Dynamic-clamp analysis of the effects of convergence on spike timing. II. Few synaptic inputs

Sensory pathways in the nervous system possess mechanisms for decreasing spike-timing variability ("jitter"), probably to increase acuity. Most studies of jitter reduction have focused on convergence of many subthreshold inputs. However, many neurons receive only a few active inputs at any given time, and jitter reduction under these conditions is not well understood. We examined this issue using dynamic-clamp recordings in slices from mouse auditory brain stem. Significant jitter reduction was possible with as few as two inputs, provided the inputs had several features. First, jitter reduction was greatest and most reliable for supra-threshold inputs. Second, significant jitter reduction occurred when the distribution of input times had a rapid onset, i.e., for alpha- but not for Gaussian-distributed inputs. Third, jitter reduction was compromised unless late inputs were suppressed by the refractory period of the cell. These results contrast with the finding in the previous paper in which many subthreshold inputs contribute to jitter reduction, whether alpha- or Gaussian-distributed. In addition, convergence of many subthreshold inputs could fail to elicit any postsynaptic response when the input distribution outlasted the refractory period of the cell. These significant differences indicate that each means of reducing jitter has advantages and disadvantages and may be more effective for different neurons depending on the properties of their inputs.     

Dynamic-clamp analysis of the effects of convergence on spike timing. I. Many synaptic inputs

Precise action potential timing is crucial in sensory acuity and motor control. Convergence of many synaptic inputs is thought to provide a means of decreasing spike-timing variability ("jitter"), but its effectiveness has never been tested in real neurons. We used the dynamic-clamp technique in mouse auditory brain stem slices to examine how convergence controls spike timing. We tested the roles of several synaptic properties that are influenced by ongoing activity in vivo: the number of active inputs (N), their total synaptic conductance (G(tot)), and their timing, which can resemble an alpha or a Gaussian distribution. Jitter was reduced most with large N, up to a factor of over 20. Variability in N is likely to occur in vivo, but this added little jitter. Jitter reduction also depended on the timing of inputs: alpha-distributed inputs were more effective than Gaussian-distributed inputs. Furthermore, the two distributions differed in their sensitivity to synaptic conductance: for Gaussian-distributed inputs, jitter was most reduced when G(tot) was 2-3 times threshold, whereas alpha-distributed inputs showed continued jitter reduction with higher G(tot). However, very high G(tot) caused the postsynaptic cell to fire multiple times, particularly when the input jitter outlasted the cell's refractory period, which interfered with jitter reduction. G(tot) also greatly affected the response latency, which could influence downstream computations. Changes in G(tot) are likely to arise in vivo through activity-dependent changes in synaptic strength. High rates of postsynaptic activity increased the number of synaptic inputs required to evoke a postsynaptic response. Despite this, jitter was still effectively reduced, particularly in cases when this increased threshold eliminated secondary spikes. Thus these studies provide insight into how specific features of converging inputs control spike timing.     

Reinforcement learning with modulated spike timing dependent synaptic plasticity

Spike timing-dependent synaptic plasticity (STDP) has emerged as the preferred framework linking patterns of pre- and postsynaptic activity to changes in synaptic strength. Although synaptic plasticity is widely believed to be a major component of learning, it is unclear how STDP itself could serve as a mechanism for general purpose learning. On the other hand, algorithms for reinforcement learning work on a wide variety of problems, but lack an experimentally established neural implementation. Here, we combine these paradigms in a novel model in which a modified version of STDP achieves reinforcement learning. We build this model in stages, identifying a minimal set of conditions needed to make it work. Using a performance-modulated modification of STDP in a two-layer feedforward network, we can train output neurons to generate arbitrarily selected spike trains or population responses. Furthermore, a given network can learn distinct responses to several different input patterns. We also describe in detail how this model might be implemented biologically. Thus our model offers a novel and biologically plausible implementation of reinforcement learning that is capable of training a neural population to produce a very wide range of possible mappings between synaptic input and spiking output.     

Retinogeniculate synaptic properties controlling spike number and timing in relay neurons

Retinal ganglion cells (RGC) transmit visual signals to thalamocortical relay neurons in the lateral geniculate nucleus via retinogeniculate synapses. Relay neuron spike patterns do not simply reflect those of RGCs, but the mechanisms controlling this transformation are not well understood. We therefore examined synaptic properties controlling the strength and precision of relay neuron firing in mouse (p28-33) brain slices using physiological stimulation patterns and a combination of current clamp and dynamic clamp. In tonic mode (-55 mV), activation of single RGC inputs elicited stereotyped responses in a given neuron. In contrast, responses in different neurons varied from unreliable, to faithfully following, to a gain in the number of spikes. Dynamic clamp experiments indicated these different responses primarily reflected variability in the amplitudes of the N-methyl-d-aspartate (NMDA) and AMPA components. Each of these components played a distinct role in transmission. The AMPA component evoked a single precisely timed, short-latency spike per stimulus, but efficacy decreased during repetitive stimulation due to desensitization and depression. The NMDA component elicited longer-latency spikes and multiple spikes per stimulus and became more effective during repetitive stimuli that led to NMDA current summation. We found that in burst mode (-75 mV), where low-threshold calcium spikes are activated, AMPA and NMDA components and synaptic plasticity influenced spike number, but no combination enabled relay cells to faithfully follow the stimulus. Thus the characteristics of AMPA and NMDA currents, the ratio of these currents and use-dependent plasticity interact to shape how RGC activity is conveyed to relay neurons.     

Characterization of reliability of spike timing in spinal interneurons during oscillating inputs

The spike timing in rhythmically active interneurons in the mammalian spinal locomotor network varies from cycle to cycle. We tested the contribution from passive membrane properties to this variable firing pattern, by measuring the reliability of spike timing, P, in interneurons in the isolated neonatal rat spinal cord, using intracellular injection of sinusoidal command currents of different frequencies (0.325-31.25 Hz). P is a measure of the precision of spike timing. In general, P was low at low frequencies and amplitudes (P = 0-0.6; 0-1.875 Hz; 0-30 pA), and high at high frequencies and amplitudes (P = 0.8-1; 3.125-31.25 Hz; 30-200 pA). The exact relationship between P and amplitude was difficult to describe because of the well-known low-pass properties of the membrane, which resulted in amplitude attenuation of high-frequency compared with low-frequency command currents. To formalize the analysis we used a leaky integrate and fire (LIF) model with a noise term added. The LIF model was able to reproduce the experimentally observed properties of P as well as the low-pass properties of the membrane. The LIF model enabled us to use the mathematical theory of nonlinear oscillators to analyze the relationship between amplitude, frequency, and P. This was done by systematically calculating the rotational number, N, defined as the number of spikes divided by the number of periods of the command current, for a large number of frequencies and amplitudes. These calculations led to a phase portrait based on the amplitude of the command current versus the frequency-containing areas [Arnold tongues (ATs)] with the same rotational number. The largest ATs in the phase portrait were those where N was a whole integer, and the largest areas in the ATs were seen for middle to high (>3 Hz) frequencies and middle to high amplitudes (50-120 pA). This corresponded to the amplitude- and frequency-evoked increase in P. The model predicted that P would be high when a cell responded with an integer and constant N. This prediction was confirmed by comparing N and P in real experiments. Fitting the result of the LIF model to the experimental data enabled us to estimate the standard deviation of the internal neuronal noise and to use these data to simulate the relationship between N and P in the model. This simulation demonstrated a good correspondence between the theoretical and experimental values. Our data demonstrate that interneurons can respond with a high reliability of spike timing, but only by combining fast and slow oscillations is it possible to obtain a high reliability of firing during rhythmic locomotor movements. Theoretical analysis of the rotation number provided new insights into the mechanism for obtaining reliable spike timing.     

Effects of noise on the spike timing precision of retinal ganglion cells

Information in a spike train is limited by variability in the spike timing. This variability is caused by noise from several sources including synapses and membrane channels; but how deleterious each noise source is and how they affect spike train coding is unknown. Combining physiology and a multicompartment model, we studied the effect of synaptic input noise and voltage-gated channel noise on spike train reliability for a mammalian ganglion cell. For tonic stimuli, the SD of the interspike intervals increased supralinearly with increasing interspike interval. When the cell was driven by current injection, voltage-gated channel noise and background synaptic noise caused fluctuations in the interspike interval of comparable amplitude. Spikes initiated on the dendrites could cause additional spike timing fluctuations. For transient stimuli, synaptic noise was dominant and spontaneous background activity strongly increased fluctuations in spike timing but decreased the latency of the first spike.     

Influence of ionic conductances on spike timing reliability of cortical neurons for suprathreshold rhythmic inputs

Spike timing reliability of neuronal responses depends on the frequency content of the input. We investigate how intrinsic properties of cortical neurons affect spike timing reliability in response to rhythmic inputs of suprathreshold mean. Analyzing reliability of conductance-based cortical model neurons on the basis of a correlation measure, we show two aspects of how ionic conductances influence spike timing reliability. First, they set the preferred frequency for spike timing reliability, which in accordance with the resonance effect of spike timing reliability is well approximated by the firing rate of a neuron in response to the DC component in the input. We demonstrate that a slow potassium current can modulate the spike timing frequency preference over a broad range of frequencies. This result is confirmed experimentally by dynamic-clamp recordings from rat prefrontal cortical neurons in vitro. Second, we provide evidence that ionic conductances also influence spike timing beyond changes in preferred frequency. Cells with the same DC firing rate exhibit more reliable spike timing at the preferred frequency and its harmonics if the slow potassium current is larger and its kinetics are faster, whereas a larger persistent sodium current impairs reliability. We predict that potassium channels are an efficient target for neuromodulators that can tune spike timing reliability to a given rhythmic input.     

Contribution of intrinsic properties and synaptic inputs to motoneuron discharge patterns: a simulation study

Motoneuron discharge patterns reflect the interaction of synaptic inputs with intrinsic conductances. Recent work has focused on the contribution of conductances mediating persistent inward currents (PICs), which amplify and prolong the effects of synaptic inputs on motoneuron discharge. Certain features of human motor unit discharge are thought to reflect a relatively stereotyped activation of PICs by excitatory synaptic inputs; these features include rate saturation and de-recruitment at a lower level of net excitation than that required for recruitment. However, PIC activation is also influenced by the pattern and spatial distribution of inhibitory inputs that are activated concurrently with excitatory inputs. To estimate the potential contributions of PIC activation and synaptic input patterns to motor unit discharge patterns, we examined the responses of a set of cable motoneuron models to different patterns of excitatory and inhibitory inputs. The models were first tuned to approximate the current- and voltage-clamp responses of low- and medium-threshold spinal motoneurons studied in decerebrate cats and then driven with different patterns of excitatory and inhibitory inputs. The responses of the models to excitatory inputs reproduced a number of features of human motor unit discharge. However, the pattern of rate modulation was strongly influenced by the temporal and spatial pattern of concurrent inhibitory inputs. Thus, even though PIC activation is likely to exert a strong influence on firing rate modulation, PIC activation in combination with different patterns of excitatory and inhibitory synaptic inputs can produce a wide variety of motor unit discharge patterns.     

Encoding the timing of inhibitory inputs

Many neuronal systems represent information by the timing of individual spikes, and it is generally assumed that spike timing predominantly encodes excitatory inputs. We show here that the timing of inhibition can also be explicitly encoded in spike times using time-dependent and voltage-dependent properties of a rapidly inactivating potassium channel (I(KIF)). In vitro recordings in rat dorsal cochlear nucleus show that the effects of inhibition on spike timing can long outlast the duration of the inhibitory potential and that this depends only on the membrane voltage change during the inhibitory postsynaptic potential. Modeling results show that small neuronal populations with a heterogeneous distribution of I(KIF) voltage dependence can robustly encode intervals of >100 ms between inhibition and excitation. Thus neuronal systems can detect and represent the precise timing of inhibition, suggesting the importance of inhibition in information encoding.     

Controlling spike timing and synchrony in oscillatory neurons

We describe an algorithm to control synchrony between two periodically firing neurons. The control scheme operates in real-time using a dynamic clamp platform. This algorithm is a low-impact stimulation method that brings the neurons toward the desired level of synchrony over the course of several neuron firing periods. As a proof of principle, we demonstrate the versatility of the algorithm using real-time conductance models and then show its performance with biological neurons of hippocampal region CA1 and entorhinal cortex.     

Amplitude and frequency dependence of spike timing: implications for dynamic regulation

The spike-time reliability of motoneurons in the Aplysia buccal motor ganglion was studied as a function of the frequency content and the relative amplitude of the fluctuations in the neuronal input, calculated as the coefficient of variation (CV). Measurements of spike-time reliability to sinusoidal and aperiodic inputs, as well as simulations of a noisy leaky integrate-and-fire neuron stimulated by spike trains drawn from a periodically modulated process, demonstrate that there are three qualitatively different CV-dependent mechanisms that determine reliability: noise-dominated (CV < 0.05 for Aplysia motoneurons) where spike timing is unreliable regardless of frequency content; resonance-dominated (CV approximately 0.05-0.25) where reliability is reduced by removal of input frequencies equal to motoneuron firing rate; and amplitude-dominated (CV >0.35) where reliability depends on input frequencies greater than motoneuron firing rate. In the resonance-dominated regime, changes in the activity of the presynaptic inhibitory interneuron B4/5 alter motoneuron spike-time reliability. The increases or decreases in reliability occur coincident with small changes in motoneuron spiking rate due to changes in interneuron activity. Injection of a hyperpolarizing current into the motoneuron reproduces the interneuron-induced changes in reliability. The rate-dependent changes in reliability can be understood from the phase-locking properties of regularly spiking motoneurons to periodic inputs. Our observations demonstrate that the ability of a neuron to support a spike-time code can be actively controlled by varying the properties of the neuron and its input.     

Reliable control of spike rate and spike timing by rapid input transients in cerebellar stellate cells

Granule cell activity in cerebellar cortex directly excites Purkinje cells via parallel fibers, but it also inhibits Purkinje cells via cerebellar cortical interneurons. This contribution of inhibitory interneurons to cerebellar cortical processing remains poorly understood. In the present study we examined the response properties of stellate cells in vitro to input patterns that may result from granule cell activity in vivo. We constructed input waveforms that represented the sum of inputs from all individual synapses and applied these waveforms to the soma of stellate cells during whole cell recordings in acute brain slices. The stimulus waveforms contained fluctuations in a broad range of frequencies and were applied at different amplitudes. To determine the contribution of synaptic shunting to stellate cell spike responses we applied the same input waveforms either as a simulated synaptic conductance using dynamic clamping or as a direct current injection stimulus. Only the dynamic clamp stimulus has the shunting properties of real synapses, i.e. leads to different-sized synaptic current as a function of membrane potential. We found that stellate cells spike with millisecond precision in response to fast temporal fluctuations in the total synaptic input. Transient increases in excitatory input frequency led to pronounced stellate cell spike responses, indicating that this pathway may be very responsive to even small assemblies of co-activated granule cells. This was observed regardless of whether the input waveform was applied as a conductance with dynamic clamping, or as a direct current injection. Thus the shunting properties of a conductance input did not play a major role in determining the control of precisely timed spiking. In contrast, a more tonic increase in excitatory conductance did not lead to a sustained spike response as obtained with prolonged positive current injection. However, even with tonic current injection the precision of spiking was lost, as previously observed. Overall, the synaptic response function of stellate cells suggests that this cell type may pick out transients in granule cell activity, and may generate precisely timed inhibition of Purkinje cells during behavior.     

Electrophysiological properties of cortical synaptic inputs of rubro-spinal neurons

Excitatory postsynaptic potentials (EPSPs) of the red nucleus neurons evoked by stimulation of the cerebellar nucleus interpositus as well as the sensorimotor and association parietal regions of the cerebral cortex were studies in acute cats. As for the first two structures, a monosynaptic connection of the association cortex with rubro-spinal neurons was shown to exist. The analyses of the time characteristics of the unitary EPSPs suggested a localization of synapses of fibers from the association cortex closer to the soma when compared with those which originated from axons of the sensorimotor cortical cells.     

Harmonic distortion from nonlinear systems with broadband inputs: Applications to lung mechanics

We present a simple index, extended harmonic distortion (k _d ), to represent the degree of system nonlinearity under sparse pseudorandom noise inputs (SPRN). The frequencies in a SPRN waveform are neither harmonics nor sums or differences of the other component frequencies. Expressed by percentage, thek _d is the square root of the ratio of output power at non-input frequencies to the total output power. We evoke three simple corrections to recover the truek _d under imperfect SPRN inputs. Simulations on two block-structured nonlinear models (Wiener and Hammerstein) demonstrate the necessity and effectiveness of these corrections especially for the Wiener-type nonlinearity. By applyingk _d to pressure-flow data of dog lungs, we found that the nonlinear harmonic interactions from a lung arise primarily from its tissues most likely the processes governing the tissue stiffness. This nonlinearity, assessed fromk _d , is stronger at higher tidal volumes and enhanced (but to a lesser degree) during bronchoconstriction. We conclude that since thek _d approach avoids the necessity for multiple-input measurements and lengthy data records, it may be useful for tracking the dynamic variations in nonlinearities of a physiological system.     

Active dendritic integration of inhibitory synaptic inputs in vivo

Synaptic integration in vivo often involves activation of many afferent inputs whose firing patterns modulate over time. In spinal motoneurons, sustained excitatory inputs undergo enormous enhancement due to persistent inward currents (PICs) that are generated primarily in the dendrites and are dependent on monoaminergic neuromodulatory input from the brain stem to the spinal cord. We measured the interaction between dendritic PICs and inhibition generated by tonic electrical stimulation of nerves to antagonist muscles during voltage clamp in motoneurons in the lumbar spinal cord of the cat. Separate samples of cells were obtained for two different states of monoaminergic input: standard (provided by the decerebrate preparation, which has tonic activity in monoaminergic axons) and minimal (the chloralose anesthetized preparation, which lacks tonic monoaminergic input). In the standard state, steady inhibition that increased the input conductance of the motoneurons by an average of 38% reduced the PIC by 69%. The range of this reduction, from <10% to >100%, was proportional to the magnitude of the applied inhibition. Thus nearly linear integration of synaptic inhibition may occur in these highly active dendrites. In the minimal state, PICs were much smaller, being approximately equal to inhibition-suppressed PICs in the standard state. Inhibition did not further reduce these already small PICs. Overall, these results demonstrate that inhibition from local spinal circuits can oppose the facilitation of dendritic PICs by descending monoaminergic inputs. As a result, local inhibition may also suppress active dendritic integration of excitatory inputs.     

Multiple neural spike train data analysis: state-of-the-art and future challenges

Multiple electrodes are now a standard tool in neuroscience research that make it possible to study the simultaneous activity of several neurons in a given brain region or across different regions. The data from multi-electrode studies present important analysis challenges that must be resolved for optimal use of these neurophysiological measurements to answer questions about how the brain works. Here we review statistical methods for the analysis of multiple neural spike-train data and discuss future challenges for methodology research.     

Differential modulation of synaptic strength and timing regulate synaptic efficacy in a motor network

Neuromodulators modify network output by altering neuronal firing properties and synaptic strength at multiple sites; however, the functional importance of each site is often unclear. We determined the importance of monoamine modulation of a single synapse for regulation of network cycle frequency in the oscillatory pyloric network of the lobster. The pacemaker kernel of the pyloric network receives only one chemical synaptic feedback, an inhibitory synapse from the lateral pyloric (LP) neuron to the pyloric dilator (PD) neurons, which can limit cycle frequency. We measured the effects of dopamine (DA), octopamine (Oct), and serotonin (5HT) on the strength of the LP→PD synapse and the ability of the modified synapse to regulate pyloric cycle frequency. DA and Oct strengthened, whereas 5HT weakened, LP→PD inhibition. Surprisingly, the DA-strengthened LP→PD synapse lost its ability to slow the pyloric oscillations, whereas the 5HT-weakened LP→PD synapse gained a greater influence on the oscillations. These results are explained by monoamine modulation of factors that determine the firing phase of the LP neuron in each cycle. DA acts via multiple mechanisms to phase-advance the LP neuron into the pacemaker's refractory period, where the strengthened synapse has little effect. In contrast, 5HT phase-delays LP activity into a region of greater pacemaker sensitivity to LP synaptic input. Only Oct enhanced LP regulation of cycle period simply by enhancing LP→PD synaptic strength. These results show that modulation of the strength and timing of a synaptic input can differentially affect the synapse's efficacy in the network.     

Reliability of SEMG spike parameters during concentric contractions

This study examined the reliability of four surface electromyographic (SEMG) spike parameters during concentric (isotonic) contractions: mean spike amplitude, mean spike frequency, mean spike slope, and the mean number of peaks per spike. Eighteen subjects performed rapid elbow flexion on a horizontal angular displacement device that was used to measure joint torque. The SEMG activity of the biceps brachii was monitored with Beckman Ag/AgCl electrodes. The testing schedule consisted of four hundred trials distributed equally over four sessions. The stability of the means across sessions and the consistency of scores within subjects was determined for the first five (1-5) and last five (96-100) trials of each session to examine the possible influence of a "warm up" effect. All measures exhibited a significant (p < 0.01) increase across test days. However, the intraclass correlation coefficients for the first five (1-5) trials ranged from 0.76 to 0.83, which was quite good. The stability and consistency for most of the criterion measures increased for the last five (96-100) trials of each session. This resulted in a higher range of coefficients from 0.85 to 0.93. Subjects became more homogeneous with respect to the mean number of peaks per spike and the R decreased to 0.65. It was concluded that the four SEMG spike parameters could be reliably measured to assess changes in muscle activity patterns. The adaptations in SEMG spike activity suggest that repetitive dynamic contractions enhanced the ability to recruit more fast-twitch motor units across test days.