Estimation of Synaptic Conductances in Presence of Nonlinear Effects Caused by Subthreshold Ionic Currents

A novel theoretical framework for simultaneous measurement of excitatory and inhibitory conductances

The firing of neurons throughout the brain is determined by the precise relations between excitatory and inhibitory inputs, and disruption of their balance underlies many psychiatric diseases. Whether or not these inputs covary over time or between repeated stimuli remains unclear due to the lack of experimental methods for measuring both inputs simultaneously. We developed a new analytical framework for instantaneous and simultaneous measurements of both the excitatory and inhibitory neuronal inputs during a single trial under current clamp recording. This can be achieved by injecting a current composed of two high frequency sinusoidal components followed by analytical extraction of the conductances. We demonstrate the ability of this method to measure both inputs in a single trial under realistic recording constraints and from morphologically realistic CA1 pyramidal model cells. Future experimental implementation of our new method will facilitate the understanding of fundamental questions about the health and disease of the nervous system.

Most neurons in the brain receive synaptic inputs from both excitatory and inhibitory neurons. Together, these inputs determine neuronal activity: excitatory synapses shift the electrical potential across the membrane towards the threshold for generation of action potentials, whereas inhibitory synapses lower this potential away from the threshold. Action potentials are the rapid electrochemical signals that transmit information to other neurons and they are critical for the information processing abilities of the brain.

Although there are many ways to measure either excitatory or inhibitory inputs, these methods have been unable to measure both at the same time. Measuring both inputs together is essential towards understanding how neurons integrate information. We developed a new analytical method to measure excitatory and inhibitory inputs at the same time from the voltage response to injection of an alternating current into a neuron. We describe the foundation of this new method and find that it works in biologically realistic simulations of neurons. By using this technique in real neurons, scientists could investigate basic principles of information processing in the healthy and diseased brain.

A computational approach for the inverse problem of neuronal conductances determination

The derivation by Alan Hodgkin and Andrew Huxley of their famous neuronal conductance model relied on experimental data gathered using the squid giant axon. However, the experimental determination of conductances of neurons is difficult, in particular under the presence of spatial and temporal heterogeneities, and it is also reasonable to expect variations between species or even between different types of neurons of the same species.We tackle the inverse problem of determining, given voltage data, conductances with non-uniform distribution in the simpler setting of a passive cable equation, both in a single or branched neurons. To do so, we consider the minimal error iteration, a computational technique used to solve inverse problems. We provide several numerical results showing that the method is able to provide reasonable approximations for the conductances, given enough information on the voltages, even for noisy data.

Determination of effective synaptic conductances using somatic voltage clamp

The interplay between excitatory and inhibitory neurons imparts rich functions of the brain. To understand the synaptic mechanisms underlying neuronal computations, a fundamental approach is to study the dynamics of excitatory and inhibitory synaptic inputs of each neuron. The traditional method of determining input conductance, which has been applied for decades, employs the synaptic current-voltage (I-V) relation obtained via voltage clamp. Due to the space clamp effect, the measured conductance is different from the local conductance on the dendrites. Therefore, the interpretation of the measured conductance remains to be clarified. Using theoretical analysis, electrophysiological experiments, and realistic neuron simulations, here we demonstrate that there does not exist a transform between the local conductance and the conductance measured by the traditional method, due to the neglect of a nonlinear interaction between the clamp current and the synaptic current in the traditional method. Consequently, the conductance determined by the traditional method may not correlate with the local conductance on the dendrites, and its value could be unphysically negative as observed in experiment. To circumvent the challenge of the space clamp effect and elucidate synaptic impact on neuronal information processing, we propose the concept of effective conductance which is proportional to the local conductance on the dendrite and reflects directly the functional influence of synaptic inputs on somatic membrane potential dynamics, and we further develop a framework to determine the effective conductance accurately. Our work suggests re-examination of previous studies involving conductance measurement and provides a reliable approach to assess synaptic influence on neuronal computation.

To understand synaptic mechanisms underlying neuronal computations, a fundamental approach is to use voltage clamp to measure the dynamics of excitatory and inhibitory input conductances. Due to the space clamp effect, the measured conductance in general deviates from the local input conductance on the dendrites, hence its biological interpretation is questionable, as we demonstrate in this work. We further propose the concept of effective conductance that is proportional to the local input conductance on the dendrites and reflects directly the synaptic impact on spike generation, and develop a framework to determine the effective conductance reliably. Our work provides a biologically plausible metric for elucidating synaptic influence on neuronal computation under the constraint of the space clamp effect.

Central pattern generators in the turtle spinal cord: selection among the forms of motor behaviors

Neuronal networks in the turtle spinal cord have considerable computational complexity even in the absence of connections with supraspinal structures. These networks contain central pattern generators (CPGs) for each of several behaviors, including three forms of scratch, two forms of swim, and one form of flexion reflex. Each behavior is activated by a specific set of cutaneous or electrical stimuli. The process of selection among behaviors within the spinal cord has multisecond memories of specific motor patterns. Some spinal cord interneurons are partially shared among several CPGs, whereas other interneurons are active during only one type of behavior. Partial sharing is a proposed mechanism that contributes to the ability of the spinal cord to generate motor pattern blends with characteristics of multiple behaviors. Variations of motor patterns, termed deletions, assist in characterization of the organization of the pattern-generating components of CPGs. Single-neuron recordings during both normal and deletion motor patterns provide support for a CPG organizational structure with unit burst generators (UBGs) whose members serve a direction of a specific degree of freedom of the hindlimb, e.g., the hip-flexor UBG, the hip-extensor UBG, the knee-flexor UBG, the knee-extensor UBG, etc. The classic half-center hypothesis that includes all the hindlimb flexors in a single flexor half-center and all the hindlimb extensors in a single extensor half-center lacks the organizational complexity to account for the motor patterns produced by turtle spinal CPGs. Thus the turtle spinal cord is a valuable model system for studies of mechanisms responsible for selection and generation of motor behaviors. NEW & NOTEWORTHY The concept of the central pattern generator (CPG) is a major tenet in motor neuroethology that has influenced the design and interpretations of experiments for over a half century. This review concentrates on the turtle spinal cord and describes studies from the 1970s to the present responsible for key developments in understanding the CPG mechanisms responsible for the selection and production of coordinated motor patterns during turtle hindlimb motor behaviors.