Synchronization in a network of fast-spiking interneurons

Experimental results revealed that in neocortex inhibitory fast-spiking (FS) interneurons interact also by electrical synapses (gap-junctions). They receive sensory information from thalamus and transfer it to principal cells by feedforward inhibition. Moreover, their synchronous discharge enhances their inhibitory control of pyramidal neurons. By using a biophysical model of FS interneurons the synchronization properties of a network of two synaptically coupled units are investigated. In the case they interact only by inhibitory synapses, well defined regions exist in the parameters space described by the strength and duration of the synaptic current, where synchronous regimes occur. Then an empirical protocol is proposed to determine approximately the borders of the synchronization manifold (SM). When electrical synapses are included, the region of synchronous discharge of the two interneurons becomes larger. In both cases, the coherent states are characterized by discharge frequencies in the gamma range. Lastly, the effects of heterogeneity, either obtained by using different stimulation currents or unidirectional inhibitory coupling, are studied.     

Computer simulation of the segmental neural network generating locomotion in lamprey by using populations of network interneurons

Realistic computer simulations of the experimentally established local spinal cord neural network generating swimming in the lamprey have been performed. Populations of network interneurons were used in which cellular properties, like cell size and membrane conductance including voltage dependent ion channels were randomly distributed around experimentally obtained mean values, as were synaptic conductances (kainate/AMPA, NMDA, glycine) and delays. This population model displayed more robust burst activity over a wider frequency range than the more simple subsample model used previously, and the pattern of interneuronal activity was appropriate. The strength of the reciprocal inhibition played a very important role in the regulation of burst frequency, and just by changing the inhibitory bias the entire physiological range could be covered. At the lower frequency range of bursting the segmental excitatory interneurons provide stability as does the activation of voltage dependent NMDA receptors. Spike frequency adaptation by means of summation of afterhyperpolarization (AHP) serves as a major burst terminating factor, and at lower rates the membrane properties conferred by the NMDA receptor activation. The lateral interneurons were not of critical importance for the burst termination. They may, however, be of particular importance for inducing a rapid burst termination during for instance steering and righting reactions. Several cellular factors combine to provide a secure and stable motor pattern in the entire frequency range.     

Contribution of stretch reflexes to locomotor control: a modeling study

It is known that the springlike properties of muscles provide automatic load compensation during weight bearing. How crucial is sensory control of the motor output given these basic properties of the locomotor system? To address this question, a neuromuscular model was used to test two hypotheses. (1) Stretch reflexes are too weak and too delayed to contribute significantly to weight-bearing. (2) The important contributions of sensory input involve state-dependent processing. We constructed a two-legged planar locomotor model with 9 segments, driven by 12 musculotendon actuators with Hill-type force-velocity and monotonic force-length properties. Electromyographic (EMG) profiles of the simulated muscle groups during slow level walking served as actuator activation functions. Spindle Ia and tendon organ Ib sensory inputs were represented by transfer functions with a latency of 35 ms, contributing 30% to the net EMG profile and gated to be active only when the receptor-bearing muscles were contracting. Locomotor stability was assessed by parametric variations of actuator maximum forces during locomotion in open-loop ("deafferented") trials and in trials with feedback control based on either sensory-evoked stretch reflexes or finite-state rules. We arrived at the following conclusions. (1) In the absence of sensory control, the intrinsic stiffness of limb muscles driven by a stereotyped rhythmical pattern can produce surprisingly stable gait. (2) When the level of central activity is low, the contribution of stretch reflexes to load compensation can be crucial. However, when central activity provides adequate load compensation, the contribution of stretch reflexes is less significant. (3) Finite-state control can greatly extend the adaptive capability of the locomotor system.     

A novel network of multipolar bursting interneurons generates theta frequency oscillations in neocortex

GABAergic interneurons can phase the output of principal cells, giving rise to oscillatory activity in different frequency bands. Here we describe a new subtype of GABAergic interneuron, the multipolar bursting (MB) cell in the mouse neocortex. MB cells are parvalbumin positive but differ from fast-spiking multipolar (FS) cells in their morphological, neurochemical, and physiological properties. MB cells are reciprocally connected with layer 2/3 pyramidal cells and are coupled with each other by chemical and electrical synapses. MB cells innervate FS cells but not vice versa. MB to MB cell as well as MB to pyramidal cell synapses exhibit paired-pulse facilitation. Carbachol selectively induced synchronized theta frequency oscillations in MB cells. Synchrony required both gap junction coupling and GABAergic chemical transmission, but not excitatory glutamatergic input. Hence, MB cells form a distinct inhibitory network, which upon cholinergic drive can generate rhythmic and synchronous theta frequency activity, providing temporal coordination of pyramidal cell output.     

A compartmental approach in modeling a neuronal network. Role of inhibitory and excitatory processes]

The conception and main principles of the compartmental approach to the modeling of neuronal networks are presented. Excitatory and inhibitory ties are described, and reducible and nonreducible neuronal networks are considered. The periodical solution in models of neuronal networks is the model of normal rhythmic (e.g., respiratory) activity. The role of external (chemoreceptor drives) is discussed. The biological interpretation of the results of modeling is given. The observed biological phenomena are considered.     

A quantitative analysis of cardiac myocyte relaxation: a simulation study

The determinants of relaxation in cardiac muscle are poorly understood, yet compromised relaxation accompanies various pathologies and impaired pump function. In this study, we develop a model of active contraction to elucidate the relative importance of the [Ca2+]i transient magnitude, the unbinding of Ca2+ from troponin C (TnC), and the length-dependence of tension and Ca2+ sensitivity on relaxation. Using the framework proposed by one of our researchers, we extensively reviewed experimental literature, to quantitatively characterize the binding of Ca2+ to TnC, the kinetics of tropomyosin, the availability of binding sites, and the kinetics of crossbridge binding after perturbations in sarcomere length. Model parameters were determined from multiple experimental results and modalities (skinned and intact preparations) and model results were validated against data from length step, caged Ca2+, isometric twitches, and the half-time to relaxation with increasing sarcomere length experiments. A factorial analysis found that the [Ca2+]i transient and the unbinding of Ca2+ from TnC were the primary determinants of relaxation, with a fivefold greater effect than that of length-dependent maximum tension and twice the effect of tension-dependent binding of Ca2+ to TnC and length-dependent Ca2+ sensitivity. The affects of the [Ca2+]i transient and the unbinding rate of Ca2+ from TnC were tightly coupled with the effect of increasing either factor, depending on the reference [Ca2+]i transient and unbinding rate.     

Temporal constraints of a gene regulatory network: Refining a qualitative simulation

The modelling of gene regulatory networks (GRNs) has classically been addressed through very different approaches. Among others, extensions of Thomas’s asynchronous Boolean approach have been proposed, to better fit the dynamics of biological systems: genes may reach different discrete expression levels, depending on the states of other genes, called the regulators: thus, activations and inhibitions are triggered conditionally on the proper expression levels of these regulators. In contrast, some fine-grained propositions have focused on the molecular level as modelling the evolution of biological compound concentrations through differential equation systems. Both approaches are limited. The first one leads to an oversimplification of the system, whereas the second is incapable to tackle large GRNs. In this context, hybrid paradigms, that mix discrete and continuous features underlying distinct biological properties, achieve significant advances for investigating biological properties. One of these hybrid formalisms proposes to focus, within a GRN abstraction, on the time delay to pass from a gene expression level to the next. Until now, no research work has been carried out, which attempts to benefit from the modelling of a GRN by differential equations, converting it into a multi-valued logical formalism of Thomas, with the aim of performing biological applications.     

The synchronization properties of a network of inhibitory interneurons depend on the biophysical model

The synchronization properties of a pair of coupled fast spiking interneurons are studied by using the theory of weakly coupled oscillators. Four different biophysical models of the single fast spiking interneuron are used and the corresponding results are compared. It is shown that for a pair of identical coupled cells, the synchronization properties are model-dependent. In particular, the firing coherence of the network is strongly affected by the reversal potential, the kinetics of the inhibitory postsynaptic current and the electrical coupling; the activation properties of the sodium and potassium currents play a significant role too.     

Functional organization of locomotor interneurons in the ventral lumbar spinal cord of the newborn rat

Although the mammalian locomotor CPG has been localized to the lumbar spinal cord, the functional-anatomical organization of flexor and extensor interneurons has not been characterized. Here, we tested the hypothesis that flexor and extensor interneuronal networks for walking are physically segregated in the lumbar spinal cord. For this purpose, we performed optical recordings and lesion experiments from a horizontally sectioned lumbar spinal cord isolated from neonate rats. This ventral hemi spinal cord preparation produces well-organized fictive locomotion when superfused with 5-HT/NMDA. The dorsal surface of the preparation was visualized using the Ca(2+) indicator fluo-4 AM, while simultaneously monitoring motor output at ventral roots L2 and L5. Using calcium imaging, we provided a general mapping view of the interneurons that maintained a stable phase relationship with motor output. We showed that the dorsal surface of L1 segment contains a higher density of locomotor rhythmic cells than the other segments. Moreover, L1 segment lesioning induced the most important changes in the locomotor activity in comparison with lesions at the T13 or L2 segments. However, no lesions led to selective disruption of either flexor or extensor output. In addition, this study found no evidence of functional parcellation of locomotor interneurons into flexor and extensor pools at the dorsal-ventral midline of the lumbar spinal cord of the rat.     

Transmitter-dependent involvement of the respiratory interneurons in the locomotor rhythm in the pulmonate mollusc Lymnaea

Pedal cell RPeD1 of the pond snail L. stagnalis becomes involved in a central rhythm identified as an activity of the central pattern generator (CPG) for locomotion. The RPeD1 rhythm developed as driven by a synaptic input in isolated CNS preparations treated with 0.05 mM serotonin (5HT) or 0.1 mM 5-hydroxytryptophan (5HTP). The 5HT-induced co-ordinated rhythmic activity was retained by each of two pedal ganglia after complete isolation thus suggesting that the respective CPG lies entirely within the pedal portion of the CNS and is paired. The findings suggest that the RPeD1 switching from one network to another represents a neurotransmitter-dependent phenomenon.     

Control of a nonsquare drug infusion system: A simulation study.

A model predictive control strategy was developed and tested on a nonlinear canine circulatory model for the regulation of hemodynamic variables under critical care conditions. Different patient conditions such as congestive heart failure, post-operative hypertension, and sepsis shock were studied in closed-loop simulations. The model predictive controller, which uses a different linear model depending on the patient condition, allowed constraints to be explicitly enforced. The controller was initially tuned on the basis of a linear plant model, then tested on the nonlinear physiological model; the simulations demonstrated the ability to handle constraints, such as drug dosage specifications, commonly desired by critical care physicians.     

Spatially structured oscillations in a two-dimensional excitatory neuronal network with synaptic depression

We study the spatiotemporal dynamics of a two-dimensional excitatory neuronal network with synaptic depression. Coupling between populations of neurons is taken to be nonlocal, while depression is taken to be local and presynaptic. We show that the network supports a wide range of spatially structured oscillations, which are suggestive of phenomena seen in cortical slice experiments and in vivo. The particular form of the oscillations depends on initial conditions and the level of background noise. Given an initial, spatially localized stimulus, activity evolves to a spatially localized oscillating core that periodically emits target waves. Low levels of noise can spontaneously generate several pockets of oscillatory activity that interact via their target patterns. Periodic activity in space can also organize into spiral waves, provided that there is some source of rotational symmetry breaking due to external stimuli or noise. In the high gain limit, no oscillatory behavior exists, but a transient stimulus can lead to a single, outward propagating target wave.     

Neural action fields for optic flow based navigation: a simulation study of the fly lobula plate network

Optic flow based navigation is a fundamental way of visual course control described in many different species including man. In the fly, an essential part of optic flow analysis is performed in the lobula plate, a retinotopic map of motion in the environment. There, the so-called lobula plate tangential cells possess large receptive fields with different preferred directions in different parts of the visual field. Previous studies demonstrated an extensive connectivity between different tangential cells, providing, in principle, the structural basis for their large and complex receptive fields. We present a network simulation of the tangential cells, comprising most of the neurons studied so far (22 on each hemisphere) with all the known connectivity between them. On their dendrite, model neurons receive input from a retinotopic array of Reichardt-type motion detectors. Model neurons exhibit receptive fields much like their natural counterparts, demonstrating that the connectivity between the lobula plate tangential cells indeed can account for their complex receptive field structure. We describe the tuning of a model neuron to particular types of ego-motion (rotation as well as translation around/along a given body axis) by its 'action field'. As we show for model neurons of the vertical system (VS-cells), each of them displays a different type of action field, i.e., responds maximally when the fly is rotating around a particular body axis. However, the tuning width of the rotational action fields is relatively broad, comparable to the one with dendritic input only. The additional intra-lobula-plate connectivity mainly reduces their translational action field amplitude, i.e., their sensitivity to translational movements along any body axis of the fly.     

A simulation study of oscillating glycolysis: a comparison between a model and experiments

Glycolysis is the best known biochemical oscillator and suitable for the exploration of the basic features of biological rhythms on a biochemical and mathematical level. Because of our detailed knowledge of its component structure (enzyme kinetics, metabolite pattern) glycolysis can be described by a set of coupled nonlinear differential equations of first order with respect to time, whose individual terms consist of enzyme velocities assuming a steady state hypothesis for the enzymatic forms. Due to the feedback control of PFK by the adenylates the system is able to oscillate. The outcomes of a simplified model, containing only the basic elements of glycolysis, show good agreements with experimental results.     

A simulation study of a time lag population model

The lack of terms representing time lags is a widely recognized weakness of the Volterra-Gause formulations of population growth and interaction. A number of analytical attempts to include time lag terms have been made in the past, but they have provided relatively little ecological insight.     

Distance models in ecological network management: A case study of patch connectivity in a grassland network

Landscape connectivity is a key issue of nature conservation and distance parameters are essential for the calculation of patch level metrics. For such calculations the so-called Euclidean and the least cost distance are the most widespread models. In the present work we tested both distance models for landscape connectivity, using connectivity metrics in the case of a grassland mosaic, and the ground beetle Pterostichus melas as a focal species. Our goal was to explore the dissimilarity between the two distance models and the consequent divergence from the calculated values of patch relevance in connectivity. We found that the two distance models calculated the distances similarly, but their estimations were more reliable over short distances (circa 500 m), than long distances (circa 3000 m). The variability in the importance of habitat patches (i.e. patch connectivity indices) was estimated by the difference between the two distance models (Euclidean vs. least cost) according to the patch size. The location of the habitat patches in the matrix seemed to be a more important factor than the habitat size in the estimation of connectivity. The uncertainty of three patch connectivity indices (Integral Index of Connectivity, Probability of Connectance and Flux) became high above a habitat size of 5 ha. Relevance of patches in maintaining connectivity varied even within small ranges depending on the estimator of distance, revealing the careful consideration of these methods in conservation planning.     

DCC mediated axon guidance of spinal interneurons is essential for normal locomotor central pattern generator function

Coordinated limb rhythmic movements take place through organized signaling in local spinal cord neuronal networks. The establishment of these circuitries during development is dependent on the correct guidance of axons to their targets. It has previously been shown that the well-known axon guidance molecule netrin-1 is required for configuring the circuitry that provides left-right alternating coordination in fictive locomotion. The attraction of commissural axons to the midline in response to netrin-1 has been shown to involve the netrin-1 receptor DCC (deleted in Colorectal Cancer). However, the role of DCC for the establishment of CPG coordination has not yet been resolved. We show that mice carrying a null mutation of DCC displayed an uncoordinated left-right activity during fictive locomotion accompanied by a loss of interneuronal subpopulations originating from commissural progenitors. Thus, DCC plays a crucial role in the formation of spinal neuronal circuitry coordinating left-right activities. Together with the previously published results from netrin-1 deficient mice, the data presented in this study suggest a role for the most ventral originating V3 interneurons in synchronous activities over the midline. Further, it provides evidence that axon crossing in the spinal cord is more intricately controlled than in previously suggested models of DCC-netrin-1 interaction.