Table 1.
Abbreviations.
Fig 1.
Optogenetic quantification of chloride extrusion in hippocampal neurons.
(A) Left, schematic of the experimental setup where a gramicidin perforated patch is made from an eNpHR-expressing hippocampal pyramidal neuron. Green light is delivered via the objective and GABA puffs (blue) directed at the cell soma. Right, top, gramicidin perforated patch voltage-clamp recording from a neuron expressing eNpHR3.0-EYFP. GABAAR currents recorded at different times, on different trials following 15s of Cl- load induced by light activation of eNpHR. Right bottom, EGABA and [Cl-]i were calculated from each GABAAR current (squares, see Methods) and plotted as a function of time after the photocurrent for a single cell. [Cl-]i recovery was fitted by a single-exponential function (black). (B) From the data in ‘A’, KCC2 Cl- extrusion rate (V) as a function of [Cl-]i was calculated. This allowed for the Cl- extrusion constant, P, to be calculated. (C) Population data from 8 neurons resulted in an average value of P of 0.001 mM-1 · s-1. A single compartmental model was then created using the NEURON simulation environment. By accounting for Cl- dynamics including Cl- extrusion via KCC2, a Cl- recovery curve and simulated GABAAR currents could be generated (orange curves in ‘A’). These closely match our experimental data.
Fig 2.
The relative amounts of inhibitory and excitatory drive produce spatial variations in neuronal chloride concentration.
(A) Top, schematic depicting the model with an axon, soma, short thick ‘proximal’ dendrite connected to a long thin ‘distal’ dendrite. Both excitatory (red) and inhibitory (blue) synaptic input were evenly distributed across the distal dendrite. Bottom, [Cl-]i concentration at the end of the 1 s simulations as a function of distance from the soma. Both inhibitory synaptic input alone (blue trace) and excitatory input alone (red trace) caused selective increases in [Cl-]i in the distal dendrite. Balanced input (purple trace) caused an even greater increase in dendritic [Cl-]i. (B) Heatmap of neuronal firing rates as a function of different numbers of excitatory and inhibitory synapses used to select “balanced” synaptic configurations: i.e. pairs of excitatory-inhibitory (E:I) synapse numbers that could transform 5 Hz balanced input into 5 Hz output under conditions of dynamic Cl- (pale squares). (C) Heatmaps of [Cl-]i (shades of green) in the distal dendrite, proximal dendrite, soma, and axon at the end of the 1 s simulations when Cl- was allowed to evolve dynamically for three pairs of synaptic numbers reflecting “weak” inhibition (left, E:I– 200:30), “moderate” inhibition (E:I– 250:300) and “strong” inhibition (E:I– 300:800) at different balanced input frequencies. Spatial variations in [Cl-]i are dictated by the number of synapses and exaggerated by higher frequencies. (D) Top, schematic as in ‘A’ but with excitatory synapses targeted at the distal dendrite and the inhibitory synapses targeted at the proximal dendrite. Bottom, as in ‘A’, peri-somatic inhibitory synaptic input also produces spatial variations in [Cl-]i, but of smaller magnitude than when inhibitory synapses are distally located. (E) Heatmap as in ‘B’ but with proximal inhibition. This allowed E:I synapse pairs which produced 5 Hz output following 5 Hz input to be identified (pale squares). (F) While functionally similar to synapse pairs with distally targeted inhibition in ‘C’, pairs with proximal inhibition produced more modest changes in [Cl-]i as a function of the subcellular domain.
Fig 3.
Dynamic chloride accumulation compromises the effectiveness of inhibition during balanced distal synaptic input.
(A) Inner left, schematic of the model, depicting excitatory synaptic input targeted toward the distal dendrite and inhibitory synapses targeted at the proximal dendrite. Left, average output firing rates over the course of a 1 s simulation as a function of balanced synaptic input for different pairs of E:I synaptic numbers (shades of green, right). Each pair resulted in a 5 Hz output following 5 Hz balanced input (as in Fig 2). Simulations were performed either with [Cl-]i able to vary dynamically (“dynamic chloride”, solid lines) or with [Cl-]i held at a constant value (“static chloride”, dashed lines). Insets with example voltage traces for simulation runs at 20 Hz input for both dynamic (top inset) and static (bottom inset) Cl- as well as [Cl-]i for the dynamic Cl- simulations (middle inset). These show that accounting for Cl- dynamics results in obvious changes in spike timing. However, chloride dynamics did not result in large changes in output firing rates. (B) Inner left, schematic demonstrating excitatory and inhibitory inputs co-targeted toward the distal dendrite. Left, output firing rates following different balanced input frequencies with different pairs of E:I synaptic numbers (shades of blue, right) as in ‘A’, but with distally targeted inhibition. Dynamic Cl- resulted in large changes to output firing rates (solid vs dashed lines) as well as spike timing (inset, example simulation runs). (C) Output firing rate given 20 Hz balanced input for different numbers of inhibitory synapses targeted to the proximal dendrite (left) or the distal dendrite (right). Adding more inhibitory synapses in the case of distally targeted inhibtion did not meaningfully impact the firing rate when Cl- was dynamic. This was not the case for static Cl- where increasing the number of inhibitory synapses continued to decrease output.
Fig 4.
The input-output function of peripherally targeted inhibition is more susceptible to the effects of chloride accumulation than proximally targeted inhibition.
(A) Schematic showing the model where both synaptic excitation and inhibition were located on the distal dendrite. Each synapse provided 5 Hz stochastic input to the neuron. (B) Left, average output firing rate over the 1 s simulation as a function of the number of excitatory synapses for different numbers of peripherally located inhibitory synapses, and where Cl- was static (dashed lines). Each dot represents the result from 1 simulation (averaged over 3 trials). Increasing the number of inhibitory synapses (shades of blue) offset the neuronal input-output curve to the right (a subtractive operation on the input-output function). Right, allowing [Cl-]i to vary in the simulations meant that increasing the number of inhibitory synapses had a reduced ability to offset the input-output curve. (C) Schematic, showing a slightly altered version of the model with synaptic inhibition located on the proximal dendrite. (D) Left, as in ‘B’ but inhibition located proximal to excitatory input, i.e. peri-somatically. With static Cl-, increasing the number of inhibitory synapses (shades of green) generated divisive gain modulation by both offsetting the threshold and reducing the maximum firing rate of the neuron. Right, output firing rates for the same number of inhibitory synapses were moderately altered with dynamic Cl-, yet with sufficient numbers of inhibitory synapses complete suppression of output could still be achieved.
Fig 5.
Chloride accumulation has a progressive degenerative effect on the input-output function of neurons.
Neuronal input-output curves from instantaneous firing rate (IFR) represented as heatmaps using synapses with continuous fluctuating conductances instead of discrete inputs. Top, example traces of neuronal membrane potential showing action potential firing over 1 s (and at 10 s) from 5 repeated simulation runs (grey-bordered squares in the heatmaps). The IFR of the neuron was taken at 20 ms, 100 ms, 500 ms 1000 ms and 10000 ms using a backward integration window (Δt) of 20 ms as an average of the 5 simulation runs. Input-output curves represented as heatmaps of IFR for relative excitatory (different columns in an individual heatmap) and inhibitory (different rows in an individual heatmap) conductances. The top row of heatmaps is where simulations were conducted with dynamic Cl-. The second row is for identical simulations with static Cl-. The third row is the difference in IFR (ΔIFR) between the two. The bottom row is the [Cl-]i at the time point for that panel (a logarithmic scale was used to visualise the small changes at 20 ms). Right inset, example input-output curve for simulations with (solid trace) and without (dashed trace) dynamic Cl-over 1 s. Note how differences in IFR and input-output curves emerge relatively rapidly over 1 second indicating a clear and progressive effect of dynamic Cl- on signalling.
Fig 6.
Chloride dynamics shift the neuronal input-output function via changes to EGABA.
(A) As in Figs 4 and 5, increasing peripherally targeted inhibition (shades of blue) offset the input-output function, with this effect reduced when Cl- was modelled as dynamic over the course of 1 s simulations (solid lines) as compared to when it was static (dashed lines). The effect of Cl- dynamics on the neuronal input-output curve was quantified using the “chloride index”. Orange traces, and equation (right) demonstrates how the chloride index is calculated using the example of a simulation with a relative inhibitory conductance of 4. Higher Cl- indices (closer to 1) indicate a reduced effect of inhibition due to Cl- being modelled as dynamic instead of static. (B) Chloride index (blue, traces) and the change in dendritic EGABA (ΔEGABA, orange traces) after a 1 s simulation for different KCC2 pump strengths (PKCC2, 100% = 1.9297 x 10−5 mA/mM2/cm2) as a function of differing levels of peripherally targeted inhibition. Simulations with increased amounts of inhibition resulted in larger shifts in chloride index and ΔEGABA. (C) As in ‘B’ but with PKCC2 held at the default level (100%, 1.9297 x 10−5 mA/mM2/cm2) and the diameter of the distal dendrite varied between 0.5 and 2 μm. Small dendritic diameters resulted in larger shifts in chloride index and ΔEGABA during the simulation. (D) Chloride index versus ΔEGABA for all the simulation runs in ‘B’ and ‘C’ as well as manipulations where we altered input resistance (S1A Fig), distal KCC2 strength (S1B Fig), the duration of the simulation (S1C Fig) and also modelled K+ as being dynamic (S1D Fig). The relationship between chloride index–the functional result of accounting for Cl- dynamics–and ΔEGABA is directly proportional and independent of underlying neuronal properties such as KCC2 strength or diameter (r = 0.94281, p < 0.00001, Pearson correlation, N = 292 simulations).
Table 2.
Constants, parameters, and default steady state values for variables.