which DNA molecules were adsorbed onto mica strongly enough to be imaged, but loosely enough to be able to diffuse on the surface. In sequential images of nonspecific complexes, RNAP was seen to slide along DNA, performing a one-dimensional random walk. Heparin, a substance known to disrupt nonspecific RNAP-DNA interactions, prevented sliding. These observations suggest that diffusion of RNAP along DNA constitutes a mechanism for accelerated promoter location. Sequential images of single, transcribing RNAP molecules were also investigated. Upon addition of 5 microM nucleoside triphosphates to stalled elongation complexes in the liquid chamber, RNAP molecules were seen to processively thread their template at rates of 1.5 nucleotide/s in a direction consistent with the promoter orientation. Transcription assays, performed with radiolabeled, mica-bound transcription complexes, confirmed this rate, which was about three times smaller than the rate of complexes in solution. This assay also showed that the pattern of pause sites and the termination site were affected by the surface. By using the Einstein-Sutherland friction-diffusion relation the loading force experienced by RNAP due to DNA-surface friction is estimated and discussed.

Adsorption↗
PubMed1999

Simulation study of a gramicidin/lipid bilayer system in excess water and lipid. II. Rates and mechanisms of water transport.

A gramicidin channel in a fluid phase DMPC bilayer with excess lipid and water has been simulated. By use of the formal correspondence between diffusion and random walk, a permeability for water through the channel was calculated, and was found to agree closely with the experimental results of Rosenberg and Finkelstein (Rosenberg, P.A., and A. Finkelstein. 1978. J. Gen. Physiol. 72:327-340; 341-350) for permeation of water through gramicidin in a phospholipid membrane. By using fluctuation analysis, components of resistance to permeation were computed for movement through the channel interior, for the transition step at the channel mouth where the water molecule solvation environment changes, and for the process of diffusion up to the channel mouth. The majority of the resistance to permeation appears to occur in the transition step at the channel mouth. A significant amount is also due to structurally based free energy barriers within the channel. Only small amounts are due to local friction within the channel or to diffusive resistance for approaching the channel mouth.

Biological Transport, Active↗
PubMed2003

Of JAKs, STATs, blind watchmakers, jeeps and trains.

Janus kinase/signal transducer and activator of transcription (JAK/STAT) signalling is essential but not sufficient for full responses to the interferons (IFNs), most cytokines and some growth factors. The IFN-gamma and interleukin-6 (IL-6) response pathways have been used as model systems to investigate both the signals involved and their organisation. Activated STAT1 diffuses freely in the cytoplasmic and nuclear compartments of the cell providing a 'random walk' element in the IFN-gamma response. Completely foreign chimeric receptors and, remarkably, in the absence of STAT3, the endogenous IL-6 receptor can efficiently mediate an IFN-gamma-like response. Accordingly all of the signals required for an IFN-gamma response can be generated through physiological levels of a foreign ligand. JAK/STAT signalling, therefore, appears 'soft-wired', modular and highly flexible with substantial overlap between different response pathways. The data are consistent with a generic or 'core' set of signals from JAK/receptor complexes with 'add-on' modulation through specific receptor motifs. The cellular background likely profoundly affects the nature of the response.

Animals↗
PubMed2004

Multi-loop decentralized PID control based on covariance control criteria: an LMI approach.

PID control is well known and widely applied in industry and many design algorithms are readily available in the literature. However, systematic design of multi-loop or decentralized PID control for multivariable processes to meet certain objectives simultaneously is still a challenging task. Designing multi-loop PID controllers such that the process variables satisfy the generalized covariance constraints is studied in this paper. A convergent computational algorithm is proposed to calculate the multi-loop PID controller for a process with stable disturbances. This algorithm is then extended to a process with random-walk disturbances. The feasibility of the proposed algorithm is verified by applying it to several simulation examples.

Journal Article↗
PubMed2000

Analysis of channel-geometry effects on separation efficiency in rectangular-capillary electrochromatography columns.

A three-dimensional random walk model was developed to evaluate the impact of column geometry on separation efficiency in chromatography systems driven by electroosmotic flow. Contributions of injection plug length, cross-sectional area of channels, and aspect ratio of rectangular channels were examined in these simulation studies. Sample plug length had no impact on efficiency until it exceeded roughly 0.4% of the channel length. Plate height increased rapidly with increasing k' as expected, almost doubling in going from k'=0.25 to 0.35. Channel geometry also had a major effect on efficiency. Plate height increased sharply in rectangular channel columns until the channel aspect ratio reached 4-8. But the effect of channel depth was even more dramatic. Minimum plate height (Hmin) was roughly half that of the channel depth in ideal cases. Hmin in a 10x2 microm channel was at 1.6 mm s(-1). Rectangular channels comparable to those obtained by microfabrication are equivalent to packed column capillary electrochromatography columns in all cases.

Algorithms↗
PubMed2000

Measurement of ingestion rate of Hydrobia ulvae (Pennant) on intertidal epipelic microalgae: the effect of mud snail density.

The individual mean ingestion rate of Hydrobia ulvae was measured experimentally in controlled microcosms, in the dark to avoid primary production during measurement and at constant temperature. The experimental design was based on the addition of prelabelled epipelic microalgae to microcosms in a constant proportion with unlabelled diatoms, and in such a way that algal food availability was not a limiting factor within the range of tested densities (0.3 to 4.1 snails cm(-2)). Results show that the individual mean ingestion rate decreased significantly from 26.6+/-1.1 ng Chl a snail(-1) h(-1) to 22.4+/-1.0 ng Chl a snail(-1) h(-1) between 0.7 and 3 snails cm(-2). We hypothesize that this sharp decrease (the threshold density was between 1.4 and 2.5 snails cm(-2)) may account for a density-dependent effect. We have tested this hypothesis by using a simple random walk model including basic behavioural processes such as a break in feeding activity when two individuals contact each other. The model represents quantitatively well the threshold effect, suggesting that behavioural processes have to be taken into account for estimating a global feeding activity of H. ulvae populations.

Journal Article↗
PubMed2002

The Escherichia coli dam DNA methyltransferase modifies DNA in a highly processive reaction.

The Escherichia coli dam adenine-N6 methyltransferase modifies DNA at GATC sequences. It is involved in post-replicative mismatch repair, control of DNA replication and gene regulation. We show that E. coli dam acts as a functional monomer and methylates only one strand of the DNA in each binding event. The preferred way of ternary complex assembly is that the enzyme first binds to DNA and then to S-adenosylmethionine. The enzyme methylates an oligonucleotide containing two dam sites and a 879 bp PCR product with four sites in a fully processive reaction. On lambda-DNA comprising 48,502 bp and 116 dam sites, E. coli dam scans 3000 dam sites per binding event in a random walk, that on average leads to a processive methylation of 55 sites. Processive methylation of DNA considerably accelerates DNA methylation. The highly processive mechanism of E. coli dam could explain why small amounts of E. coli dam are able to maintain the methylation state of dam sites during DNA replication. Furthermore, our data support the general rule that solitary DNA methyltransferase modify DNA processively whereas methyltransferases belonging to a restriction-modification system show a distributive mechanism, because processive methylation of DNA would interfere with the biological function of restriction-modification systems.

Bacteriophage lambda↗
PubMed1984

Chemicomechanical transduction performed by enzymes activated by polymers.

Kinetic models for the mode of action of processive and non-processive DNA-helicases are detailed. Fluxes at the steady state are analyzed, and the random walk of the enzymes on the DNA is studied in connection with the rate constants of the chemical reactions involved in the transformation of substrate to products. Finally, the constants of the kinetic model for the processive helicase are related to the parameters of an analogous viscoelastic model.

Adenosine Triphosphatases↗
PubMed1986

Energy storage during DNA girase activity.

In this work, we develop a minimal two-cycle model for the action of DNA girase. One of the cycles describes the ATP dependent chemicomechanical transduction performed by the enzyme. The other cycle describes the relaxing activity exhibited by girase on supercoiled DNA in the absence of substrates. Supercoiling of DNA is described as a random walk on a topological index. The mechanical energy storage in DNA is manifested in the fact that in general, the kinetic constants for the cycles do not satisfy Wegscheider relations. Finally, a connection is established between the degree of DNA supercoiling and the hydrolysis of ATP.

Adenosine Triphosphate↗
PubMed2000

A mathematical model for the roles of pericytes and macrophages in the initiation of angiogenesis. I. The role of protease inhibitors in preventing angiogenesis.

In this paper, a simple mathematical model developed in H.A. Levine, B.D. Sleeman, M. Nilsen-Hamilton [J. Math. Biol., in press] to describe the initiation of capillary formation in tumor angiogenesis is extended to include the roles of pericytes and macrophages in regulating angiogenesis. The model also allows for the presence of anti-angiogenic (angiostatic) factors. The model is based on the observation that angiostatin can prevent the degradation of fibronectin in the basal lamina by inhibiting the catalytic action of active proteolytic enzyme. That is, it is proposed that the inhibitor 'deactivates' the protease but that it does not reduce the over all concentration of the protease. It consequently explores the possibility of preventing neovascular capillaries from migrating through the extra-cellular matrix toward the tumor by inhibiting protease action. The model is based on the theory of reinforced random walks coupled with Michaelis-Menten mechanisms which view endothelial cell receptors as the catalysts for transforming both tumor and macrophage derived angiogenic factors into proteolytic enzyme which in turn degrade the basal lamina. A simple catalytic reaction is proposed for the degradation of the basal lamina by the active proteases. A mechanism, in which the angiostatin acts as a protease inhibitor is discussed which has been substantiated experimentally. A second mechanism for the production of protease inhibitor from angiostatin by endothelial cells is proposed to be of Michaelis-Menten type. Mathematically, this mechanism includes the former as a subcase.

Angiogenesis Inducing Agents↗
PubMed2003

Metapopulation dynamics with quasi-local competition.

Stepping-stone models for the ecological dynamics of metapopulations are often used to address general questions about the effects of spatial structure on the nature and complexity of population fluctuations. Such models describe an ensemble of local and spatially isolated habitat patches that are connected through dispersal. Reproduction and hence the dynamics in a given local population depend on the density of that local population, and a fraction of every local population disperses to neighboring patches. In such models, interesting dynamic phenomena, e.g. the persistence of locally unstable predator-prey interactions, are only observed if the local dynamics in an isolated patch exhibit non-equilibrium behavior. Therefore, the scope of these models is limited. Here we extend these models by making the biologically plausible assumption that reproductive success in a given local habitat not only depends on the density of the local population living in that habitat, but also on the densities of neighboring local populations. This would occur if competition for resources occurs between neighboring populations, e.g. due to foraging in neighboring habitats. With this assumption of quasi-local competition the dynamics of the model change completely. The main difference is that even if the dynamics of the local populations have a stable equilibrium in isolation, the spatially uniform equilibrium in which all local populations are at their carrying capacity becomes unstable if the strength of quasi-local competition reaches a critical level, which can be calculated analytically. In this case the metapopulation reaches a new stable state, which is, however, not spatially uniform anymore and instead results in an irregular spatial pattern of local population abundance. For large metapopulations, a huge number of different, spatially non-uniform equilibrium states coexist as attractors of the metapopulation dynamics, so that the final state of the system depends critically on the initial conditions. The existence of a large number of attractors has important consequences when environmental noise is introduced into the model. Then the metapopulation performs a random walk in the space of all attractors. This leads to large and complicated population fluctuations whose power spectrum obeys a red-shifted power law. Our theory reiterates the potential importance of spatial structure for ecological processes and proposes new mechanisms for the emergence of non-uniform spatial patterns of abundance and for the persistence of complicated temporal population fluctuations.

Competitive Behavior↗
PubMed2002

Global speed processing: evidence for local averaging within, but not across two speed ranges.

A primary task of the visual system is to extract the direction and speed of animate objects from the retinal image. We examined global speed processing by determining how local speeds are integrated and whether integration occurs across all speeds or within fixed speed ranges. The first experiment addressed how local motion signals are combined to determine the speed of an object in motion. Observers judged the speed of a moving cloud of dots that took a random walk in direction while the dots inside the cloud moved somewhat independently of the cloud itself. The apparent speed of the cloud of dots is found to change in proportion with the dot speed and is well predicted by calculating the average speed resulting from nearest neighbour matches across stimulus frames. The second experiment addressed whether local speeds are combined across all speeds or within fixed speed ranges for the detection of global motion. Global dot motion (GDM) stimuli that moved in a radial or rotational directions moving at a low speed of 1.2 degrees /s or a high speed of 9.6 degrees /s were used to measure the thresholds for detecting structured motion as a function of the speed of noise dots (0 degrees /s-10.8 degrees /s) added to the stimulus. With low-speed targets, only additional noise dots moving at low speeds interfered with signal detection. High-speed targets were only interfered with by dots moving at high speeds. This finding established the existence of at least two independent speed tuned systems in the range of speeds tested. Experiment 3 investigated how speed signals are combined within a system to determine the global speed. Using sectored radial GDM stimuli the perceived speed of the fastest dots was measured as a function of whether the speed of the dots in alternate sectors either activated the high or low-speed systems. Averaging only occurred when dots were all within the sensitivity range of the high-speed system, however, if alternate sectors activated separate speed systems, averaging did not occur. Thus local speeds are averaged, independent of direction, to derive a global speed estimate, but averaging only occurs within, and not across, speed tuned mechanisms.

Adult↗
PubMed2000

Human cortical areas underlying the perception of optic flow: brain imaging studies.

In summary, we have reviewed electrophysiological and brain imaging studies of motion and optic-flow processing. Single-unit studies indicate that MST (V5a) is a site of optic-flow extraction and that this information can be used to guide pursuit eye movements and to estimate heading. The EEG and MEG studies point to a localized electrical dipole in occipitotemporal cortex evoked by visual motion. We have also discussed the evidence from functional imaging studies for response specificity of the rCBF and BOLD effects in posterior cortex to visual motion and optic flow. Focal attention modulates the amplitude of the BOLD signal evoked by visual motion stimulation. Retinotopic mapping techniques have been used to locate region borders within the visual cortex. Our results indicate that striate (V1) and extrastriate areas (V2, V3/V3a) respond robustly to optic flow. However, with exception of a more pronounced response in V3/V3a to random walk, we found little evidence for response selectivity with respect to flow type and disparity in these early visual areas. In a similar fashion, the human V5/V5a complex responds well to optic flow, but these responses do not vary significantly with the type of flow field and do not seem to depend on disparity. In contrast, the kinetic occipital area (KO/V3b) responds well to optic-flow information, and it is the only area that produces more pronounced activation to the disparity in the flow fields. These initial results are promising because they suggest that the fMRI method can be sensitive to changes in stimulus parameters that define flow fields. More work will be required to explore the extent to which these responses reflect the neuronal processing of optic flow. Eye position tracking is now possible during fMRI experiments. We have demonstrated that the eye movements affect the BOLD responses in motion-sensitive areas (Kimming et al., 1999). Further experiments in our laboratory are aimed at understanding the effects of eye movements on the neuronal coding of complex optic-flow fields (Schira et al., 1999).

Animals↗