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PubMed2006

Distinguishing the noise and attractor strength of coordinated limb movements using recurrence analysis.

The variability of coupled rhythmic limb movements is assumed to be a consequence of the strength of a movement's attractor dynamic and a constant stochastic noise process that continuously perturbs the movement system away from this dynamic. Recently, it has been suggested that the nonlinear technique of recurrence analysis can be used to index the effects of noise and attractor strength on movement variability. To test this, three experiments were conducted in which the attractor strength of bimanual wrist-pendulum movements (using coordination mode, movement frequency and detuning), as well as the magnitude of stochastic perturbations affecting the variability of these movements (using a temporally fluctuating visual metronome) was manipulated. The results of these experiments demonstrate that recurrence analysis can index parametric changes in the attractor strength of coupled rhythmic limb movements and the magnitude of metronome induced stochastic perturbations independently. The results of Experiments 1 and 2 also support the claim that differences between the variability of inphase and antiphase coordination, and between slow and fast movement frequencies are due to differences in attractor strength. In contrast to the standard assumption that the noise that characterizes interlimb coordination remains constant for different magnitudes of detuning (Delta omega) the results of Experiment 3 suggest that the magnitude of noise increases with increases in |Delta omega|.

Biomechanical Phenomena↗
PubMedDate not supplied

Feedback stabilization of fed-batch bioreactors: non-monotonic growth kinetics.

This paper deals with the design of a feedback controller for fed-batch microbial conversion processes that forces the substrate concentration C(S) to a desired setpoint, starting from an arbitrary (initial) substrate concentration when non-monotonic growth kinetics apply. This problem is representative for a lot of industrial fermentation processes, with the baker's yeast fermentation as a well-known example. It is assumed that the specific growth rate mu is function of the substrate concentration only. A first approach exploits the availability of on-line measurements of both the substrate and biomass concentration. A second approach is merely based on on-line measurements of the biomass concentration, which provide an estimate for the specific growth rate. After a reformulation of the substrate concentration setpoint into a specific growth rate setpoint, it is demonstrated that the fed-batch process can still be stabilized around any desired operating point along the non-monotonic kinetics.

Algorithms↗
PubMedDate not supplied

Visual discrimination and short-term memory for random patterns in patients with a focal cortical lesion.

Visual discrimination and short-term recognition memory for computer-generated random patterns were explored in 23 patients with a postsurgical lesion in one of the cortical hemispheres. Their results are compared with those of 23 age-matched volunteers. In a same-different forced-choice discrimination task, d' and log beta (measures of sensitivity and bias), as well as reaction time (RT) were determined. All participants viewed patterns defined either by luminance contrast or isoluminant red-green color contrast, the amplitude of which was adjusted to be 10 times the respective detection threshold level. Block patterns consisting of a 6 x 6 matrix of light and dark (red and green) checks were randomly configured on each presentation. They were presented in pairs, randomly in two visual quadrants for a duration of 200 msec. Three presentation conditions were used: simultaneous presentation of reference and test stimulus, sequential presentation with a short delay (interstimulus interval, ISI = 3 s), and sequential presentation with a long delay (ISI = 6 s). The results indicate that patients with a lesion in the occipitotemporal cortex, the superior temporal cortex and the frontal cortex were significantly impaired on both luminance-contrast and color-contrast pattern discrimination. Patients with damage in the anterior inferotemporal cortex showed no overall impairment. The results suggest that performance in visual discrimination and recognition memory tasks rely on distributed neural processes with more than one neocortical location.

Adult↗
PubMed1993

Coding of odor intensity.

A model for coding of odor intensity in the first two neuronal layers of olfactory systems is proposed. First, the occupation and activation by odorant molecules of receptor proteins of different types borne by the first order neurons are described as birth and death processes. The occupation (birth) rate depends on the concentration of the odorant, whereas the probability of activation of an occupied receptor depends on the type of the odorant. Second, the spike generation mechanism proposed for the first order neuron depends on the level of the generator potential evoked by the activated receptors and on a time-decaying threshold which is reset to infinity after each spike. The various resulting stochastic regimes of firing activity at different concentrations are described. Third, each second order neuron is influenced by excitation coming from numerous first order neurons, lateral inhibition from other second order neurons, and self-inhibition. All these incoming signals are integrated at the second order neuron. The firing activity of the first and second order neurons is modeled by a first passage time scheme. For both types of neuron the shapes of the curves predicted by the model for the mean firing frequency as a function of stimulus concentration are shown to be in accordance with available experimental results.

Animals↗
PubMed1987

On the overdispersed molecular clock.

Rates of molecular evolution at some loci are more irregular than described by simple Poisson processes. Three situations under which molecular evolution would not follow simple Poisson processes are reevaluated from the viewpoint of the neutrality hypothesis: concomitant or multiple substitutions in a gene, fluctuating substitution rates in time caused by coupled effects of deleterious mutations and bottlenecks, and changes in the degree of selective constraints against a gene (neutral space) caused by successive substitutions. The common underlying assumption that these causes are lineage nonspecific excludes the case where mutation rates themselves change systematically among lineages or taxonomic groups, and severely limits the extent of variation in the number of substitutions among lineages. Even under this stringent condition, however, the third hypothesis, the fluctuating neutral space model, can generate fairly large variation. This is described by a time-dependent renewal process, which does not exhibit any episodic nature of molecular evolution. It is argued that the observed elevated variances in the number of nucleotide or amino acid substitutions do not immediately call for positive Darwinian selection in molecular evolution.

Animals↗
PubMed2004

Random drift and culture change.

We show that the frequency distributions of cultural variants, in three different real-world examples--first names, archaeological pottery and applications for technology patents--follow power laws that can be explained by a simple model of random drift. We conclude that cultural and economic choices often reflect a decision process that is value-neutral; this result has far-reaching testable implications for social-science research.

Computer Simulation↗
PubMedDate not supplied

Mammalian genes as molecular clocks?

In analyzing the silent nucleotide substitutions in some mammalian mitochondrial mRNA coding genes, we had found that the frequency of each of the four nucleotides in rat, mouse, and cow, but not in humans, is the same in the silent third codon position (Lanave C, Preparata G, Saccone C, Serio G (1984) J Mol Evol 20:86-93). Because our findings for these three species were compatible with a stationary Markov process for the evolution of nucleotide sequences, we applied such a model to calculate the effective evolutionary silent substitution rate (vs) and the divergence times among the species. In this paper we have analyzed the first and second codon positions in the same mammalian mitochondrial genes. We found that in the first and second codon positions the human mitochondrial genes satisfy the stationarity conditions. This has allowed us to use the stochastic model mentioned above to calculate the divergence times among mouse, rat, cow, and human. Furthermore, we have analyzed the silent substitution rate in one nuclear gene for these four mammals. We found that in this gene the effective silent substitution rate is about 3 times lower than in mitochondrial genes, and that humans are in this case stationary with respect to the other three mammals in the third codon position as well. Application of our Markov model to this latter gene yields divergence times consistent with our previous determinations.

Animals↗
PubMed2006

How lifetimes shape epigenotype within and across generations.

Despite our detailed characterization of the human genome at the level of the primary DNA sequence, we are still far from understanding the molecular events underlying phenotypic variation. Epigenetic modifications to the DNA sequence and associated chromatin are known to regulate gene expression and, as such, are a significant contributor to phenotype. Studies of inbred mice and monozygotic twins show that variation in the epigenotype can be seen even between genetically identical individuals and that this, in some cases at least, is associated with phenotypic differences. Moreover, recent evidence suggests that the epigenome can be influenced by the environment and these changes can last a lifetime. However, we also know that epigenetic states in real-time are in continual flux and, as a result, the epigenome exhibits instability both within and across generations. We still do not understand the rules governing the establishment and maintenance of the epigenotype at any particular locus. The underlying DNA sequence itself and the sequence at unlinked loci (modifier loci) are certainly involved. Recent support for the existence of transgenerational epigenetic inheritance in mammals suggests that the epigenetic state of the locus in the previous generation may also play a role. Over the next decade, many of these processes will be better understood, heralding a greater capacity for us to correlate measurable molecular marks with phenotype and providing the opportunity for improved diagnosis and presymptomatic healthcare.

Animals↗
PubMed2001

Unexpected coherence and conservation.

The effects of migration in a network of patch populations, or metapopulation, are extremely important for predicting the possibility of extinctions both at a local and a global scale. Migration between patches synchronizes local populations and bestows upon them identical dynamics (coherent or synchronous oscillations), a feature that is understood to enhance the risk of global extinctions. This is one of the central theoretical arguments in the literature associated with conservation ecology. Here, rather than restricting ourselves to the study of coherent oscillations, we examine other types of synchronization phenomena that we consider to be equally important. Intermittent and out-of-phase synchronization are but two examples that force us to reinterpret some classical results of the metapopulation theory. In addition, we discuss how asynchronous processes (for example, random timing of dispersal) can paradoxically generate metapopulation synchronization, another non-intuitive result that cannot easily be explained by the standard theory.

Animal Migration↗
PubMed2004

Role of clustering and gridlike ordering in epidemic spreading.

The spreading of an epidemic is determined by the connectivity patterns which underlie the population. While it has been noted that a virus spreads more easily on a network in which global distances are small, it remains a great challenge to find approaches that unravel the precise role of local interconnectedness. Such topological properties enter very naturally in the framework of our two-time-step description, also providing an approach to track a probabilistic system. The method is elaborated for SIS-type epidemic processes, leading to a quantitative interpretation of the role of loops up to length 4 in the onset of an epidemic.

Cluster Analysis↗
PubMed2001

Pattern recognition in a compartmental model of a CA1 pyramidal neuron.

Computer simulation of a CA1 hippocampal pyramidal neuron is used to estimate the effects of synaptic and spatio-temporal noise on such a cell's ability to accurately calculate the weighted sum of its inputs, presented in the form of transient patterns of activity. Comparison is made between the pattern recognition capability of the cell in the presence of this noise and that of a noise-free computing unit in an artificial neural network model of a heteroassociative memory. Spatio-temporal noise due to the spatial distribution of synaptic input and quantal variance at each synapse degrade the accuracy of signal integration and consequently reduce pattern recognition performance in the cell. It is shown here that a certain degree of asynchrony in action potential arrival at different synapses, however, can improve signal integration. Signal amplification by voltage-dependent conductances in the dendrites, provided by synaptic NMDA receptors, and sodium and calcium ion channels, also improves integration and pattern recognition. While the biological sources of noise are significant when few patterns are stored in the associative memory of which the cell is a part, when large numbers of patterns are stored the noise from the other stored patterns comes to dominate the pattern recognition process. In this situation, the pattern recognition performance of the pyramidal cell is within a factor of two of that of the computing unit in the artificial neural network model.

Action Potentials↗
PubMed2005

Lifesaving explains mortality decline with time.

Mortality rates of human populations in developed countries are declining with time. We show that this effect can be explained via a 'lifesaving' methodology. Our approach is based on considering a non-homogeneous Poisson process of potentially harmful events. Each of these events can be 'cured' with a given probability or can result in a termination of the Poisson process (death) with a complementary probability. A lifesaving ratio, defining the corresponding relative increase in life expectancy for homogeneous and heterogeneous populations is analyzed. Some generalizations are discussed. Several simple examples are considered.

Humans↗
PubMed2002

Grouped-neural network modeling for model predictive control.

A group of feed-forward neural networks (NNs), each providing the prediction of an individual process output at a future step, is used as the dynamic prediction model for the model-based predictive control (MPC) scheme in the proposed work. These NNs are parallel (independent) rather than cascaded--they are trained and implemented in parallel. Therefore, the complexity and effort in the training stage is decreased and compounded error propagation is eliminated from the prediction. A new strategy of compensating for the process-model mismatch under this grouped-NN model structure is also developed. Effectiveness of the scheme as a general nonlinear MPC is demonstrated by simulation results.

Algorithms↗
PubMed2006

Discrete stimulus estimation from neural responses in the turtle retina.

In this paper, we investigate the decoding of flashed, full-field visual stimuli while recording from a population of retinal ganglion cells. We present a direct statistical method for determining the likelihood that a response was evoked by a particular stimulus, and use this method to estimate stimuli based on microelectrode array recordings in the turtle retina. This method uses the well-known time-varying Poisson model of neural firing, along with extensions to accommodate neural refractory periods. Unlike other approaches commonly used for Poisson processes, the specific formulation presented here is bin free and requires few user-specified parameters. Statistical dependency issues and the effects of stationarity on the estimation method are also discussed.

Action Potentials↗
PubMed2005

Coarse-grained model of proteins incorporating atomistic detail of the active site.

We present a novel approach to explore the conformational space of globular proteins near their native state. It combines the advantages of coarse-grained models with those of all-atoms simulations, required to treat molecular recognition processes. The comparison between calculated structural properties with those obtained with all-atoms molecular dynamics simulations establishes the accuracy of the model. Our method has the potential to be extended to molecular recognition processes in systems whose characteristic size and time scale prevent an analysis based on all-atoms molecular dynamics.

Amyloid Precursor Protein Secretases↗
PubMed2003

Intercellular communication via intracellular calcium oscillations.

In this letter, we present the results of a simple model for intercellular communication via calcium oscillations, motivated in part by a recent experimental study. The model describes two cells (a "donor" and "sensor") whose intracellular dynamics involve a calcium-induced, calcium release process. The cells are coupled by assuming that the input of the sensor cell is proportional to the output of the donor cell. As one varies the frequency of calcium oscillations of the donor cell, the sensor cell passes through a sequence of N : M phase-locked regimes and exhibits a "Devil's staircase" behavior. Such a phase-locked response has been seen experimentally in pulsatile stimulation of single cells. We also study a stochastic version of the coupled two-cell model. We find that phase locking holds for realistic choices for the cell volume.

Animals↗
PubMed2003

Development of a biologically-based controlled growth and differentiation model for developmental toxicology.

Amathematical model is developed with a highly controlled birth and death process for precursor cells. This model is both biologically- and statistically-based. The controlled growth and differentiation (CGD) model limits the number of replications allowed in the development of a tissue or organ and thus, more closely reflects the presence of a true stem cell population. Leroux et al. (1996) presented a biologically-based dose-response model for developmental toxicology that was derived from a partial differential equation for the generating function. This formulation limits further expansion into more realistic models of mammalian development. The same formulae for the probability of a defect (a system of ordinary differential equations) can be derived through the Kolmogorov forward equations due to the nature of this Markov process. This modified approach is easily amenable to the expansion of more complicated models of the developmental process such as the one presented here. Comparisons between the Leroux et al. (1996) model and the controlled growth and differentiation (CGD) model as developed in this paper are also discussed.

Animals↗
PubMed2001

Is there chaos in the brain? I. Concepts of nonlinear dynamics and methods of investigation.

In the light of results obtained during the last two decades in a number of laboratories, it appears that some of the tools of nonlinear dynamics, first developed and improved for the physical sciences and engineering, are well-suited for studies of biological phenomena. In particular it has become clear that the different regimes of activities undergone by nerve cells, neural assemblies and behavioural patterns, the linkage between them, and their modifications over time, cannot be fully understood in the context of even integrative physiology, without using these new techniques. This report, which is the first of two related papers, is aimed at introducing the non expert to the fundamental aspects of nonlinear dynamics, the most spectacular aspect of which is chaos theory. After a general history and definition of chaos the principles of analysis of time series in phase space and the general properties of chaotic trajectories will be described as will be the classical measures which allow a process to be classified as chaotic in ideal systems and models. We will then proceed to show how these methods need to be adapted for handling experimental time series; the dangers and pitfalls faced when dealing with non stationary and often noisy data will be stressed, and specific criteria for suspecting determinism in neuronal cells and/or assemblies will be described. We will finally address two fundamental questions, namely i) whether and how can one distinguish, deterministic patterns from stochastic ones, and, ii) what is the advantage of chaos over randomness: we will explain why and how the former can be controlled whereas, notoriously, the latter cannot be tamed. In the second paper of the series, results obtained at the level of single cells and their membrane conductances in real neuronal networks and in the study of higher brain functions, will be critically reviewed. It will be shown that the tools of nonlinear dynamics can be irreplaceable for revealing hidden mechanisms subserving, for example, neuronal synchronization and periodic oscillations. The benefits for the brain of adopting chaotic regimes with their wide range of potential behaviours and their aptitude to quickly react to changing conditions will also be considered.

Animals↗