Modeling different regimes of bioelectrical activity in the brain in normal subjects and in "increased readiness" in a network of neuron-like elements

Desynchronous (low voltage fast activity), synchronous (high voltage slow waves) as well as convulsive brain activities were stimulated by a computer model of neuronal population. Network excitatory and inhibitory elements possessed fundamental dynamic properties of real neurones. Being independent both of the excitability of elements and of external influence efficacy, synchronous (desynchronous) network activity resulted from the increase (decrease) of the average power of "neuronal" interconnections which imitated mutual and recurrent excitation and inhibition. The inhibition efficacy being reduced as compared with excitation, synchronization of elements became intensified. As a consequence, the rhythmic activity amplitude increased and the appearance of self-sustained oscillations simulating convulsive activity was facilitated. The probable mechanism of EEG activation by virtue of the reduction of mutual and recurrent excitation and inhibition efficacy as well as the significance of inhibitory mechanism deficiency for epileptogenesis are discussed.     

Calculation of parameters of neuronal network model on the basis of analysis of power spectra of rat brain biopotentials

On the basis of neuronal network a linearized model of power spectrum of the network stable activity was calculated with the approximation of external input by "white" noise. The power spectrum function obtained was used for approximation of the power spectra of the rats motor cortex potentials by the least squares method. As a result the network parameters modelling excitatory and inhibitory cellular and synaptic mechanisms were calculated for two rat strains differing in seizure readiness. As a result of calculations genetically predisposed to seizures KM rats were assumed to differ from unpredisposed to seizures Wistar rats in the increase of efficacy of neuronal interactions (excitatory and inhibitory) as a consequence of the enhanced neuronal "reactivity".     

Simulation and Parameter Estimation Study of a Simple Neuronal Model of Rhythm Generation: Role of NMDA and Non-NMDA Receptors

Simple neural network models of the Xenopus embryo swimming CPG, based on the one originally developed by Roberts and Tunstall (1990), were used to investigate the role of the voltage-dependent N-methyl-D-aspartate (NMDA) receptor channels, in conjunction with faster non-NMDA components of synaptic excitation, in rhythm generation. The voltage-dependent NMDA current "follows" the membrane potential, leading to a postinhibitory rebound that is more efficient than one without voltage dependency and allows neurons to fire more than one action potential per cycle. Furthermore, the model demonstrated limited rhythmic activity in the absence of synaptic inhibition, supporting the hypothesis that the NMDA channels provide a basic mechanism for rhythmicity. However, the rhythmic properties induced by the NMDA current were observed only when there was moderate activation of the non-NMDA synaptic channels, suggesting a modulatory role for this component. The simulations also show that the voltage dependency of the NMDA conductance, as well as the fast non-NMDA current, stabilizes the alternation pattern versus synchrony. To verify that these effects and their implications on the mechanism of swimming and transition to other types of activity take place in the real preparation, constraints on parameter values have to be specified. A method to estimate synaptic parameters was tested with generated data. It is shown that a global analysis, based on multiple iterations of the optimization process (Foster et al., 1993), gives a better understanding of the parameter subspace describing network activity than a standard fit with a sensitivity analysis for an individual solution.     

Predictive power of "a minima" models in biology

Many apparently complex mechanisms in biology, especially in embryology and molecular biology, can be explained easily by reasoning at the level of the "efficient cause" of the observed phenomenology: the mechanism can then be explained by a simple geometrical argument or a variational principle, leading to the solution of an optimization problem, for example, via the co-existence of a minimization and a maximization problem (a min-max principle). Passing from a microscopic (or cellular) level (optimal min-max solution of the simple mechanistic system) to the macroscopic level often involves an averaging effect (linked to the repetition of a large number of such microscopic systems with possible random choice of the parameters of each of them) that gives birth to a global functional feature (e.g. at the tissue level). We will illustrate these general principles by building in four different domains of application "a minima" models and showing the main properties of their solutions: (1) extraction of a minimal RNA structure functioning as the first "peptidic machine," a kind of ancestral ribosome; (2) study of a genetic regulatory network of Drosophila centred on Engrailed gene and expressing successively two genes inside a limit cycle; (3) study of a genetic network regulating neural activity and proliferation in mammals; and (4) study of a simple geometric model of epiboly in zebrafish.     

Voltage-dependent behavior of a "ball-and-chain" gramicidin channel.

The channel-forming properties of two analogs of gramicidin, gramicidin-ethylenediamine (gram-EDA), and gramicidin-N,N-dimethylethylenediamine (gram-DMEDA) were studied in planar lipid bilayers, using protons as the permeant ion. These peptides have positively charged amino groups tethered to their C-terminal ends via a linker containing a carbamate group. Gram-DMEDA has two extra methyl groups attached to the terminal amino group, making it a bulkier derivative. The carbamate groups undergo thermal cis-trans isomerization on the 10-100-ms time scale. The conductance behavior of gram-EDA is found to be markedly voltage dependent, whereas the behavior of gram-DMEDA is not. In addition, voltage affects the cis-trans ratios of the carbamate groups of gram-EDA, but not those of gram-DMEDA. A model is proposed to account for these observations, in which voltage can promote the binding of the terminal amino group of gram-EDA to the pore in a "ball-and-chain" fashion. The bulkiness of the gram-DMEDA derivative prevents this binding.     

A study of the "outward potassium channel" (OPC) in the frog oocyte. I. A study of the "cell-attached" configuration

A single channel current was studied in the membrane of the immature oocyte of the european frog (Rana esculenta) by using the "patch clamp" technique in the "cell attached" configuration. Single channel activity appeared as short outward currents when membrane potential was made positive inside; full activation required seconds to be complete, no inactivation being appreciable. Deactivation (or current block) upon membrane repolarization was so fast that no inward current could be detected in any case. The reversal potential, estimated by interpolating the I/V diagrams, was -30 mV using standard Ringer as electrode filling solution, and the elementary conductance was 95 pS. Neither reversal potential nor elementary conductance were affected by removal of external Ca2+ (Mg2+ or Ba2+ substitution) or external Cl- (methanesulphonate substitution). The reversal potential moved towards positive potentials by substituting external Na+ with K+, the magnitude of the shifts being consistent with a ratio PK/PNa = 6.4. A distinctive property of the current/voltage relation for this K-current is its anomalous bell-shape, the outward current displaying a maximum at membrane potentials around 75 mV with standard Ringer as electrode filling solution and tending to zero with more positive potentials.     

Computer simulation for studying calcium dependent abnormalities in firing mechanism of molluscan neurones

Computer modelling technique is proposed to assist in physiological research on invertebrate neuronal membranes. The firing mechanism of a single patch of invertebrate neuronal membrane has been studied in dependence on maximum Ca++ conductance. The calculations are based on modification of Hodgkin-Huxley's data completed by a straight line approximation between experimental points of the kinetic parameters of Ca++ current and early transient potassium current. The time course of conductance changes is assumed to be proportional to m2h for Ca++ current. Three distinct potassium currents are involved into the model, viz. transient potassium current, delayed potassium current and Ca++-dependent potassium current. The modified Euler method run on a digital computer has been used for numerical integration of kinetic equations. Significant effects of Ca++ conductance on spike broadening, plateau development and spike afterhyperpolarization are represented. In the range of small Ca++ conductance an infinite spontaneous activity can be triggered by a short (suprathreshold) current pulse which may be considered a model of pacemaker activity. Plateau development resulting from potassium blocking or decreasing potassium equilibrium is facilitated by Ca++ conductance in the range of greater Ca++ conductance. The effects of voltage sensitivity of the coupling coefficient describing the current of Ca++-dependent K+ channels were studied and compared to the voltage independent case. The coupling coefficient seems to be a crucial factor in broadening the range of Ca++ conductance responsible for pacemaker activity. For greater values of Ca++ conductance, a decrease of the coupling coefficient leads to a transition from prolonged bursting to interruption of burst activity by burst-afterhyperpolarization. The blocking effect of 4-aminopyridine on fast outward current has been studied by the model which has a practical significance considering that aminopyridine is known as a convulsive agent. We suppose that it is reasonable to study the convulsive effects of aminopyridine by the model based on the kinetics of the isolated neuronal membrane. The model may help in understanding the ionic background underlying abnormal network activity during epileptic discharges of mammalian neurones.     

Dynamics of spontaneous activity in random networks with multiple neuron subtypes and synaptic noise

During slow-wave sleep, brain electrical activity is dominated by the slow (< 1 Hz) electroencephalogram (EEG) oscillations characterized by the periodic transitions between active (or Up) and silent (or Down) states in the membrane voltage of the cortical and thalamic neurons. Sleep slow oscillation is believed to play critical role in consolidation of recent memories. Past computational studies, based on the Hodgkin-Huxley type neuronal models, revealed possible intracellular and network mechanisms of the neuronal activity during sleep, however, they failed to explore the large-scale cortical network dynamics depending on collective behavior in the large populations of neurons. In this new study, we developed a novel class of reduced discrete time spiking neuron models for large-scale network simulations of wake and sleep dynamics. In addition to the spiking mechanism, the new model implemented nonlinearities capturing effects of the leak current, the Ca²⁺ dependent K⁺ current and the persistent Na⁺ current that were found to be critical for transitions between Up and Down states of the slow oscillation. We applied the new model to study large-scale two-dimensional cortical network activity during slow-wave sleep. Our study explained traveling wave dynamics and characteristic synchronization properties of transitions between Up and Down states of the slow oscillation as observed in vivo in recordings from cats. We further predict a critical role of synaptic noise and slow adaptive currents for spike sequence replay as found during sleep related memory consolidation.     

A versatile ODE approximation to a network model for the spread of sexually transmitted diseases

 We develop a moment closure approximation (MCA) to a network model of sexually transmitted disease (STD) spread through a steady/casual partnership network. MCA has been used previously to approximate static, regular lattices, whereas application to dynamic, irregular networks is a new endeavour, and application to sociologically-motivated network models has not been attempted. Our goals are 1) to investigate issues relating to the application of moment closure approximations to dynamic and irregular networks, and 2) to understand the impact of concurrent casual partnerships on STD transmission through a population of predominantly steady monogamous partnerships. We are able to derive a moment closure approximation for a dynamic irregular network representing sexual partnership dynamics, however, we are forced to use a triple approximation due to the large error of the standard pair approximation. This example underscores the importance of doing error analysis for moment closure approximations. We also find that a small number of casual partnerships drastically increases the prevalence and rate of spread of the epidemic. Finally, although the approximation is derived for a specific network model, we can recover approximations to a broad range of network models simply by varying model parameters which control the structure of the dynamic network. Thus our moment closure approximation is very flexible in the kinds of network models it can approximate. Received: 26 August 2001 / Revised version: 15 March 2002 / Published online: 23 August 2002 C.T.B. was supported by the NSF. Key words or phrases: Moment closure approximation – Network model – Pair approximation – Sexually transmitted diseases – Steady/casual partnership network     

LsrR quorum sensing "switch" is revealed by a bottom-up approach

Quorum sensing (QS) enables bacterial multicellularity and selective advantage for communicating populations. While genetic "switching" phenomena are a common feature, their mechanistic underpinnings have remained elusive. The interplay between circuit components and their regulation are intertwined and embedded. Observable phenotypes are complex and context dependent. We employed a combination of experimental work and mathematical models to decipher network connectivity and signal transduction in the autoinducer-2 (AI-2) quorum sensing system of E. coli. Negative and positive feedback mechanisms were examined by separating the network architecture into sub-networks. A new unreported negative feedback interaction was hypothesized and tested via a simple mathematical model. Also, the importance of the LsrR regulator and its determinant role in the E. coli QS "switch", normally masked by interfering regulatory loops, were revealed. Our simple model allowed mechanistic understanding of the interplay among regulatory sub-structures and their contributions to the overall native functioning network. This "bottom up" approach in understanding gene regulation will serve to unravel complex QS network architectures and lead to the directed coordination of emergent behaviors.     

Oscillatory network with self-organized dynamical connections for synchronization-based image segmentation

An oscillatory network of columnar architecture located in 3D spatial lattice was recently designed by the authors as oscillatory model of the brain visual cortex. Single network oscillator is a relaxational neural oscillator with internal dynamics tunable by visual image characteristics - local brightness and elementary bar orientation. It is able to demonstrate either activity state (stable undamped oscillations) or "silence" (quickly damped oscillations). Self-organized nonlocal dynamical connections of oscillators depend on oscillator activity levels and orientations of cortical receptive fields. Network performance consists in transfer into a state of clusterized synchronization. At current stage grey-level image segmentation tasks are carried out by 2D oscillatory network, obtained as a limit version of the source model. Due to supplemented network coupling strength control the 2D reduced network provides synchronization-based image segmentation. New results on segmentation of brightness and texture images presented in the paper demonstrate accurate network performance and informative visualization of segmentation results, inherent in the model.     

Reproducibility of swallow-induced cortical BOLD positive and negative fMRI activity

Functional MRI (fMRI) studies have demonstrated that a number of brain regions (cingulate, insula, prefrontal, and sensory/motor cortices) display blood oxygen level-dependent (BOLD) positive activity during swallow. Negative BOLD activations and reproducibility of these activations have not been systematically studied. The aim of our study was to investigate the reproducibility of swallow-related cortical positive and negative BOLD activity across different fMRI sessions. We studied 16 healthy volunteers utilizing an fMRI event-related analysis. Individual analysis using a general linear model was used to remove undesirable signal changes correlated with motion, white matter, and cerebrospinal fluid. The group analysis used a mixed-effects multilevel model to identify active cortical regions. The volume and magnitude of a BOLD signal within each cluster was compared between the two study sessions. All subjects showed significant clustered BOLD activity within the known areas of cortical swallowing network across both sessions. The cross-correlation coefficient of percent fMRI signal change and the number of activated voxels across both positive and negative BOLD networks were similar between the two studies (r ≥ 0.87, P < 0.0001). Swallow-associated negative BOLD activity was comparable to the well-defined "default-mode" network, and positive BOLD activity had noticeable overlap with the previously described "task-positive" network. Swallow activates two parallel cortical networks. These include a positive and a negative BOLD network, respectively, correlated and anticorrelated with swallow stimulus. Group cortical activity maps, as well as extent and amplitude of activity induced by volitional swallowing in the cortical swallowing network, are reproducible between study sessions.     

Topology selection by chaotic neurons of a pyloric central pattern generator

The pyloric Central Pattern Generator (CPG) in the lobster has an architecture in which every neuron receives at least one connection from another member of the CPG. We call this a "non-open" network topology. An "open" topology, where at least one neuron does not receive synapses from any other CPG member, is found neither in the pyloric nor in the gastric mill CPG. Here we investigate a possible reason for this topological structure using the ability to perform a biologically functional task as a measure of the efficacy of the network. When the CPG is composed of model neurons that exhibit regular membrane voltage oscillations, open topologies are as able to maximize this functionality as non-open topologies. When we replace these models by neurons which exhibit chaotic membrane voltage oscillations, the functional criterion selects non-open topologies. As isolated neurons from invertebrate CPGs are known in some cases to undergo chaotic oscillations, this suggests that there is a biological basis for the class of non-open network topologies that we observe.     

Reverse engineering gene regulatory networks from measurement with missing values

Background

Gene expression time series data are usually in the form of high-dimensional arrays. Unfortunately, the data may sometimes contain missing values: for either the expression values of some genes at some time points or the entire expression values of a single time point or some sets of consecutive time points. This significantly affects the performance of many algorithms for gene expression analysis that take as an input, the complete matrix of gene expression measurement. For instance, previous works have shown that gene regulatory interactions can be estimated from the complete matrix of gene expression measurement. Yet, till date, few algorithms have been proposed for the inference of gene regulatory network from gene expression data with missing values.

Results

We describe a nonlinear dynamic stochastic model for the evolution of gene expression. The model captures the structural, dynamical, and the nonlinear natures of the underlying biomolecular systems. We present point-based Gaussian approximation (PBGA) filters for joint state and parameter estimation of the system with one-step or two-step missing measurements. The PBGA filters use Gaussian approximation and various quadrature rules, such as the unscented transform (UT), the third-degree cubature rule and the central difference rule for computing the related posteriors. The proposed algorithm is evaluated with satisfying results for synthetic networks, in silico networks released as a part of the DREAM project, and the real biological network, the in vivo reverse engineering and modeling assessment (IRMA) network of yeast Saccharomyces cerevisiae.

Conclusion

PBGA filters are proposed to elucidate the underlying gene regulatory network (GRN) from time series gene expression data that contain missing values. In our state-space model, we proposed a measurement model that incorporates the effect of the missing data points into the sequential algorithm. This approach produces a better inference of the model parameters and hence, more accurate prediction of the underlying GRN compared to when using the conventional Gaussian approximation (GA) filters ignoring the missing data points.

     

Electron microscopic-cytochemical study of the enzyme activity of energy metabolism in "dark" and "light" neurons of the rat cerebral cortex

The ultrastructural localization of succinate dehydrogenase (SDH) and lactate dehydrogenase (LDH) activity in "dark" and "light" neurons of the intact rat's frontal brain cortex has been studied. The enzymes' activity was detected with using potassium ferricyanide as artificial acceptor of electrons. In the "light" cells SDH activity is localized in the mitochondria and plasma membranes. LDH activity is localized in the mitochondria, plasma membranes and hyaloplasm. SDH and LDH activity was not found in the "dark" cells.     

A model of slow conduction in bullfrog atrial trabeculae.

The success or failure of the propagation of electrical activity in cardiac tissue is dependent on both cellular membrane characteristics and intercellular coupling properties. This paper considers a linear arrangement of individual bullfrog atrial cells that are resistively coupled end to end to form a cylindrical strand. The strand, in turn, is encased by an endothelial sheath that provides a restricted extracellular space and an ion diffusion barrier to the outer bathing medium. This encased strand serves as an idealized model of an atrial trabeculum. Excitable membrane characteristics of the atrial cell are specified in terms of a Hodgkin-Huxley type of model that is quantitatively based on single-microelectrode voltage clamp data from bullfrog atrial myocytes. This membrane model can simulate the behavior of normal cells as well as of ischemic cells that exhibit depressed electrophysiological behavior (e.g., decreased resting potential, upstroke velocity, peak height, and action potential duration). Depressed activity can be easily simulated with variation of a single model parameter, the gain of the Na+/K+ pump current (INaK). Intercellular coupling properties are specified in terms of a lumped resistive T-type network between adjacent cells. The atrial strand model provides a means for studying the theoretical aspects of slow conduction in a "hybrid" strand that consists of a central region of cells having abnormal membrane or coupling properties, flanked on either side by normal atrial cells. Both uniform and discontinuous conduction are simulated by means of appropriate changes in the coupling resistance between cells. In addition, by varying either the degree of depressed electrical activity or the intercalated disc resistance in the central zone of the strand, slow conduction or complete conduction block in that region is demonstrated. Since the cellular model used in this study is based on experimental data and closely mimics both the atrial action potential and the underlying membrane currents, it has the potential to (1) accurately represent the current and voltage wave-forms occurring in the region of intercalated discs and (2) provide detailed information regarding the mechanisms in intercellular current spread in the region of slow conduction.     

The threshold for radiation stochastic effects: arguments "pro" and "contra". Applied realization

This study represents the analysis of the data available in the literature and the author's findings concerning the issue of a shape of the dose stochastic effect curve in the range of low levels of radiation (LLR). The data obtained from radioepidemiological and experimental investigations are used. Also considered are the arguments "pro" and "contra" regarding approximation of these curves by means of a linear function (linear non-threshold conception) or as a quasi-plateau (threshold conception). The above analysis allows us to conclude that the threshold conception is more reliable than the non-threshold one from the standpoint of the analysis of postulate bases, theoretical paradigms, the mechanisms for radiobiological effects, epidemiological and experimental data. It is suggested that a separate radiogenic cancer risk estimation should be used in case of LLR and high level radiation instead of one overall estimation by means of the linear non-threshold model.     

Systematic mutational analysis of the active-site threonine of HIV-1 proteinase: rethinking the "fireman's grip" hypothesis

Aspartic proteinases share a conserved network of hydrogen bonds (termed "fireman's grip"), which involves the hydroxyl groups of two threonine residues in the active site Asp-Thr-Gly triplets (Thr26 in the case of human immunodeficiency virus type 1 (HIV-1) PR). In the case of retroviral proteinases (PRs), which are active as symmetrical homodimers, these interactions occur at the dimer interface. For a systematic analysis of the "fireman's grip," Thr26 of HIV-1 PR was changed to either Ser, Cys, or Ala. The variant enzymes were tested for cleavage of HIV-1 derived peptide and polyprotein substrates. PR(T26S) and PR(T26C) showed similar or slightly reduced activity compared to wild-type HIV-1 PR, indicating that the sulfhydryl group of cysteine can substitute for the hydroxyl of the conserved threonine in this position. PR(T26A), which lacks the "fireman's grip" interaction, was virtually inactive and was monomeric in solution at conditions where wild-type PR exhibited a monomer-dimer equilibrium. All three mutations had little effect when introduced into only one chain of a linked dimer of HIV-1 PR. In this case, even changing both Thr residues to Ala yielded residual activity suggesting that the "fireman's grip" is not essential for activity but contributes significantly to dimer formation. Taken together, these results indicate that the "fireman's grip" is crucial for stabilization of the retroviral PR dimer and for overall stability of the enzyme.     

The effects of herbal oxytocics on the isolated "stripped" myometrium model

Decoctions of Agapanthus africanus and Clivia miniata are used as oxytocic agents in South African traditional herbal medicine. Aqueous extracts of A. africanus and C. miniata leaves have been shown to possess similar uterotonic activities in the isolated whole uterus preparation. The uterus however, comprises a myometrial and an endometrial layer and the activity of both oxytocin and the prostaglandins differs in these layers. The aim of this study was to determine the uterotonic activity of the herbal remedies in an endometrium-free preparation (i.e. "stripped" myometrium) and, if active, whether this effect could be related to prostaglandin synthesis or to interaction with specific receptors. The effects of the herbal extracts were tested on the isolated "stripped" rat myometrium preparation. Both herbal extracts caused a direct contractile response by the isolated tissue. Pretreatment of the myometrium with either plant extract augmented the initial response to acetylcholine. Preincubation with atropine inhibited the response to cumulative dosage of Agapanthus extract but had no effect on the response to Clivia. Indomethacin administration did not affect the response of the myometrium to cumulative dosage of acetylcholine, oxytocin or Clivia extract but inhibited the response to Agapanthus extract. These results clearly indicate that the Agapanthus and Clivia herbal extracts exhibited uterotonic activity in this model. The study illustrates that the "stripped" myometrium model has successfully differentiated between the mechanisms of action of two herbal oxytocics compared to the whole uterus preparation where their uterotonic activity was thought to be similar.     

Using the Guttman scale to define and estimate measurement error in items over time: the case of cognitive decline and the meaning of "points lost"

We used a Guttman model to represent responses to test items over time as an approximation of what is often referred to as "points lost" in studies of cognitive decline or interventions. To capture this meaning of "point loss", over four successive assessments, we assumed that once an item is incorrect, it cannot be correct at a later visit. If the loss of a point represents actual decline, then failure of an item to fit the Guttman model over time can be considered measurement error. This representation and definition of measurement error also permits testing the hypotheses that measurement error is constant for items in a test, and that error is independent of "true score", which are two key consequences of the definition of "measurement error"--and thereby, reliability--under Classical Test Theory. We tested the hypotheses by fitting our model to, and comparing our results from, four consecutive annual evaluations in three groups of elderly persons: a) cognitively normal (NC, N?=?149); b) diagnosed with possible or probable AD (N?=?78); and c) cognitively normal initially and a later diagnosis of AD (converters, N?=?133). Of 16 items that converged, error-free measurement of "cognitive loss" was observed for 10 items in NC, eight in converters, and two in AD. We found that measurement error, as we defined it, was inconsistent over time and across cognitive functioning levels, violating the theory underlying reliability and other psychometric characteristics, and key regression assumptions.