Stochastic constancy,variability and adaptation of spike generation: Performance of a giant neuron in the visual system of the fly

The stochastic structure of the spike activity generated by a movement processing wide-field element in the visual system of the fly has been studied over the whole performance area of the neuron. The structure of this discharge is described in terms of an Adaptive Integrate-to-Threshold model for a wide variety of spatio-temporal stimuli as well as steady-state stimuli. In order to reproduce the experimental results it is shown that the source of randomness in the model (e.g. the threshold) behaves like a random variable which is distributed according to a two-state Markov renewal process. In the case of stationary discharges generated by moving sinewave patterns the shape of the interspike interval distribution (which, in the Integrate-to-Threshold model, reflects the shape of the threshold distribution) changes continuously from a two-state distribution at low firing rates to a one-state distribution at high firing rates. In dynamic conditions of the discharge, generated by temporal dynamic stimuli, the experimental results show that the shape of the (demodulated) interval distribution of the discharge is determined by the highest instantaneous firing rate with an adaptation time constant of a few seconds. The physioligical origin of this intriguing behaviour remains — up till now — out of the picture.     

Prestress and Adhesion Site Dynamics Control Cell Sensitivity to Extracellular Stiffness

This study aims at improving the understanding of mechanisms responsible for cell sensitivity to extracellular environment. We explain how substrate mechanical properties can modulate the force regulation of cell sensitive elements primarily adhesion sites. We present a theoretical and experimental comparison between two radically different approaches of the force regulation of adhesion sites that depends on their either stationary or dynamic behavior. The most classical stationary model fails to predict cell sensitivity to substrate stiffness whereas the dynamic model predicts extracellular stiffness dependence. This is due to a time dependent reaction force in response to actomyosin traction force exerted on cell sensitive elements. We purposely used two cellular models, i.e., alveolar epithelial cells and alveolar macrophages exhibiting respectively stationary and dynamic adhesion sites, and compared their sensitivity to theoretical predictions. Mechanical and structural results show that alveolar epithelial cells exhibit significant prestress supported by evident stress fibers and lacks sensitivity to substrate stiffness. On the other hand, alveolar macrophages exhibit low prestress and exhibit sensitivity to substrate stiffness. Altogether, theory and experiments consistently show that adhesion site dynamics and cytoskeleton prestress control cell sensitivity to extracellular environment with an optimal sensitivity expected in the intermediate range.     

Estimation of the spatial autocorrelation function: consequences of sampling dynamic populations in space and time

The estimation of spatial autocorrelation in spatially- and temporally-referenced data is fundamental to understanding an organism's population biology. I used four sets of census field data, and developed an idealized space-time dynamic system, to study the behavior of spatial autocorrelation estimates when a practical method of sampling is employed. Estimates were made using both a classical geostatistical approach and a recently developed non-parametric approach. In field data, the estimate of the local spatial autocorrelation (i.e. autocorrelation as the distance between pairs of sampling points approaches 0), was greatly affected by sample size, while the range of spatial dependence (i.e. the distance at which the autocorrelation becomes negligible) was fairly stable. Similar patterns were seen in the theoretical system, as well as greater variability in local spatial autocorrelation during the invasion stage of colonization. When sampling for the purposes of quantifying spatial patterns, improved estimates of spatial autocorrelation may be obtained by increasing the number of pairs of points that are close in space at the expense of attempting to cover the entire region of interest with equidistant sampling points. Also, results from the theoretical space-time system suggested that greater resolution in sampling may be required in newly establishing populations relative to those already established.     

Salt effects on the structure and internal dynamics of superhelical DNAs studied by light scattering and Brownian dynamics.

Using laser light scattering, we have measured the static and dynamic structure factor of two different superhelical DNAs, p1868 (1868 bp) and simian virus 40 (SV40) (5243 bp), in dilute aqueous solution at salt concentrations between 1 mM and 3 M NaCl. For both DNA molecules, Brownian dynamics (BD) simulations were also performed, using a previously described model. A Fourier mode decomposition procedure was used to compute theoretical light scattering autocorrelation functions (ACFs) from the BD trajectories. Both measured and computed autocorrelation functions were then subjected to the same multiexponential decomposition procedure. Simulated and measured relaxation times as a function of scattering angle were in very good agreement. Similarly, computed and measured static structure factors and radii of gyration agreed within experimental error. One main result of this study is that the amplitudes of the fast-relaxing component in the ACF show a peak at 1 M salt concentration. This nonmonotonic behavior might be caused by an initial increase in the amplitudes of internal motions due to diminishing long-range electrostatic repulsions, followed by a decrease at higher salt concentration due to a compaction of the structure.     

Laser light-scattering analysis of protoplasmic streaming in the slime mold Physarum polycephalum

Laser light scattering is shown to be an effective means of obtaining a rapid, objective assessment of dynamic changes in the intact plasmodium of the myxomycete Physarum polycephalum during bidirectional (shuttle) streaming. The motion of material in a 100 mum diameter region of a plasmodial vein was studied by following changes in the autocorrelation function of the fluctuations in the scattered light intensity. The autocorrelation function was recorded at 10 s intervals and analyzed to follow changes in the flow velocity of protoplasm associated with shuttle streaming. Rhythmic velocity changes and a "beating" pattern of velocity maxima were readily observed. In an attempt to locate the site of underlying structural changes in the vein responsible for the changing pattern of flow, the average scattered intensity was separated into components derived from moving and stationary scatterers. Periodic variations in the light intensity due to stationary scatterers are related to the streaming cycle and indicate the occurrence of important structural changes in the vein walls. Two possible interpretations of the data are offered; one involving gross dynamic changes in vein structure, the other involving the formation, contraction, or breakdown of fibrillar material in the vein wall during the streaming cycle.     

On the autocorrelation of one class of non-stationary random point processes

The autocorrelation of those non-stationary random point processes that can be transformed by a time transformation into a stationary process is derived. As an application, a closed form formula is obtained for the autocorrelation of those processes where the average number of points is sinusoidally modulated and the corresponding stationary process is defined by independent intervals identically distributed according to a gamma density of integer order.     

A computer program for linear nonparametric and parametric identification of biological data

A computer program package for parametric and nonparametric linear system identification of both static and dynamic biological data, written for an LSI-11 minicomputer with 28 K of memory, is described. The program has 11 possible commands including an instructional help command. A user can perform nonparametric spectral analysis and estimation of autocorrelation and partial autocorrelation functions of univariate data and estimate nonparametrically the transfer function and possibly an associated noise series of bivariate data. In addition, the commands provide the user the means to derive a parametric autoregressive moving average model for univariate data, to derive a parametric transfer function and noise model for bivariate data, and to perform several model evaluation tests such as pole-zero cancellation, examination of residual whiteness and uncorrelatedness with the input. The program, consisting of a main program and driver subroutine as well as six overlay segments, may be run interactively or automatically.     

Laser light-scattering analysis of protoplasmic streaming in the slime mold physarum polycephalum

Laser light scattering is shown to be an effective means of obtaining a rapid, objective assessment of dynamic changes in the intact plasmodium of the myxomycete Physarum polycephalum during bidirectional (shuttle) streaming. The motion of material in a 100 μm diameter region of a plasmodial vein was studied by following changes in the autocorrelation function of the fluctuations in the scattered light intensity. The autocorrelation function was recorded at 10 s intervals and analyzed to follow changes in the flow velocity of protoplasm associated with shuttle streaming. Rhythmic velocity changes and a “beating” pattern of velocity maxima were readily observed. In an attempt to locate the site of underlying structural changes in the vein responsible for the changing pattern of flow, the average scattered intensity was separated into components derived from moving and stationary scatterers. Periodic variations in the light intensity due to stationary scatterers are related to the streaming cycle and indicate the occurrence of important structural changes in the vein walls. Two possible interpretations of the data are offered; one involving gross dynamic changes in vein structure, the other involving the formation, contraction, or breakdown of fibrillar material in the vein wall during the streaming cycle.     

The structure of optimal time- and age-dependent harvesting in the Lotka-McKendrik population model

The paper analyzes optimal harvesting of age-structured populations described by the Lotka-McKendrik model. It is shown that the optimal time- and age-dependent harvesting control involves only one age at natural conditions. This result leads to a new optimization problem with the time-dependent harvesting age as an unknown control. The integral Lotka model is employed to explicitly describe the time-varying age of harvesting. It is proven that in the case of the exponential discounting and infinite horizon the optimal strategy is a stationary solution with a constant harvesting age. A numeric example on optimal forest management illustrates the theoretical findings. Discussion and interpretation of the results are provided.     

On estimating critical population size for an endangered species in the presence of environmental stochasticity

A stationary second order autoregressive process with Gaussian noise, which was linked to survivorship and reproductive success by logistic transformations, was used as a model for an environmental process. Computer experiments in Monte Carlo integration, with the objective of exploring the sensitivity of estimates of mean critical population size to variations in the parameters of the environmental process, were then conducted. These experiments suggest that estimates of mean critical population size are very sensitive to the form of the autocorrelation function of the stationary environmental process. For the most part, those experiments in which the autocorrelation function was strictly positive not only resulted in the largest estimates of mean critical population size but also led to the highest levels of environmental stochasticity as measured by its coefficient of variation. As in previous work, these experiments suggest that concerted efforts should be made to model those environmental factors that are critical to the survivability of an endangered species in assessing its chances for continued existence.     

A dynamic and spatial model with migration generating the log-Gaussian field of population densities

A spatial version of a dynamic population model leading to the lognormal distribution is defined. The model establishes relations between the joint spatial and temporal autocorrelation and biological concepts like environmental stochasticity, migration and strength of local density-regulation. The model is generalized to describe communities of species leading to a dynamic and spatial lognormal species abundance model with migration.     

An updated perspective on the role of environmental autocorrelation in animal populations

Ecological theory predicts that the presence of temporal autocorrelation in environments can considerably affect population extinction risk. However, empirical estimates of autocorrelation values in animal populations have not decoupled intrinsic growth and density feedback processes from environmental autocorrelation. In this study, we first discuss how the autocorrelation present in environmental covariates can be reduced through nonlinear interactions or by interactions with multiple limiting resources. We then estimated the degree of environmental autocorrelation present in the Global Population Dynamics Database using a robust, model-based approach. Our empirical results indicate that time series of animal populations are affected by low levels of environmental autocorrelation, a result consistent with predictions from our theoretical models. Claims supporting the importance of autocorrelated environments have been largely based on indirect empirical measures and theoretical models seldom anchored in realistic assumptions. It is likely that a more nuanced understanding of the effects of autocorrelated environments is necessary to reconcile our conclusions with previous theory. We anticipate that our findings and other recent results will lead to improvements in understanding how to incorporate fluctuating environments into population risk assessments.     

Single-channel autocorrelation functions: the effects of time interval omission.

We present a general mathematical framework for analyzing the dynamic aspects of single channel kinetics incorporating time interval omission. An algorithm for computing model autocorrelation functions, incorporating time interval omission, is described. We show, under quite general conditions, that the form of these autocorrelations is identical to that which would be obtained if time interval omission was absent. We also show, again under quite general conditions, that zero correlations are necessarily a consequence of the underlying gating mechanism and not an artefact of time interval omission. The theory is illustrated by a numerical study of an allosteric model for the gating mechanism of the locust muscle glutamate receptor-channel.     

Spatio-temporal self-organization of bone mineral metabolism and trabecular structure of primary bone

A nonlinear two-variable reaction-diffusion model of bone mineral metabolism, built from an overall self-oscillatory compartmental model of calcium metabolism in vivo, has been studied for its ability to generate spatial and spatio-temporal self-organizations in a two-dimensional space. Analytical and numerical results confirm the theoretical properties previously described for this kind of model. In particular, it is shown that, for a given set of reactional parameter values and certain values of the ratio of the two diffusion coefficients, there exists a set of unstable wavenumbers leading spontaneously to the development, from the homogeneous steady state, of either different types of stationary spatial patterns (hexagonal, striped and re-entrant hexagonal patterns) or more or less complex spatio-temporal expressions. We discuss the relevance of analogies established between some spatial or spatio-temporal structures predicted by the model and some peculiar features of the primary bone trabecular architecture which appear during embryonic ossification.     

A note on the sample serial autocorrelation function of stationary spike trains

The computation of the sample serial autocorrelation of a spike train is reasonable under the condition that the underlying process is stationary and linear. If these conditions are not fulfilled, the sample serial autocorrelation is random and any interpretation of it is erroneous: On the other hand, if the conditions are proved to hold, there is little need for the computation of the sample serial correlation, since in nearly all practical cases the stationarity is approximated by stationarity in the wide sense, which means that the deterministic autocorrelation of the process is already known.     

Stochastic approach to molecular interactions and computational theory of metabolic and genetic regulations

The underlying molecular mechanisms of metabolic and genetic regulations are computationally identical and can be described by a finite state Markov process. We establish a common computational model for both regulations based on the stationary distribution of the Markov process with the aim of establishing a unified, quantitative model of general biological regulations. Various existing results regarding intracellular regulations are derived including the classical Michaelis-Menten equation and its generalization to more complex allosteric enzymes in a systematic way. The notion of probability flow is introduced to distinguish the equilibrium stationary distribution from the non-equilibrium one; it plays a crucial role in the analysis of stationary state equations. A graphical criterion to guarantee the existence of an equilibrium stationary distribution is derived, which turns out to be identical to the classical Wegscheider condition. Simple graphical methods to compute the equilibrium and non-equilibrium stationary distributions are derived based crucially on the probability flow, which dramatically simplifies the classical methods still used in enzymology.     

Stick-and-diffuse and caged diffusion: a comparison of two models of synaptic vesicle dynamics

Two models were recently proposed to enable us to understand the dynamics of synaptic vesicles in hippocampal neurons. In the caged diffusion model, the vesicles diffuse in small circular cages located randomly in the bouton, while in the stick-and-diffuse model the vesicles bind and release from a cellular cytomatrix. In this article, we obtain analytic expressions for the fluorescence correlation spectroscopy (FCS) autocorrelation function for the two models and test their predictions against our earlier FCS measurements of the vesicle dynamics. We find that the stick-and-diffuse model agrees much better with the experiment. We find also that, due to the slow dynamics of the vesicles, the finite experimental integration time has an important effect on the FCS autocorrelation function and demonstrate its effect for the different models. The two models of the dynamics are also relevant to other cellular environments where mobile species undergo slow diffusionlike motion in restricted spaces or bind and release from a stationary substrate.     

Microtubules cut and run

There is broad agreement that cells reconfigure their microtubules through rapid bouts of assembly and disassembly, as described by the mechanism known as dynamic instability. However, many cell types have complex patterns of microtubule organization that are not entirely explicable by dynamic instability. There is growing evidence that microtubules can be moved into new patterns of organization by forces generated by molecular motor proteins. Studies on several cell types support a model called 'cut and run' in which long microtubules are stationary, but relatively short microtubules are mobile. In this model, cells mobilize their microtubules by severing them into short pieces, using enzymes such as katanin and spastin that break the lattice of the microtubule polymer. After being reorganized, the short microtubules can once again elongate and lose their mobility. Microtubule severing is also crucial for a variation of 'cut and run' in which the severed microtubules are reorganized by means of treadmilling.