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 underlying synaptic mechanisms, a fundamental approach is to study the dynamics of excitatory and inhibitory conductances of each neuron. The traditional method of determining conductance employs the synaptic current-voltage (I-V) relation obtained via voltage clamp. Using theoretical analysis, electrophysiological experiments, and realistic simulations, here we demonstrate that the traditional method conceptually fails to measure the conductance due to the neglect of a nonlinear interaction between the clamp current and the synaptic current. Consequently, it incurs substantial measurement error, even giving rise to unphysically negative conductance as observed in experiments. To elucidate synaptic impact on neuronal information processing, we introduce the concept of effective conductance and propose a framework to determine it accurately. Our work suggests re-examination of previous studies involving conductancemeasurement and provides a reliable approach to assess synaptic influence on neuronal computation. Neurons receive myriad excitatory (E) and inhibitory (I) synaptic inputs at dendrites. The spatiotemporal interaction between these E and I inputs are crucial for neuronal computation[18, 32, 12], for instance, to shape neural activity [27, 33], to enhance feature selectivity [21, 24], to modulate neural oscillations [6], and to balance network dynamics [26, 11]. To understand synaptic mechanisms underlying neuronal computation, it is important to investigate the dynamics of the pure E and I inputs to a neuron via electrophysiological recording techniques. Somatic voltage clamp has become a popular approach to achieve this both in vitro and in vivo studies over the last thirty years [19]. For instance, voltage clamp has been extensively applied to areas including visual [4, 5, 1], auditory [34, 27, 28, 31], and prefrontal cortex [23, 14]. To reveal quantitative information of E and I conductances, data collected in voltage clamp mode needs to be further processed to determine the conductance values. In the traditional method, by assuming the neuron as an electrically compact point and the synaptic conductance of this point neuron being independent of the injected clamp current, the dynamics of its voltage can be described as [16] c dV dt = −gL(V − εL)− gE(V − εE)− gI(V − εI) + Iinj , (1) where c is the membrane capacitance, V is the membrane potential, gL, gE and gI are the leak, E, and I conductances, respectively, εL, εE and εI are the corresponding reversal potentials, respectively, and Iinj is the externally injected current. Here all potentials are relative to the resting potential. Using the voltage clamp to hold the somatic voltage V at different levels, one can obtain the corresponding synaptic