Dynamic properties of cortical evoked (10 Hz) oscillations: theory and experiment

Experiments probed the dynamic properties of stimulus-evoked (10 Hz) oscillations in somatosensory cortex of anesthetized rats. Experimental paradigms and statistical time series analysis were based on theoretical ideas from a dynamic approach to temporal patterns of neuronal activity. From the results of a double-stimulus paradigm we conclude that the neuronal response contains two components with different dynamics and different coupling to the stimulus. Based on this result a quantitative dynamic model is derived, making use of normal form theory for bifurcating vector fields. The variables used are abstract, but measurable, dynamic components. The model parameters capture the dynamic properties of neuronal response and are related to experimental results. A structural interpretation of the model can be given in terms of the collective dynamics of neuronal groups, their mutual interaction, and their coupling to peripheral stimuli. The model predicts the stimulusdependent lifetime of the oscillations as observed in experiment. We show that this prediction relies on the basic concept of dynamic bistability and does not depend on the modeling details.     

Nonparametric estimation of stage occupation probabilities in a multistage model with current status data

Multistage models are used to describe individuals (or experimental units) moving through a succession of "stages" corresponding to distinct states (e.g., healthy, diseased, diseased with complications, dead). The resulting data can be considered to be a form of multivariate survival data containing information about the transition times and the stages occupied. Traditional survival analysis is the simplest example of a multistage model, where individuals begin in an initial stage (say, alive) and move irreversibly to a second stage (death). In this article, we consider general multistage models with a directed tree structure (progressive models) in which individuals traverse through stages in a possibly non-Markovian manner. We construct nonparametric estimators of stage occupation probabilities and marginal cumulative transition hazards. Empirical calculations of these quantities are not possible due to the lack of complete data. We consider current status information which represents a more severe form of censoring than the commonly used right censoring. Asymptotic validity of our estimators can be justified using consistency results for nonparametric regression estimators. Finite-sample behavior of our estimators is studied by simulation, in which we show that our estimators based on these limited data compare well with those based on complete data. We also apply our method to a real-life data set arising from a cardiovascular diseases study in Taiwan.     

Parametric models of ontogenetic diversities

Modeling of morphogenesis demonstrates that they form rather wide regions of structural stability and narrow zones of instability in parametric space. Within instability zones, small parameter shifts lead to drastic changes in the morphology of buds. These particular zones are the sources of ontogenetic diversities and represent the reserve for evolutionary variation. A topical problem is to construct models based on universal schemes of negative feedbacks between dynamic components of ontogenesis; moreover, the specificity of ontogenesis should be determined by the values of genetic and epigenetic parameters.     

Consideration of a priori information and type of an experimental error using the method of system identification based on the minimal quadratic discrepancy criterion

The variants of the identification method were considered that take the a priori information about the evolution of a system under study and the type of experimental errors of the dynamic parameters of the system into account. An example of using this method for the identification of a biochemical reaction is given where the error in measuring the dynamic parameters (concentration of substances) has both an absolute and a relative components.     

Dynamic health policies for controlling the spread of emerging infections: influenza as an example

The recent appearance and spread of novel infectious pathogens provide motivation for using models as tools to guide public health decision-making. Here we describe a modeling approach for developing dynamic health policies that allow for adaptive decision-making as new data become available during an epidemic. In contrast to static health policies which have generally been selected by comparing the performance of a limited number of pre-determined sequences of interventions within simulation or mathematical models, dynamic health policies produce "real-time" recommendations for the choice of the best current intervention based on the observable state of the epidemic. Using cumulative real-time data for disease spread coupled with current information about resource availability, these policies provide recommendations for interventions that optimally utilize available resources to preserve the overall health of the population. We illustrate the design and implementation of a dynamic health policy for the control of a novel strain of influenza, where we assume that two types of intervention may be available during the epidemic: (1) vaccines and antiviral drugs, and (2) transmission reducing measures, such as social distancing or mask use, that may be turned "on" or "off" repeatedly during the course of epidemic. In this example, the optimal dynamic health policy maximizes the overall population's health during the epidemic by specifying at any point of time, based on observable conditions, (1) the number of individuals to vaccinate if vaccines are available, and (2) whether the transmission-reducing intervention should be either employed or removed.     

On the comparison of Feller and Ornstein-Uhlenbeck models for neural activity

 Diffusion processes have been extensively used to describe membrane potential behavior. In this approach the interspike interval has a theoretical counterpart in the first-passage-time of the diffusion model employed. Since the mathematical complexity of the first-passage-time problem increases with attempts to make the models more realistic it seems useful to compare the features of different models in order to highlight their relative performance. In this paper we compare the Feller and Ornstein–Uhlenbeck models under three different criteria derived from the level of information available about their parameters. We conclude that the Feller model is preferable when complete knowledge of the characterizing parameters is assumed. On the other hand, when only limited information about the parameters is available, such as the mean firing time and the histogram shape, no advantage arises from using this more complex model. Received: 8 November 1994/Accepted in revised form : 23 May 1995     

Gustatory processing is dynamic and distributed

The process of gustatory coding consists of neural responses that provide information about the quantity and quality of food, its generalized sensation, its hedonic value, and whether it should be swallowed. Many of the models presently used to analyze gustatory signals are static in that they use the average neural firing rate as a measure of activity and are unimodal in the sense they are thought to only involve chemosensory information. We have recently elaborated upon a dynamic model of gustatory coding that involves interactions between neurons in single as well as in spatially separate, gustatory and somatosensory regions. We propose that the specifics of gustatory responses grow not only out of information ascending from taste receptor cells, but also from the cycling of information around a massively interconnected system.     

Toward a new approach in tumor cell heterogeneity studies using the concept of order

A new methodology was developed to study dynamic processes topographically in biological systems by means of a graph-theoretical method. It is based upon order parameters obtained from a minimal spanning tree analysis coupled with computer simulations. The method was used to analyse the heterogeneous behavior of two neoplastic cell lines after treatment with laminin. The laminin-induced cell detachment was quantitated and shown to be inversely related to cell population density and thus to cellular interactions. Our statistical analysis is a very powerful tool to obtain information from seemingly disorderly heterogeneous biological models.     

Task and content modulate amygdala-hippocampal connectivity in emotional retrieval

The ability to remember emotional events is crucial for adapting to biologically and socially significant situations. Little is known, however, about the nature of the neural interactions supporting the integration of mnemonic and emotional information. Using fMRI and dynamic models of effective connectivity, we examined regional neural activity and specific interactions between brain regions during a contextual memory retrieval task. We independently manipulated emotional context and relevance of retrieved emotional information to task demands. We show that retrieval of emotionally valenced contextual information is associated with enhanced connectivity from hippocampus to amygdala, structures crucially involved with encoding of emotional events. When retrieval of emotional information is relevant to current behavior, amygdala-hippocampal connectivity increases bidirectionally, under modulatory influences from orbitofrontal cortex, a region implicated in representation of affective value and behavioral guidance. Our findings demonstrate that both memory content and behavioral context impact upon large scale neuronal dynamics underlying emotional retrieval.     

The time course of cellular responses to iontophoretically applied drugs.

Simple models of two-species ecosystems are usually analyzed in terms of the existence and stability of a static equilibrium state. We examine the way in which perturbations, in the form of periodic reductions in both species, lead to stable coexistence in a state of dynamic equilibrium. We establish general criteria for the occurrence of such dynamic equilibrium states. We show that coexistence in a dynamic equilibrium occurs for a fairly wide range of model parameters, and that dynamic equilibrium states are a rather robust feature of simple models.     

Joint modelling of repeated transitions in follow-up data--a case study on breast cancer data

In longitudinal studies where time to a final event is the ultimate outcome often information is available about intermediate events the individuals may experience during the observation period. Even though many extensions of the Cox proportional hazards model have been proposed to model such multivariate time-to-event data these approaches are still very rarely applied to real datasets. The aim of this paper is to illustrate the application of extended Cox models for multiple time-to-event data and to show their implementation in popular statistical software packages. We demonstrate a systematic way of jointly modelling similar or repeated transitions in follow-up data by analysing an event-history dataset consisting of 270 breast cancer patients, that were followed-up for different clinical events during treatment in metastatic disease. First, we show how this methodology can also be applied to non Markovian stochastic processes by representing these processes as "conditional" Markov processes. Secondly, we compare the application of different Cox-related approaches to the breast cancer data by varying their key model components (i.e. analysis time scale, risk set and baseline hazard function). Our study showed that extended Cox models are a powerful tool for analysing complex event history datasets since the approach can address many dynamic data features such as multiple time scales, dynamic risk sets, time-varying covariates, transition by covariate interactions, autoregressive dependence or intra-subject correlation.     

Accounting for Errors in Data Improves Divergence Time Estimates in Single-cell Cancer Evolution

Single-cell sequencing provides a new way to explore the evolutionary history of cells. Compared to traditional bulk sequencing, where a population of heterogeneous cells is pooled to form a single observation, single-cell sequencing isolates and amplifies genetic material from individual cells, thereby preserving the information about the origin of the sequences. However, single-cell data are more error-prone than bulk sequencing data due to the limited genomic material available per cell. Here, we present error and mutation models for evolutionary inference of single-cell data within a mature and extensible Bayesian framework, BEAST2. Our framework enables integration with biologically informative models such as relaxed molecular clocks and population dynamic models. Our simulations show that modeling errors increase the accuracy of relative divergence times and substitution parameters. We reconstruct the phylogenetic history of a colorectal cancer patient and a healthy patient from single-cell DNA sequencing data. We find that the estimated times of terminal splitting events are shifted forward in time compared to models which ignore errors. We observed that not accounting for errors can overestimate the phylogenetic diversity in single-cell DNA sequencing data. We estimate that 30–50% of the apparent diversity can be attributed to error. Our work enables a full Bayesian approach capable of accounting for errors in the data within the integrative Bayesian software framework BEAST2.     

Bayesian Finite Markov Mixture Model for Temporal Multi‐Tissue Polygenic Patterns

Finite mixture models can provide the insights about behavioral patterns as a source of heterogeneity of the various dynamics of time course gene expression data by reducing the high dimensionality and making clear the major components of the underlying structure of the data in terms of the unobservable latent variables. The latent structure of the dynamic transition process of gene expression changes over time can be represented by Markov processes. This paper addresses key problems in the analysis of large gene expression data sets that describe systemic temporal response cascades and dynamic changes to therapeutic doses in multiple tissues, such as liver, skeletal muscle, and kidney from the same animals. Bayesian Finite Markov Mixture Model with a Dirichlet Prior is developed for the identifications of differentially expressed time related genes and dynamic clusters. Deviance information criterion is applied to determine the number of components for model comparisons and selections. The proposed Bayesian models are applied to multiple tissue polygenetic temporal gene expression data and compared to a Bayesian model‐based clustering method, named CAGED. Results show that our proposed Bayesian Finite Markov Mixture model can well capture the dynamic changes and patterns for irregular complex temporal data (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimized grid-based protein-protein docking as a global search tool followed by incorporating experimentally derivable restraints

Unbound protein docking, or the computational prediction of the structure of a protein complex from the structures of its separated components, is of importance but still challenging. A practical approach toward reliable results for unbound docking is to incorporate experimentally derived information with computation. To this end, truly systematic search of the global docking space is desirable. The fast Fourier transform (FFT) docking is a systematic search method with high computational efficiency. However, by using FFT to perform unbound docking, possible conformational changes upon binding must be treated implicitly. To better accommodate the implicit treatment of conformational flexibility, we develop a rational approach to optimize "softened" parameters for FFT docking. In connection with the increased "softness" of the parameters in this global search step, we use a revised rule to select candidate models from the search results. For complexes designated as of low and medium difficulty for unbound docking, these adaptations of the original FTDOCK program lead to substantial improvements of the global search results. Finally, we show that models resulted from FFT-based global search can be further filtered with restraints derivable from nuclear magnetic resonance (NMR) chemical shift perturbation or mutagenesis experiments, leading to a small set of models that can be feasibly refined and evaluated using computationally more expensive methods and that still include high-ranking near-native conformations.     

Postprocessing of genealogical trees

We consider inference for demographic models and parameters based upon postprocessing the output of an MCMC method that generates samples of genealogical trees (from the posterior distribution for a specific prior distribution of the genealogy). This approach has the advantage of taking account of the uncertainty in the inference for the tree when making inferences about the demographic model and can be computationally efficient in terms of reanalyzing data under a wide variety of models. We consider a (simulation-consistent) estimate of the likelihood for variable population size models, which uses importance sampling, and propose two new approximate likelihoods, one for migration models and one for continuous spatial models.     

水/乙醇混合溶剂中的阿奇霉素结晶动力学

利用粒数密度和粒度之间的关系判别晶体生长模型;采用间歇动态法,以粒数衡算方程、溶质质量守恒和McCabe定律为基础,利用Beer-Lambert定律,借助光学关联的方法,建立了包含透光率变量的伴有成核和晶体生长的动力学模型;通过在线测量溶液密度与透光率数据,采用非线性最小二乘法拟合得到了晶体成核和生长动力学经验方程,并以实时浓度为目标验证了动力学参数的准确性以及模型表达式的正确性。     

Parameter estimation and change-point detection from Dynamic Contrast Enhanced MRI data using stochastic differential equations

Dynamic Contrast Enhanced imaging (DCE-imaging) following a contrast agent bolus allows the extraction of information on tissue micro-vascularization. The dynamic signals obtained from DCE-imaging are modeled by pharmacokinetic compartmental models which integrate the Arterial Input Function. These models use ordinary differential equations (ODEs) to describe the exchanges between the arterial and capillary plasma and the extravascular-extracellular space. Their least squares fitting takes into account measurement noises but fails to deal with unpredictable fluctuations due to external/internal sources of variations (patients’ anxiety, time-varying parameters, measurement errors in the input function, etc.). Adding Brownian components to the ODEs leads to stochastic differential equations (SDEs). In DCE-imaging, SDEs are discretely observed with an additional measurement noise. We propose to estimate the parameters of these noisy SDEs by maximum likelihood, using the Kalman filter. In DCE-imaging, the contrast agent injected in vein arrives in plasma with an unknown time delay. The delay parameter induces a change-point in the drift of the SDE and ODE models, which is estimated also. Estimations based on the SDE and ODE pharmacokinetic models are compared to real DCE-MRI data. They show that the use of SDE provides robustness in the estimation results. A simulation study confirms these results.     

Information Flow in Networks and the Law of Diminishing Marginal Returns: Evidence from Modeling and Human Electroencephalographic Recordings

We analyze simple dynamical network models which describe the limited capacity of nodes to process the input information. For a proper range of their parameters, the information flow pattern in these models is characterized by exponential distribution of the incoming information and a fat-tailed distribution of the outgoing information, as a signature of the law of diminishing marginal returns. We apply this analysis to effective connectivity networks from human EEG signals, obtained by Granger Causality, which has recently been given an interpretation in the framework of information theory. From the distributions of the incoming versus the outgoing values of the information flow it is evident that the incoming information is exponentially distributed whilst the outgoing information shows a fat tail. This suggests that overall brain effective connectivity networks may also be considered in the light of the law of diminishing marginal returns. Interestingly, this pattern is reproduced locally but with a clear modulation: a topographic analysis has also been made considering the distribution of incoming and outgoing values at each electrode, suggesting a functional role for this phenomenon.     

A phylogenetic approach to the evolution of fish behaviour

Summary WHAT HAVE WE LEARNED?As I indicated in the introduction, this is a non-traditional review. I have not asked What generalizations can we draw about the evolution of fish behaviour based upon information gleaned from phylogenetically based studies? Instead, I have presented detailed discussions of those studies. The reason for this approach is quite simple: if all studies in such a wide area of investigation can be discussed at length in one relatively short paper, then the database is not large enough to warrant the move from information collection to information synthesis. The purpose of this review, then, has been to capture the enthusiasm of the phylogenetically orientated fish ethologists and to highlight their discoveries, in the hopes that this will stimulate further research. If successful, the next review of phylogeny and the evolution of fish behaviour will follow a more familiar pathway.Although the database does not allow us to draw generalizations about the evolution of specific behavioural characters in fishes, the studies to date have uncovered a number of more general evolutionary insights. First, phylogenetic conservatism is evident at all levels of analysis, from the muscle activity patterns that underlie behavioural characters (Lauder 1986; Westneat and Wainwright, 1989; Westneat 1991; Wainwright and Lauder, 1992) through foraging preferences (Winterbottom and McLennan, 1993) and egg deposition strategies (Johnston and Page, 1992) to parental care (Stiassney and Gerstner, 1992). This conservatism forms the backbone against which the appearance of novel behaviours (apomorphies) can be highlighted. Each species' behavioural repertoire is thus a unique combination of very old (plesiomorphic), relatively old (synapomorphic) and recently derived (autapomorphic) characters. Second, phylogenetic analysis has allowed us to investigate models of behavioural evolution that were constructed from a variety of microevolutionary fitness parameters. The macroevolutionary patterns have corroborated some parts of those models (transition from biparental to female-only care: Gross and Sargent, 1985; Stiassney and Gerstner, 1992; transition from fresh water to anadromy: Gross et al., 1988; Stearley, 1992) and highlighted other parts of the models that would benefit from a re-examination of the basic assumptions (transition from biparental or female-only to male-only care: Gross and Sargent, 1985; Stiassney and Gerstner, 1992). Third, expanding our evolutionary perspective to include clades of organisms has allowed researchers to formulate new theories of behavioural evolution incroporating information about the patterns of character origin and diversification as well as information about character maintenance (Ryan, 1900a; Ryan and Rand, 1990; Ryan et al., 1990a). And finally, examination of macroevolutionary correlations between the origin and diversification of behavioural characters has allowed us to make predictions about the forces influencing the evolution of those characters that can then be tested experimentally (McLennan et al., 1988; Basolo, 1990a,b, 1991; McLennan, 1991). The studies presented in this paper have spanned a wide theoretical arena. They have revealed a number of interesting insights about the evolution of behaviour, and in so doing, have demonstrated the hybrid vigour of a research programme based upon integrating phylogeny and experimental ethology, phylogeny and functional morphology, and phylogeny and behavioural ecology. The question to be answered now is:WHERE DO WE GO FROM HERE?If this fledgling research programme is to remain vigorous, we need to do two things. First, channels of communication must be re-opened between systematists and ethologists. Specifically, we need to encourage systematists to construct robust phylogenetic trees for groups of fish that either have already been well studied behaviourally and ecologically, or would be of interest to ethologists if a phylogeny existed (the belontiids, poeciliids, and rivulines come to mind, to name just a few). In the absence of such critical information, behavioural ecologists are faced with the option of investigating their ethological data based upon trees reconstructed from old classification schemes or phenograms, neither of which produces a robust phylogenetic hypothesis of genealogy. Researchers who have opted for this approach preface their investigations with the caveat that the analysis and conclusions are only preliminary because of the unsatisfactory nature of the phylogenetic hypotheses available to them. The importance of a preliminary analysis cannot be understimated for researchers who are frustrated by their inability to apply the phylogenetic approach to their burgeoning data sets. It is, however, critical to remember that a preliminary analysis can, at best, produce only tentative results. If the data themselves are both incomplete and ambiguous, this will compound the problems arising from the absence of a rigorous phylogenetic framework, which will produce a confusing picture of behavioural evolution. It is also important to realize that even the most robust phylogenetic tree is still only a hypothesis of genealogical relationships, a hypothesis that may change with the discovery of new data.Second, links must be forged between comparative ethology and behavioural ecology. All of the examples discussed in this paper uncovered a phylogenetic component in patterns of behavioural origin and diversification. The discovery of this phylogenetic influence, however, is only the first step in developing a comprehensive evolutionary picture because phylogenetic patterns can tell us very little about the processes underlying those patterns. In order to explore questions of process, we must incorporate information about the fitness parameters of behavioural characters into our evolutionary picture. For example, optimizing such parameters onto a phylogenetic tree may allow us to investigate whether there are any macroevolutionary correlations between the origin and divergence of a behaviour and a change in one (or more) of the fitness components. We must also incorporate information about the genetic, developmental and physiological control of behaviour into our comparative framework (Brooks and McLennan, 1991; Willis et al., 1991; Lauder et al., 1993). This is perhaps the most neglected aspect of comparative ethology and will thus be the most difficult to remedy. Details of the genetic and developmental systems underlying behaviour are known for only a handful of taxa and for only a handful of behaviours within those taxa. The physiological control of behaviour is better studied, but has yet to be placed within a phylogenetic context (but see e.g. Stearley, 1992, for an example of the insights that can be gained from such a study). The results of such a multilevel approach will be a more robust estimate of the relative roles for the effects of both phylogenetic heritage and environmental factors in the evolution of behaviour in fishes.