Magnus J. E. Richardson

Velocity and curvature in human locomotion along complex curved paths : a comparison with hand movements

Abstract There is extensive experimental evidence linking instantaneous velocity to curvature in drawing and hand-writing movements. The empirical relationship between these characteristics of motion and path is well described by a power law in which the velocity varies in proportion to the one-third power of the radius of curvature. It was recently shown that a similar relationship can be observed during locomotion along curved elliptical paths raising the possibility that these very different motor activities might, at some level, share the same planning strategies. It has, however, been noted that the ellipse is a special case with respect to the one-third power law and therefore these previous results might not provide strong evidence that the one-third power law is a general feature of locomotion around curved paths. For this reason the experimental study of locomotion and its comparison with hand writing is extended here to non-elliptical paths. Subjects walked along predefined curved paths consisting of two complex shapes drawn on the ground: the cloverleaf and the limacon. It was found that the data always supported a close relationship between instantaneous velocity and curvature. For these more complex paths, however, the relationship is shape-dependent—although velocity and curvature can still be linked by a power law, the exponent depends on the geometrical form of the path. The results demonstrate the existence of a close relationship between instantaneous velocity and curvature in locomotion that is more general than the one-third power law. The origins of this relationship and its possible explanation in the mechanical balance of forces and in central planning are discussed.

Synaptic Shot Noise and Conductance Fluctuations Affect the Membrane Voltage with Equal Significance

The subthreshold membrane voltage of a neuron in active cortical tissue is a fluctuating quantity with a distribution that reflects the firing statistics of the presynaptic population. It was recently found that conductance-based synaptic drive can lead to distributions with a significant skew. Here it is demonstrated that the underlying shot noise caused by Poissonian spike arrival also skews the membrane distribution, but in the opposite sense. Using a perturbative method, we analyze the effects of shot noise on the distribution of synaptic conductances and calculate the consequent voltage distribution. To first order in the perturbation theory, the voltage distribution is a gaussian modulated by a prefactor that captures the skew. The gaussian component is identical to distributions derived using current-based models with an effective membrane time constant. The well-known effective-time-constant approximation can therefore be identified as the leading-order solution to the full conductance-based model. The higher-order modulatory prefactor containing the skew comprises terms due to both shot noise and conductance fluctuations. The diffusion approximation misses these shot-noise effects implying that analytical approaches such as the Fokker-Planck equation or simulation with filtered white noise cannot be used to improve on the gaussian approximation. It is further demonstrated that quantities used for fitting theory to experiment, such as the voltage mean and variance, are robust against these non-Gaussian effects. The effective-time-constant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added.

Extracting non-linear integrate-and-fire models from experimental data using dynamic I – V curves

The dynamic I–V curve method was recently introduced for the efficient experimental generation of reduced neuron models. The method extracts the response properties of a neuron while it is subject to a naturalistic stimulus that mimics in vivo-like fluctuating synaptic drive. The resulting history-dependent, transmembrane current is then projected onto a one-dimensional current–voltage relation that provides the basis for a tractable non-linear integrate-and-fire model. An attractive feature of the method is that it can be used in spike-triggered mode to quantify the distinct patterns of post-spike refractoriness seen in different classes of cortical neuron. The method is first illustrated using a conductance-based model and is then applied experimentally to generate reduced models of cortical layer-5 pyramidal cells and interneurons, in injected-current and injected- conductance protocols. The resulting low-dimensional neuron models—of the refractory exponential integrate-and-fire type—provide highly accurate predictions for spike-times. The method therefore provides a useful tool for the construction of tractable models and rapid experimental classification of cortical neurons.

Spike-train spectra and network response functions for non-linear integrate-and-fire neurons

Reduced models have long been used as a tool for the analysis of the complex activity taking place in neurons and their coupled networks. Recent advances in experimental and theoretical techniques have further demonstrated the usefulness of this approach. Despite the often gross simplification of the underlying biophysical properties, reduced models can still present significant difficulties in their analysis, with the majority of exact and perturbative results available only for the leaky integrate-and-fire model. Here an elementary numerical scheme is demonstrated which can be used to calculate a number of biologically important properties of the general class of non-linear integrate-and-fire models. Exact results for the first-passage-time density and spike-train spectrum are derived, as well as the linear response properties and emergent states of recurrent networks. Given that the exponential integrate-fire model has recently been shown to agree closely with the experimentally measured response of pyramidal cells, the methodology presented here promises to provide a convenient tool to facilitate the analysis of cortical-network dynamics.

Multiquantal release underlies the distribution of synaptic efficacies in the neocortex.

Inter-pyramidal synaptic connections are characterized by a wide range of EPSP amplitudes. Although repeatedly observed at different brain regions and across layers, little is known about the synaptic characteristics that contribute to this wide range. In particular, the range could potentially be accounted for by differences in all three parameters of the quantal model of synaptic transmission, i.e. the number of release sites, release probability and quantal size. Here, we present a rigorous statistical analysis of the transmission properties of excitatory synaptic connections between layer-5 pyramidal neurons of the somato-sensory cortex. Our central finding is that the EPSP amplitude is strongly correlated with the number of estimated release sites, but not with the release probability or quantal size. In addition, we found that the number of release sites can be more than an order of magnitude higher than the typical number of synaptic contacts for this type of connection. Our findings indicate that transmission at stronger synaptic connections is mediated by multiquantal release from their synaptic contacts. We propose that modulating the number of release sites could be an important mechanism in regulating neocortical synaptic transmission.

Single neuron dynamics and computation

At the single neuron level, information processing involves the transformation of input spike trains into an appropriate output spike train. Building upon the classical view of a neuron as a threshold device, models have been developed in recent years that take into account the diverse electrophysiological make-up of neurons and accurately describe their input-output relations. Here, we review these recent advances and survey the computational roles that they have uncovered for various electrophysiological properties, for dendritic arbor anatomy as well as for short-term synaptic plasticity.

Short-term synaptic plasticity orchestrates the response of pyramidal cells and interneurons to population bursts.

The synaptic drive from neuronal populations varies considerably over short time scales. Such changes in the pre-synaptic rate trigger many temporal processes absent under steady-state conditions. This paper examines the differential impact of pyramidal cell population bursts on post-synaptic pyramidal cells receiving depressing synapses, and on a class of interneuron that receives facilitating synapses. In experiment a significant shift of the order of one hundred milliseconds is seen between the response of these two cell classes to the same population burst. It is demonstrated here that such a temporal differentiation of the response can be explained by the synaptic and membrane properties without recourse to elaborate cortical wiring schemes. Experimental data is first used to construct models of the two types of dynamic synaptic response. A population-based approach is then followed to examine analytically the temporal synaptic filtering effects of the population burst for the two post-synaptic targets. The peak-to-peak delays seen in experiment can be captured by the model for experimentally realistic parameter ranges. It is further shown that the temporal separation of the response is communicated in the outgoing action potentials of the two post-synaptic cells: pyramidal cells fire at the beginning of the burst and the class of interneuron receiving facilitating synapses fires at the end of the burst. The functional role of such delays in the temporal organisation of activity in the cortical microcircuit is discussed.

The dynamics of single spike-evoked adenosine release in the cerebellum

Adenosine modulates brain activity in both health and disease. Although we know a lot about adenosine action, we know little about how it is released and its cellular sources. We have previously shown that adenosine can be released in the cerebellum by a train of action potentials. Here we have used a pharmacological agent to enhance adenosine release and can thus study release in response to a single action potential. The release follows a waveform that is well described by a minimal diffusion model from a temporally sharp release event. Adenosine release has a complex, history‐dependent dynamics: it can be either depressed or enhanced depending on the stimulation pattern – similar properties to those of fast neurotransmitters such as glutamate. Our results demonstrate that the dynamics of adenosine release will depend strongly on the pattern of neural activity and thus constitutes a highly complex signalling pathway in the nervous system.

Matched Pre- and Post-Synaptic Changes Underlie Synaptic Plasticity over Long Time Scales

Modifications of synaptic efficacies are considered essential for learning and memory. However, it is not known how the underlying functional components of synaptic transmission change over long time scales. To address this question, we studied cortical synapses from young Wistar rats before and after 12 h intervals of spontaneous or glutamate-induced spiking activity. We found that, under these conditions, synaptic efficacies can increase or decrease by up to 10-fold. Statistical analyses reveal that these changes reflect modifications in the number of presynaptic release sites, together with postsynaptic changes that maintain the quantal size per release site. The quantitative relation between the presynaptic and postsynaptic transmission components was not affected when synaptic plasticity was enhanced or reduced using a broad range of pharmacological agents. These findings suggest that ongoing synaptic plasticity results in matched presynaptic and postsynaptic modifications, in which elementary modules that span the synaptic cleft are added or removed as a function of experience.

Adenosine A1 receptor activation mediates the developmental shift at layer 5 pyramidal cell synapses and is a determinant of mature synaptic strength

•  Neocortical layer 5 pyramidal cell synapses exhibit a developmental reduction in neurotransmitter release probability. Mature synapses are weaker, less reliable and show greater facilitation than immature connections. •  Using paired intracellular recordings our study identifies the mechanism that mediates this developmental change as being due to an increased activation of presynaptic adenosine A1 receptors. •  Unlike immature connections, which showed little A1 receptor activation, mature connections demonstrated a broad range of activation that was inversely correlated to mature synaptic strength. •  We show that the functional efficacy of A1 receptors does not change over development and so our evidence points to concentrations of extracellular adenosine at synapses increasing locally over development. •  The increased adenosine levels significantly affect synaptic efficacy suggesting that the emplacement of adenosine sources and sinks might be a novel mechanism for long‐term plasticity at layer 5 pyramidal cell synapses.