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PubMed2000

A

A solid state, electronically addressable, bistable [2]catenane-based molecular switching device was fabricated from a single monolayer of the [2]catenane, anchored with phospholipid counterions, and sandwiched between an n-type polycrystalline silicon bottom electrode and a metallic top electrode. The device exhibits hysteretic (bistable) current/voltage characteristics. The switch is opened at +2 volts, closed at -2 volts, and read at approximately 0.1 volt and may be recycled many times under ambient conditions. A mechanochemical mechanism for the action of the switch is presented and shown to be consistent with temperature-dependent measurements of the device operation.

Journal Article↗
PubMed2002

Regulation of the mammalian cell cycle: a model of the G1-to-S transition.

We have formulated a mathematical model for regulation of the G(1)-to-S transition of the mammalian cell cycle. This mathematical model incorporates the key molecules and interactions that have been identified experimentally. By subdividing these critical molecules into modules, we have been able to systematically analyze the contribution of each to dynamics of the G(1)-to-S transition. The primary module, which includes the interactions between cyclin E (CycE), cyclin-dependent kinase 2 (CDK2), and protein phosphatase CDC25A, exhibits dynamics such as limit cycle, bistability, and excitable transient. The positive feedback between CycE and transcription factor E2F causes bistability, provided that the total E2F is constant and the retinoblastoma protein (Rb) can be hyperphosphorylated. The positive feedback between active CDK2 and cyclin-dependent kinase inhibitor (CKI) generates a limit cycle. When combined with the primary module, the E2F/Rb and CKI modules potentiate or attenuate the dynamics generated by the primary module. In addition, we found that multisite phosphorylation of CDC25A, Rb, and CKI was critical for the generation of dynamics required for cell cycle progression.

Animals↗
PubMed2006

A mathematical model for the mating-induced prolactin rhythm of female rats.

For the first 10 days of pregnancy and the first 12 days of pseudopregnancy, the secretion of prolactin (PRL) from pituitary lactotrophs is rhythmic, with two surges/day. This rhythm can also be triggered by bolus injection of oxytocin (OT). We describe a mathematical model for the initiation, maintenance, and termination of the OT-induced PRL rhythm. In our model, the mechanism for this circadian rhythm is mutual interaction between lactotrophs and neuroendocrine dopamine (DA) neurons. This rhythm is, under normal lighting conditions, entrained by the suprachiasmatic nucleus (SCN) but persists in the absence of input from the SCN. We postulate that OT injection triggers the rhythm by activating a population of bistable hypothalamic neurons that innervate and inhibit DA neurons. The bistable nature of these neurons allows them to act as a memory device, maintaining the rhythm long after OT has been cleared from the blood. The mechanism for this memory device and the arguments supporting it are detailed with computer simulations. Finally, we consider potential targets for a rhythm-terminating factor and make predictions that may be used to determine which mechanism is operational in terminating the OT- or mating-induced PRL rhythm.

Animals↗
PubMed2003

Short duty cycle destabilizes a half-center oscillator, but gap junctions can restabilize the anti-phase pattern.

Mutually inhibitory pacemaker neurons with duty cycle close to 50% operate as a half-center oscillator (anti-phase coordination, i.e., 180 degrees out of phase), even in the presence of weak to modest gap junctional coupling. For electrical coupling strength above a critical value synchronization occurs. But, as shown here with modeling studies, the effects of electrical coupling depend critically on a cell's duty cycle. Instead of oscillating either in-phase or anti-phase, model cells with short duty cycle express additional rhythmic patterns, and different transitions between them, depending on electrical coupling strength. For weak or no electrical coupling, cells do not oscillate in anti-phase but instead exhibit almost in-phase activity. Strengthening this weak coupling leads to stable anti-phase activity. With yet stronger electrical coupling stable inphase (synchrony) emerges but it coexists with the anti-phase pattern. Thus the network shows bistability for an intermediate range of coupling strength. For sufficiently strong electrical coupling synchrony is the network's only attracting rhythmic state. Our results, numerical and analytical (phase plane analysis), are based on a minimal but biophysically motivated pacemaker model for the slowly oscillating envelope of bursting neurons. However, illustrations for an Hodgkin-Huxley model suggest that some of our results for short duty cycle may extend to patterning of repetitive spikes. In particular, electrical coupling of intermediate strength may promote anti-phase activity and provide bistability of anti-phase and in-phase spiking.

Biological Clocks↗
PubMed2003

Modeling interactions between electrical activity and second-messenger cascades in Aplysia neuron R15.

The biophysical properties of neuron R15 in Aplysia endow it with the ability to express multiple modes of oscillatory electrical activity, such as beating and bursting. Previous modeling studies examined the ways in which membrane conductances contribute to the electrical activity of R15 and the ways in which extrinsic modulatory inputs alter the membrane conductances by biochemical cascades and influence the electrical activity. The goals of the present study were to examine the ways in which electrical activity influences the biochemical cascades and what dynamical properties emerge from the ongoing interactions between electrical activity and these cascades. The model proposed by Butera et al. in 1995 was extended to include equations for the binding of Ca(2+) to calmodulin (CaM) and the actions of Ca(2+)/CaM on both adenylyl cyclase and phosphodiesterase. Simulations indicated that levels of cAMP oscillated during bursting and that these oscillations were approximately antiphasic to the oscillations of Ca(2+). In the presence of cAMP oscillations, brief perturbations could switch the electrical activity between bursting and beating (bistability). Compared with a constant-cAMP model, oscillations of cAMP substantially expanded the range of bistability. Moreover, the integrated electrical/biochemical model simulated some early experimental results such as activity-dependent inactivation of the anomalous rectifier. The results of the present study suggest that the endogenous activity of R15 depends, in part, on interactions between electrical activity and biochemical cascades.

Adenylyl Cyclases↗
PubMed1989

Bifurcation analysis of nonlinear retinal horizontal cell models. I. Properties of isolated cells.

1. Bifurcation theory is used to study properties of nonlinear analytical and computational models of isolated retinal horizontal cells. The analytical model is based on the published data of Shingai and Christensen describing steady-state I-V characteristics of horizontal cells isolated from catfish (Ictalurus punctatus) retina. The computational model is based on I-V characteristics of distinct macroscopic membrane currents observed in horizontal cells isolated from goldfish (Carassius auratus) retina. Slow-model dynamics are analyzed assuming that excitatory processes occur rapidly with respect to the time course of inactivation of the inward Ca2+ and outward K+ currents. 2. A global bifurcation diagram plotting the location and stability properties of critical points as a function of photoreceptor-evoked horizontal-cell postsynaptic membrane conductance Gsyn is derived for the analytical model. The automated bifurcation analysis software AUTO is used to compute global bifurcation diagrams for the computational model. Bifurcation diagrams exhibit a bistable regime at small Gsyn values characterized by two stable and one unstable critical point and a monostable regime at larger Gsyn values characterized by a single globally attracting stable critical point. The transition between bistable and monostable behavior occurs at a Gsyn value of roughly 0.9 nS for the computational model and 1.7 nS for the analytical model. Estimates of horizontal-cell glutamate-channel conductance suggest that this transition corresponds to the activation of as few as 400-700 glutamate channels. Dark-evoked release of neurotransmitter from photoreceptors may therefore set horizontal-cell synaptic conductance Gsyn to a value within the monostable regime. 3. Photoreceptor-evoked horizontal-cell membrane conductance, total Ca2+ channel conductance, and inactivation of the inward Ca2+ current are shown to be the major factors controlling the bifurcation structure of the computational model. Inactivation of the inward Ca2+ current is required to account for the dark resting potential of horizontal cells as well as light-evoked hyperpolarizing responses. Inactivation of the outward K+ current has little effect on model properties. 4. Isolated horizontal cells generate Ca2+ action potentials whereas cells in the intact retina normally do not. Simple procedures for modeling the slow dynamics of isolated horizontal-cell Ca2+ action potentials are described.(ABSTRACT TRUNCATED AT 400 WORDS)

Algorithms↗
PubMed1990

Bifurcation analysis of nonlinear retinal horizontal cell models. II. Network properties.

1. We have previously presented a model of horizontal-cell soma isolated from fish retina. The model consists of a synaptic conductance representing input from photoreceptors in parallel with voltage-dependent membrane currents. Membrane-current models are based on I-V curves measured in isolated fish horizontal cells. Bifurcation theory was used to analyze model properties. The major findings of this study were 1) the inward Ca2+ current must be inactivated to account for horizontal-cell resting potentials and hyperpolarizing responses to light stimuli in a background of dark, and 2) the synaptic conductance controls the bifurcation structure of the model, with bistable behavior occurring at small and monostable behavior occurring at larger values of the synaptic conductance. The synaptic conductance at the point of transition from bistable to monostable behavior corresponds to the activation of as few as 100 synaptic channels. Thus tonic synaptic input from photoreceptors and inactivation of the inward Ca2+ current act to "linearize" responses of isolated horizontal-cell models. 2. The model described in this paper extends these analyses to large networks of horizontal cells in which each cell is coupled resistively to its nearest neighbors and is modeled with the use of the full complement of nonlinear membrane currents. Network responses to arbitrary patterns of conductance change (simulating inputs from photoreceptors), current-, or voltage-clamp stimuli are computed using the Newton iteration. The Newton descent direction is computed using either conjugate gradient (CG) or preconditioned CG algorithms. 3. An analysis of network stability properties is performed. Network I-V curves are computed by voltage-clamping the center node and computing the current required to maintain the clamp voltage. Computations are performed on networks of model cells in which the Ca2+ current is fully activated and the synaptic conductance is zero, thus making each cell as nonlinear as possible. Coupling conductance values slightly greater than 100 pS provide a current shunt sufficient to prevent the generation of Ca2+ action potentials in the network. This coupling conductance corresponds to the conductance of as few as two gap-junction channels and is more than two orders of magnitude less than the coupling known to exist between pairs of cultured horizontal cells.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗
PubMed1993

A variable-threshold motoneuron model that incorporates time- and voltage-dependent potassium and calcium conductances.

1. A "threshold-crossing" motoneuron model was developed to relate recently described biophysical features of cat alpha-motoneurons to motoneuron discharge behavior. This model incorporated three features not included in precedent models: 1) a low-threshold, persistent calcium current; 2) realistic voltage dependencies of the major ionic conductances; and 3) a variable spike threshold. The effects of these additional biophysical features on model behavior were investigated by successively adding them to a fixed threshold model with a single potassium conductance. 2. Fixed-threshold models with either one or two potassium conductances could not produce appropriate discharge behavior. Steady-state frequency-current (F-I) relations were characterized by a continuously increasing slope, unlike the piecewise linear relations observed in real motoneurons. These models also produced unrealistically high discharge rates at the highest levels of "injected" current. 3. The addition of a variable spike threshold, which was made to increase linearly with the magnitude of injected current, could limit maximum discharge rates to more realistic levels. However, steady-state F-I relations still did not exhibit the appropriate shape. 4. The incorporation of a low-threshold calcium current led to a good quantitative agreement between the steady-state F-I relations produced by the model and those obtained in real motoneurons. In addition, the steady-state relation between total membrane current and membrane voltage (I-V relation) of the model was very similar to those measured in real motoneurons. The model's I-V and F-I relations were both very sensitive to the exact form of the steady-state relation between the magnitude of the calcium conductance and membrane voltage. 5. Additional modifications, which included a second calcium conductance and a factor relating spike threshold to membrane voltage, helped to produce more realistic afterhyperpolarizations and first-interval F-I relations. 6. Bistable discharge behavior could be produced by reducing the slow potassium conductance and increasing the time constants governing the activation and deactivation of the low-threshold calcium conductance. 7. The final model thus reproduces a wide range of motoneuron behaviors including subthreshold rectification, piecewise linear first interval and steady-state F-I relations, and, with appropriate modifications, bistable discharge behavior. Nonetheless, by simplifying the representation of fast spike conductances as well as the kinetics of the other ionic conductances, the model remains simple enough to be incorporated into a larger neural network.

Animals↗
PubMed2005

Switching time of nanowire memory.

Cadmium sulfide nanowires of 10-nm diameter, electrodeposited in porous anodic alumina films, exhibit an electronic bistability that can be harnessed for non-volatile memory. The current-voltage characteristics of the wires show two stable conductance states that are well-separated (conductances differ by more than 4 orders of magnitude) and long lived (longevity > 1 year at room temperature). These two states can encode binary bits 0 and 1. Here we report measurements of the switching time to switch from the high- to the low-conductance state. These measurements also shed some light on the physical mechanisms underlying the bistability.

Cadmium Compounds↗
PubMed2002

Nonlinear dynamics of a Bragg cell under intensity feedback in the near-Bragg, four-order regime.

A detailed examination of the nonlinear dynamical behavior of an acousto-optic Bragg cell in the near-Bragg regime of operation for the case of four scattered orders under intensity feedback is carried out. This problem is an extension of the standard ideal-Bragg feedback model whereby traditionally bistability, hysteresis, and chaotic oscillations are observed under zeroth- or first-order feedback of the scattered light. For the present case, the closed-loop equations are developed from a priori knowledge of the open-loop analytical solutions for four-order near-Bragg scattering. The results, obtained via computer simulation, reveal a variety of interesting dynamics, including bistability, bifurcation, hysteresis, chaotic oscillations (including in this case the relatively uncommon period-three behavior, in addition to the more usual period-doubling phenomenon en route to chaos), and potentially useful parametric dependence of these features. The observed results are interpreted in terms of system behavior for varying feedback gain and bias, the so-called Klein-Cook parameter Q, and time delay, and are compared with earlier work based on the ideal Bragg regime.

Journal Article↗
PubMed2005

Dynamical hysteresis in a three-level atomic system.

We have experimentally investigated dynamical hysteresis behavior by changing the sweeping frequency of the cavity input field in the optical bistability of rubidium atoms (in a three-level atomic-type configuration) inside an optical cavity. The shape, width (or area), and direction of the hysteresis cycle are sensitive functions of the sweeping frequency for such an optical bistable system.

Journal Article↗
PubMed2006

Transcriptional dynamics of the embryonic stem cell switch.

Recent ChIP experiments of human and mouse embryonic stem cells have elucidated the architecture of the transcriptional regulatory circuitry responsible for cell determination, which involves the transcription factors OCT4, SOX2, and NANOG. In addition to regulating each other through feedback loops, these genes also regulate downstream target genes involved in the maintenance and differentiation of embryonic stem cells. A search for the OCT4-SOX2-NANOG network motif in other species reveals that it is unique to mammals. With a kinetic modeling approach, we ascribe function to the observed OCT4-SOX2-NANOG network by making plausible assumptions about the interactions between the transcription factors at the gene promoter binding sites and RNA polymerase (RNAP), at each of the three genes as well as at the target genes. We identify a bistable switch in the network, which arises due to several positive feedback loops, and is switched on/off by input environmental signals. The switch stabilizes the expression levels of the three genes, and through their regulatory roles on the downstream target genes, leads to a binary decision: when OCT4, SOX2, and NANOG are expressed and the switch is on, the self-renewal genes are on and the differentiation genes are off. The opposite holds when the switch is off. The model is extremely robust to parameter changes. In addition to providing a self-consistent picture of the transcriptional circuit, the model generates several predictions. Increasing the binding strength of NANOG to OCT4 and SOX2, or increasing its basal transcriptional rate, leads to an irreversible bistable switch: the switch remains on even when the activating signal is removed. Hence, the stem cell can be manipulated to be self-renewing without the requirement of input signals. We also suggest tests that could discriminate between a variety of feedforward regulation architectures of the target genes by OCT4, SOX2, and NANOG.

Animals↗
PubMed2005

Activation in visual cortex correlates with the awareness of stereoscopic depth.

Using event-related functional magnetic resonance imaging, we studied the activation correlating with the awareness of stereoscopic depth using a bistable slanted surface (slant rivalry). Bistability resulted from incongruence between two slant-defining cues: binocular disparity and monocular perspective. The stimulus was perceived as alternating between the perspective-dominated percept (monocular depth) and the disparity-dominated percept (stereopsis), while sensory input remained constant, enabling us to study changes in awareness of depth associated with either cue. Transient activation relating to perceptual alternations was found bilaterally in the caudal part of the intraparietal sulcus, in the right-hemispheric anterior intraparietal sulcus, within visual area V4d-topo, and inferior to area MT+. Transient activation correlating specifically with alternations toward the disparity-dominated percept was found in a number of visual areas, including dorsal visual areas V3A, V7, and V4d-topo and visual areas MT+ and lateral occipital complex. No activation was found for alternations toward the perspective-dominated percept. Our results show that of all visual areas responsive to disparity-defined depth, V4d-topo shows the most robust signal changes correlating with the instigation of stereoscopic depth awareness (stereopsis).

Awareness↗
PubMed2006

Persistent responses to brief stimuli: feedback excitation among brainstem neurons.

The ability of brief stimuli to trigger prolonged neuronal activity is a fundamental requirement in nervous systems, common to motor responses and short-term memory. Bistable membrane properties and network feedback excitation have both been proposed as suitable mechanisms to sustain such persistent responses. There is now good experimental evidence for membrane bistability. In contrast, the long-standing hypotheses based on positive feedback excitation have yet to be supported by direct evidence for mutual excitatory connections between appropriate neurons. In young frog tadpoles (Xenopus), we show that a small region of caudal hindbrain and rostral spinal cord is sufficient to generate prolonged swimming in response to a brief stimulus. We used paired whole-cell patch recordings to identify hindbrain neurons in this region that actively excite spinal neurons to drive sustained swimming. We show directly that some of these hindbrain neurons make reciprocal excitatory connections with each other. We use a population model of the hindbrain network to illustrate how feedback excitation can provide a robust mechanism to generate persistent responses. Our recordings provide direct evidence for feedback excitation among neurons within a network that drives a prolonged response. Its presence in a lower brain region early in development suggests that it is a basic feature of neuronal network design.

Animals↗
PubMed2006

Slow state transitions of sustained neural oscillations by activity-dependent modulation of intrinsic excitability.

Little is known about the dynamics and mechanisms of transitions between tonic firing and bursting in cortical networks. Here, we use a computational model of a neocortical circuit with extracellular potassium dynamics to show that activity-dependent modulation of intrinsic excitability can lead to sustained oscillations with slow transitions between two distinct firing modes: fast run (tonic spiking or fast bursts with few spikes) and slow bursting. These transitions are caused by a bistability with hysteresis in a pyramidal cell model. Balanced excitation and inhibition stabilizes a network of pyramidal cells and inhibitory interneurons in the bistable region and causes sustained periodic alternations between distinct oscillatory states. During spike-wave seizures, neocortical paroxysmal activity exhibits qualitatively similar slow transitions between fast run and bursting. We therefore predict that extracellular potassium dynamics can cause alternating episodes of fast and slow oscillatory states in both normal and epileptic neocortical networks.

Animals↗
PubMed2006

Akt versus p53 in a network of oncogenes and tumor suppressor genes regulating cell survival and death.

The tumor suppressor protein, p53, and the oncoprotein, Akt, are involved in a cross talk that could be at the core of a cell's control machinery for switching between survival and death. This cross talk is a combination of reciprocally antagonistic pathways emanating from p53 and Akt, and also involves another tumor suppressor gene, PTEN, and another oncogene, Mdm2; such a connected network of cancer-relevant genes must be significant and demands a critical study. The p53-Akt network is shown in this report to possess the potential to exhibit bistability, a phenomenon in which two stable steady states of the system coexist for a fixed set of control parameter values. A hierarchy of qualitative networks and abstract kinetic models are analyzed and simulated on a computer to demonstrate the robustness of the bistable behavior, which, as argued in this study, is a likely candidate mechanism for a cellular survival-death switch. The analysis applies to cells that are neither p53-null nor Akt-null. The models presented here offer experimental predictions on the identity of control parameters of apoptotic thresholds and on network perturbations (including DNA damage and Akt inhibition) that are sufficient to generate switching between pro-survival and pro-death cellular states.

Apoptosis↗
PubMed2006

Entropy and barrier-controlled fluctuations determine conformational viscoelasticity of single biomolecules.

Biological macromolecules have complex and nontrivial energy landscapes, endowing them with a unique conformational adaptability and diversity in function. Hence, understanding the processes of elasticity and dissipation at the nanoscale is important to molecular biology and emerging fields such as nanotechnology. Here we analyze single molecule fluctuations in an atomic force microscope, using a generic model of biopolymer viscoelasticity that includes local "internal" conformational dissipation. Comparing two biopolymers, dextran and cellulose (polysaccharides with and without local bistable transitions), demonstrates that signatures of simple conformational change are minima in both the elastic and internal friction constants around a characteristic force. A novel analysis of dynamics on a bistable energy landscape provides a simple explanation: an elasticity driven by the entropy, and friction by a barrier-controlled hopping time of populations between states, which is surprisingly distinct to the well-known relaxation time. This nonequilibrium microscopic analysis thus provides a means of quantifying new dynamical features of the energy landscape of the glucopyranose ring, revealing an unexpected underlying roughness and information on the shape of the barrier of the chair-boat transition in dextran. The results presented herein provide a basis toward probing the viscoelasticity of macromolecular conformational transitions on more complex energy landscapes, such as during protein folding.

Biopolymers↗