Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Random walk”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 991 records · Page 55Linked to original sources
PubMed2002

Concentration fluctuations in a mesoscopic oscillating chemical reaction system.

Under sustained pumping, kinetics of macroscopic nonlinear biochemical reaction systems far from equilibrium either can be in a stationary steady state or can execute sustained oscillations about a fixed mean. For a system of two dynamic species X and Y, the concentrations n(x) and n(y) will be constant or will repetitively trace a closed loop in the (n(x), n(y)) phase plane, respectively. We study a mesoscopic system with n(x) and n(y) very small; hence the occurrence of random fluctuations modifies the deterministic behavior and the law of mass action is replaced by a stochastic model. We show that n(x) and n(y) execute cyclic random walks in the (n(x), n(y)) plane whether or not the deterministic kinetics for the corresponding macroscopic system represents a steady or an oscillating state. Probability distributions and correlation functions for n(x)(t) and n(y)(t) show quantitative but not qualitative differences between states that would appear as either oscillating or steady in the corresponding macroscopic systems. A diffusion-like equation for probability P(n(x), n(y), t) is obtained for the two-dimensional Brownian motion in the (n(x), n(y)) phase plane. In the limit of large n(x), n(y), the deterministic nonlinear kinetics derived from mass action is recovered. The nature of large fluctuations in an oscillating nonequilibrium system and the conceptual difference between "thermal stochasticity" and "temporal complexity" are clarified by this analysis. This result is relevant to fluorescence correlation spectroscopy and metabolic reaction networks.

Journal Article↗
PubMed2003

Osmotic water transport through carbon nanotube membranes.

We use molecular dynamics simulations to study osmotically driven transport of water molecules through hexagonally packed carbon nanotube membranes. Our simulation setup comprises two such semipermeable membranes separating compartments of pure water and salt solution. The osmotic force drives water flow from the pure-water to the salt-solution compartment. Monitoring the flow at molecular resolution reveals several distinct features of nanoscale flows. In particular, thermal fluctuations become significant at the nanoscopic length scales, and as a result, the flow is stochastic in nature. Further, the flow appears frictionless and is limited primarily by the barriers at the entry and exit of the nanotube pore. The observed flow rates are high (5.8 water molecules per nanosecond and nanotube), comparable to those through the transmembrane protein aquaporin-1, and are practically independent of the length of the nanotube, in contrast to predictions of macroscopic hydrodynamics. All of these distinct characteristics of nanoscopic water flow can be modeled quantitatively by a 1D continuous-time random walk. At long times, the pure-water compartment is drained, and the net flow of water is interrupted by the formation of structured solvation layers of water sandwiched between two nanotube membranes. Structural and thermodynamic aspects of confined water monolayers are studied.

Membranes, Artificial↗
PubMed2000

Anterograde flow of cargo across the golgi stack potentially mediated via bidirectional "percolating" COPI vesicles.

How do secretory proteins and other cargo targeted to post-Golgi locations traverse the Golgi stack? We report immunoelectron microscopy experiments establishing that a Golgi-restricted SNARE, GOS 28, is present in the same population of COPI vesicles as anterograde cargo marked by vesicular stomatitis virus glycoprotein, but is excluded from the COPI vesicles containing retrograde-targeted cargo (marked by KDEL receptor). We also report that GOS 28 and its partnering t-SNARE heavy chain, syntaxin 5, reside together in every cisterna of the stack. Taken together, these data raise the possibility that the anterograde cargo-laden COPI vesicles, retained locally by means of tethers, are inherently capable of fusing with neighboring cisternae on either side. If so, quanta of exported proteins would transit the stack in GOS 28-COPI vesicles via a bidirectional random walk, entering at the cis face and leaving at the trans face and percolating up and down the stack in between. Percolating vesicles carrying both post-Golgi cargo and Golgi residents up and down the stack would reconcile disparate observations on Golgi transport in cells and in cell-free systems.

Amino Acid Sequence↗
PubMed2002

The Brownian web.

Arratia, [Arratia, R. (1979) Ph.D. thesis (University of Wisconsin, Madison) and unpublished work] and later Toth and Werner [Toth, B. & Werner, W. (1998) Probab. Theory Relat. Fields 111, 375-452] constructed random processes that formally correspond to coalescing one-dimensional Brownian motions starting from every space-time point. We extend their work by constructing and characterizing what we call the Brownian Web as a random variable taking values in an appropriate (metric) space whose points are (compact) sets of paths. This leads to general convergence criteria and, in particular, to convergence in distribution of coalescing random walks in the scaling limit to the Brownian Web.

Journal Article↗
PubMed2001

Explaining mortality rate plateaus.

We propose a stochastic model of aging to explain deviations from exponential growth in mortality rates commonly observed in empirical studies. Mortality rate plateaus are explained as a generic consequence of considering death in terms of first passage times for processes undergoing a random walk with drift. Simulations of populations with age-dependent distributions of viabilities agree with a wide array of experimental results. The influence of cohort size is well accounted for by the stochastic nature of the model.

Aging↗
PubMed1976

Kinetics of branch migration in double-stranded DNA.

The rate of branch migration in double stranded DNA has been measured by the use of a unique substrate formed by the action of the EcoRI restriction endonuclease on the dimeric figure-8 configuration of the replicative form DNA of phage G4. The figure-8 and the X-form derived from it contain a junction of the kind postulated to occur in the Holliday structure and to be an essential feature of a number of models of recombination. In the X-form this junction can branch migrate to an irreversible terminal configuration consisting of two linear monomers. The disappearance of X-forms was measured by electron microscopy. A treatment of branch migration as a random walk process was developed to permit the determination of the rate of the intrinsic process, a step movement of the junction by a distance of one base pair. A value of about 6 kilobase pairs per sec at 37 degrees was obtained.

Bacteriophages↗
PubMed1989

A case at last for age-phased reduction in equity.

Maximizing expected utility over a lifetime leads one who has constant relative risk aversion and faces random-walk securities returns to be "myopic" and hold the same fraction of portfolio in equities early and late in life--a defiance of folk wisdom and casual introspection. By assuming one needs to assure at retirement a minimum ("subsistence") level of wealth, the present analysis deduces a pattern of greater risk-taking when young than when old. When a subsistence minimum is needed at every period of life, the rentier paradoxically is least risk tolerant in youth--the Robert C. Merton paradox that traces to the decline with age of the present discounted value of the subsistence-consumption requirements. Conversely, the decline with age of capitalized human capital reverses the Merton effect.

Aging↗
PubMed1990

Prediction of the three-dimensional structure of Escherichia coli 30S ribosomal subunit: a molecular mechanics approach.

We introduce a computer-assisted procedure for folding large RNA chains into three-dimensional conformations consistent with their secondary structure and other known experimental constraints. The RNA chain is modeled using pseudoatoms at different levels of detail--from a single pseudoatom per helix to a single pseudoatom for each nucleotide. A stepwise procedure is used, starting with a simple representation of the macromolecule that is refined and then extrapolated into higher resolution for further refinement. The procedure is capable of folding different random-walk chains by using energy minimization, allowing generation of a range of conformations consistent with given experimental data. We use this procedure to generate several possible conformations of the 16S RNA in the 30S ribosomal subunit of Escherichia coli by using secondary structure and the neutron-scattering map of the 21 proteins in the small subunit. The RNA chain is modeled using a single pseudoatom per helix. RNA-RNA and RNA-protein crosslinks, reported in current literature, are included in our model. Footprinting data for different ribosomal proteins in the 16S RNA are also used. Several conformations of the 16S RNA are generated and compared to predict gross structural features of the 30S subunit as well as to identify regions of the 16S RNA that cannot be well-defined with current experimental data.

Escherichia coli↗
PubMed1992

Graviton scattering and matter distribution.

In this model gravitation results from the emission and absorption of quanta (gravitons) that are scattered a few times in crossing a typical galaxy. Many features of the universe can be explained in terms of this model, although theoretical justification for the scattering of gravitons is lacking. Gravitons follow a random walk and diffuse through the outer regions of a galaxy. As a result the force of attraction follows a 1/R law, matching observed galactic rotation curves and explaining galactic dynamics without the need of dark matter. The model makes predictions regarding early stages in the expansion of the universe and the establishment of the mass distribution. It may be assumed that a nearly uniform expanding cloud of gas was present that was subject to collapse under gravitational forces. The 1/R law of attraction due to graviton diffusion is orders of magnitude more effective for initiation of collapse than the inverse square law, and it applies to blocks of gas larger than the graviton mean free path. Delay in the spread of gravitational attraction by diffusion sets a time-dependent range beyond which the attractive force is zero. In the model this causes arrays of matter to collapse locally into zones with a spacing set by the length of the range of the attractive force. An initial examination indicates that under these conditions the background radiation could have been released from a nearly uniform distribution at the time of decoupling of radiation and matter, followed by gravitational collapse into blocks of galactic mass. In the model the diffusion of gravitons continued and collapse became possible on a larger scale, initiating the formation of galactic clusters and still larger structures. The slow rate of diffusion then prevented the largest structures from attracting each other and permitted the formation of the voids on a very large scale. The model predicts that on the largest scale there is a three-dimensional repeated array of structures separated by voids. Ultimately structures larger than galactic clusters outran the diffusion of the gravitons and have since been freely expanding.

Journal Article↗
PubMed1993

A physical model for the translocation and helicase activities of Escherichia coli transcription termination protein Rho.

Transcription termination protein Rho of Escherichia coli interacts with newly synthesized RNA chains and brings about their release from elongation complexes paused at specific Rho-dependent termination sites. Rho is thought to accomplish this by binding to a specific Rho "loading site" on the nascent RNA and then translocating preferentially along the transcript in a 5'-->3' direction. On reaching the elongation complex, Rho releases the nascent RNA by a 5'-->3' RNA.DNA helicase activity. These translocation and helicase activities are driven by the RNA-dependent ATPase activity of Rho. In this paper we propose a mechanism for these processes that is based on the structure and properties of the Rho protein. Rho is a hexamer of identical subunits that are arranged as a trimer of asymmetric dimers with D3 symmetry. The binding of ATP and RNA to Rho also reflects this pattern; the Rho hexamer carries three strong and three weak binding sites for each of these entities. The asymmetric dimers of Rho correspond to functional dimers that can undergo conformational transitions driven by ATP hydrolysis. We propose that the quaternary structure of Rho coordinates the ATP-driven RNA binding and release processes to produce a biased random walk of the Rho hexamer along the RNA, followed by RNA.DNA helicase activity and transcript release. The proposed model may have implications for other hexameric DNA.DNA, RNA.DNA, and RNA.RNA helicases that function in replication and transcription.

Escherichia coli↗
PubMed1996

Least activation path for protein folding: investigation of staphylococcal nuclease folding by stopped-flow circular dichroism.

Is the pathway of protein folding determined by the relative stability of folding intermediates, or by the relative height of the activation barriers leading to these intermediates? This is a fundamental question for resolving the Levinthal paradox, which stated that protein folding by a random search mechanism would require a time too long to be plausible. To answer this question, we have studied the guanidinium chloride (GdmCl)-induced folding/unfolding of staphylococcal nuclease [(SNase, formerly EC 3.1.4.7; now called microbial nuclease or endonuclease, EC 3.1.31.1] by stopped-flow circular dichroism (CD) and differential scanning microcalorimetry (DSC). The data show that while the equilibrium transition is a quasi-two-state process, kinetics in the 2-ms to 500-s time range are triphasic. Data support the sequential mechanism for SNase folding: U3 <--> U2 <--> U1 <--> N0, where U1, U2, and U3 are substates of the unfolded protein and N0 is the native state. Analysis of the relative population of the U1, U2, and U3 species in 2.0 M GdmCl gives delta-G values for the U3 --> U2 reaction of +0.1 kcal/mol and for the U2 --> U1 reaction of -0.49 kcal/mol. The delta-G value for the U1 --> N0 reaction is calculated to be -4.5 kcal/mol from DSC data. The activation energy, enthalpy, and entropy for each kinetic step are also determined. These results allow us to make the following four conclusions. (i) Although the U1, U2, and U3 states are nearly isoenergetic, no random walk occurs among them during the folding. The pathway of folding is unique and sequential. In other words, the relative stability of the folding intermediates does not dictate the folding pathway. Instead, the folding is a descent toward the global free-energy minimum of the native state via the least activation path in the vast energy landscape. Barrier avoidance leads the way, and barrier height limits the rate. Thus, the Levinthal paradox is not applicable to the protein-folding problem. (ii) The main folding reaction (U1 --> N0), in which the peptide chain acquires most of its free energy (via van der Waals' contacts, hydrogen bonding, and electrostatic interactions), is a highly concerted process. These energy-acquiring events take place in a single kinetic phase. (iii) U1 appears to be a compact unfolded species; the rate of conversion of U2 to U1 depends on the viscosity of solution. (iv) All four relaxation times reported here depend on GdmCl concentrations: it is likely that none involve the cis/trans isomerization of prolines. Finally, a mechanism is presented in which formation of sheet-like chain conformations and a hydrophobic condensation event precede the main-chain folding reaction.

Circular Dichroism↗
PubMed1998

Charge transfer and transport in DNA.

We explore charge migration in DNA, advancing two distinct mechanisms of charge separation in a donor (d)-bridge ([Bj])-acceptor (a) system, where [Bj] = B1,B2, . , BN are the N-specific adjacent bases of B-DNA: (i) two-center unistep superexchange induced charge transfer, d*[Bj]a --> d[Bj]a+/-, and (ii) multistep charge transport involves charge injection from d* (or d+) to [Bj], charge hopping within [Bj], and charge trapping by a. For off-resonance coupling, mechanism i prevails with the charge separation rate and yield exhibiting an exponential dependence approximately exp(-betaR) on the d-a distance (R). Resonance coupling results in mechanism ii with the charge separation lifetime tau approximately Neta and yield Y approximately (1 + Neta)-1 exhibiting a weak (algebraic) N and distance dependence. The power parameter eta is determined by charge hopping random walk. Energetic control of the charge migration mechanism is exerted by the energetics of the ion pair state dB1+/-B2 . BNa relative to the electronically excited donor doorway state d*B1B2 . BNa. The realization of charge separation via superexchange or hopping is determined by the base sequence within the bridge. Our energetic-dynamic relations, in conjunction with the energetic data for d*/d- and for B/B+, determine the realization of the two distinct mechanisms in different hole donor systems, establishing the conditions for "chemistry at a distance" after charge transport in DNA. The energetic control of the charge migration mechanisms attained by the sequence specificity of the bridge is universal for large molecular-scale systems, for proteins, and for DNA.

DNA↗
PubMed2000

The asymptotic distribution of canonical correlations and variates in cointegrated models.

The cointegrated model considered here is a nonstationary vector autoregressive process in which some linear functions are stationary and others are random walks. The first difference of the process (the "error-correction form") is stationary. Statistical inference, such as reduced rank regression estimation of the coefficients of the process and tests of hypotheses of dimensionality of the stationary part, involves the canonical correlations between the difference vector and the relevant vector of the past of the process. The asymptotic distributions of the canonical correlations and the canonical vectors under the assumption that the process is Gaussian are found.

Journal Article↗
PubMed1996

Preparation of figure 8 and cruciform DNAs and their use in studies of the kinetics of branch migration.

We have re-examined the kinetics of the branch migration of double-stranded DNA that is mediated by the stepwise movement of the Holliday junction. This work revises and extends our previous treatment (Thompson, B. J., Camien, M. N., and Warner, R. C. (1976) Proc. Natl. Acad. Sci. U.S.A. 73, 2299-2303). New methodology and new highly purified substrates have been used. The latter include figure 8s prepared from phage G4 DNA by annealing single-stranded components and two sizes of a novel cruciform. We treat the process as a one-dimensional diffusion based on the random walk, the mathematical basis of which is discussed in detail. The step rate is shown to be 3 orders of magnitude slower than we reported previously. The most important contribution to the erroneously high rate was a result of the presence of EDTA in the spreading solution used for electron microscopy at that time. A second contribution of about 4-fold resulted from catalysis by EcoRI and other proteins. The rates reported here are for the uncatalyzed reaction.

Base Sequence↗
PubMed1998

The Influence of Flow on the Concentration of Platelet Active Substances in the Vicinity of Mural Microthrombi.

The flow effect on the concentration of platelet active substances in the vicinity of a mural microthrombus is investigated numerically. A three-dimensional model is employed in which the mural microthrombus is modelled as a semisphere attached to a plane surface. The description of the blood flow uses the three-dimensional incompressible Navier-Stokes equations for Newtonian fluids, and the mass transport and reaction kinetics are modelled applying a system of coupled convection-diffusion equations with reaction terms. The numerical approach employs the finite element method and a streamline upwind stabilization due to the high Peclet numbers. To verify the calculated concentrations a random walk model for the simulation of the convective diffusion of thrombogenic substances is employed. The results show flow recirculations directly upstream and downstream of the microthrombus which cause local concentration maxima in these regions. The resulting thrombin concentration exceeds the required level for platelet activation at shear rates and thrombus sizes under consideration. The resulting concentrations of thromboxane A(2) (TxA(2) ) and adenosine diphosphate (ADP) exceed the corresponding activation levels only at low shear rates and for large aggregates. For an aggregate diameter of 20 µm at the shear rate [formula: see text] the maximum TxA(2) concentration at a distance from the wall of 3 µm is 0.69 µM, which exceeds the required level of 0.6 µM. Increasing the shear rate to [formula: see text] causes a decrease of the maximum concentration to 0.43 µM.

Journal Article↗
PubMedDate not supplied

The development of structure and function in the postnatal human cerebral cortex from birth to 72 months: changes in thickness of layers II and III co-relate to the onset of new age-specific behaviors.

HYPOTHESIS: The thickness of a cortical layer is a composite measure of neuronal, axonal, dendritic, synaptic, and glial numbers and sizes that may relate to thefunction of a cortical area. METHODS: 35 age-specific behaviors with defined cortical localization whose onset lies between birth and 72 months were selected. Each behavior's function localized to one or more of 12 cytoarchitectonic areas (Brodmann areas 4, with homuncular subdivisions for leg, trunk, face, and hand, plus 17, 18, 19, 20, 21, 24, 36, and 37). Data on cortical thickness for each layer of 41 cytoarchitectonic areas (including the 12 above) of the postnatal human cerebral cortex from birth of 72 months were analyzed for general patterns of change. For the 12 cortical areas functionally related to theage-specific behaviors, we searched for layer thickness changes that co-related to when the behaviors began. RESULTS: Without exception, all layers of the 41 cortical areas of the postnatal human cerebral cortex studied develop through a series of repeated thinning and thickening in a wave-like fashion. With regard to the co-relation of behavioral onset and changes in cortical layer thickness, from birth to 15 months, only layer II has agreater than expected frequency of being the layer with the greatest relative change in thickness (relative to its previous value). From 15 to 72 months, only layer IlI has a greater than expected frequency of being the layer with the greatest absolute change in thickness (81% involved a change in its direction of growth (thinning <--> thickening)). The co-occurrence of directional growth change and having the greatest layer thickness change were only statistically significant for layer III when an age-specific behavior began and was not seen for the 41 cortical areas overall (p = 0.014). CONCLUSIONS: Cortical laminar development exhibits aprocess that is mathematically consistent with a random walk with drift and with boundaries so that uncontrolled proliferation and pruning are prevented. The directional changes in layer growth could be controlled by feedback coupled with growth promoting and growth inhibiting factors. Layer II, with its function of establishing local corticocortical connections, appears to be most important in establishing age-specific behaviors of infants from birth to 15 months. Such a process tends to produce relatively simpler behaviors. LayerIII, with its function of establishing longer distance corticocortical connections, appears to be most important in establishing age-specific behaviors of children from 15 to 72 months. This process tends to produce richer, more cross-modal behaviors than those mediated primarily by local corticocortical interactions.

Aging↗
PubMed1995

Statistical description of nucleic acid secondary structure folding.

A simple statistical model describing the folding of nucleic acids is proposed. For long sequences the real configuration of the secondary structure is a quasi equilibrium state that cannot be characterised by minimal free energy. This is because the time required to achieve complete thermal equilibrium considerably exceeds the life-time of the molecule. The formation of the secondary structure is represented as a random walk process in the space of all possible molecular configurations. The quasi equilibrium structure is obtained by successive linking and disruptions of helix segments with probabilities determined by the rate constants of corresponding unimolecular reactions. The probabilities of configurations consisting of all possible compatible helices are calculated. Structures of some t-RNAs and ribosomal RNAs are analysed.

Algorithms↗
PubMed2004

The role of the angiopoietins in tumour angiogenesis.

Angiogenesis--the growth of new blood vessels from existing ones--is a prerequisite for the growth of solid tumours beyond a diameter of approximately 2 mm. In recent years, the angiopoietins have emerged as important regulators of angiogenesis. They mediate a delicate balance between vascular quiescence, regression and new growth, but their mechanism of action is not fully understood. This work attempts to provide a mathematical description of the role of the angiopoietins in angiogenesis. The model is formulated within the framework of reinforced random walks, which allows easy transition between the continuum (macroscopic) and discrete (microscopic) forms. Model predictions are in qualitative agreement with experimental observations, and may have implications for antiangiogenic cancer therapies.

Angiopoietin-1↗