Sharing of Phosphatases Promotes Response Plasticity in Phosphorylation Cascades

Sharing of positive or negative regulators between multiple targets is frequently observed in cellular signaling cascades. For instance, phosphatase sharing between multiple kinases is ubiquitous within the MAPK pathway. Here we investigate how such phosphatase sharing could shape robustness and evolvability of the phosphorylation cascade. Through modeling and evolutionary simulations, we demonstrate that 1) phosphatase sharing dramatically increases robustness of a bistable MAPK response, and 2) phosphatase-sharing cascades evolve faster than nonsharing cascades. This faster evolution is particularly pronounced when evolving from a monostable toward a bistable phenotype, whereas the transition speed of a population from a bistable to monostable response is not affected by phosphatase sharing. This property may enable the phosphatase-sharing design to adapt better in a changing environment. Analysis of the respective mutational landscapes reveal that phosphatase sharing reduces the number of limiting mutations required for transition from monostable to bistable responses, hence facilitating a faster transition to such response types. Taken together, using MAPK cascade as an example, our study offers a general theoretical framework to explore robustness and evolutionary plasticity of signal transduction cascades.     

Some properties of randomly connected networks of neuron-like elements with refractory

Dynamic properties of randomly connected networks consisting of neuron-like elements with refractory are investigated from a macroscopic point of view. Equations describing the transition of the activity level of the network — a macroscopic state — are derived under some hypotheses on the stochastic properties of the network. The equations are characterized by a set of parameters which are determined by distributions of the threshold values of elements and the weighting values of connection between elements. It is shown that a network behaves like a monostable, bistable or astable circuit when its refractory period is less than one time unit and that a network is monostable or bistable when its refractory period is longer than two time units. An oscillatory network, on the other hand, is always realized if the network has a feedback mechanism which decreases the excitability of neurons when high activity level is sustained. Some results of computer simulation of randomly connected neuron networks are also presented.     

The Two-Photon Reversible Reaction of the Bistable Jumping Spider Rhodopsin-1

Bistable opsins are photopigments expressed in both invertebrates and vertebrates. These light-sensitive G-protein-coupled receptors undergo a reversible reaction upon illumination. A first photon initiates the cis to trans isomerization of the retinal chromophore—attached to the protein through a protonated Schiff base—and a series of transition states that eventually results in the formation of the thermally stable and active Meta state. Excitation by a second photon reverts this process to recover the original ground state. On the other hand, monostable opsins (e.g., bovine rhodopsin) lose their chromophore during the decay of the Meta II state (i.e., they bleach). Spectroscopic studies on the molecular details of the two-photon cycle in bistable opsins are limited. Here, we describe the successful expression and purification of recombinant rhodopsin-1 from the jumping spider Hasarius adansoni (JSR1). In its natural configuration, spectroscopic characterization of JSR1 is hampered by the similar absorption spectra in the visible spectrum of the inactive and active states. We solved this issue by separating their absorption spectra by replacing the endogenous 11-cis retinal chromophore with the blue-shifted 9-cis JSiR1. With this system, we used time-resolved ultraviolet-visible spectroscopy after pulsed laser excitation to obtain kinetic details of the rise and decay of the photocycle intermediates. We also used resonance Raman spectroscopy to elucidate structural changes of the retinal chromophore upon illumination. Our data clearly indicate that the protonated Schiff base is stable throughout the entire photoreaction. We additionally show that the accompanying conformational changes in the protein are different from those of monostable rhodopsin, as recorded by light-induced FTIR difference spectroscopy. Thus, we envisage JSR1 as becoming a model system for future studies on the reaction mechanisms of bistable opsins, e.g., by time-resolved x-ray crystallography.     

Self-organization effects induced by ion-conformational interaction in biomembrane channels

It is shown that phenomena of molecular self-organization can take place in biomembrane channels. A strong interaction between charged groups of channel-forming protein and ion flux passing through the channel causes bistable or steady limit cycle regimes. These regimes are possible only far from the equilibrium state when the ion flux exceeds a certain threshold value. A number of such synergetic models is reviewed. Each time, only the simplest (monostable) regime takes place near the zero value of the ion flux. Some experimental data may be explained by this approach.     

Design of the lac gene circuit revisited

The lactose (lac) operon of Escherichia coli serves as the paradigm for gene regulation, not only for bacteria, but also for all biological systems from simple phage to humans. The details of the systems may differ, but the key conceptual framework remains, and the original system continues to reveal deeper insights with continued experimental and theoretical study. Nearly as long lasting in impact as the pivotal work of Jacob and Monod is the classic experiment of Novick and Weiner in which they demonstrated all-or-none gene expression in response to an artificial inducer. These results are often cited in claims that normal gene expression is in fact a discontinuous bistable phenomenon. In this paper, I review several levels of analysis of the lac system and introduce another perspective based on the construction of the system design space. These represent variations on a theme, based on a simply stated design principle, that captures the key qualitative features of the system in a largely mechanism-independent fashion. Moreover, this principle can be readily interpreted in terms of specific mechanisms to make predictions regarding monostable vs. bistable behavior. The regions of design space representing bifurcations are compared with the corresponding regions identified through bifurcation analysis. I present evidence based on biological considerations as well as modeling and analysis to suggest that induction of the lac system in its natural setting is a monostable continuously graded phenomenon. Nevertheless, it must be acknowledged that the lac stability question remains unsettled, and it undoubtedly will remain so until there are definitive experimental results.     

Do variables that affect similar bistable apparent-movement displays result in similar changes in perception?

Two bistable apparent-movement displays (i.e. ones that generate two qualitatively different kinds of movement percepts under different conditions) were compared. They were designed to be as similar as possible spatially, and were studied with identical stimulus manipulations to see whether changes in balance between their bistable percepts would be similar. Results show that the two displays had different response characteristics to the same stimulus manipulations. Two models of motion perception that have previously predicted at least one kind of bistable apparent motion were considered in terms of how well they address the current data. As yet, neither model has been shown to predict the motion states and bistable behavior of the two displays studied here. It is concluded that results of the type described here (specifically, differences in the psychophysical functions yielded by two structurally similar but qualitatively different bistable displays) present a challenge for theories of motion perception.     

Some properties of transmission lines composed of random networks

This paper discusses some properties of a nerve-axon-like transmission line made up from random networks of threshold elements. A random network contains a large number of threshold elements of which the threshold values are Gaussian random variables, and it can act as a monostable or a bistable multivibrator. The signal wave propagation in a transmission line is analyzed by a statistical method. The results show that a signal wave can propagate along the line and that its waveform is shaped, during propagation, into a specific form peculiar to the line. A self-oscillatory system that consists of two random networks is also analyzed. Even in this simple system, various modes of oscillation can exist, with periods varying over a wide range according to the values of system parameters. Examples of self-oscillations obtained by a graphical method are presented, and also some results of computer experiments are shown.     

Study on dynamic characteristics’ change of hippocampal neuron reduced models caused by the Alzheimer’s disease

In the paper, based on the electrophysiological experimental data, the Hippocampal neuron reduced model under the pathology condition of Alzheimer’s disease (AD) has been built by modifying parameters’ values. The reduced neuron model’s dynamic characteristics under effect of AD are comparatively studied. Under direct current stimulation, compared with the normal neuron model, the AD neuron model’s dynamic characteristics have obviously been changed. The neuron model under the AD condition undergoes supercritical Andronov–Hopf bifurcation from the rest state to the continuous discharge state. It is different from the neuron model under the normal condition, which undergoes saddle-node bifurcation. So, the neuron model changes into a resonator with monostable state from an integrator with bistable state under AD’s action. The research reveals the neuron model’s dynamic characteristics’ changing under effect of AD, and provides some theoretic basis for AD research by neurodynamics theory.     

The coupled dynamics of human socio-economic choice and lake water system: the interaction of two sources of nonlinearity

We study a mathematical model for the coupled dynamics of human socio-economic choice and lake water system. In the model, many players choose one of the two options: a cooperative and costly option with low phosphorus discharge, and an economical option with high phosphorus discharge. The choice is affected by an economic cost, a social concern about water pollution, and a conformist tendency. The pollution level in the lake is determined by total phosphorus discharge by the players, the sedimentation and the outflow of phosphorus, and the recycling of phosphorus from the sediment. The model has two sources of nonlinearity: the cooperation level tends to be bistable due to conformist tendency of people (social hysteresis) and pollution level tends to be bistable because phosphorus recycling occurs faster in more eutrophic lakes (ecological hysteresis). The combination of these two sources may cause multiple stable equilibria or oscillations with a long periodicity. Small economic cost and strong social concern about pollution level can decrease the pollution level, but may not be very effective in enhancing the cooperation level. In contrast, strong conformist tendency produces a stable state with a high cooperation level and a low pollution level. We discuss implications of these results to the water quality management.     

Effects of the anesthetic agent propofol on neural populations

The neuronal mechanisms of general anesthesia are still poorly understood. Besides several characteristic features of anesthesia observed in experiments, a prominent effect is the bi-phasic change of power in the observed electroencephalogram (EEG), i.e. the initial increase and subsequent decrease of the EEG-power in several frequency bands while increasing the concentration of the anaesthetic agent. The present work aims to derive analytical conditions for this bi-phasic spectral behavior by the study of a neural population model. This model describes mathematically the effective membrane potential and involves excitatory and inhibitory synapses, excitatory and inhibitory cells, nonlocal spatial interactions and a finite axonal conduction speed. The work derives conditions for synaptic time constants based on experimental results and gives conditions on the resting state stability. Further the power spectrum of Local Field Potentials and EEG generated by the neural activity is derived analytically and allow for the detailed study of bi-spectral power changes. We find bi-phasic power changes both in monostable and bistable system regime, affirming the omnipresence of bi-spectral power changes in anesthesia. Further the work gives conditions for the strong increase of power in the δ-frequency band for large propofol concentrations as observed in experiments.     

Electrical bistability in a neuron model with monostable dendritic and axosomatic membranes

In a two-compartment mathematical model, we studied the reason for and conditions of manifestation of electrical bistability in a neuron composed of monostable parts. One compartment of the model simulated the dendrites; their membrane was monostable at high depolarization and characterized by an N-shaped steady current-voltage (I–V) characteristic endowed by inward synaptic current through voltage-dependent channels sensitive to N-methyl-D-aspartate (NMDA). Another compartment simulated the axosomatic region with a positively sloped linearizedI–V characteristic of the membrane monostable at the resting membrane potential. For the whole cell, bistability was obvious at a subcritical intensity of NMDA activation; the reason was the current directed from the more depolarized dendritic region into the somatic region, and the necessary condition was that the above somatopetal core current must exceed the net inward transmembrane current (the latter was the sum of the inward synaptic and outward passive extrasynaptic currents) of the dendritic compartment. This relation essentially depended on the size of the dendrites. Neirofiziologiya/Neurophysiology, Vol. 32, No. 2, pp. 98–101, March–April, 2000.     

A bistable Rb-E2F switch underlies the restriction point

The restriction point (R-point) marks the critical event when a mammalian cell commits to proliferation and becomes independent of growth stimulation. It is fundamental for normal differentiation and tissue homeostasis, and seems to be dysregulated in virtually all cancers. Although the R-point has been linked to various activities involved in the regulation of G1-S transition of the mammalian cell cycle, the underlying mechanism remains unclear. Using single-cell measurements, we show here that the Rb-E2F pathway functions as a bistable switch to convert graded serum inputs into all-or-none E2F responses. Once turned ON by sufficient serum stimulation, E2F can memorize and maintain this ON state independently of continuous serum stimulation. We further show that, at critical concentrations and duration of serum stimulation, bistable E2F activation correlates directly with the ability of a cell to traverse the R-point.     

Expression and comparative characterization of Gq-coupled invertebrate visual pigments and melanopsin

A non-visual pigment melanopsin, which is localized in photosensitive retinal ganglion cells and is involved in the circadian photoentrainment and pupillary responses in mammals, is phylogenetically close to the visual pigments of invertebrates, such as insects and cephalopods. Recent studies suggested that melanopsin is a bistable pigment and drives a Gq-mediated signal transduction cascade, like the invertebrate visual pigments. Because detailed electrophysiological properties are somewhat different between the visual cells and the photosensitive ganglion cells, we here expressed and purified the invertebrate visual pigment and melanopsin to comparatively investigate their Gq-activation abilities. We successfully expressed and purified UV and blue light-sensitive visual pigments of the honeybee as well as the amphioxus melanopsin. Although the purified UV-sensitive pigment and the melanopsin lost their bistable nature during purification, reconstitution of the pigments in lipid vesicles resulted in return of the bistable nature. The light-dependent Gq-activation abilities among these reconstituted pigments are similar, suggesting that the electrophysiological differences do not depend on the Gq-activation step but rather on the other signal transduction steps and/or on cell properties. Our findings are also important in that this is the first report describes a heterologous large-scale expression of the Gq-coupled invertebrate visual pigments in cultured cells.     

Steady-state properties of a model ternary substrate cycle: theoretical predictions.

Numerous ternary substrate cycles are metabolically operative in vivo. The relative concentrations of the interconverted substrates are generally correlated with different physiological states. These cycles often include reversible and/or substrate-inhibited enzymic steps. The switch between one steady state (metabolic state) and another may be the consequence of either the effect of an exogeneous metabolite or signal, or the alteration of a cycle internal parameter. The interpretation of results obtained with currently designed experiments on substrate cycles seldom take into account the very dynamic and regulatory properties inherent in the cyclic and often autocatalytic nature of the pathway. In the present report, the various dynamic properties of a model ternary substrate cycle, bounded by moiety conservation, are investigated. Three situations with increasing complexity are considered: (i) the three enzymes are michaelian and catalyse irreversible steps; (ii) one of the enzymic steps is reversible; and (iii) one step is subjected to a destabilizing factor, i.e. inhibition by excess of substrate. The behavior(s) of the whole cycle is mainly controlled by four parameters, that is, ST, the total concentration of the substrate pool, and the three enzyme maximal velocities, VMi (i = 1,2,3). As ST (= S1 + S2 + S3) is constant, the Si steady-state concentrations (stable or not) can be represented in barycentric coordinates in a triangle (simplex). This convenient representation allows us to predict the different states of the system when one enzyme maximal activity is varied. The steady-state concentration dependencies as a function of one or several parameters may be either monostable (possibility of zero-order ultrasensitivity) or bistable (with or without reversible transitions). The physiological and experimental relevances of these observations are emphasized.