Self-tuning of neural circuits through short-term synaptic plasticity
D. Sussillo and T. Toyoizumi and W. Maass
J Neurophysiol 97 4079-95 (2007)
Numerous experimental data show that cortical networks of neurons are not silent in the absence of external inputs, but rather maintain a low spontaneous firing activity. This aspect of cortical networks is likely to be important for their computational function, but is hard to reproduce in models of cortical circuits of neurons because the low-activity regime is inherently unstable. Here we show-through theoretical analysis and extensive computer simulations-that short-term synaptic plasticity endows models of cortical circuits with a remarkable stability in the low-activity regime. This short-term plasticity works as a homeostatic mechanism that stabilizes the overall activity level in spite of drastic changes in external inputs and internal circuit properties, while preserving reliable transient responses to signals. The contribution of synaptic dynamics to this stability can be predicted on the basis of general principles from control theory.
Diversity of intrinsic frequency encoding patterns in rat cortical neurons--mechanisms and possible functions
J. Kang and H. P. C. Robinson and J. Feng
PLoS One 5 e9608 (2010)
Extracellular recordings of single neurons in primary and secondary somatosensory cortices of monkeys in vivo have shown that their firing rate can increase, decrease, or remain constant in different cells, as the external stimulus frequency increases. We observed similar intrinsic firing patterns (increasing, decreasing or constant) in rat somatosensory cortex in vitro, when stimulated with oscillatory input using conductance injection (dynamic clamp). The underlying mechanism of this observation is not obvious, and presents a challenge for mathematical modelling. We propose a simple principle for describing this phenomenon using a leaky integrate-and-fire model with sinusoidal input, an intrinsic oscillation and Poisson noise. Additional enhancement of the gain of encoding could be achieved by local network connections amongst diverse intrinsic response patterns. Our work sheds light on the possible cellular and network mechanisms underlying these opposing neuronal responses, which serve to enhance signal detection.
Metabolic cost as a unifying principle governing neuronal biophysics
A. Hasenstaub and S. Otte and E. Callaway and T. J. Sejnowski
Proc Natl Acad Sci U S A 107 12329-34 (2010)
The brain contains an astonishing diversity of neurons, each expressing only one set of ion channels out of the billions of potential channel combinations. Simple organizing principles are required for us to make sense of this abundance of possibilities and wealth of related data. We suggest that energy minimization subject to functional constraints may be one such unifying principle. We compared the energy needed to produce action potentials singly and in trains for a wide range of channel densities and kinetic parameters and examined which combinations of parameters maximized spiking function while minimizing energetic cost. We confirmed these results for sodium channels using a dynamic current clamp in neocortical fast spiking interneurons. We find further evidence supporting this hypothesis in a wide range of other neurons from several species and conclude that the ion channels in these neurons minimize energy expenditure in their normal range of spiking.
A statistical analysis of information-processing properties of lamina-specific cortical microcircuit models
S. Haeusler and W. Maass
Cereb Cortex 17 149-62 (2007)
A major challenge for computational neuroscience is to understand the computational function of lamina-specific synaptic connection patterns in stereotypical cortical microcircuits. Previous work on this problem had focused on hypothesized specific computational roles of individual layers and connections between layers and had tested these hypotheses through simulations of abstract neural network models. We approach this problem by studying instead the dynamical system defined by more realistic cortical microcircuit models as a whole and by investigating the influence that its laminar structure has on the transmission and fusion of information within this dynamical system. The circuit models that we examine consist of Hodgkin-Huxley neurons with dynamic synapses, based on detailed data from Thomson and others (2002), Markram and others (1998), and Gupta and others (2000). We investigate to what extent this cortical microcircuit template supports the accumulation and fusion of information contained in generic spike inputs into layer 4 and layers 2/3 and how well it makes this information accessible to projection neurons in layers 2/3 and layer 5. We exhibit specific computational advantages of such data-based lamina-specific cortical microcircuit model by comparing its performance with various types of control models that have the same components and the same global statistics of neurons and synaptic connections but are missing the lamina-specific structure of real cortical microcircuits. We conclude that computer simulations of detailed lamina-specific cortical microcircuit models provide new insight into computational consequences of anatomical and physiological data.
Integrated mechanisms of anticipation and rate-of-change computations in cortical circuits
G. D. Puccini and M. V. Sanchez-Vives and A. Compte
PLoS Comput Biol 3 e82 (2007)
Local neocortical circuits are characterized by stereotypical physiological and structural features that subserve generic computational operations. These basic computations of the cortical microcircuit emerge through the interplay of neuronal connectivity, cellular intrinsic properties, and synaptic plasticity dynamics. How these interacting mechanisms generate specific computational operations in the cortical circuit remains largely unknown. Here, we identify the neurophysiological basis of both the rate of change and anticipation computations on synaptic inputs in a cortical circuit. Through biophysically realistic computer simulations and neuronal recordings, we show that the rate-of-change computation is operated robustly in cortical networks through the combination of two ubiquitous brain mechanisms: short-term synaptic depression and spike-frequency adaptation. We then show how this rate-of-change circuit can be embedded in a convergently connected network to anticipate temporally incoming synaptic inputs, in quantitative agreement with experimental findings on anticipatory responses to moving stimuli in the primary visual cortex. Given the robustness of the mechanism and the widespread nature of the physiological machinery involved, we suggest that rate-of-change computation and temporal anticipation are principal, hard-wired functions of neural information processing in the cortical microcircuit.
A microcircuit model of the frontal eye fields
J. Heinzle and K. Hepp and K. A. C. Martin
J Neurosci 27 9341-53 (2007)
The cortical control of eye movements is highly sophisticated. Not only can eye movements be made to the most salient target in a visual scene, but they can also be controlled by top-down rules as is required for visual search or reading. The cortical area called frontal eye fields (FEF) has been shown to play a key role in the visual to oculomotor transformations in tasks requiring an eye movement pattern that is not completely reactive, but follows a previously learned rule. The layered, local cortical circuit, which provides the anatomical substrate for all cortical computation, has been studied extensively in primary sensory cortex. These studies led to the concept of a "canonical circuit" for neocortex (Douglas et al., 1989; Douglas and Martin, 1991), which proposes that all areas of neocortex share a common basic circuit. However, it has not ever been explored whether in principle the detailed canonical circuit derived from cat area 17 (Binzegger et al., 2004) could implement the quite different functions of prefrontal cortex. Here, we show that the canonical circuit can, with a few modifications, model the primate FEF. The spike-based network of integrate-and-fire neurons was tested in tasks that were used in electrophysiological experiments in behaving macaque monkeys. The dynamics of the model matched those of neurons observed in the FEF, and the behavioral results matched those observed in psychophysical experiments. The close relationship between the model and the cortical architecture allows a detailed comparison of the simulation results with physiological data and predicts details of the anatomical circuit of the FEF.
Role of interneuron diversity in the cortical microcircuit for attention
C. I. Buia and P. H. Tiesinga
J Neurophysiol 99 2158-82 (2008)
Receptive fields of neurons in cortical area V4 are large enough to fit multiple stimuli, making V4 the ideal place to study the effects of selective attention at the single-neuron level. Experiments have revealed evidence for stimulus competition and have characterized the effect thereon of spatial and feature-based attention. We developed a biophysical model with spiking neurons and conductance-based synapses. To account for the comprehensive set of experimental results, it was necessary to include in the model, in addition to regular spiking excitatory (E) cells, two types of interneurons: feedforward interneurons (FFI) and top-down interneurons (TDI). Feature-based attention was mediated by a projection of the TDI to the FFI, stimulus competition was mediated by a cross-columnar excitatory connection to the FFI, whereas spatial attention was mediated by an increase in activity of the feedforward inputs from cortical area V2. The model predicts that spatial attention increases the FFI firing rate, whereas feature-based attention decreases the FFI firing rate and increases the TDI firing rate. During strong stimulus competition, the E cells were synchronous in the beta frequency range (15-35 Hz), but with feature-based attention, they became synchronous in the gamma frequency range (35-50 Hz). We propose that the FFI correspond to fast-spiking, parvalbumin-positive basket cells and that the TDI correspond to cells with a double-bouquet morphology that are immunoreactive to calbindin or calretinin. Taken together, the model results provide an experimentally testable hypothesis for the behavior of two interneuron types under attentional modulation.
Specific synapses develop preferentially among sister excitatory neurons in the neocortex
Y.-C. Yu and R. S. Bultje and X. Wang and S.-H. Shi
Nature 458 501-4 (2009)
Neurons in the mammalian neocortex are organized into functional columns. Within a column, highly specific synaptic connections are formed to ensure that similar physiological properties are shared by neuron ensembles spanning from the pia to the white matter. Recent studies indicate that synaptic connectivity in the neocortex is sparse and highly specific to allow even adjacent neurons to convey information independently. How this fine-scale microcircuit is constructed to create a functional columnar architecture at the level of individual neurons largely remains a mystery. Here we investigate whether radial clones of excitatory neurons arising from the same mother cell in the developing neocortex serve as a substrate for the formation of this highly specific microcircuit. We labelled ontogenetic radial clones of excitatory neurons in the mouse neocortex by in utero intraventricular injection of enhanced green fluorescent protein (EGFP)-expressing retroviruses around the onset of the peak phase of neocortical neurogenesis. Multiple-electrode whole-cell recordings were performed to probe synapse formation among these EGFP-labelled sister excitatory neurons in radial clones and the adjacent non-siblings during postnatal stages. We found that radially aligned sister excitatory neurons have a propensity for developing unidirectional chemical synapses with each other rather than with neighbouring non-siblings. Moreover, these synaptic connections display the same interlaminar directional preference as those observed in the mature neocortex. These results indicate that specific microcircuits develop preferentially within ontogenetic radial clones of excitatory neurons in the developing neocortex and contribute to the emergence of functional columnar microarchitectures in the mature neocortex.
Decorrelated neuronal firing in cortical microcircuits
A. S. Ecker and P. Berens and G. A. Keliris and M. Bethge and N. K. Logothetis and A. S. Tolias
Science 327 584-7 (2010)
Correlated trial-to-trial variability in the activity of cortical neurons is thought to reflect the functional connectivity of the circuit. Many cortical areas are organized into functional columns, in which neurons are believed to be densely connected and to share common input. Numerous studies report a high degree of correlated variability between nearby cells. We developed chronically implanted multitetrode arrays offering unprecedented recording quality to reexamine this question in the primary visual cortex of awake macaques. We found that even nearby neurons with similar orientation tuning show virtually no correlated variability. Our findings suggest a refinement of current models of cortical microcircuit architecture and function: Either adjacent neurons share only a few percent of their inputs or, alternatively, their activity is actively decorrelated.
Similar network activity from disparate circuit parameters
A. A. Prinz and D. Bucher and E. Marder
Nat Neurosci 7 1345-52 (2004)
It is often assumed that cellular and synaptic properties need to be regulated to specific values to allow a neuronal network to function properly. To determine how tightly neuronal properties and synaptic strengths need to be tuned to produce a given network output, we simulated more than 20 million versions of a three-cell model of the pyloric network of the crustacean stomatogastric ganglion using different combinations of synapse strengths and neuron properties. We found that virtually indistinguishable network activity can arise from widely disparate sets of underlying mechanisms, suggesting that there could be considerable animal-to-animal variability in many of the parameters that control network activity, and that many different combinations of synaptic strengths and intrinsic membrane properties can be consistent with appropriate network performance.
Variability, compensation and homeostasis in neuron and network function
E. Marder and J.-M. Goaillard
Nat Rev Neurosci 7 563-74 (2006)
Neurons in most animals live a very long time relative to the half-lives of all of the proteins that govern excitability and synaptic transmission. Consequently, homeostatic mechanisms are necessary to ensure stable neuronal and network function over an animal's lifetime. To understand how these homeostatic mechanisms might function, it is crucial to understand how tightly regulated synaptic and intrinsic properties must be for adequate network performance, and the extent to which compensatory mechanisms allow for multiple solutions to the production of similar behaviour. Here, we use examples from theoretical and experimental studies of invertebrates and vertebrates to explore several issues relevant to understanding the precision of tuning of synaptic and intrinsic currents for the operation of functional neuronal circuits.
Variability v.s. synchronicity of neuronal activity in local cortical network models with different wiring topologies
K. Kitano and T. Fukai
J Comput Neurosci 23 237-50 (2007)
Dynamical behavior of a biological neuronal network depends significantly on the spatial pattern of synaptic connections among neurons. While neuronal network dynamics has extensively been studied with simple wiring patterns, such as all-to-all or random synaptic connections, not much is known about the activity of networks with more complicated wiring topologies. Here, we examined how different wiring topologies may influence the response properties of neuronal networks, paying attention to irregular spike firing, which is known as a characteristic of in vivo cortical neurons, and spike synchronicity. We constructed a recurrent network model of realistic neurons and systematically rewired the recurrent synapses to change the network topology, from a localized regular and a "small-world" network topology to a distributed random network topology. Regular and small-world wiring patterns greatly increased the irregularity or the coefficient of variation (Cv) of output spike trains, whereas such an increase was small in random connectivity patterns. For given strength of recurrent synapses, the firing irregularity exhibited monotonous decreases from the regular to the random network topology. By contrast, the spike coherence between an arbitrary neuron pair exhibited a non-monotonous dependence on the topological wiring pattern. More precisely, the wiring pattern to maximize the spike coherence varied with the strength of recurrent synapses. In a certain range of the synaptic strength, the spike coherence was maximal in the small-world network topology, and the long-range connections introduced in this wiring changed the dependence of spike synchrony on the synaptic strength moderately. However, the effects of this network topology were not really special in other properties of network activity.
Probing the dynamics of identified neurons with a data-driven modeling approach
T. Nowotny and R. Levi and A. I. Selverston
PLoS One 3 e2627 (2008)
In controlling animal behavior the nervous system has to perform within the operational limits set by the requirements of each specific behavior. The implications for the corresponding range of suitable network, single neuron, and ion channel properties have remained elusive. In this article we approach the question of how well-constrained properties of neuronal systems may be on the neuronal level. We used large data sets of the activity of isolated invertebrate identified cells and built an accurate conductance-based model for this cell type using customized automated parameter estimation techniques. By direct inspection of the data we found that the variability of the neurons is larger when they are isolated from the circuit than when in the intact system. Furthermore, the responses of the neurons to perturbations appear to be more consistent than their autonomous behavior under stationary conditions. In the developed model, the constraints on different parameters that enforce appropriate model dynamics vary widely from some very tightly controlled parameters to others that are almost arbitrary. The model also allows predictions for the effect of blocking selected ionic currents and to prove that the origin of irregular dynamics in the neuron model is proper chaoticity and that this chaoticity is typical in an appropriate sense. Our results indicate that data driven models are useful tools for the in-depth analysis of neuronal dynamics. The better consistency of responses to perturbations, in the real neurons as well as in the model, suggests a paradigm shift away from measuring autonomous dynamics alone towards protocols of controlled perturbations. Our predictions for the impact of channel blockers on the neuronal dynamics and the proof of chaoticity underscore the wide scope of our approach.
Reliable circuits from irregular neurons: a dynamical approach to understanding central pattern generators
A. I. Selverston and M. I. Rabinovich and H. D. Abarbanel and R. Elson and A. Szücs and R. D. Pinto and R. Huerta and P. Varona
J Physiol Paris 94 357-74 (2000)
Central pattern generating neurons from the lobster stomatogastric ganglion were analyzed using new nonlinear methods. The LP neuron was found to have only four or five degrees of freedom in the isolated condition and displayed chaotic behavior. We show that this chaotic behavior could be regularized by periodic pulses of negative current injected into the neuron or by coupling it to another neuron via inhibitory connections. We used both a modified Hindmarsh-Rose model to simulate the neurons behavior phenomenologically and a more realistic conductance-based model so that the modeling could be linked to the experimental observations. Both models were able to capture the dynamics of the neuron behavior better than previous models. We used the Hindmarsh-Rose model as the basis for building electronic neurons which could then be integrated into the biological circuitry. Such neurons were able to rescue patterns which had been disabled by removing key biological neurons from the circuit.
Using a model to assess the role of the spatiotemporal pattern of inhibitory input and intrasegmental electrical coupling in the intersegmental and side-to-side coordination of motor neurons by the leech heartbeat central pattern generator
P. S. García and T. M. Wright and I. R. Cunningham and R. L. Calabrese
J Neurophysiol 100 1354-71 (2008)
Previously we presented a quantitative description of the spatiotemporal pattern of inhibitory synaptic input from the heartbeat central pattern generator (CPG) to segmental motor neurons that drive heartbeat in the medicinal leech and the resultant coordination of CPG interneurons and motor neurons. To begin elucidating the mechanisms of coordination, we explore intersegmental and side-to-side coordination in an ensemble model of all heart motor neurons and their known synaptic inputs and electrical coupling. Model motor neuron intrinsic properties were kept simple, enabling us to determine the extent to which input and electrical coupling acting together can account for observed coordination in the living system in the absence of a substantive contribution from the motor neurons themselves. The living system produces an asymmetric motor pattern: motor neurons on one side fire nearly in synchrony (synchronous), whereas on the other they fire in a rear-to-front progression (peristaltic). The model reproduces the general trends of intersegmental and side-to-side phase relations among motor neurons, but the match with the living system is not quantitatively accurate. Thus realistic (experimentally determined) inputs do not produce similarly realistic output in our model, suggesting that motor neuron intrinsic properties may contribute to their coordination. By varying parameters that determine electrical coupling, conduction delays, intraburst synaptic plasticity, and motor neuron excitability, we show that the most important determinant of intersegmental and side-to-side phase relations in the model was the spatiotemporal pattern of synaptic inputs, although phasing was influenced significantly by electrical coupling.
The electrotonic structure of pyramidal neurons contributing to prefrontal cortical circuits in macaque monkeys is significantly altered in aging
D. Kabaso and P. J. Coskren and B. I. Henry and P. R. Hof and S. L. Wearne
Cereb Cortex 19 2248-68 (2009)
Whereas neuronal numbers are largely preserved in normal aging, subtle morphological changes occur in dendrites and spines, whose electrotonic consequences remain unexplored. We examined age-related morphological alterations in 2 types of pyramidal neurons contributing to working memory circuits in the macaque prefrontal cortex (PFC): neurons in the superior temporal cortex forming "long" projections to the PFC and "local" projection neurons within the PFC. Global dendritic mass homeostasis, measured by 3-dimensional scaling analysis, was conserved with aging in both neuron types. Spine densities, dendrite diameters, lengths, and branching complexity were all significantly reduced in apical dendrites of long projection neurons with aging, but only spine parameters were altered in local projection neurons. Despite these differences, voltage attenuation due to passive electrotonic structure, assuming equivalent cable parameters, was significantly reduced with aging in the apical dendrites of both neuron classes. Confirming the electrotonic analysis, simulated passive backpropagating action potential efficacy was significantly higher in apical but not basal dendrites of old neurons. Unless compensated by changes in passive cable parameters, active membrane properties, or altered synaptic properties, these effects will increase the excitability of pyramidal neurons, compromising the precisely tuned activity required for working memory, ultimately resulting in age-related PFC dysfunction.
Neuronal firing sensitivity to morphologic and active membrane parameters
C. M. Weaver and S. L. Wearne
PLoS Comput Biol 4 e11 (2008)
Both the excitability of a neuron's membrane, driven by active ion channels, and dendritic morphology contribute to neuronal firing dynamics, but the relative importance and interactions between these features remain poorly understood. Recent modeling studies have shown that different combinations of active conductances can evoke similar firing patterns, but have neglected how morphology might contribute to homeostasis. Parameterizing the morphology of a cylindrical dendrite, we introduce a novel application of mathematical sensitivity analysis that quantifies how dendritic length, diameter, and surface area influence neuronal firing, and compares these effects directly against those of active parameters. The method was applied to a model of neurons from goldfish Area II. These neurons exhibit, and likely contribute to, persistent activity in eye velocity storage, a simple model of working memory. We introduce sensitivity landscapes, defined by local sensitivity analyses of firing rate and gain to each parameter, performed globally across the parameter space. Principal directions over which sensitivity to all parameters varied most revealed intrinsic currents that most controlled model output. We found domains where different groups of parameters had the highest sensitivities, suggesting that interactions within each group shaped firing behaviors within each specific domain. Application of our method, and its characterization of which models were sensitive to general morphologic features, will lead to advances in understanding how realistic morphology participates in functional homeostasis. Significantly, we can predict which active conductances, and how many of them, will compensate for a given age- or development-related structural change, or will offset a morphologic perturbation resulting from trauma or neurodegenerative disorder, to restore normal function. Our method can be adapted to analyze any computational model. Thus, sensitivity landscapes, and the quantitative predictions they provide, can give new insight into mechanisms of homeostasis in any biological system.
Complex parameter landscape for a complex neuron model
P. Achard and E. De Schutter
PLoS Comput Biol 2 e94 (2006)
The electrical activity of a neuron is strongly dependent on the ionic channels present in its membrane. Modifying the maximal conductances from these channels can have a dramatic impact on neuron behavior. But the effect of such modifications can also be cancelled out by compensatory mechanisms among different channels. We used an evolution strategy with a fitness function based on phase-plane analysis to obtain 20 very different computational models of the cerebellar Purkinje cell. All these models produced very similar outputs to current injections, including tiny details of the complex firing pattern. These models were not completely isolated in the parameter space, but neither did they belong to a large continuum of good models that would exist if weak compensations between channels were sufficient. The parameter landscape of good models can best be described as a set of loosely connected hyperplanes. Our method is efficient in finding good models in this complex landscape. Unraveling the landscape is an important step towards the understanding of functional homeostasis of neurons.
Cellular, synaptic, network, and modulatory mechanisms involved in rhythm generation
R. L. Calabrese
Curr Opin Neurobiol 8 710-7 (1998)
The membrane properties and the synaptic interactions of individual neurons, as well as the interactions between neuronal networks, all contribute to the formation of the complex patterns of activity that underlie rhythmic motor patterns and slow-wave sleep rhythms. These properties and interactions are potential points of modulation for further refining network output. Recent work illustrates the range of these properties and interactions and suggests how they may be modulated.
A central pattern generator producing alternative outputs: temporal pattern of premotor activity
B. J. Norris and A. L. Weaver and L. G. Morris and A. Wenning and P. A. García and R. L. Calabrese
J Neurophysiol 96 309-26 (2006)
The central pattern generator for heartbeat in medicinal leeches constitutes seven identified pairs of segmental heart interneurons. Four identified pairs of heart interneurons make a staggered pattern of inhibitory synaptic connections with segmental heart motor neurons. Using extracellular recording from multiple interneurons in the network in 56 isolated nerve cords, we show that this pattern generator produces a side-to-side asymmetric pattern of intersegmental coordination among ipsilateral premotor interneurons. This pattern corresponds to a similarly asymmetric fictive motor pattern in heart motor neurons and asymmetric constriction pattern of the two tubular hearts, synchronous and peristaltic. We provide a quantitative description of the firing pattern of all the premotor interneurons, including phase, duty cycle, and intraburst frequency of this premotor activity pattern. This analysis identifies two stereotypical coordination modes corresponding to synchronous and peristaltic, which show phase constancy over a broad range of periods as do the fictive motor pattern and the heart constriction pattern. Coordination mode is controlled through one segmental pair of heart interneurons (switch interneurons). Side-to-side switches in coordination mode are a regular feature of this pattern generator and occur with changes in activity state of these switch interneurons. Associated with synchronous coordination of premotor interneurons, the ipsilateral switch interneuron is in an active state, during which it produces rhythmic bursts, whereas associated with peristaltic coordination, the ipsilateral switch interneuron is largely silent. We argue that timing and pattern elaboration are separate functions produced by overlapping subnetworks in the heartbeat central pattern generator.
Using constraints on neuronal activity to reveal compensatory changes in neuronal parameters
A. V. Olypher and R. L. Calabrese
J Neurophysiol 98 3749-58 (2007)
In this study, we developed a general description of parameter combinations for which specified characteristics of neuronal or network activity are constant. Our approach is based on the implicit function theorem and is applicable to activity characteristics that smoothly depend on parameters. Such smoothness is often intrinsic to neuronal systems when they are in stable functional states. The conclusions about how parameters compensate each other, developed in this study, can thus be used even without regard to the specific mathematical model describing a particular neuron or neuronal network. We showed that near a generic point in the parameter space there are infinitely many other points, or parameter combinations, for which specified characteristics of activity are the same as in the original point. These parameter combinations form a smooth manifold. This manifold can be extended as long as the gradients of characteristics are defined and independent. All possible variations of parameters compensating each other are simply all possible charts of the same manifold. The number of compensating parameters (but not parameters themselves) is fixed and equal to the number of the independent characteristics maintained. The algorithm that we developed shows how to find compensatory functional dependencies between parameters numerically. Our method can be used in the analysis of the homeostatic regulation, neuronal database search, model tuning and other applications.
How does maintenance of network activity depend on endogenous dynamics of isolated neurons?
A. V. Olypher and R. L. Calabrese
Neural Comput 21 1665-82 (2009)
Robust activity of some networks, such as central pattern generators, suggests the existence of physiological mechanisms that maintain the most important characteristics, for example, the period and spike frequency of the pattern. Whatever these mechanisms are, they change the appropriate model parameters to or along the isomanifolds on which the characteristics of the pattern are constant, while their sensitivities to parameters may be different. Setting synaptic connections to zero at the points of isomanifolds allows for dissecting the maintenance mechanisms into components involving synaptic transmission and components involving intrinsic currents. The physiological meaning of the intrinsic current changes might be revealed by analysis of their impact on endogenous neuronal dynamics. Here, we sought answers to two questions: (1) Do parameter variations in insensitive directions (along isomanifolds) change endogenous dynamics of the network neurons? (2) Do sensitive and insensitive directions for network pattern characteristics depend on endogenous dynamics of the network neurons? We considered a leech heartbeat half-center oscillator model network and analyzed isomanifolds on which the burst period or spike frequency of the model, or both, are constant. Based on our analysis, we hypothesize that the dependence on endogenous dynamics of the isolated neurons is the stronger the more characteristics of the pattern have to be maintained. We also found that in general, the network was more flexible when it consisted of endogenously tonically spiking rather than bursting or silent neurons. Finally, we discuss the physiological implications of our findings.
Consistent dynamics suggests tight regulation of biophysical parameters in a small network of bursting neurons
A. Szücs and A. I. Selverston
J Neurobiol 66 1584-601 (2006)
The neuronal firing patterns in the pyloric network of crustaceans are remarkably consistent among animals. Although this characteristic of the pyloric network is well-known, the biophysical mechanisms underlying the regulation of the systems output are receiving renewed attention. Computer simulations of the pyloric network recently demonstrated that consistent motor output can be achieved from neurons with disparate biophysical parameters among animals. Here we address this hypothesis by pharmacologically manipulating the pyloric network and analyzing the emerging voltage oscillations and firing patterns. Our results show that the pyloric network of the lobster stomatogastric ganglion maintains consistent and regular firing patterns even when entire populations of specific voltage-gated channels and synaptic receptors are blocked. The variations of temporal parameters used to characterize the burst patterns of the neurons as well as their intraburst spike dynamics do not display statistically significant increase after blocking the transient K-currents (with 4-aminopyridine), the glutamatergic inhibitory synapses (with picrotoxin), or the cholinergic synapses (with atropine) in pyloric networks from different animals. These data suggest that in this very compact circuit, the biophysical parameters are cell-specific and tightly regulated.
Models wagging the dog: are circuits constructed with disparate parameters?
T. Nowotny and A. Szücs and R. Levi and A. I. Selverston
Neural Comput 19 1985-2003 (2007)
In a recent article, Prinz, Bucher, and Marder (2004) addressed the fundamental question of whether neural systems are built with a fixed blueprint of tightly controlled parameters or in a way in which properties can vary largely from one individual to another, using a database modeling approach. Here, we examine the main conclusion that neural circuits indeed are built with largely varying parameters in the light of our own experimental and modeling observations. We critically discuss the experimental and theoretical evidence, including the general adequacy of database approaches for questions of this kind, and come to the conclusion that the last word for this fundamental question has not yet been spoken.
Determining Burst Firing Time Distributions from Multiple Spike Trains
L. F. Lago-Fernández and A. Szücs and P. Varona
Neural Comput 21 973-90 (2009)
Recent experimental findings have shown the presence of robust and cell-type-specific intraburst firing patterns in bursting neurons. We address the problem of characterizing these patterns under the assumption that the bursts exhibit well-defined firing time distributions. We propose a method for estimating these distributions based on a burst alignment algorithm that minimizes the overlap among the firing time distributions of the different spikes within the burst. This method provides a good approximation to the burst's intrinsic temporal structure as a set of firing time distributions. In addition, the method allows labeling the spikes in any particular burst, establishing a correspondence between each spike and the distribution that best explains it, and identifying missing spikes. Our results on both simulated and experimental data from the lobster stomatogastric ganglion show that the proposed method provides a reliable characterization of the intraburst firing patterns and avoids the errors derived from missing spikes. This method can also be applied to nonbursting neurons as a general tool for the study and the interpretation of firing time distributions as part of a temporal neural code.
Robust microcircuit synchronization by inhibitory connections
A. Szücs and R. Huerta and M. I. Rabinovich and A. I. Selverston
Neuron 61 439-53 (2009)
Microcircuits in different brain areas share similar architectural and biophysical properties with compact motor networks known as central pattern generators (CPGs). Consequently, CPGs have been suggested as valuable biological models for understanding of microcircuit dynamics and particularly, their synchronization. We use a well known compact motor network, the lobster pyloric CPG to study principles of intercircuit synchronization. We couple separate pyloric circuits obtained from two animals via artificial synapses and observe how their synchronization depends on the topology and kinetic parameters of the computer-generated synapses. Stable in-phase synchronization appears when electrically coupling the pacemaker groups of the two networks, but reciprocal inhibitory connections produce more robust and regular cooperative activity. Contralateral inhibitory connections offer effective synchronization and flexible setting of the burst phases of the interacting networks. We also show that a conductance-based mathematical model of the coupled circuits correctly reproduces the observed dynamics illustrating the generality of the phenomena.
Consistency and diversity of spike dynamics in the neurons of bed nucleus of stria terminalis of the rat: a dynamic clamp study
A. Szücs and F. Berton and T. Nowotny and P. Sanna and W. Francesconi
PLoS One 5 e11920 (2010)
Neurons display a high degree of variability and diversity in the expression and regulation of their voltage-dependent ionic channels. Under low level of synaptic background a number of physiologically distinct cell types can be identified in most brain areas that display different responses to standard forms of intracellular current stimulation. Nevertheless, it is not well understood how biophysically different neurons process synaptic inputs in natural conditions, i.e., when experiencing intense synaptic bombardment in vivo. While distinct cell types might process synaptic inputs into different patterns of action potentials representing specific "motifs" of network activity, standard methods of electrophysiology are not well suited to resolve such questions. In the current paper we performed dynamic clamp experiments with simulated synaptic inputs that were presented to three types of neurons in the juxtacapsular bed nucleus of stria terminalis (jcBNST) of the rat. Our analysis on the temporal structure of firing showed that the three types of jcBNST neurons did not produce qualitatively different spike responses under identical patterns of input. However, we observed consistent, cell type dependent variations in the fine structure of firing, at the level of single spikes. At the millisecond resolution structure of firing we found high degree of diversity across the entire spectrum of neurons irrespective of their type. Additionally, we identified a new cell type with intrinsic oscillatory properties that produced a rhythmic and regular firing under synaptic stimulation that distinguishes it from the previously described jcBNST cell types. Our findings suggest a sophisticated, cell type dependent regulation of spike dynamics of neurons when experiencing a complex synaptic background. The high degree of their dynamical diversity has implications to their cooperative dynamics and synchronization.
Neuromodulation of spike-timing precision in sensory neurons
C. P. Billimoria and R. A. DiCaprio and J. T. Birmingham and L. F. Abbott and E. Marder
J Neurosci 26 5910-9 (2006)
The neuropeptide allatostatin decreases the spike rate in response to time-varying stretches of two different crustacean mechanoreceptors, the gastropyloric receptor 2 in the crab Cancer borealis and the coxobasal chordotonal organ (CBCTO) in the crab Carcinus maenas. In each system, the decrease in firing rate is accompanied by an increase in the timing precision of spikes triggered by discrete temporal features in the stimulus. This was quantified by calculating the standard deviation or "jitter" in the times of individual identified spikes elicited in response to repeated presentations of the stimulus. Conversely, serotonin increases the firing rate but decreases the timing precision of the CBCTO response. Intracellular recordings from the afferents of this receptor demonstrate that allatostatin increases the conductance of the neurons, consistent with its inhibitory action on spike rate, whereas serotonin decreases the overall membrane conductance. We conclude that spike-timing precision of mechanoreceptor afferents in response to dynamic stimulation can be altered by neuromodulators acting directly on the afferent neurons.
Understanding circuit dynamics using the stomatogastric nervous system of lobsters and crabs
E. Marder and D. Bucher
Annu Rev Physiol 69 291-316 (2007)
Studies of the stomatogastric nervous systems of lobsters and crabs have led to numerous insights into the cellular and circuit mechanisms that generate rhythmic motor patterns. The small number of easily identifiable neurons allowed the establishment of connectivity diagrams among the neurons of the stomatogastric ganglion. We now know that (a) neuromodulatory substances reconfigure circuit dynamics by altering synaptic strength and voltage-dependent conductances and (b) individual neurons can switch among different functional circuits. Computational and experimental studies of single-neuron and network homeostatic regulation have provided insight into compensatory mechanisms that can underlie stable network performance. Many of the observations first made using the stomatogastric nervous system can be generalized to other invertebrate and vertebrate circuits.
Reliable neuromodulation from circuits with variable underlying structure
R. Grashow and T. Brookings and E. Marder
Proc Natl Acad Sci U S A 106 11742-6 (2009)
Recent work argues that similar network performance can result from highly variable sets of network parameters, raising the question of whether neuromodulation can be reliable across individuals with networks with different sets of synaptic strengths and intrinsic membrane conductances. To address this question, we used the dynamic clamp to construct 2-cell reciprocally inhibitory networks from gastric mill (GM) neurons of the crab stomatogastric ganglion. When the strength of the artificial inhibitory synapses (g(syn)) and the conductance of an artificial I(h) (g(h)) were varied with the dynamic clamp, a variety of network behaviors resulted, including regions of stable alternating bursting. Maps of network output as a function of g(syn) and g(h) were constructed in normal saline and again in the presence of serotonin or oxotremorine. Both serotonin and oxotremorine depolarize and excite isolated individual GM neurons, but by different cellular mechanisms. Serotonin and oxotremorine each increased the size of the parameter regions that supported alternating bursting, and, on average, increased burst frequency. Nonetheless, in both cases some parameter sets within the sample space deviated from the mean population response and decreased in frequency. These data provide insight into why pharmacological treatments that work in most individuals can generate anomalous actions in a few individuals, and they have implications for understanding the evolution of nervous systems.
Functional consequences of animal-to-animal variation in circuit parameters
J.-M. Goaillard and A. L. Taylor and D. J. Schulz and E. Marder
Nat Neurosci 12 1424-30 (2009)
How different are the neuronal circuits for a given behavior across individual animals? To address this question, we measured multiple cellular and synaptic parameters in individual preparations to see how they correlated with circuit function, using neurons and synapses in the pyloric circuit of the stomatogastric ganglion of the crab Cancer borealis. There was considerable preparation-to-preparation variability in the strength of two identified synapses, in the amplitude of a modulator-evoked current and in the expression of six ion channel genes. Nonetheless, we found strong correlations across preparations among these parameters and attributes of circuit performance. These data illustrate the importance of making multidimensional measurements from single preparations for understanding how variability in circuit output is related to the variability of multiple circuit parameters.