# Balance of excitation and inhibition

Curator and Contributors

1.00 - Ilan Lampl

In the context of neurophysiology, balance of excitation and inhibition refers to the relative contributions of excitatory and inhibitory synaptic inputs corresponding to some neuronal event, such as oscillation or response evoked by sensory stimulation. In the current literature, owing to the extremely wide range of conditions in which the term excitatory-inhibitory balance is applied, it has several different, albeit related, meanings. As described in more detail below, the precise meaning depends on various considerations, such as averaging across time or population of neurons that is involved; the relevant timescale; whether the synaptic activity is sustained or transient, spontaneous or evoked. In general, excitatory and inhibitory inputs of a neuron are said to be balanced if across a range of conditions of interest the ratio between the two inputs is constant.

In the cortex, interneurons responsible for inhibition comprise just a small fraction of the neurons, yet they have an important function in regulating activity of principal cells. When inhibition is blocked pharmacologically, cortical activity becomes epileptic (Dichter and Ayala, 1987), and neurons may lose their selectivity to different stimulus features (Sillito, 1975). These and other data indicate that the interplay between excitation and inhibition has an important role in determining the cortical computation. Our understanding of the relationships between these two opposing forces has advanced significantly during the recent years, mainly due to the growing use of in-vivo intracellular recording techniques.

## Indirect evidence for excitatory-inhibitory balance

Cortical neurons receive synaptic inputs from thousands of other, mostly excitatory, neurons, each of which evokes only a sub-millivolt response (Bruno and Sakmann, 2006; Lefort et al., 2009). If these inputs arrive from neurons that fire at independent random times, they are expected to produce an almost constant depolarization leading to a regular firing. However, spike trains extracellularly recorded from single cortical neurons exhibit high variability. For instance, the coefficient of variation of the inter spike intervals (ISIs) of neurons firing in response to a sensory input for a period of several seconds, is approximately equal to 1, as expected from a Poisson process (Softky and Koch, 1993). This apparent paradox between simple probabilistic considerations and the observed statistics of cortical spike trains led to several proposed resolutions.

One early resolution was that excitatory and inhibitory synaptic currents of cortical neurons are approximately balanced in strength, causing the membrane potential to hover somewhat below the spiking threshold, crossing it at random times (Shadlen and Newsome, 1994, 1998). Simulations, based on the random walk model of (Gerstein and Mandelbrot, 1964) demonstrated that under such a regime of synaptic inputs the ISI variability is in agreement with experimental observations (Shadlen and Newsome, 1994, 1998). Furthermore, computational studies of spontaneous activity in neuronal networks showed that such a balance between excitation and inhibition emerges naturally if the network is sparsely connected (van Vreeswijk and Sompolinsky, 1996), see also a review in (Vogels et al., 2005). However, these early theoretical studies were based on crude estimates of the relevant parameters, and therefore cannot be regarded as definitive. In fact, several follow-up studies suggested that other factors, such as synchrony, are required in order to explain the observed ISI statistics, e.g., (Stevens and Zador, 1998). Indeed, as described below, it appears that although excitation and inhibition are balanced, the membrane potential of cortical neurons does not necessarily follow the random walk trajectory predicted by these early models (DeWeese et al, 2006).

The possibility of excitation and inhibition having a comparable strength might seem implausible at first, since interneurons comprise only 15% - 25% of the population of cortical neurons. However, the synaptic strength and firing rates of inhibitory interneurons are substantially higher than in excitatory neurons, and at the same time the depression of inhibitory synapses due to sustained activation is less pronounced (Markram et al., 2004). Thus inhibitory interneurons may have an impact disproportionate to their relatively small number.

## Intracellular measurement of the excitatory and inhibitory synaptic inputs

Figure 1: Computation of synaptic conductance evoked by sensory stimulus. The average response to whisker deflection in a spiny stellate neuron in layer IV of the rat primary somatosensory cortex is recorded in current-clamp mode while injecting 4 different currents (left panel). In addition, neuron’s capacitance and leak conductance are measured (not shown). By fitting the responses to equation (1) the average excitatory and inhibitory synaptic conductances evoked by the stimulus are recovered (right panel). Adapted from (Heiss et al., 2008).

In a pioneering study, Borg-Graham and colleagues used intracellular recordings to estimate directly the synaptic conductance changes evoked in cortical neurons by visual stimulation (Borg-Graham et al., 1996, 1998). The average synaptic current evoked by a stimulus is recorded in voltage-clamp mode, using several different clamping voltages. Alternatively, the subthreshold response is recorded in the current-clamp mode at several different clamping currents. The behavior of the membrane potential is approximated using a passive, single compartment, conductance-based model of the neuron, described by

$$CdV/dt = -G_{leak}(V(t)-E_{leak}) - G_{ex}(t)(V(t)-E_{ex}) - G_{in}(t)(V(t)-E_{in})+I_{inj}, \;\;\;\; (1)$$

where $$E_{leak}$$ is the resting membrane potential of the neuron, $$C$$ is its capacitance, $$G_{leak}$$ is the mean conductance in absence of stimulation (the inverse of input resistance), $$E_{ex}$$ and $$E_{in}$$ are the reversal potentials of excitation and inhibition, and $$I_{inj}$$ is the current injected through the recording pipette. By fitting equation (1) to the average responses at different holding potentials, the synaptic conductances evoked by the stimulus, $$G_{ex}(t)$$ and $$G_{in}(t)\ ,$$ can be computed (see Figure 1). For an in-depth review of the method and its caveats an interested reader is referred to (Monier et al., 2008).

## Selectivity of cortical excitation and inhibition to sensory stimulation

Early models of the visual cortex suggested that the selectivity of cortical cells to sensory stimulation emerges from feedforward inputs. Later models, however, questioned this view by suggesting that cortical inhibition plays a significant role in enhancing the selectivity of cortical response. The best known example for this controversy is the emergence of orientation selectivity. The feedfoward model (Hubel and Wiesel, 1962) was supported by various studies (Alonso and Martinez, 1998; Chung and Ferster, 1998; Martinez and Alonso, 2001), but it was also challenged by others (Sillito, 1975;Volgushev et al., 1996). These latter experimental studies supported models in which cortical inhibition sharpens the selectivity of the cells by shunting excitation at non-preferred stimuli (Ben-Yishai et al., 1995; Somers et al., 1995; Hansel and Sompolinsky, 1996). Similarly, inhibition was suggested to account for the selectivity of neurons in the primary auditory cortex (Calford and Semple, 1995; Sutter et al., 1999; Wang et al., 2002).

A breakthrough in the ability to test these models was introduced by the in-vivo intracellular conductance measurement method described above. This technique was used in the past decade to examine the role of inhibition not only in the emergence of orientation selectivity of cortical cells in the visual cortex (Anderson et al., 2000) but also in their length tuning (Anderson et al., 2001) and the selectivity to the direction of motion (Priebe and Ferster, 2005). These and other studies indicate that excitation and inhibition in the visual cortex are similarly tuned, suggesting that the selectivity of the neurons is unlikely to emerge due to suppression of the response to non-preferred stimuli (Priebe and Ferster, 2008). Along the same line, the frequency and intensity tuning curves of excitation and inhibition in the primary auditory cortex, as measured by intracellular in-vivo recordings, were found to be similar to each other (Wehr and Zador, 2003), see Figure 2. These results suggest that as in the visual cortex, the selectivity of auditory cortex neurons is not established by inhibition.

Figure 2: An example of a neuron in the auditory cortex with frequency and intensity co-tuned excitatory and inhibitory inputs. (a) Excitatory and inhibitory synaptic conductances evoked by stimuli of different frequencies and preferred intensity have a similar tuning. The measured conductances are shown at the bottom (green – excitatory conductance, red - inhibitory conductance, black – total conductance). (b) The excitatory and inhibitory inputs are also intensity co-tuned, notation as in (a). Adapted from (Wehr and Zador, 2003).

In the auditory and somatosensory cortices sensory stimulation often evokes stereotypic sequence of excitation followed within a few milliseconds by inhibition (Wehr and Zador, 2003; Higley and Contreras, 2006). Although excitation and inhibition are similarly tuned and hence are said to be balanced, a large imbalance occurs at the millisecond time scale, as inhibition lags behind excitation by several milliseconds. This lag between excitation and inhibition is likely to determine the integration window for excitation, affecting the number and precise timing of action potentials (Gabernet et al., 2005). In the auditory cortex the lag is independent of the frequency tuning of the cells (Wehr and Zador, 2003). In the somatosensory cortex, however, the delay between excitation and inhibition might be related to the stimulus tuning of the neuron, such that at the preferred stimuli the lag between excitation and inhibition is larger than at the non-preferred ones (Wilent and Contreras, 2005). Hence, a wider time window is available for integration of excitation for the stimuli which the neuron prefers.

The similar tuning of excitatory and inhibitory inputs to different features of the stimuli space appears to be a rather general organizational principle in the sensory areas, however the co-tuning is not necessarily precise. For example, in the auditory cortex the frequency tuning of inhibition appears to be somewhat wider than of the excitation (Wu et al., 2008). Another such example was found in the barrel cortex, where the intensity co-tuning of excitation and inhibition is not preserved for very weak whisker stimuli (Heiss et al., 2008). In certain special cases the co-tuning of excitation and inhibition breaks altogether. For instance, in the auditory cortex some intensity-tuned neurons receive excitatory inputs which peak at the preferred intensity, whereas their inhibitory inputs increase monotonically with the stimulus strength (Wu et al., 2006).

One of the central roles traditionally attributed to inhibition is suppression of neuronal responses during temporal integration of sensory inputs. A widely known example is forward suppression in the auditory cortex, in which the response to a second click presented shortly after the first one is much weaker. Another example is in the barrel cortex, where a response to whisker stimulation is largely suppressed if it is preceded by a stimulation of a neighboring whisker. Such forward suppression was widely believed to be due to inhibition evoked by the first stimuli. However, intracellular conductance measurements found that the duration of inhibitory synaptic input evoked by the first click is too short to account for the duration of forward suppression, so that the above explanation is incomplete at the best (Wehr and Zador, 2003, 2005). Similarly, an intracellular recording study in the barrel cortex has shown that cross whisker suppression cannot be fully explained by a postsynaptic inhibitory mechanism (Higley and Contreras, 2003). Although inhibition is not the primary cause for forward suppression, in other cases the ratio between the excitatory and inhibitory inputs to a neuron in a primary sensory area does depend not only on the instantaneous properties of the stimuli (its contrast, frequency, intensity, etc.) but also on its past history. One particular example is adaptation to repeated stimuli, such as clicks or whisker deflections, which under certain conditions can skew the ratio between excitatory and inhibitory inputs toward excitation (Wehr and Zador, 2005; Heiss et al., 2008).

## Balance during spontaneous activity

Under some anesthesia conditions and during slow wave sleep, the membrane potential of cortical neurons fluctuates between a depolarized state and hyperpolarized state. This behavior is known as Up-Down activity. During the Down state the neurons receive almost no synaptic inputs, so that the membrane stays near its resting potential. In the Up state a barrage of synaptic input produces a reliable depolarization of 10-20 mV, which occasionally causes spiking (see Figure 1 in Up and down states).

The relation between the average amounts of excitatory and inhibitory synaptic inputs during the Up state was studied using the conductance measurement method described above. These experiments, conducted both in vitro (Shu et al., 2003) and in vivo (Haider et al., 2006), have shown that excitatory and inhibitory conductances are balanced throughout the Up state. In the beginning of the Up state, both the excitatory and the inhibitory synaptic conductances are high and they tend to progressively decrease, but their ratio remains constant and approximately equal to 1. The high-conductance state in an awake animal is similar to a continuous Up state (Destexhe et al., 2007). According to a recent intracellular study in the cortex of awake cats, during spontaneous activity the neurons are continuously bombarded by both excitatory and inhibitory inputs, where the total inhibitory conductance is several times higher than the excitatory one (Rudolph et al., 2007). All these findings provide a confirmation for the balanced excitation-inhibition hypothesis put forward by (Shadlen and Newsome, 1994).

Figure 3: Excitatory and inhibitory inputs are synchronized during spontaneous activity. Two nearby neurons are simultaneously recorded when (a) both are at their resting potential, close to the reversal potential of inhibition (hyperpolarized-hyperpolarized mode); (b) both neurons are depolarized close to the reversal potential of excitation (depolarized-depolarized mode); (c-d) one of the neurons is in the hyperpolarized mode while the other is in the depolarized mode. In (a) the activity is dominated by excitatory inputs, which are seen to be highly synchronized between the neurons. Similarly, in (b) the activity is dominated by inhibitory inputs which are also highly synchronized. Finally, the mixed mode recordings (c-d) demonstrate that the excitatory and inhibitory inputs possess a high degree of synchrony. Adapted from (Okun and Lampl, 2008).

An activity pattern quite different from Up-Down dynamics or continuous Up state can be observed in rodents that are awake or under certain anesthesia conditions. It is characterized by rather short depolarizations ('bumps') and membrane potential distribution that is not bimodal, e.g., (DeWeese and Zador, 2006; Poulet and Petersen, 2008). Since there are no stereotypic Up events nor does the activity resemble a single continuous Up state, the single-electrode conductance measurement method which requires averaging over multiple repeats of some stereotypic event, recorded at different holding potentials, cannot be applied. However, the substantial synchrony of synaptic inputs to closely located neurons (Lampl et al., 1999; Hasenstaub et al., 2005; Okun and Lampl, 2008; Poulet and Petersen, 2008) which exists in this case allows to continuously monitor both the excitatory and the inhibitory activity in the local network. Toward this end simultaneous recording from a nearby pair of neurons are used, where one cell is hyperpolarized close to the reversal potential of inhibition and the other cell is depolarized sufficiently close to the reversal potential of excitation (Okun and Lampl, 2008), Figure 3. This method reveals that in this type of spontaneous activity the excitatory and inhibitory inputs are interlocked in time, with inhibition lagging by several milliseconds behind excitation. Furthermore, the strength of excitatory and inhibitory inputs is (positively) correlated – large bumps typically contain both a strong excitatory and a strong inhibitory components, whereas small bumps are due to weak synaptic inputs, rather than strong inhibition that quenches the excitatory input. These correlations strongly suggest that inhibition plays important role in controlling the excitability of cortical networks at fast time scale.

## Conclusions

The available data, collected under a wide variety of conditions and in distinct cortical areas indicates that co-activation of inhibition and excitation is a basic functional principle underlying various cortical activities, occurring with a high temporal precision of a few milliseconds. Although the balance between excitatory and inhibitory synaptic inputs was studied most extensively in the cortex, similar principles manifest themselves in many CNS structures, such as the hippocampus (Atallah and Scanziani, 2009), superior colliculus (Populin, 2005), brain stem (Magnusson et al., 2008), spinal cord (Berg et al., 2007), and others.

While the role of the tight coupling between excitation and inhibition is not fully clear, it is most likely to serve as a major gain mechanism that increases the accuracy and speed of neuronal response. By counterbalancing the excitatory drive, inhibitory inputs greatly extend the dynamic range of excitation, allowing a fine and rapid control over the amount of depolarization of the membrane potential. It is apparent that achieving a certain depolarization without a counteracting inhibitory force would have required a much weaker excitatory input, increasing the error and variability of the response.

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