Stationary states and transients in neural populations

The dynamics of populations of neurons are studied analytically and by computer simulation. The nets are probabilistic but may be coupled into systems of interacting populations in accordance with the netlet approach, first described by Harth et al., 1970a, Harth et al., 1970b. The analysis is here extended to include the situation in which the neuronal activity is given by finite difference equations of order two or greater. It is shown that the formalism developed here can take into account any combination of refractory periods, summation times and effective delays that may exist in a net. Stationary states are represented as the results of an eigenvalue problem. For slowly varying excitatory or inhibitory inputs these states exhibit marked hysteresis effects. Transient behavior is investigated and found to consist generally of damped oscillations about the stationary states.     

Stationary gene frequency distribution in the environment fluctuating between two distinct states

Summary A general method is given to obtain a stationary distribution in a stochastic one-dimensional dynamical system in which an environmental parameter specifying the dynamical system is a stationary Markov process with only two states. By applying this method, the exact stationary gene frequency distribution is obtained for a genic selection model in the environment fluctuating between two distinct states. Several limiting stationary distributions are obtained therefrom, and one of them is shown to coincide with a stationary solution of the diffusion equation heuristically derived by us for more general cases. Discussion is given on the relationship between the diffusion equations obtained by various authors starting from discrete, non-overlapping generation models.     

An evolutionary model of low mood states

It has been suggested that low mood in humans is an adaptive response to unfavourable circumstances, and that the anhedonia, pessimism and fatigue that often accompany it function to minimise risk until circumstances improve. While this is plausible, it would be possible to make the opposite prediction equally plausibly: individuals in bad circumstances should take greater risks in order to improve their situations. Here, I present a simple analytical model adapted from the risk-sensitive foraging literature. It shows that in dire states, individuals should be risk-prone, in poor states, risk-averse, and in good states, risk-prone again. I discuss how the various kinds of mood state observed in humans might be understood as mechanisms for adaptively adjusting behavioural risk-taking to the current situation.     

About a three states molecular evolution model

The Eigen model of molecular evolution has recently been reconsidered by taking into account the existence of non-reproducing sequences. New results obtained with this model are presented here: several time-scales characterize the population dynamics and the location of the error threshold, shifted towards larger values of the probability of mutation, depends on both the size of the population and time. Thus this model can be used to analyse extinction events. The distribution of individuals in sequence space beyond the threshold is also discussed.     

Using thermal stress to model aspects of disease states

Exposure to acute heat or cold stress elicits numerous physiological responses aimed at maintaining body temperatures. Interestingly, many of the physiological responses, mediated by the cardiovascular and autonomic nervous systems, resemble aspects of, or responses to, certain disease states. The purpose of this Perspective is to highlight some of these areas in order to explore how they may help us better understand the pathophysiology underlying aspects of certain disease states. The benefits of using this human thermal stress approach are that (1) no adjustments for inherent comparative differences in animals are needed, (2) non-medicated healthy humans with no underlying co-morbidities can be studied in place of complex patients, and (3) more mechanistic perturbations can be safely employed without endangering potentially vulnerable populations. Cold stress can be used to induce stable elevations in blood pressure. Cold stress may also be used to model conditions where increases in myocardial oxygen demand are not met by anticipated increases in coronary blood flow, as occurs in older adults. Lower-body negative pressure has the capacity to model aspects of shock, and the further addition of heat stress improves and expands this model because passive-heat exposure lowers systemic vascular resistance at a time when central blood volume and left-ventricular filling pressure are reduced. Heat stress can model aspects of heat syncope and orthostatic intolerance as heat stress decreases cerebral blood flow and alters the Frank–Starling mechanism resulting in larger decreases in stroke volume for a given change in left-ventricular filling pressure. Combined, thermal perturbations may provide in vivo paradigms that can be employed to gain insights into pathophysiological aspects of certain disease states.     

A simple vaccination model with multiple endemic states

A simple two-dimensional SIS model with vaccination exhibits a backward bifurcation for some parameter values. A two-population version of the model leads to the consideration of vaccination policies in paired border towns. The results of our mathematical analysis indicate that a vaccination campaign φ meant to reduce a disease's reproduction number R(φ) below one may fail to control the disease. If the aim is to prevent an epidemic outbreak, a large initial number of infective persons can cause a high endemicity level to arise rather suddenly even if the vaccine-reduced reproduction number is below threshold. If the aim is to eradicate an already established disease, bringing the vaccine-reduced reproduction number below one may not be sufficient to do so. The complete bifurcation analysis of the model in terms of the vaccine-reduced reproduction number is given, and some extensions are considered.     

Describing behavioral states using a system model of the primate brain.

A system model of the primate neocortex is presented, based mainly on the neuroanatomy of the rhesus macaque monkey and consisting of a set of processing modules arranged as a perception-action hierarchy. These modules correspond to regions of the neocortex and their connectivity to that of the neocortex. A computational approach based on predicate logic is explained, and the results of a computer implementation of the model are reported, which demonstrate social behaviors involving affiliation and social conflict. The behavioral states of primates involved in these behaviors can be represented by the states of the system model, which have a logical representation and a diagrammatic form. It is shown how the behavioral states in goal-directed behaviors can be represented and also their short term moment-to-moment development in time. It is then shown how the state of social interaction among two or more primates can be represented, using their individual behavioral states, with interindividual action and perception. The causal dynamics of behavioral states is explained and also a control mechanism, namely, the use of confirmation signals, which stabilizes behavioral states and their dynamics. Stabilized behavioral states are seen as corresponding to coherent activations of the system, resulting from successful selection of module activations and intermodule communication with confirmation.     

Explicit-duration hidden Markov model inference of UP-DOWN states from continuous signals

Neocortical neurons show UP-DOWN state (UDS) oscillations under a variety of conditions. These UDS have been extensively studied because of the insight they can yield into the functioning of cortical networks, and their proposed role in putative memory formation. A key element in these studies is determining the precise duration and timing of the UDS. These states are typically determined from the membrane potential of one or a small number of cells, which is often not sufficient to reliably estimate the state of an ensemble of neocortical neurons. The local field potential (LFP) provides an attractive method for determining the state of a patch of cortex with high spatio-temporal resolution; however current methods for inferring UDS from LFP signals lack the robustness and flexibility to be applicable when UDS properties may vary substantially within and across experiments. Here we present an explicit-duration hidden Markov model (EDHMM) framework that is sufficiently general to allow statistically principled inference of UDS from different types of signals (membrane potential, LFP, EEG), combinations of signals (e.g., multichannel LFP recordings) and signal features over long recordings where substantial non-stationarities are present. Using cortical LFPs recorded from urethane-anesthetized mice, we demonstrate that the proposed method allows robust inference of UDS. To illustrate the flexibility of the algorithm we show that it performs well on EEG recordings as well. We then validate these results using simultaneous recordings of the LFP and membrane potential (MP) of nearby cortical neurons, showing that our method offers significant improvements over standard methods. These results could be useful for determining functional connectivity of different brain regions, as well as understanding network dynamics.     

Thermal aggregation of a model allosteric protein in different conformational states

Protein aggregation is of crucial importance in a wide variety of situations. High temperatures, combined with other denaturing conditions, have been used very extensively to decipher some of the fundamentals related to formation of amorphous and fibrillar protein aggregates. The present study reports on the dependency of thermal aggregation of bovine liver glutamate dehydrogenase (GDH), a well-characterized allosteric enzyme, on its conformational state. The initial phases of thermal aggregation of this protein was followed in the presence of a number of well-known allosteric ligands. Positive effectors were found to decrease the rate and extent of aggregation in a concentration dependent manner, while negative effectors did the reverse. ADP, one of the most characterized GDH activators was found to stabilize a specific protein conformation resulting in loss of propensity to aggregate. The importance of this observation related to control of protein–protein interactions leading to protein aggregation is discussed.     

Transfer RNA docking pair model in the ribosomal pre- and post-translocational states.

A consensus has been reached that the conformation of the anticodon-codon interactions of two adjacent tRNA molecules on the ribosome is a Sundaralingam-type (S-type). Even if it is kept to the S-type, there are still various possibilities. Various experimental data have been supporting an idea that the conformation of A-site tRNA is different from that of P-site tRNA. Those data as well as the recent result of Brimacombe and co-workers that U20:1 of lupin tRNAmMetbound to the A-site was cross-linked to a region, 875-905, of 23S rRNA in combination with the other recent findings of Nierhaus and co-workers about the spin-contrast method of neutron diffraction of the ribosome and the better accessible nucleotide patterns of phosphorothioated tRNAs on the ribosome have led to a new tRNA docking pair model, in which the highly conserved G18 and G19 of D-loop in A-site tRNA and C56 and C61 of TpsiC-loop in P-site tRNA base pair along with the conventional base pairs of adjacent codon-anticodon interactions. This A-P tRNA pair model can be translocated to the P-E tRNA pair model without changing the conformation except the ACCA termini, keeping the position of the growing nascent polypeptide chain.     

Stationary phase in yeast

Eukaryotic cell proliferation is controlled by specific growth factors and the availability of essential nutrients. If either of these signals is lacking, cells may enter into a specialized nondividing resting state, known as stationary phase or G(0). The entry into such resting states is typically accompanied by a dramatic decrease in the overall growth rate and an increased resistance to a variety of environmental stresses. Since most cells spend most of their life in these quiescent states, it is important that we develop a full understanding of the biology of the stationary phase/G(0) cell. This knowledge would provide important insights into the control of two of the most fundamental aspects of eukaryotic cell biology: cell proliferation and long-term cell survival. This review will discuss some recent advances in our understanding of the stationary phase of growth in the budding yeast, Saccharomyces cerevisiae.     

An atomic model of the thin filament in the relaxed and Ca2+-activated states

Contraction of striated muscles is regulated by tropomyosin strands that run continuously along actin-containing thin filaments. Tropomyosin blocks myosin-binding sites on actin in resting muscle and unblocks them during Ca2+-activation. This steric effect controls myosin-crossbridge cycling on actin that drives contraction. Troponin, bound to the thin filaments, couples Ca2+-concentration changes to the movement of tropomyosin. Ca2+-free troponin is thought to trap tropomyosin in the myosin-blocking position, while this constraint is released after Ca2+-binding. Although the location and movements of tropomyosin are well known, the structural organization of troponin on thin filaments is not. Its mechanism of action therefore remains uncertain. To determine the organization of troponin on the thin filament, we have constructed atomic models of low and high-Ca2+ states based on crystal structures of actin, tropomyosin and the "core domain" of troponin, and constrained by distances between filament components and by their location in electron microscopy (EM) reconstructions. Alternative models were also built where troponin was systematically repositioned or reoriented on actin. The accuracy of the different models was evaluated by determining how well they corresponded to EM images. While the initial low and high-Ca2+ models fitted the data precisely, the alternatives did not, suggesting that the starting models best represented the correct structures. Thin filament reconstructions were generated from the EM data using these starting models as references. In addition to showing the core domain of troponin, the reconstructions showed additional detail not present in the starting models. We attribute this to an extension of TnI linking the troponin core domain to actin at low (but not at high) Ca2+, thereby trapping tropomyosin in the OFF-state. The bulk of the core domain of troponin appears not to move significantly on actin, regardless of Ca2+ level. Our observations suggest a simple model for muscle regulation in which troponin affects the charge balance on actin and hence tropomyosin position.     

Molecular tectonic model of virus structural transitions: the putative cell entry states of poliovirus

Upon interacting with its receptor, poliovirus undergoes conformational changes that are implicated in cell entry, including the externalization of the viral protein VP4 and the N terminus of VP1. We have determined the structures of native virions and of two putative cell entry intermediates, the 135S and 80S particles, at approximately 22-A resolution by cryo-electron microscopy. The 135S and 80S particles are both approximately 4% larger than the virion. Pseudoatomic models were constructed by adjusting the beta-barrel domains of the three capsid proteins VP1, VP2, and VP3 from their known positions in the virion to fit the 135S and 80S reconstructions. Domain movements of up to 9 A were detected, analogous to the shifting of tectonic plates. These movements create gaps between adjacent subunits. The gaps at the sites where VP1, VP2, and VP3 subunits meet are plausible candidates for the emergence of VP4 and the N terminus of VP1. The implications of these observations are discussed for models in which the externalized components form a transmembrane pore through which viral RNA enters the infected cell.