Gennady Cymbalyuk

A multiconductance silicon neuron with biologically matched dynamics

We have designed, fabricated, and tested an analog integrated-circuit architecture to implement the conductance-based dynamics that model the electrical activity of neurons. The dynamics of this architecture are in accordance with the Hodgkin-Huxley formalism, a widely exploited, biophysically plausible model of the dynamics of living neurons. Furthermore the architecture is modular and compact in size so that we can implement networks of silicon neurons, each of desired complexity, on a single integrated circuit. We present in this paper a six-conductance silicon-neuron implementation, and characterize it in relation to the Hodgkin-Huxley formalism. This silicon neuron incorporates both fast and slow ionic conductances, which are required to model complex oscillatory behaviors (spiking, bursting, subthreshold oscillations).

Using a Hybrid Neural System to Reveal Regulation of Neuronal Network Activity by an Intrinsic Current

The generation of rhythmic patterns by neuronal networks is a complex phenomenon, relying on the interaction of numerous intrinsic and synaptic currents, as well as modulatory agents. To investigate the functional contribution of an individual ionic current to rhythmic pattern generation in a network, we constructed a hybrid system composed of a silicon model neuron and a heart interneuron from the heartbeat timing network of the medicinal leech. When the model neuron and a heart interneuron are connected by inhibitory synapses, they produce rhythmic activity similar to that observed in the heartbeat network. We focused our studies on investigating the functional role of the hyperpolarization-activated inward current (Ih) on the rhythmic bursts produced by the network. By introducing changes in both the model and the heart interneuron, we showed that Ih determines both the period of rhythmic bursts and the balance of activity between the two sides of the network, because the amount and the activation/deactivation time constant of Ih determines the length of time that a neuron spends in the inhibited phase of its burst cycle. Moreover, we demonstrated that the model neuron is an effective replacement for a heart interneuron and that changes made in the model can accurately mimic similar changes made in the living system. Finally, we used a previously developed mathematical model (Hill et al. 2001) of two mutually inhibitory interneurons to corroborate these findings. Our results demonstrated that this hybrid system technique is advantageous for investigating neuronal properties that are inaccessible with traditional techniques.

A modular artificial neural net for controlling a six-legged walking system

A system that controls the leg movement of an animal or a robot walking over irregular ground has to ensure stable support for the body and at the same time propel it forward. To do so, it has to react adaptively to unpredictable features of the environment. As part of our study of the underlying mechanisms, we present here a model for the control of the leg movement of a 6-legged walking system. The model is based on biological data obtained from the stick insect. It represents a combined treatment of realistic kinematics and biologically motivated, adaptive gait generation. The model extends a previous algorithmic model by substituting simple networks of artificial neurons for the algorithms previously used to control leg state and interleg coordination. Each system controlling an individual leg consists of three subnets. A hierarchically superior net contains two sensory and two ‘premotor’ units; it rhythmically suppresses the out-put of one or the other of the two subordinate nets. These are continuously active. They might be called the ‘swing module’ and the ‘stance module’ because they are responsible for controlling the swing (return stroke) and the stance (power stroke) movements, respectively. The swing module consists of three motor units and seven sensory units. It can produce appropriate return stroke movements for a broad range of initial and final positions, can cope with mechanical disturbances of the leg movement, and is able to react to an obstacle which hinders the normal performance of the swing movement. The complete model is able to walk at different speeds over irregular surfaces. The control system rapidly reestablishes a stable gait when the movement of the legs is disturbed.

Coexistence of Tonic Spiking Oscillations in a Leech Neuron Model

The leech neuron model studied here has a remarkable dynamical plasticity. It exhibits a wide range of activities including various types of tonic spiking and bursting. In this study we apply methods of the qualitative theory of dynamical systems and the bifurcation theory to analyze the dynamics of the leech neuron model with emphasis on tonic spiking regimes. We show that the model can demonstrate bi-stability, such that two modes of tonic spiking coexist. Under a certain parameter regime, both tonic spiking modes are represented by the periodic attractors. As a bifurcation parameter is varied, one of the attractors becomes chaotic through a cascade of period-doubling bifurcations, while the other remains periodic. Thus, the system can demonstrate co-existence of a periodic tonic spiking with either periodic or chaotic tonic spiking. Pontryagin’s averaging technique is used to locate the periodic orbits in the phase space.

AnimatLab: A 3D graphics environment for neuromechanical simulations

The nervous systems of animals evolved to exert dynamic control of behavior in response to the needs of the animal and changing signals from the environment. To understand the mechanisms of dynamic control requires a means of predicting how individual neural and body elements will interact to produce the performance of the entire system. AnimatLab is a software tool that provides an approach to this problem through computer simulation. AnimatLab enables a computational model of an animals body to be constructed from simple building blocks, situated in a virtual 3D world subject to the laws of physics, and controlled by the activity of a multicellular, multicompartment neural circuit. Sensor receptors on the body surface and inside the body respond to external and internal signals and then excite central neurons, while motor neurons activate Hill muscle models that span the joints and generate movement. AnimatLab provides a common neuromechanical simulation environment in which to construct and test models of any skeletal animal, vertebrate or invertebrate. The use of AnimatLab is demonstrated in a neuromechanical simulation of human arm flexion and the myotactic and contact-withdrawal reflexes.

Modeling Alternation to Synchrony with Inhibitory Coupling: A Neuromorphic VLSI Approach

We developed an analog very large-scale integrated system of two mutually inhibitory silicon neurons that display several different stable oscillations. For example, oscillations can be synchronous with weak inhibitory coupling and alternating with relatively strong inhibitory coupling. All oscillations observed experimentally were predicted by bifurcation analysis of a corresponding mathematical model. The synchronous oscillations do not require special synaptic properties and are apparently robust enough to survive the variability and constraints inherent in this physical system. In biological experiments with oscillatory neuronal networks, blockade of inhibitory synaptic coupling can sometimes lead to synchronous oscillations. An example of this phenomenon is the transition from alternating to synchronous bursting in the swimming central pattern generator of lamprey when synaptic inhibition is blocked by strychnine. Our results suggest a simple explanation for the observed oscillatory transitions in the lamprey central pattern generator network: that inhibitory connectivity alone is sufficient to produce the observed transition.

In-phase and antiphase self-oscillations in a model of two electrically coupled pacemakers

The dynamic behavior of a model of two electrically coupled oscillatory neurons was studied while the external polarizing current was varied. It was found that the system with weak coupling can demonstrate one of five stable oscillatory modes: (1) in-phase oscillations with zero phase shift; (2) antiphase oscillations with halfperiod phase shift; (3) oscillations with any fixed phase shift depending on the value of the external polarizing current; (4) both in-phase and antiphase oscillations for the same current value, where the oscillation type depends on the initial conditions; (5) both in-phase and quasiperiodic oscillations for the same current value. All of these modes were robust, and they persisted despite small variations of the oscillator parameters. We assume that similar regimes, for example antiphase oscillations, can be detected in neurophysiological experiments. Possible applications to central pattern generator models are discussed.

Six Types of Multistability in a Neuronal Model Based on Slow Calcium Current

Background Multistability of oscillatory and silent regimes is a ubiquitous phenomenon exhibited by excitable systems such as neurons and cardiac cells. Multistability can play functional roles in short-term memory and maintaining posture. It seems to pose an evolutionary advantage for neurons which are part of multifunctional Central Pattern Generators to possess multistability. The mechanisms supporting multistability of bursting regimes are not well understood or classified. Methodology/Principal Findings Our study is focused on determining the bio-physical mechanisms underlying different types of co-existence of the oscillatory and silent regimes observed in a neuronal model. We develop a low-dimensional model typifying the dynamics of a single leech heart interneuron. We carry out a bifurcation analysis of the model and show that it possesses six different types of multistability of dynamical regimes. These types are the co-existence of 1) bursting and silence, 2) tonic spiking and silence, 3) tonic spiking and subthreshold oscillations, 4) bursting and subthreshold oscillations, 5) bursting, subthreshold oscillations and silence, and 6) bursting and tonic spiking. These first five types of multistability occur due to the presence of a separating regime that is either a saddle periodic orbit or a saddle equilibrium. We found that the parameter range wherein multistability is observed is limited by the parameter values at which the separating regimes emerge and terminate. Conclusions We developed a neuronal model which exhibits a rich variety of different types of multistability. We described a novel mechanism supporting the bistability of bursting and silence. This neuronal model provides a unique opportunity to study the dynamics of networks with neurons possessing different types of multistability.

Serotonin Transduction Cascades Mediate Variable Changes in Pyloric Network Cycle Frequency in Response to the Same Modulatory Challenge

A fundamental question in systems biology addresses the issue of how flexibility is built into modulatory networks such that they can produce context-dependent responses. Here we examine flexibility in the serotonin (5-HT) response system that modulates the cycle frequency (cf) of a rhythmic motor output. We found that depending on the preparation, the same 5-min bath application of 5-HT to the pyloric network of the California spiny lobster, Panulirus interruptus, could produce a significant increase, decrease, or no change in steady-state cf relative to baseline. Interestingly, the mean circuit output was not significantly different among preparations prior to 5-HT application. We developed pharmacological tools to examine the preparation-to-preparation variability in the components of the 5-HT response system. We found that the 5-HT response system consisted of at least three separable components: a 5-HT(2betaPan)-like component mediated a rapid decrease followed by a sustained increase in cf; a 5-HT(1alphaPan)-like component produced a small and usually gradual increase in cf; at least one other component associated with an unknown receptor mediated a sustained decrease in cf. The magnitude of the change in cf produced by each component was highly variable, so that when summed they could produce either a net increase, decrease, or no change in cf depending on the preparation. Overall, our research demonstrates that the balance of opposing components of the 5-HT response system determines the direction and magnitude of 5-HT-induced change in steady-state cf relative to baseline.

Neuromechanical simulation of the locust jump

SUMMARY The neural circuitry and biomechanics of kicking in locusts have been studied to understand their roles in the control of both kicking and jumping. It has been hypothesized that the same neural circuit and biomechanics governed both behaviors but this hypothesis was not testable with current technology. We built a neuromechanical model to test this and to gain a better understanding of the role of the semi-lunar process (SLP) in jump dynamics. The jumping and kicking behaviors of the model were tested by comparing them with a variety of published data, and were found to reproduce the results from live animals. This confirmed that the kick neural circuitry can produce the jump behavior. The SLP is a set of highly sclerotized bands of cuticle that can be bent to store energy for use during kicking and jumping. It has not been possible to directly test the effects of the SLP on jump performance because it is an integral part of the joint, and attempts to remove its influence prevent the locust from being able to jump. Simulations demonstrated that the SLP can significantly increase jump distance, power, total energy and duration of the jump impulse. In addition, the geometry of the joint enables the SLP force to assist leg flexion when the leg is flexed, and to assist extension once the leg has begun to extend.