Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session B22: Focus Session: Fluctuations and Fluctuation Analysis in Biological Systems |
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Sponsoring Units: DBP Chair: Peter Hanggi, University Augsburg Room: LACC 409B |
Monday, March 21, 2005 11:15AM - 11:51AM |
B22.00001: Stochastic signalling in excitable ion channel clusters Invited Speaker: The electric properties of axonal cell membranes are predominantly determined by the dynamics of the voltage-dependent gating of potassium and sodium ion channels. The inherent stochastic dynamics of the gating process generates the so-called channel noise. These fluctuations of the number of open ion channels initiate spontaneous excitations. By use of a stochastic generalization of the Hodgkin-Huxley model we investigate the dependency of the spike production on the number of ion channels within a cluster. There exist an optimal cluster size for which solely the internal noise causes a most regular spontaneous generation of action potentials -- the effect of intrinsic coherence resonance -- and an optimal system size induced Stochastic Resonance in presence of external driving [1,2]. In addition to the variation of the size of ion channel clusters, the living organisms may adopt the densities of different ion channels in order to regulate the spontaneous spiking activity. We vary the densities, i.e. the number of the specific ion channels for a given membrane patch size by poisoning the potassium, or the sodium ion channels yielding either an increase or decrease of the regularity of the spiking dynamics [3].\\ We also investigate the influence of the gating charge on spontaneous spiking: the ion channels contribute to the membrane capacity, since the switching of the channel gates between an open and a closed configuration is always connected with charge movement within the cell membrane. Especially, for the case of relatively large densities of ion channels (such as in nodes of Ranvier), this may play a crucial role for nerve excitation. Surprisingly, the gating charge do not dramatically change the excitation behavior. This even holds true even for extremely dense ion channel assemblies; instead the membrane capacity at rest exhibits a bell-shaped dependence on the ion channel density. \\ \noindent [1] G. Schmid, I. Goychuk and P. H\"anggi, Europhys. Lett {\bf 56}, 22 (2001).\\ \noindent [2] G. Schmid, I. Goychuk, P. H\"anggi, S. Zeng, and P. Jung, Fluct. Noise Lett. {\bf 4}, L33 (2004).\\ \noindent [3] G. Schmid, I. Goychuk, and P. H\"anggi, Physical Biology {\bf 1}, 61 (2004). [Preview Abstract] |
Monday, March 21, 2005 11:51AM - 12:03PM |
B22.00002: The Dynamics of Small Excitable Systems Peter Jung, Jian-Wei Shuai We consider clusters of sodium ion channels similar as found in the nodes of Ranvier in myelinated neurons. The cluster behaves like excitable systems in the limit of large numbers of ion channels. Small clusters of channels, i.e. {\it small excitable systems}, exhibit spontaneous action potentials. We show that {\it small} excitable systems exhibit maxima of the spontaneous firing rate and of the response to external stimuli at multiple specific cluster sizes that are universally determined by arithmetic properties of small numbers. [Preview Abstract] |
Monday, March 21, 2005 12:03PM - 12:15PM |
B22.00003: Langevin Formalism as the Basis for the Unification of Population Dynamics Harold P. de Vladar We are presenting a simple reformulation to population dynamics that generalizes many growth functions. The reformulation consists of two equations, one for population size, and one for the growth rate. The model shows that even when a population is density-dependent the dynamics of its growth rate does not depend explicitly neither on population size nor on the carrying capacity. Actually, the growth rate is uncoupled from the population size equation. The model has only two parameters: a Malthusian parameter $\rho$ and an interaction coefficient $\theta$. Distinct values of these parameters reproduce the family of $\theta$-logistics, the van Bertalanffy, Gompertz and Potential Growth equations, among other possibilities. Stochastic perturbations to the Malthusian parameter leads to a Langevin form of stochastic differential equation consisting of a family of cubic potentials perturbed with multiplicative noise. Using these equtions, we derive the stationary Fokker Plank distribution which which shows that in the stationary dynamics, density dependent populations fluctuate around a mean size that is shifted from the carrying capacity proportionally to the noise intensity. We also study which kinds of populations are susceptible to noise induced transitions. [Preview Abstract] |
Monday, March 21, 2005 12:15PM - 12:51PM |
B22.00004: Ion current fluctuations in abiotic mimics of voltage-gated biochannels Invited Speaker: We have been investigating voltage-gating properties of single abiotic nanopores in polymer films. The pores have a shape of a tapered cone with the opening diameter of the tip as small as several nanometers. We have designed two nanotube systems, which exhibit ion current rectification through two distinct mechanisms (i) electrostatic interactions, based on asymmetric shape of electrostatic potential inside the pore, and (ii) electro-mechanical gate placed at the entrance of the conical pore, responsive to the external field applied across the membrane. We have also shown that transient transport properties of nanotubes can be modulated by change of chemistry of the pore walls. We have designed nanotubes, which produce voltage-dependent ion current fluctuations with the kinetics of openings and closings similar to voltage-gated ion channels in biological membranes. An abiotic equivalent of calcium-gated potassium channel will be discussed as well. I will also describe application of voltage-gating nanopores as platforms in biosensing. Recognition sites were incorporated into the pore walls, introducing selectivity for a given analyte. Sensors can be developed from these modified pores based on current-voltage characteristics or on the stochastic detection of analyte molecules as they translocate the membrane. [Preview Abstract] |
Monday, March 21, 2005 12:51PM - 1:03PM |
B22.00005: Strong-coupling dynamics of chemotaxis Ramon Grima, Timothy Newman In this talk we present a stochastic model of cell-cell interactions. This model has recently been introduced to study the role of fluctuations in chemotaxis and related cell movement phenomena. The strong-coupling behavior of the model is studied by means of an asymptotic analysis. For the case of the cell diffusion coefficient less than the chemical diffusion coefficient, it is possible to show that for positive chemotaxis we obtain renormalization of the cell diffusion coefficient for all coupling strengths, ruling out self- localization of a single cell due to auto-chemotaxis. For negative chemotaxis, the model predicts renormalized diffusive behavior for weak coupling and ballistic behavior at larger coupling strengths in one and two dimensions. In three dimensions this transition is only manifest subject to a constraint. The case of auto-chemotaxis is also studied via a cellular automaton model. We show that the temporal dynamics are very sensitive to microscopic details, in particular as to whether the chemical field is modeled through individual random walkers moving on an underlying spatial grid or through a deterministic diffusion equation. [Preview Abstract] |
Monday, March 21, 2005 1:03PM - 1:15PM |
B22.00006: Time-Delay Induced Oscillations in Gene-Regulatory Networks Dmitry Bratsun, Dmitri Volfson, Jeff Hasty, Lev Tsimring We develop both deterministic and stochastic models of transriptionalregulation in small genetic circuits taking into account the effect of time delay occuring in the production of protein monomers. We show that delayed transcription and translation can drastically change the behavior of the system from stationary to oscillatory. Neutral curves of the Hopf bifurcation are derived and studied as a function of the system parameters. In the framework of the stochastic description based on the master equation we analyze the role of fluctuations in the transition to oscillations. We derive the analytical expression for the correlation function and compare it with the results of numerical simulations based on direct Gillespie method. [Preview Abstract] |
Monday, March 21, 2005 1:15PM - 1:27PM |
B22.00007: Single Enzyme Pathways and Substrate Fluctuations Marianne Stefanini, Alan McKane, Timothy Newman In this talk we discuss the validity of the well-known Michaelis-Menten equation (MME), which is used to connect enzyme-substrate reaction rate to substrate concentration. In particular, we are interested in the role of stochastic fluctuations at very low enzyme concentrations, and whether the MME needs to be modified in this case. We find that the MME is valid if the concentration of substrate molecules is maintained at a constant level with microscopic precision (using a Maxwell Demon). However, if this concentration is maintained only on average (by some macroscopic means) then the MME fails and is replaced by a new and fairly simple form. Interestingly, this new form can distinguish between enzyme reactions which occur via a single or multiple pathways, and may therefore be of interest to experimentalists probing intra-molecular enzyme kinetics. [Preview Abstract] |
Monday, March 21, 2005 1:27PM - 1:39PM |
B22.00008: The implications of microtubule dynamic instability on chromosome dynamics in metaphase David Lubin, Buddhapriya Chakrabarti, Alex J. Levine We present a model of chromosome oscillations during late metaphase based on the postulates of the stochastic detachment/reattachment of kinetochore microtubules and the dynamic instability model for microtubules dynamics. In this approach the motion of the chromosomes is analyzed by treating them as Brownian particles subject to a fluctuating force arising from the varying number of microtubules attached to the kinetochore at a given time. Furthermore, we predict observable changes in the chromosome dynamics in response to antimitotic drugs (e.g. taxol) that affects the microtubule dynamics. This approach may facilitate the use of the stochastic time series of chromosome position data as a complement to more traditional approaches in the elucidation of the mechanisms of chromosome alignment during metaphase of cell division. [Preview Abstract] |
Monday, March 21, 2005 1:39PM - 1:51PM |
B22.00009: Beyond Linear Decomposition: Maximizing Information Transmission with Curved Manifolds Tatyana Sharpee, William Bialek We consider how to optimally separate multidimensional signals into two categories in order to maximize information transmission. Our motivation comes from the nervous system, where neurons process multidimensional signals into a binary sequence of responses (spikes). We derive a local equation for the decision boundary which relates the curvature of its contour, scaled by the noise level, to the probability distribution of input signals. In the case of correlated Gaussian inputs, straight lines are shown to provide optimal separation. For non-Gaussian inputs, however, the straight-line solution is not always optimal. For example, in the case of a 2D exponential probability distribution the exact solution for the optimal decision boundary is a hyperbola-type curve, and the angle between its asymptotes is fixed across nearly all spike probabilities. The ubiquity of non-Gaussian signals in nature, particularly the exponential distribution considered here, makes these results relevant for neurons across different sensory modalities. The predicted curvature of the optimal decision boundaries should be observable as sensitivity of neurons to multiple stimulus dimensions rather than just a single receptive field. [Preview Abstract] |
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