Reduced models for binocular rivalry

Binocular rivalry occurs when two very different images are presented to the two eyes, but a subject perceives only one image at a given time. A number of computational models for binocular rivalry have been proposed; most can be categorised as either “rate” models, containing a small number of variables, or as more biophysically-realistic “spiking neuron” models. However, a principled derivation of a reduced model from a spiking model is lacking. We present two such derivations, one heuristic and a second using recently-developed data-mining techniques to extract a small number of “macroscopic” variables from the results of a spiking neuron model simulation. We also consider bifurcations that can occur as parameters are varied, and the role of noise in such systems. Our methods are applicable to a number of other models of interest.     

Reduced kinetic models of facilitative transport

In spite of the highly complex structural dynamics of globular proteins, the processes mediated by them can usually be described in terms of relatively simple kinetic diagrams. How do complex proteins, characterized by undergoing transitions among a possibly very large number of intermediate states, exhibit functional properties that can be interpreted in terms of kinetic diagrams consisting of only a small number of states? One possible way of explaining this apparent contradiction is that, under some conditions, a reduction of the actual complete kinetic diagram that describes all of the macromolecular states and transitions takes place. In this work, we contribute with a formal basis to this interpretation, by generalizing the procedure of diagram reduction to the case of multicyclic kinetic diagrams. As an example, we apply the procedure to a complex kinetic model of facilitative transport. We develop Monte Carlo simulations to obtain the kinetic parameters of the complex model and we compare them with the ones analytically obtained from the reduced model. We confirm that, under some conditions, the kinetic behavior of the complex transporter is indistinguishable from the one of a four-state simple carrier model, derived from the former by diagram reduction. Besides introducing some novel methodological aspects, this work further contributes to the idea that, under many physiological and experimental conditions, a reduction occurs of the complete kinetic diagram that describes the dynamics of a globular protein.     

Reduced kinetic models of neutral transport in the tokamak plasma

A method for constructing reduced models of neutrals transport for problems with a reduced dimension has been proposed on the basis of the kinetic equation. The case of a cylindrically symmetric plasma column, which is a good approximation for the tokamak geometry, has been thoroughly analyzed. For this geometry, the kinetic model of neutrals in the isotropic approximation is implemented using an algorithm based on energy grouping of neutrals; this algorithm for atomic hydrogen isotopes is integrated in the ASTRA code.     

Reduced models of networks of coupled enzymatic reactions

The Michaelis-Menten equation has played a central role in our understanding of biochemical processes. It has long been understood how this equation approximates the dynamics of irreversible enzymatic reactions. However, a similar approximation in the case of networks, where the product of one reaction can act as an enzyme in another, has not been fully developed. Here we rigorously derive such an approximation in a class of coupled enzymatic networks where the individual interactions are of Michaelis-Menten type. We show that the sufficient conditions for the validity of the total quasi-steady state assumption (tQSSA), obtained in a single protein case by Borghans, de Boer and Segel can be extended to sufficient conditions for the validity of the tQSSA in a large class of enzymatic networks. Secondly, we derive reduced equations that approximate the network's dynamics and involve only protein concentrations. This significantly reduces the number of equations necessary to model such systems. We prove the validity of this approximation using geometric singular perturbation theory and results about matrix differentiation. The ideas used in deriving the approximating equations are quite general, and can be used to systematize other model reductions.     

Invasion models of vegetation dynamics

Since communities change as a result of their successful invasion by new species it seems logical to attempt to predict future vegetation change by focussing on the invasion process. Several such invasion models are reviewed, and one particular model, based on dynamic game theory is developed further. This model can be used as an alternative to linear (e.g. Markov chain) models for the prediction of vegetation dynamics, and also to compare invasive abilities of species and resistance to invasion of communities. The main advantage of the model lies in the fact that it operates at a sufficiently high level of integration to allow for model calibration (in spite of the large number of underlying processes), and yet has an obvious population biological interpretation (in terms of the success of invading populations). The model can be calibrated using either time course data or experimental data, and it may be helpful in understanding what determines the fate of an invading population. It is used here to analyze two published vegetation dynamics data sets.This work was financially supported by operating grant A8115 from the Natural Sciences and Engineering Research Council of Canada.     

Structured models of metapopulation dynamics

I develop models of metapopulation dynamics that describe changes in the numbers of individuals within patches. These models are analogous to structured population models, with patches playing the role of individuals. Single species models which do not include the effect of immigration on local population dynamics of occupied patches typically lead to a unique equilibrium. The models can be used to study the distributions of numbers of individuals among patches, showing that both metapopulations with local outbreaks and metapopulations without outbreaks can occur in systems with no underlying environmental variability. Distributions of local population sizes (in occupied patches) can vary independently of the total population size, so both patterns of distributions of local population sizes are compatible with either rare or common species. Models which include the effect of immigration on local population dynamics can lead to two positive equilibria, one stable and one unstable, the latter representing a threshold between regional extinction and persistence.     

Stochastic models of neuronal dynamics

Cortical activity is the product of interactions among neuronal populations. Macroscopic electrophysiological phenomena are generated by these interactions. In principle, the mechanisms of these interactions afford constraints on biologically plausible models of electrophysiological responses. In other words, the macroscopic features of cortical activity can be modelled in terms of the microscopic behaviour of neurons. An evoked response potential (ERP) is the mean electrical potential measured from an electrode on the scalp, in response to some event. The purpose of this paper is to outline a population density approach to modelling ERPs.We propose a biologically plausible model of neuronal activity that enables the estimation of physiologically meaningful parameters from electrophysiological data. The model encompasses four basic characteristics of neuronal activity and organization: (i) neurons are dynamic units, (ii) driven by stochastic forces, (iii) organized into populations with similar biophysical properties and response characteristics and (iv) multiple populations interact to form functional networks. This leads to a formulation of population dynamics in terms of the Fokker-Planck equation. The solution of this equation is the temporal evolution of a probability density over state-space, representing the distribution of an ensemble of trajectories. Each trajectory corresponds to the changing state of a neuron. Measurements can be modelled by taking expectations over this density, e.g. mean membrane potential, firing rate or energy consumption per neuron. The key motivation behind our approach is that ERPs represent an average response over many neurons. This means it is sufficient to model the probability density over neurons, because this implicitly models their average state. Although the dynamics of each neuron can be highly stochastic, the dynamics of the density is not. This means we can use Bayesian inference and estimation tools that have already been established for deterministic systems. The potential importance of modelling density dynamics (as opposed to more conventional neural mass models) is that they include interactions among the moments of neuronal states (e.g. the mean depolarization may depend on the variance of synaptic currents through nonlinear mechanisms).Here, we formulate a population model, based on biologically informed model-neurons with spike-rate adaptation and synaptic dynamics. Neuronal sub-populations are coupled to form an observation model, with the aim of estimating and making inferences about coupling among sub-populations using real data. We approximate the time-dependent solution of the system using a bi-orthogonal set and first-order perturbation expansion. For didactic purposes, the model is developed first in the context of deterministic input, and then extended to include stochastic effects. The approach is demonstrated using synthetic data, where model parameters are identified using a Bayesian estimation scheme we have described previously.     

Spatial models of virus-immune dynamics

To date, the majority of theoretical models describing the dynamics of infectious diseases in vivo are based on the assumption of well-mixed virus and cell populations. Because many infections take place in solid tissues, spatially structured models represent an important step forward in understanding what happens when the assumption of well-mixed populations is relaxed. Here, we explore models of virus and virus-immune dynamics where dispersal of virus and immune effector cells was constrained to occur locally. The stability properties of our spatial virus-immune dynamics models remained robust under almost all biologically plausible dispersal schemes, regardless of their complexity. The various spatial dynamics were compared to the basic non-spatial dynamics and important differences were identified: When space was assumed to be homogeneous, the dynamics generated by non-spatial and spatially structured models differed substantially at the peak of the infection. Thus, non-spatial models may lead to systematic errors in the estimates of parameters underlying acute infection dynamics. When space was assumed to be heterogeneous, spatial coupling not only changed the equilibrium properties of the uncoupled populations but also equalized the dynamics and thereby reduced the likelihood of dynamic elimination of the infection. In line with experimental and clinical observations, long-lasting oscillation periods were virtually absent. When source-sink dynamics were considered, the long-term outcome of the infection depended critically on the degree of spatial coupling. The infection collapsed when emigration from source sites became too large. Finally, we discuss the implications of spatially structured models on medical treatment of infectious diseases, and note that a huge gap exists in data accurately describing infection dynamics in solid tissues.     

Protein dynamics under light control

A stochastic view of allostery is providing quantitative estimates of the energy made available through protein photoswitches.     

Live cell division dynamics monitoring in 3D large spheroid tumor models using light sheet microscopy

Background

Multicellular tumor spheroids are models of increasing interest for cancer and cell biology studies. They allow considering cellular interactions in exploring cell cycle and cell division mechanisms. However, 3D imaging of cell division in living spheroids is technically challenging and has never been reported.

Results

Here, we report a major breakthrough based on the engineering of multicellular tumor spheroids expressing an histone H2B fluorescent nuclear reporter protein, and specifically designed sample holders to monitor live cell division dynamics in 3D large spheroids using an home-made selective-plane illumination microscope.

Conclusions

As illustrated using the antimitotic drug, paclitaxel, this technological advance paves the way for studies of the dynamics of cell divion processes in 3D and more generally for the investigation of tumor cell population biology in integrated system as the spheroid model.     

HIV感染动力学模型概述

自1981年美国首次发现艾滋病以来,艾滋病在世界范围内广泛传播,引起医学专家、生物学家、数学家和物理学家等的极大关注。近年来,HIV动力学模型成为HIV治疗领域的研究热点。HIV基本动力学模型的研究有助于实现对未来疾病发展状况的描述与预测,HIV感染控制模型的研究有助于改善HIV病毒患者的治疗方案,对控制模型的优化有利于发现对HIV患者的有效治疗策略。本文概述了几种基本的HIV感染动力学模型,分析比较了它们的性能差异和各自存在的优缺点,介绍了HIV控制模型及其优化控制模型的计算机Matlab/simulink模拟。     

On stochastic models of light absorption

Previously developed light absorption models have treated the effective quantity of light-absorbing material within the experimental environment as a constant, i.e. a parameter. These models are, however, probabilistic in nature and are properly applied and interpreted only in a statistical sense. Thus, it is clearly logical to regard the effective quantity of light-absorbing material to be a random variable. In this paper an asymptotic distribution is derived for this random quantity, and it is shown how this distribution may be incorporated into present models. These results may be applied to light absorption by plant and crop canopies as well as to liquid or solid media. Furthermore, previous models are based upon the assumption that light is parallel, or effectively so, as for solar light. Such models may be inadequate for an artificial (laboratory) environment which utilizes point source light. Present models for estimating light interception and radiation intensity are modified so as to accommodate a proximate point source of light. Numerical examples are included to illustrate the theory.     

Considering nuclear compartmentalization in the light of nuclear dynamics

Many proteins are concentrated in compartments within the nucleus. Chromatin is also compartmentalized at different nuclear sites. However, nuclear proteins have now been shown to be highly mobile. This review considers the formation and function of nuclear compartments in a situation in which proteins are rapidly moving through the nuclear volume.     

Inferring models of gene expression dynamics

We study the problem of identifying genetic networks in which expression dynamics are modeled by a differential equation that uses logical rules to specify time derivatives. We make three main contributions. First, we describe computationally efficient procedures for identifying the structure and dynamics of such networks from expression time series. Second, we derive predictions for the expected amount of data needed to identify randomly generated networks. Third, if expression values are available for only some of the genes, we show that the structure of the network for these "visible" genes can be identified and that the size and overall complexity of the network can be estimated. We validate these procedures and predictions using simulation experiments based on randomly generated networks with up to 30,000 genes and 17 distinct regulators per gene and on a network that models floral morphogenesis in Arabidopsis thaliana.     

Learning generative models of molecular dynamics

We introduce three algorithms for learning generative models of molecular structures from molecular dynamics simulations. The first algorithm learns a Bayesian-optimal undirected probabilistic model over user-specified covariates (e.g., fluctuations, distances, angles, etc). L1 regularization is used to ensure sparse models and thus reduce the risk of over-fitting the data. The topology of the resulting model reveals important couplings between different parts of the protein, thus aiding in the analysis of molecular motions. The generative nature of the model makes it well-suited to making predictions about the global effects of local structural changes (e.g., the binding of an allosteric regulator). Additionally, the model can be used to sample new conformations. The second algorithm learns a time-varying graphical model where the topology and parameters change smoothly along the trajectory, revealing the conformational sub-states. The last algorithm learns a Markov Chain over undirected graphical models which can be used to study and simulate kinetics. We demonstrate our algorithms on multiple molecular dynamics trajectories.     

Comparing internal models of the dynamics of the visual environment

It is well known that the human postural control system responds to motion of the visual scene, but the implicit assumptions it makes about the visual environment and what quantities, if any, it estimates about the visual environment are unknown. This study compares the behavior of four models of the human postural control system to experimental data. Three include internal models that estimate the state of the visual environment, implicitly assuming its dynamics to be that of a linear stochastic process (respectively, a random walk, a general first-order process, and a general second-order process). In each case, all of the coefficients that describe the process are estimated by an adaptive scheme based on maximum likelihood. The fourth model does not estimate the state of the visual environment. It adjusts sensory weights to minimize the mean square of the control signal without making any specific assumptions about the dynamic properties of the environmental motion.We find that both having an internal model of the visual environment and its type make a significant difference in how the postural system responds to motion of the visual scene. Notably, the second-order process model outperforms the human postural system in its response to sinusoidal stimulation. Specifically, the second-order process model can correctly identify the frequency of the stimulus and completely compensate so that the motion of the visual scene has no effect on sway. In this case the postural control system extracts the same information from the visual modality as it does when the visual scene is stationary. The fourth model that does not simulate the motion of the visual environment is the only one that reproduces the experimentally observed result that, across different frequencies of sinusoidal stimulation, the gain with respect to the stimulus drops as the amplitude of the stimulus increases but the phase remains roughly constant. Our results suggest that the human postural control system does not estimate the state of the visual environment to respond to sinusoidal stimuli.