Imperfect Space Clamp Permits Electrotonic Interactions between Inhibitory and Excitatory Synaptic Conductances, Distorting Voltage Clamp Recordings

The voltage clamp technique is frequently used to examine the strength and composition of synaptic input to neurons. Even accounting for imperfect voltage control of the entire cell membrane (“space clamp”), it is often assumed that currents measured at the soma are a proportional indicator of the postsynaptic conductance. Here, using NEURON simulation software to model somatic recordings from morphologically realistic neurons, we show that excitatory conductances recorded in voltage clamp mode are distorted significantly by neighboring inhibitory conductances, even when the postsynaptic membrane potential starts at the reversal potential of the inhibitory conductance. Analogous effects are observed when inhibitory postsynaptic currents are recorded at the reversal potential of the excitatory conductance. Escape potentials in poorly clamped dendrites reduce the amplitude of excitatory or inhibitory postsynaptic currents recorded at the reversal potential of the other conductance. In addition, unclamped postsynaptic inhibitory conductances linearize the recorded current-voltage relationship of excitatory inputs comprising AMPAR and NMDAR-mediated components, leading to significant underestimation of the relative contribution by NMDARs, which are particularly sensitive to small perturbations in membrane potential. Voltage clamp accuracy varies substantially between neurons and dendritic arbors of different morphology; as expected, more reliable recordings are obtained from dendrites near the soma, but up to 80% of the synaptic signal on thin, distant dendrites may be lost when postsynaptic interactions are present. These limitations of the voltage clamp technique may explain how postsynaptic effects on synaptic transmission could, in some cases, be attributed incorrectly to presynaptic mechanisms

Effects of Neural Morphology and Input Distribution on Synaptic Processing by Global and Focal NMDA-Spikes.

Cortical neurons can respond to glutamatergic stimulation with regenerative N-Methyl-D-aspartic acid (NMDA)-spikes. NMDA-spikes were initially thought to depend on clustered synaptic activation. Recent work had shown however a new variety of a global NMDA-spike, which can be generated by randomly distributed inputs. Very little is known about the factors that influence the generation of these global NMDA-spikes, as well the potentially distinct rules of synaptic integration and the computational significance conferred by the two types of NMDA-spikes. Here I show that the input resistance (RIN) plays a major role in influencing spike initiation; while the classical, focal NMDA-spike depended upon the local (dendritic) RIN, the threshold of global NMDA-spike generation was set by the somatic RIN. As cellular morphology can exert a large influence on RIN, morphologically distinct neuron types can have dissimilar rules for NMDA-spikes generation. For example, cortical neurons in superficial layers were found to be generally prone to global NMDA-spike generation. In contrast, electric properties of cortical layer 5b cells clearly favor focal NMDA-spikes. These differences can translate into diverse synaptic integration rules for the different classes of cortical cells; simulated superficial layers neurons were found to exhibit strong synaptic interactions between different dendritic branches, giving rise to a single integrative compartment mediated by the global NMDA-spike. In these cells, efficiency of postsynaptic activation was relatively little dependent on synaptic distribution. By contrast, layer 5b neurons were capable of true multi-unit computation involving independent integrative compartments formed by clustered synaptic input which could trigger focal NMDA-spikes. In a sharp contrast to superficial layers neurons, randomly distributed synaptic inputs were not very effective in driving firing the layer 5b cells, indicating a possibility for different computation performed by these important cortical neurons

Examples of simulated focal and global NMDA-spikes.

<p>Simulated glutamatergic inputs were activated either on a single dendritic location (focal distribution, A1, marked by the green point), or on all the branches of the cell (global distribution, A2, blue points). A, Somatic voltage waveforms for different activation intensities (4, 8, 16 and 32 synapses) for the focal distribution (A1), and 10, 20, 40 and 80 synapses for the global distribution (A2). Synaptic activation of both distributions produced NMDA-spikes, as was evident by a large supralinear increase in the somatic amplitude. For comparison, AMPA-only EPSPs for similar intensities of activation are shown in brown.B, Peak somatic EPSP amplitude as a function of stimulation intensity for the two distributions. Dotted lines denote a linear extrapolation of a unitary EPSP. Color coding as in A.</p

Voltage gated potassium channels have a differential effect on focal and global NMDA-spike amplitudes.

<p>A1, Somatic EPSP responses in a simulated layer 2/3 cell to 80 focally distributed synaptic inputs for a passive cell (solid), and in the presence of low or high dendritic potassium conductances (dotted). AMPA-only EPSP for the control case is shown in brown. A2, Peak somatic EPSP for the different potassium loads as a function of the number of synaptic inputs. Control, green; AMPA-only, brown. The dotted black line represents a linear extrapolation of a unitary EPSP. B, same as A for global distribution. C, Summary of the peak nonlinearity of the somatic EPSP as a function of the dendritic (C1) and somatic (C2) potassium conductances.</p

Morphological differences between principal cortical neurons predict distinct rules of NMDA-spike initiation.

<p>A, Examples of the morphologies and the input-output relations in simulated cortical layer 2/3 pyramidal (left), layer 4 spiny stellate (middle) and layer 5b pyramidal (right) neurons. For each cell class the plots show the peak somatic EPSPs evoked by a representative focal (green) or global (blue) synaptic distribution for basal and apical (where applicable) dendritic trees. For comparison, AMPA-only stimulation is shown in brown (solid for global and dotted for focal distributions). For layer 5b pyramidal neurons inserts show the full scale of the responses. B, Summary of the peak somatic NMDA-spike amplitude for the different dendritic trees (apical ▼ and basal ▲) in the three classes of cells for the focal (green) and the global (blue) synaptic distributions. C, The number of synaptic inputs (synaptic threshold) required to generate the NMDA-spikes, color coding as in B. Open symbols show the average number of synapses per each branch that lead to global NMDA-spike initiation. D, The ratio between the synaptic thresholds for global and focal NMDA-spikes is significantly different between superficial and deep cortical neurons (***p<0.001, ANOVA, Tukey’s HSD test)</p

The impact of cellular morphology on the properties of the NMDA-spikes.

<p>The morphology of the artificial cell was varied as follows; in A The diameter of all dendrites was changed between 0.3 and 3μm, in B The length of the dendrites varied between 30 and 300μm, in C the membrane size of the soma scaled from 44 to 1170 μm² and in D the number of dendrites increased from 6 to 16. For each manipulation, the following information is displayed: top, somatic (solid) and dendritic (dotted) R_IN. Middle, synaptic threshold for focal (green) and global (blue) NMDA-spikes. For comparison, the dotted blue trace shows the number of synapses on a single branch that initiated a global NMDA-spike. Focal/global spike thresholds were well correlated with the inverse of the dendritic (dotted grey)/somatic (solid grey) R_IN values. Bottom, peak somatic (solid) and dendritic (dotted) spike amplitudes for the focal (green) and global (blue) NMDA-spikes. The somatic amplitude of the focal NMDA-spike was almost identical to the ratio between the somatic to the dendritic R_IN values (dotted grey).</p

Dendritic and somatic Input Resistances determine NMDA-spike properties in realistic neuronal morphologies.

<p>A,B, The correlation between the number of synapses required for a global NMDA-spike generation in the basal dendrites and the inverse of somatic input resistance (A), soma size (B, grey) and the cumulative length of the dendritic trees (B, black) for the cortical cellular morphologies. Here and in the next plots the solid line indicates a linear fit to the data. C, D, A good correlation was found between the number of synapses required for focal NMDA-spike generation to the inverse of the focal dendritic input resistance(C) but not to the length of the stimulated branch (D), both in basal (black) and apical (grey) dendrites. E, F, A high correlation was found between somatic amplitude of the focal NMDA to the ratio between the somatic and dendritic input resistances (E) but not to the length of the stimulated branch.</p

Simulated suprathreshold dendritic summation is supra-linear in superficial but not in deep layers cortical neurons.

<p>A and B, Axosomatic spike count resulting from dendritic summation between two (A) and five (B) dendrites was highly supralinear in a cortical layer 2/3 pyramidal neuron morphology. Linearity was tested by comparing between Actual synaptic activation to response to somatic injection of summed EPSPs from all active dendrites (Expected). A1, B1, cartoon of the number and distribution of synaptic inputs (left) and representative somatic potentials (right).Purple, actual simultaneous activation of all synapses. Black, expected somatic response to somatic current injection. A2, B2, The actual vs. expected AP counts for 3000 simulated suprathreshold summations. Circle size and color code for occurrence rate. Solid line, linear fit to the dataset, dotted line, linear summation. A3, B3, Axosomatic spike count as a function of the total number of activated synapses for the actual (purple) and expected (grey) summations. The data was fitted with sigmoid curves. A4, B4, The degree of non-linearity of the firing responses as a function of the number of activated inputs. Positive values indicate larger actual (A) responses that expected (E), zero is the linear case (actual = expected) and negative values for actual>expected cases. The dataset was analyzed with a moving average (purple curve). C and D, similar to A and B for cortical layer 5b pyramidal cell. The suprathreshold summation was remarkably linear between all branch number tested (2–10 branches).</p

Subthreshold dendritic summation follows different rules in superficial and deep cortical layers neuronal morphologies.

<p>Synaptic summation was probed by comparing between the linear summation of somatic responses following input activation on individual dendrites (Expected) to the simultaneous activation of all synaptic inputs (Actual). A, Synaptic input summation between two dendrites was almost linear (A1), whereas five dendrites summed supralinearly (A2) in a simulated layer 5b pyramidal cell. Left, example of the somatic EPSP following activation of single dendrite (grey), the ‘Expected’ linear summation of individual dendrites (black) and the ‘Actual’ response (cyan). The cartoon on left shows the number of active branches and the number of synaptic inputs on each branch. Right, summary of the actual vs. expected EPSP amplitudes for 1000 trials (black).Bold trace, moving average. Dotted line, linear summation. B, same as A for cortical layer 2/3 pyramidal cell morphology. Actual (magenta) synaptic input summation was highly supralinear both between two (B1) and five (B2). C, The degree of supralinearity (measured as the ratio between the actual to the expected responses) for the three classes of cortical neurons for summation between different number of dendrites in basal (C1) and apical (C2) dendritic trees. *p<0.05,***p<0.001 between superficial and deep layers (ANOVA, Tukey’s HSD test).</p