We used a single-compartment, conductance-based Morris-Lecar model (Morris and Lecar, 1981). The basic equations describing the dynamic behavior of membrane potential (V) and recovery variable (w) were: dVdt=−1Cap(gNa¯(V−ENa)0.5(1+tanh(V−v1v2))             +gk¯w(V−EK)+ginh(V−EGABA)+gexc(V−Eexc)             +gL(V−EL)+Iahp+ICa),dwdt=φ(0.5(1+tanh(V−v3v4))−w)sech(V−v32v4), where Cap = 2 μF/cm², φ = 0.25, v₁ = −1.2 mV, v₂ = 18 mV, v₃ = −9 mV, v₄ = 10 mV (Prescott et al., 2008). The value of E_GABA (in mV) was given by the Goldman-Hodgkin-Katz equation: EGABA=1000(RTF)ln(4[Cl-]i+[HCO3-]i4[Cl-]o+[HCO3-]o), where T = 310 K stands for absolute temperature, R = 8.3 J/(K·mol) for the perfect gas constant, and F = 96 485 C/mole for the Faraday constant. Except for [Cl⁻]_i and [Ca²⁺]_i, other ionic concentrations were treated as constant: E_Na = 45 mV and E_K = −85 or −95 mV (Hille, 2001). The intra and extra cellular bicarbonate concentrations were set to [HCO3−]_i = 11.8 mM and [HCO3−]_o = 25 mM (Staley and Proctor, 1999). Leak reversal potential (E_L) was set at −70 mV (Hille, 2001), the reversal potential of excitatory synapses (E_exc) was set to 0 mV (Jahr and Stevens, 1993) and [Cl⁻]_o was fixed at 120 mM. Chloride reversal potential (E_Cl) in units of mV was computed using Nernst equation: ECl=1000(RTF)ln([Cl-]i[Cl-]o).

The Cl⁻ efflux through KCC2 was given by the linear approximation g_KCC2(E_K-E_Cl) which is a simplification of more comprehensive models (Williams et al., 1999; Williams and Payne, 2004). Intracellular [Cl⁻] was updated according to: d[Cl-]idt=SAVgKCC2(ECl-EK)-xginh(Vm-ECl)F, where SAV is the is the surface area to volume ratio of the cell taken to be surface the surface area to volume ratio of a sphere so that SAV = 10⁻¹ s/r where s = 3 for a sphere and r = 6 μm (Ratté and Prescott, 2011) unless otherwise indicated. The variable x describes the fraction of the GABA_A mediated current that is due to the flux of Cl⁻ ions (Ratté and Prescott, 2011) namely: x=V-EClV-EGABA.

We also modeled changes in [Ca²⁺]_i according to: d[Ca2+]idt=SAVICa2·F+[Ca2+]i,rest-[Ca2+]iτCa, as described in De Schutter and Somlen (1998) with [Ca²⁺]i,rest=10-4 mM (Collins et al., 1991; Nakajima et al., 1993) and τ_Ca = 50 ms (Traub and Llinas, 1977). The calcium current, I_Ca was given in μA/cm² by the equation: ICa=gCa¯(V-ECa)11+exp[-(V-Vlt)∕kl], with gCa¯=0.5 mS/cm², V_lt = −5 mV and k_l = 5 mV (Benison et al., 2001). The value of E_ca was computed using [Ca²⁺]_o = 5·10⁻³ M (Jahr and Stevens, 1993). Calcium concentration was then used to determine the kinetics of Ca²⁺ activated K⁺ channels limiting high frequency spiking. The dynamics of those channels were described by the following equations: Iahp=gahp¯mahp(V-EK), with gahp¯=1 mS/cm² (Destexhe and Paré, 1999) and mahp=[Ca2+]i2KCa2+[Ca2+]i2 with KCa=10-3 mM (Moczydlowski and Latorre, 1983). Model parameters related to Cl⁻ dynamics were validated by comparing the Cl⁻ extrusion rate when [Cl⁻]_i = 15 mM to the half maximal extrusion rate reported in Staley et al. (1995). All simulations were performed with MATLAB software and equations were integrated using forward Euler method.

In simulations of Figures 3, 7 the signal was generated through an Ornstein-Uhlenbeck process (Uhlenbeck and Ornstein, 1930). The time evolution of the signal strength x_t is described by the following equation dxt=θ(μ-xt)dt+σdWt where W_t represent a Wiener process, μ is the mean of the process equal to 0. In simulations of Figure 2, the same Ornstein-Uhlenbeck process was used to generate noise added to a sinusoidal signal. For the simulations in Figure 3 we used the following parameters: θ = 11 s⁻¹ and σ=2.2 mS∕cm2s. The simulations in Figure 7 were performed with different values of μ and σ to adjust the mean value and standard deviation of the process in accordance to the descriptions in the figure section and the figure legends.

Mutual information between two variables X and Y was computed using Shannon's mutual information formula (Shannon, 1949):

Alternatively, the mutual information between X and Y is given by I(X,Y) = H(X) − H(X|Y) where H(X) stands for the Shannon's entropy of the variable X which is given by: H(X)=-∫p(x)log(p(x))dx and X|Y is the conditional distribution of X knowing Y. Computations were performed using distributions discretized into 100 bins.

Power spectrums in Figure 3 were computed using fast-Fourier-transform functions in MATLAB. Autocorrelation of a quantity X at delay time δ was computed according to the formula: ∫0L−δX(t)X(t+δ)dt−(∫0L−δX(t)dt)2∫0L−δX2(t)dt−(∫0L−δX(t)dt)2, where L is the time length of the simulation. Cross-correlation between two time vectors X and Y was computed according to the equation: ∫0L−δX(t)Y(t+δ)dt−(∫0L−δX(t)dt)(∫0L−δY(t)dt)∫0L−δX2(t)dt−(∫0L−δX(t)dt)2∫0L−δY2(t)dt−(∫0L−δY(t)dt)2.

To compute the transfer functions in Figure 3, we submitted the model neuron to a series of sinusoidal inhibitory inputs with g_inh oscillating between 0 and 2 mS/cm² at frequencies between 0.01 and 1 Hz. For each input frequency, we computed the amplitude of the Cl⁻ fluctuation [Δ [Cl⁻]_i = max([Cl⁻]_i) – min([Cl⁻]_i)] after initial convergence as well as phase delay [[Time_max(Cl) - Time_max(ginh)]/Per] where Per is the period of input oscillations.

For the ROC analysis performed in Figure 7, the model neuron was submitted to excitatory and inhibitory inputs generated with an Ornstein-Uhlenbeck process as described above. For each KCC2 level and excitation-inhibition ratio, we measured ISR histograms. For thresholds running from the minimum ISR obtained to the maximum ISR value, we computed the proportion of ISR from input with g_inh/g_exc = 1 smaller than this threshold and the proportion of ISR from input with g_inh/g_exc = 1 smaller than this threshold. When plotted against each other, these two probabilities yielded the ROC curves.

In healthy adult central neurons, Cl⁻ influx via GABA_A receptors is counterbalanced by Cl⁻ efflux via KCC2 and the equilibrium value of [Cl⁻]_i depends on the strength of each process. Intracellular [Cl⁻] can thus change with time if GABA_A input (i.e., conductance) and/or Cl⁻ driving force vary, where changes in the latter can arise from variations in E_GABA or by membrane depolarization caused by concurrent synaptic excitation (Figure 1D; Thompson and Gahwiler, 1989; Doyon et al., 2011). Relationships identified in Figure 1D raise important points. First, inhibitory current (I_inh) and E_GABA form a negative feedback loop, the gain of which is inversely related to the strength of KCC2 activity. The negative nature of the feedback is liable to convey a counterproductive form of plasticity in which inhibition weakens under precisely the conditions in which it is most needed. Second, ISR is assumed to reflect the ratio of excitatory and inhibitory input, implying that we can infer (decode) that input from ISR; however, that assumption is violated if driving forces vary. Since stability of the Cl⁻ driving force depends on the feedback loop between I_inh and E_GABA, the gain of which depends on KCC2 (see Figure 1D), it stands to reason that ability to decode synaptic input from ISR is dependent on KCC2. Having established these relationships qualitatively, we sought to quantify their impact on neural coding.

To quantify the impact of Cl⁻ dynamics on the encoding of inhibitory input, we first simulated a 0.2 Hz sinusoidal inhibitory conductance g_inh (Figure 2A top) in a model in which [Cl⁻]_i fluctuates freely for comparison with a model in which [Cl⁻]_i is artificially fixed. To isolate the effects of Cl⁻ lability, the fixed [Cl⁻]_i value was chosen to equal the mean value of [Cl⁻]_i under dynamic conditions (Figure 2A middle). When plotted against time, ISR exhibited a seemingly trivial phase difference between the two models (Figure 2A bottom). However, the elliptical orbit revealed by plotting [Cl⁻]_i against g_inh shows that [Cl⁻]_i differs between the ascending and descending phases of the stimulus (Figure 2B)—this results from changes in [Cl⁻]_i lagging behind changes in the input. The efficacy of inhibition depends on Cl⁻ current (see above), which means that time-dependent variation in [Cl⁻]_i, by affecting that current through E_GABA and driving force, will produce time-dependent modulation of ISR. Consequently, whereas ISR is a well-defined function of g_inh in the model with static [Cl⁻]_i, ISR becomes ambiguously related to g_inh in the model with dynamic [Cl⁻]_i (Figure 2C, red and black curves, respectively).

The slow Cl⁻ fluctuations described above evidently preclude the value of g_inh at time t from being unambiguously decoded from ISR. To quantify this effect, we added noise to a sinusoidally varying g_inh “signal” and measured the amount of information transmitted by ISR on that signal in dynamic vs. static [Cl⁻]_i conditions. Information transfer was calculated based on conditional entropy, which, in a very generic way, quantifies how much more confidently one can predict the input when one knows the output. The relationship between ISR and g_inh having two branches for dynamic [Cl⁻]_i conditions results in greater conditional entropy, which equates with ISR providing less information about g_inh, as illustrated in Figure 2D (note the broader and bimodal conditional distribution of g_inh in the case of fluctuating [Cl⁻]_i) for an arbitrarily chosen response of 30 spikes/s to g_inh sinusoidally modulated at 0.2 Hz. The more broadly those branches are separated (Supplementary Figure 1), the greater the conditional entropy and the less information ISR provides about g_inh. Re-testing with different sinusoidal g_inh frequencies shows that the loss of information attributable to dynamic [Cl⁻]_i was highest for the lowest frequencies tested and became negligible for frequencies >1 Hz (Figure 2E). These results show that lability of [Cl⁻]_i occurs to the detriment of information transmission when the cell experiences relatively slow variation in inhibitory input.

The observation that slower inputs drive larger fluctuations (Supplementary Figure 1) suggests that [Cl⁻]_i is a low-pass filtered reflection of inhibitory synaptic input. To characterize that filtering, we stimulated the model neuron with noisy inhibitory input that accurately recapitulates background synaptic activity (Destexhe et al., 2001). As expected, fluctuations in [Cl⁻]_i were sluggish compared with the rapid changes in g_inh and ISR (Figure 3A). Indeed, the power spectrum for g_inh is flat between 0.01 and 10 Hz whereas the one for [Cl⁻]_i falls off beyond 0.1 Hz, consistent with low-pass filtering (Figure 3B). The slow nature of Cl⁻ fluctuations led us to postulate that [Cl⁻]_i at any given time should reflect past values of [Cl⁻]_i as well as predict its future values. This was tested by computing the auto-correlation function for both [Cl⁻]_i and g_inh (Figure 3C). Results show that g_inh fluctuations with an autocorrelation time of 84 ms yielded fluctuations in [Cl⁻]_i with a much longer autocorrelation time of 8 s. Consequently, [Cl⁻]_i at a given time is a good predictor of what [Cl⁻]_i will be 5–10 s later whereas g_inh is forgotten within milliseconds. The inset in Figure 3C shows that [Cl⁻]_i autocorrelation time is inversely related to KCC2 level, indicating that KCC2 downregulation results in slower Cl⁻ fluctuations (see below). Since [Cl⁻]_i affects ISR, it follows that [Cl⁻]_i at time t should be predictive of both ISR at that time t as well as ISR a few seconds into the future, whereas this should not be the case for g_inh, given its short autocorrelation time. To test this, we measured the cross-correlation between [Cl⁻]_i and ISR as well as between g_inh and ISR. As predicted, cross-correlation between [Cl⁻]_i and ISR remained positive for a few seconds whereas g_inh was forgotten within milliseconds (Figure 3D).

The above data confirm that Cl⁻ fluctuations reflect low-pass filtering of g_inh fluctuations, the details of which presumably depend on a variety of post-synaptic factors that influence the balance of Cl⁻ influx and efflux. To investigate those factors, we measured the transfer function by submitting the model neuron to sinusoidal g_inh of different frequencies but equal amplitude. For each input frequency, we computed the amplitude of [Cl⁻]_i fluctuations as well as the phase delay between fluctuations in g_inh and [Cl⁻]_i under a variety of conditions (Figure 4A). We hypothesized that cell radius would be an important determinant of filtering given its effects on the surface area-to-volume (SAV) ratio. As expected, the corner frequency of the Cl⁻ response decreased as the SAV ratio was reduced by increasing radius (Figure 4B top). We also found that the corner frequency was significantly affected by KCC2 level (Figure 4C top). Unlike varying radius, reducing KCC2 allowed for larger [Cl⁻]_i fluctuations at low input frequencies (Figure 4C top). The magnitude of excitatory input g_exc also influenced the magnitude of [Cl⁻]_i fluctuations (because depolarization increases Cl⁻ driving force; see Figure 1D), but it had little effect on the corner frequency (Figure 4D top). Under all conditions (Figures 4B–D bottom), phase delay was near zero for very low frequency inputs (indicating that [Cl⁻]_i tracks slow changes in input) but increased toward π/2 as input frequency was increased (indicating that [Cl⁻]_i lags behind faster changes in input). These results highlight that the amplitude and kinetics of Cl⁻ fluctuations are likely to differ quantitatively between different cells, or even between different subcellular compartments. One can thus predict, for example, that the axon hillock, with its small diameter, low KCC2 level (Stafstrom, 2009; Bender and Trussell, 2012) and dense GABAergic innervation will exhibit large time dependent Cl⁻ fluctuations in comparison with the soma.

The fact that decreasing KCC2 function yielded both increasing maximum [Cl⁻]_i fluctuation amplitude and decreasing corner frequency reflects a combination of weak and slow Cl⁻ regulation, or, in other words, increased Cl⁻ lability and settling time. It follows that an abrupt but sustained increase in g_inh will elicit a large change in [Cl⁻]_i, but [Cl⁻]_i will be slow to reach its new steady-state. Since ISR depends on the present values of g_inh and [Cl⁻]_i, and since the present value of [Cl⁻]_i depends on past values of g_inh, (until [Cl⁻]_i converges to steady-state), ISR will depend on both present and past values of g_inh. This history-dependence, or ionic memory, will naturally compromise decoding of the present value of g_inh from ISR, as demonstrated below.

To quantify the impact of Cl⁻ dynamics on information transfer, we simulated abrupt step-changes in g_inh applied at 10 s intervals where each value of g_inh was chosen from a Gaussian distribution (Figure 5A). This was repeated for different levels of KCC2 but, for each KCC2 level, we adjusted the mean of the distribution from which g_inh was chosen such that combinations of g_KCC2 and mean g_inh yielded equivalent inhibition across all KCC2 levels (i.e., reduction of ISR from 80 spikes/s without inhibition to 30 spikes/s with inhibition; see Supplementary Figure 2 for the relationship between mean g_inh, mean [Cl⁻]_i and g_KCC2). By choosing this paradigm, we tested how KCC2 hypofunction affects the robustness and kinetics of Cl⁻ regulation without affecting the mean ISR by unbalancing excitation and inhibition. This is important because disinhibition caused by an arbitrarily applied shift in E_GABA can, depending on the degree of change, be offset by an increase in g_inh (Prescott et al., 2006; Knabl et al., 2008; Asiedu et al., 2010; Doyon et al., 2011). Critically, such compensation will not offset weak and slow Cl⁻ regulation resulting from KCC2 hypofunction and instead, would tend to exacerbate such changes. Indeed, our simulations reveal a tendency for ISR to overshoot and converge slowly in response to abrupt change in g_inh (Figure 5A).

We computed mutual information between ISR (at different time points after the step change in g_inh) and the present and previous value of g_inh using the approach introduced in Figure 2D. This was repeated for multiple KCC2 levels. In effect, we asked how well g_inh can be decoded from ISR. The time-dependent changes in ISR, which parallel the time-dependent changes in [Cl⁻]_i (see Figure 5A), tend to impair that decoding. Our analysis quantifies the impairment as a function of KCC2 level; later, we will address how ionic fluctuations affect other aspects of neural coding. Here, we refer to information available from ISR about the present value of g_inh as transmitted information and to information available about the previous value of g_inh as ionic memory (Figure 5B). We compared transmitted information calculated for dynamic Cl⁻ conditions against transmitted information calculated for static Cl⁻ conditions; this does not imply that constant [Cl⁻]_i is necessarily optimal but, instead, serves simply to isolate the effects of dynamic changes in [Cl⁻]_i.

Figure 5C shows transmitted information calculated at times immediately and 10 s after the step change in g_inh and plotted against KCC2 level. For comparison, transmitted information was also calculated for static [Cl⁻]_i conditions, with [Cl⁻]_i set to the time-averaged value associated with each KCC2 level (see Supplementary Figure 2). As predicted, less information was transmitted when KCC2 was reduced, but whereas information loss measured after 10 s remained small until large reductions in KCC2, information loss immediately after the change in g_inh was evident even for small reductions in KCC2 (Figures 5C,D). This differential loss of information pinpoints the effects of the slow equilibration of [Cl⁻]_i—increased settling time—which is also evident by plotting transmitted information as a function of time elapsed since the step change in g_inh normalized to transmitted information with constant [Cl⁻]_i (Figure 5D). Patterns of transmitted information (Figures 5C,D) are inversely related to patterns of ionic memory (Figures 5E,F).

These results show that mild KCC2 hypofunction impairs information transfer on both short and long time scales. On short time scales, information loss is related to ionic memory, which is a direct consequence of slow Cl⁻ regulation (i.e., long settling times). On longer time scales, information loss is due to instability of the [Cl⁻]_i steady-state, which is a direct consequence of weak Cl⁻ regulation (i.e., increased lability). The slowing and weakening of Cl⁻ regulation are obviously linked—[Cl⁻]_i would not drift toward new steady-state values if steady-state was static—but our results highlight that the effects of slow Cl⁻ settling time are more readily manifested in terms of information loss. Based on our testing paradigm, we can also conclude that these effects are not prevented by compensating for reduced Cl⁻ driving force by increasing the level of GABA_A conductance.

Thus far, we have focused on the encoding and decoding of inhibitory input because of its direct connection with Cl⁻ flux. However, excitatory synaptic input also affects E_GABA, albeit indirectly, since depolarization caused by synaptic excitation contributes to a depolarizing shift in E_GABA (Figure 1D). As an aside, excitatory and inhibitory input co-vary during realistic stimulation (Seriés et al., 2003; Haider et al., 2006). But putting aside co-variations (until Figure 7), g_exc fluctuations could cause Cl⁻ fluctuations even if g_inh remains constant, which led us to hypothesize that Cl⁻ instability could also form an ionic substrate for memory of past g_exc and that it could impair encoding of the present value of g_exc. To test this, we repeated the simulations reported in Figure 5 but this time g_inh was kept constant while g_exc underwent intermittent step-changes. We computed transmitted information about g_exc based on ISR immediately and 10 s after the step change in g_inh. For comparison, we also calculated transmitted information with [Cl⁻]_i held constant at the average value of [Cl⁻]_i associated with each KCC2 level (Figure 6A).

Like for encoding of g_inh, the information transmitted about g_exc immediately after the step change in conductance decreased for low KCC2 levels. But interestingly, and unexpectedly, compared with static [Cl⁻]_i conditions, transmitted information was increased after waiting long enough for [Cl⁻]_i to reach steady state. This is best illustrated by plotting transmitted information as a function of time elapsed since the step change in conductance normalized to transmitted information with constant [Cl⁻]_i (Figure 6B). Computations confirmed that fluctuations in ionic concentrations create a Cl⁻-based memory of past g_exc (Figures 6C,D) that was much weaker than the memory of past g_inh (cf. Figure 5) but interestingly, could still affect information transfer.

Like for g_inh, g_exc modulates ISR via two distinct pathways: its immediate and direct effect via excitatory current, and the slower and indirect effect via [Cl⁻]_i, where the latter affects the influence of concurrent inhibition on ISR. A critical issue is whether the direct and indirect effects oppose or reinforce one another. In the case of g_inh, a large conductance will reduce ISR but the associated shift in E_GABA will undermine that effect (see Figure 1D). In contrast, in the case of g_exc, a large conductance will increase ISR and the associated shift in E_GABA will enhance that effect (by reducing the efficacy of inhibition), meaning the direct and indirect effects are reinforcing. This may, under certain conditions, be beneficial: for low KCC2 levels, weak excitatory inputs (that would normally fail to elicit spiking) can, if sustained for long enough, cause progressive Cl⁻ accumulation and thus disinhibition to the point where spiking is elicited (Figure 6E). Re-testing with inputs of different durations and strengths reveals that weak but sustained g_exc stimuli that would go undetected under normal conditions can be decoded from the steady-state firing rate when KCC2 is downregulated (Figure 6F). Thus, detection of sustained weak stimuli can be enhanced by reduced KCC2 activity, which could be beneficial or deleterious depending on context. For example, this could allow subtle mechanical stimuli such as movement of clothes over the skin to activate nociceptive spinal neurons in neuropathic pain conditions—a deleterious effect—but it may also facilitate the establishment of excitatory synapses during early stages of development—a beneficial effect. Furthermore, the same changes would be detrimental for discrimination of stimuli near the upper end of the dynamic range (see below).

The decrease in information transmission studied in Figures 5, 6 provides a generic demonstration of how mild Cl⁻ dysregulation may impair neural coding. To provide physiological context, we also simulated a scenario in which tuning curves for excitation and inhibition define a receptive field (RF): excitation and inhibition are both strongest at the RF center, but because inhibition has a broader tuning curve, the g_inh/g_exc ratio is greater at the RF periphery (Figure 7A). In this commonly occurring pattern (Ben-Yishai et al., 1995; Suga, 1997; Seriés et al., 2003), inhibition serves to sharpen the tuning curve for net excitation and, in this way, improves spatial acuity or feature selectivity (Marr, 1982). As a preliminary step to assess the impact of Cl⁻ dysregulation on discrimination, we computed the output firing rate of a model neuron as a function of the stimulus location in its RF as parameterized by the g_inh/g_exc ratio for different stimulus strengths and KCC2 levels (Figure 7B).

The input-output curves in Figure 7B exhibit features indicative of deteriorated neural coding such as failure of gain control and contraction of dynamic range. To investigate this more quantitatively, we first computed the gain of the input-output curves for a given stimulus strength (g_exc = 0.3 mS/cm²; Figure 7C) which revealed how increasing the g_inh/g_exc ratio leads to a linear decrease in input-output gain for a normal KCC2 level whereas gain control failed when KCC2 level was reduced (Figure 7C top). Such a failure prevents inhibition from extending the dynamic range, which effectively leads to contraction of the dynamic range when KCC2 level is reduced (Figure 7C bottom). As neurons can efficiently encode stimulus strength only if the stimulus distribution falls within the dynamic range, we hypothesized that contraction of dynamic range caused by Cl⁻ dysregulation would impair encoding of broadly distributed input. This was confirmed by plotting Shannon-Weaver mutual information as a function of the width of the input distribution in scenarios of both efficient and compromised KCC2 activity (Figure 7D). As predicted, contraction of dynamic range caused by mildly reduced KCC2 level led to reduced information about input strength and this degradation worsened in proportion to the width of the input distribution.

Having shown that Cl⁻ dysregulation can impair information about input strength, we hypothesized that it could also impair encoding of stimulus location within the RF since input-output curves corresponding to different stimulus locations get closer to each other when KCC2 level is reduced (see Figure 7B). This implies decreased discriminability. To test this hypothesis, we investigated whether the proportionality constant between g_inh and g_exc could be unambiguously inferred from ISR for scenarios of normal and reduced KCC2 levels (Figure 7E). We submitted the model neuron to inputs whose g_inh/g_exc ratio corresponds to stimulation within the center or periphery of the RF and we compared the distributions of the resulting ISR vectors. Whereas, the separation between the two ISR distributions is broad for normal KCC2 levels, it becomes narrower when KCC2 level is reduced. Intuitively, broader separation of ISR distributions enables clearer discrimination of stimulus location. Quantifying this with Shannon-Weaver mutual information requires assumptions about the prior probability of the stimulus location; for illustration sake, we assumed each location to have equal probability. The computed mutual information between the input location and ISR was decreased in conditions of impaired KCC2 activity (Figure 7F right inset).

To quantify changes in discriminability using independent methodology, we turned to signal detection theory and receiver-operating-characteristic (ROC) analysis (Marr, 1982; Green and Swets, 1988). For any observed ISR value, one can decide if this value arises from a stimulus within the RF center or periphery based on whether the observed ISR lies above or below a given decision threshold. Determination of the optimal value of the decision threshold is based on the tradeoff between false positive and false negative decisions and does not, therefore, require any assumption about the prior distribution. That said, the quality of discrimination can be assessed through ROC diagrams obtained by varying the decision threshold and then plotting the probability of correct detection against the probability of false alarms (Zweig and Campbell, 1993; Figure 7F). The ROC curve for pure chance is a straight line at 45° and the quality of discrimination increases as the actual ROC curve diverges from this diagonal. The ROC curve obtained with a high KCC2 level indicates near perfect discriminability while these obtained for reduced KCC2 levels tend toward chance levels.

In conclusion, testing the impact of Cl⁻ dysregulation in the context of a receptive field showed, in a physiologically relevant paradigm, how modest KCC2 hypofunction disrupts neural coding. This together with other metrics (e.g., reduced mutual information) and the observed disruption of processes like gain control all demonstrate the degradation of neural coding that occurs when Cl⁻ regulation is compromised.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The reviewer Michael E. Hildebrand and handling Editor Gerald W. Zamponi declared a current/past collaboration and the handling Editor states that the process nevertheless met the standards of a fair and objective review.