Variability of quantal synaptic currents in thalamocortical neurons

Abstract

Broad amplitude variability and skewed distributions are characteristic features of quantal synaptic currents (minis) at central synapses. The relative contributions of the various underlying sources are still debated. Through computational models of thalamocortical neurons, we separated intra- from extra-synaptic sources. Our simulations indicate that the external factors of local input resistance and dendritic filtering generate equally small amounts of negatively skewed synaptic variability. The ability of these two factors to reduce positive skew increased as their contribution to variability increased, which in control trials for morphological, biophysical, and experimental parameters never exceeded 10% of the range. With these dendritic factors ruled out, we tested multiple release models, which led to distributions with clearly non-physiological multiple peaks. We conclude that intra-synaptic organization is the primary determinant of synaptic variability in thalamocortical neurons and, due to extra-synaptic mechanisms, is more potent than the data suggested. Thalamortical neurons, especially in rodents, constitute a remarkably favorable system for molecular genetic studies of synaptic variability and its functional consequence.

Fig. 1

Dendritic morphology and synapse distributions: (A) thalamocortical relay neuron (TCN) from the ventrobasal complex of the somatosensory thalamus of rat. Note the rapid reduction of dendrite diameter, long terminal branches and short primary and intermediate branches that are characteristic of TCNs and are defining characteristics of bushy neurons. Morphology is shown flattened to viewing plane (not projected). Additional morphology data appears in Fig. 8. Electrophysiological recordings from this neuron as well as its 3D reconstruction data and were used to create a computational model. The second panel depicts each compartment (N = 1416) of the model, with the areas of squares being proportional to compartment membrane area. (B) Uniform area density of inhibitory synapses (heavy lines; top (Sato et al., 1997), bottom (Sato et al., 1997; Liu et al., 1995)) contrasts with non-uniform densities of excitatory synapses from “cortical” (upper thin line) and “sensory” (lower thin line) afferents. Based on serial reconstructive electron microscopy data (Sato et al., 1997; Liu et al., 1995). Individual TCNs receive approximately 1500 inhibitory synapses, which, in rodent ventrobasal complex, derive from the reticular thalamic nucleus only.

Fig. 2

Paradigm 1: synaptic variability due to resistive–capacitive filtering. Identical predetermined synaptic currents I_pre = I_syn(t) were injected alternately into each of 1416 dendritic compartments. I_pre followed a double exponential time course, which we constrained with cesium based whole cell recordings of mIPSCs in TCNs of rat ventrobasal slice preparations maintained in vitro (Cox et al., 1997; LeFeuvre et al., 1997). These dendritic injections were recorded though a somatic voltage clamp. (A) Dashed trace depicts I_pre. Solid traces depict five example somatic voltage clamp recordings (mPREs). (B) Sites of five injections recorded somatically in (A). (C) mPRE data scatter plot, with marginal histograms. Each square marks the rise time and peak amplitude of the recording of an event at one of the compartments. The large crosshair marks the median rise time and median peak amplitude, with the closest mPRE defined as the median. Even though all injected currents were identical, their recordings were variable. This variability reflects how events at different dendritic sites are subjected to different degrees of low-pass filtering when viewed from the soma. The low-pass filtering is due to three factors: (1) membrane resistance, (2) membrane capacitance, and (3) morphology of the dendritic arbor. Note that the mIPSC amplitudes have the opposite skew of the mPRE amplitudes. Also note that the range of mPRE amplitudes is less than 10% of the range of mIPSC amplitudes. (D) Three histograms superimposed: one mPRE data set and two mIPSC data sets (Cox et al., 1997; LeFeuvre et al., 1997). Note the positive skew of mIPSC amplitude data. Each in vitro histogram is composed of several hundred events. Corrections were made for the differences in net ionic drive between the two studies; bin widths are 2 and 10 pA. (E) Bold open squares mark five synapses lying on and spanning the least squares line in (C). Uppermost square marks median in (C). Triangles and circles mark locations where the injected current resulted in an mPRE lying along the lines of the crosshair.

Fig. 3

Temporal measures: cross plot of two different measures of the rising phase of the somatic recordings. Each square marks the corresponding values of the recording of an event in one of the compartments. Note that the 0–100% rise time can be accurately estimated from 10 to 90% rise time. Equation of the least square line is given in text.

Fig. 4

Control trials: currents and parameters. Black squares indicate baseline settings in this report. (A) Inclusion of 4.7 nA of the low threshold Ca²⁺ T-current led to mPREs that were slightly smaller than when excluded. All active currents, except for those carried by Ca²⁺, had been blocked during experiments. (B) Higher settings for the voltage clamp's series resistance led to more precise (low scatter), but less accurate (offset) recordings of synaptic currents. (C) Recording chamber temperature influenced variability through I_pre kinetics, with cooler temperatures being both more precise and more accurate. (D) Doubling the number of compartments and halving the integration time step led to minute changes, indicating that mPRE scatter (Fig. 2C) is a signature of the dendritic arbor. (E) Drastic changes in somatic R_in led to small changes in amplitudes, suggesting that recording solutions are free to be chosen based on functions other than rendering the neuron more “compact”. (F) Specific membrane capacitance influenced amplitude variability and temporal variability to roughly equal extents. (A–F) Note the preserved spatial relations (approximate co-linearity and relative inter-point distances) between the data of the five synapses.

Fig. 5

Paradigm 2: synaptic variability due to filtering, input resistance, and space clamp. Conductance based synaptic currents I_dyn = I_syn(t, V_m) were injected alternately in each of 1416 dendritic compartments. The conductance time course g_syn(t) was defined by a double-exponential time course constrained such that the location that had yielded the median mPRE (uppermost square in Fig. 2E) now yielded a matching mDYN. (A) Spatial variation in local R_in and local space clamp quality led to a different I_dyn at each location. Five example I_dyns and mDYNs are given, corresponding to locations in Fig. 2B. Note the two-fold increase in variability of peak amplitude relative to Fig. 2A. (B) Perisynaptic escape voltages reflect space clamp quality and local R_in (see also Fig. 9B4). (C) mDYN data scatter plot, with marginal histograms. Each square marks the rise time and peak amplitude of the recording of an event at one of the compartments. The large crosshair marks the median rise time and median peak amplitude, with the closest mDYN defined as the median. Even though the conductances used at all locations were identical, their recordings of their currents were variable. This variability reflects how conductance based events at different dendritic sites are subjected differentially to three factors: (1) local input resistance, (2) local space clamp quality, and (3) low-pass resistive–capacitive filtering when viewed from the soma. The low-pass filtering is due to three factors: (1) membrane resistance, (2) membrane capacitance, and (3) morphology of the dendritic arbor. Note that, like the mPREs, the mDYN amplitude data is negatively skewed. The dashed curved is a re-plot of the mPRE envelope in Fig. 2C. Note the two-fold increase in amplitude variability. (D) Three histograms superimposed: one mDYN data set and two mIPSC data sets (Cox et al., 1997; LeFeuvre et al., 1997). Note that the mIPSC amplitudes have the opposite skew of the mDYN amplitudes. Also note that the range of mDYN amplitudes is less than 10% of the range of mIPSC amplitudes. (E) Triangles and circles correspond to mDYNs closest to the median crosshair lines given in (C). Compare with Fig. 2E.

Fig. 6

Synaptic current vs. synaptic conductance. The mDYN data from the conductance based currents, I_dyn = I_syn(t, V_m) = g_syn(t) × (V_m − E_syn), shows twice the range of peak amplitude variability compared to mPRE data from the predetermined current modeling, I_pre = I_syn(t) = P × W(t). mDYN data is shaped by local R_in and local space clamp quality, as well as resistive–capacitive filtering whereas only resistive–capacitive shapes the mPRE data. These differences between paradigms impact peak amplitudes, as shown in the left panel, which is a cross plot of amplitude data. The differences do not impact temporal measures, as shown in the middle panel, which contains two cross plots: one for each of the indicated measures of the rising phase. The right panel depicts the superposition of Figs. 2E and 5E.

Fig. 7

Uniform rescaling: to extend the present results across nuclei and species we created three new models with alternative morphologies based on our reconstructed neuron and on the literature. Here, uniform rescalings included length doubling, diameter thickening and diameter thinning. These are the only ways in which rodent ventrobasal thalamocortical neurons are known to differ from each other (Ohara and Havton, 1994; Ohara et al., 1995), however we have greatly exceeded the natural range of variation in order to extend the results to other nuclei and species. Simulations were run on these new models. Associated mDYN data envelopes are plotted for each, along with marginal histograms of peak amplitudes. Range of variability in peak amplitude remained less than 10% of the range of mIPSC in vitro data. The skew of peak amplitudes continued to be opposite of mIPSC in vitro data.

Fig. 8

Diameters at branch points: to further extend the present results across nuclei and species we created three more models with new alternative morphologies. Diameters were tuned to homogenize the 3/2 ratios to values of the unperturbed maximum, unperturbed minimum, or unity, given by $\Sigma d_i^{3∕2}∕D^{3∕2}$ for daughter branch diameters d_i and parent branch diameter D. In the top panel, cross marks are placed at branch position and order and are sized to reflect D, revealing the characteristically rapid reduction in dendrite diameter. The 108 terminal branches are sorted by remoteness of the proximal end, stretched out horizontally and shown in grey. Second panel plots the 3/2 ratio of the 69 branch points. Vertical lines mark the median branch point distance (left), and the distance marking the 50/50 split of membrane area into distal and proximal halves (right). This left/right relationship reflects the bushy nature of thalamocortical arbors. Simulations were run on these new models, and resulting mDYN data envelopes are plotted, along with histograms of peak amplitudes. Again, range of variability in peak amplitude remained less than 10% of the range of mIPSC in vitro data. Except for the morphology with 3/2 ratios homogenized to the maximum, the skew of peak amplitudes continued to be opposite of mIPSC in vitro data.

Fig. 9

Multiple events, heterogeneous conductances: multiple quantal events appear as distinct modes in amplitude histograms, even with heterogeneous synapses. In contrast, in vitro histograms are unimodal. (A) Joint histograms of single and double quantal events, for the two cases of identical and heterogeneous synapses. Heterogeneity was implemented as site dependent variation in peak conductances. Thus the histograms reflect the net heterogeneity in all parameters that shape the postsynaptic current. The heterogeneous histogram was constructed using a 10:7 ratio of single and double events so as yield a histogram similar to in vitro mIPSC data. However, this high proportion of double events is not plausible given the 4 Hz in vitro rate of mIPSCs. (B1) Single quantal events from heterogeneous synapses given by a lognormal distribution. Lognormal parameters were chosen to yield a distribution similar to in vitro mIPSC data. (B2) Peak conductances shown as a function (random) of distance from the soma, for the lognormal paradigm. (B3) The mDYN data under lognormal heterogeneity. (B4) Two plots: black marks are a cross plot of perisynaptic escape voltage amplitudes with and without somatic voltage clamp. Escape voltages diminish the net drive of the ions through the chloride channels (V_m − E_syn = 46 mV) by up to 40%. Perisynaptic transients differ between clamped and unclamped conditions by less than 2 mV, as indicated by the dashed line y = x + 2. Since this is less than 5% of the net driving force, it indicates that local R_in has a much greater influence than space clamp quality. Second plot consisting of grey marks show the escape voltage peaks as a function of location for the unclamped scenario. (C) In vitro mIPSC data (Cox et al., 1997; LeFeuvre et al., 1997) re-plotted from Figs. 2D and 5D.