# Balance of excitation and inhibition

Post-publication activity

Curator: Ilan Lampl

In the context of neurophysiology, balance of excitation and inhibition (E/I balance) 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 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 E/I balance

Cortical neurons receive synaptic inputs from thousands of other, mainly excitatory, neurons, most of which evoke 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 E/I balance emerges naturally if the network is sparsely connected (van Vreeswijk and Sompolinsky, 1996; 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 (Crochet and Petersen, 2006; DeWeese and Zador, 2006; Poulet and Petersen, 2008; Okun et al., 2010; Polack et al., 2013; Sachidhanandam et al., 2013; Tan et al., 2014). 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, thus inhibitory interneurons 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 directly estimate 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 (Anderson et al., 2000). 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 in primary visual cortex. The feedforward model (Hubel and Wiesel, 1962) was supported by various studies (Nelson et al., 1994; Alonso and Martinez, 1998; Chung and Ferster, 1998; Martinez and Alonso, 2001), while being challenged by others (Sillito, 1975; Volgushev et al., 1996). The feedforward model, however, failed to predict several key experimental findings, and in particular the contrast invariance of orientation tuning (Ferster and Miller, 2000). Alternative models proposed that the tuning of inhibitory inputs is wider, so that excitation and inhibition form a 'Mexican hat' interaction pattern which sharpens the selectivity of the cells (Ben-Yishai et al., 1995; Somers et al., 1995; Hansel and Sompolinsky, 1996). In the primary auditory cortex inhibition was similarly suggested to account for the sensory selectivity of the neurons (Calford and Semple, 1995; Sutter et al., 1999; Wang et al., 2002).

A breakthrough in the ability to test these models was achieved by the in-vivo intracellular conductance measurement methods described above. Over the last 15 years this approach was used in many studies to examine the sensory selectivity of excitatory and inhibitory synaptic inputs in primary sensory areas of several mammalian species. Direct measurements showed that to a first approximation the excitatory and inhibitory inputs are either similarly tuned, or that inhibitory inputs have a somewhat wider tuning. In cat primary visual cortex excitatory and inhibitory synaptic inputs are similarly tuned for orientation (Anderson et al., 2000), as well as for length (Anderson et al., 2001) and the direction of motion (Priebe and Ferster, 2005). In the rodent primary auditory cortex inhibition is tuned similarly or somewhat wider than excitation for both frequency and intensity (Wehr and Zador, 2003; Wu et al., 2008; Zhou et al., 2014), see Figure 2. Therefore, in these cases the selectivity of the neurons is unlikely to emerge through inhibitory suppression of the response to non-preferred stimuli.

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).

The similar tuning of excitatory and inhibitory inputs to different features of the stimuli space appears to be a rather common organizational principle in the sensory areas, however there are several notable exceptions. The most prominent deviation from co-tuning was observed for orientation selectivity in the mouse primary visual cortex, where the inhibitory input is substantially more broadly tuned than the excitatory input, possibly because rodent primary visual cortex lacks orientation columns (Liu et al., 2011; Atallah et al., 2012; Li et al., 2012; Harris and Mrsic-Flogel, 2013). An opposite scenario, where inhibitory inputs have narrower selectivity, was observed for frequency tuning in layer V intrinsically-bursting (but not regular-spiking) neurons of the primary auditory cortex (Sun et al., 2013). Also 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), representing a case where the co-tuning of excitation and inhibition appears to break altogether. Finally, it should be noted that the tuning of inhibitory and excitatory inputs alone is not sufficient to substantiate specific theoretical models for feature selectivity in the cortex, because broad tuning of inhibition may either reflect non-specific convergence of inputs from a population of inhibitory cells that demonstrate highly selective but non-overlapping orientation tuning curves, or simply result from the wide tuning curves of their innervating inhibitory neurons (Shapley and Xing, 2013; Section 6 below).

## Temporal structure of sensory evoked excitation and inhibition

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 fine 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 preferred stimuli, producing more action potentials.

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 stimulus (its contrast, frequency, intensity, etc.) but also on its 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). Paradoxically, because of a slower recovery of inhibitory inputs from adaptation, neurons become hypersensitive shortly after the termination of the adapting stimulation (Cohen-Kashi Malina et al., 2013), which might explain why neurons in the barrel cortex respond better to non-periodic stimulation (Lak et al., 2008).

## E/I 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 phase the neurons receive almost no synaptic inputs, so that the membrane stays near its resting potential. In the Up phase a barrage of synaptic inputs 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 phase 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 phase. In the beginning of the Up phase, 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.

In awake, drug-free animals the membrane potential dynamics exhibits an entire spectrum of distinct, brain state dependent activity patterns. The highly desynchronized high-conductance state, which is similar to a continuous Up phase (Crochet and Petersen 2006; Destexhe et al., 2007) represents one end of this spectrum. According to an intracellular study in the cortex of awake cats, in this condition 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), providing 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).

The other end of the spectrum of brain states in awake mammals is the quiet wakefulness condition, which is somewhat similar to light anesthesia, and 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). In the quiet wakefulness condition and light state of anesthesia there are no stereotypic Up events nor does the activity resemble a single continuous Up phase, therefore 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 scales.

## Current research directions

In the recent years a whole range of new genetic tools became available, particularly for the mouse (Mus musculus) species. In addition, working with awake head-fixed mice is relatively straightforward. These and other recent developments are heavily relied upon in the current research which, in addition to the directions discussed in the previous sections, focuses on new aspects of E/I balance, as described in more detail below.

#### E/I balance across brain states

To date, only few works investigated how brain state modulation affects E/I balance. A study of primary visual cortex found that in awake mice, when compared to animals under anesthesia, the spatial tuning of inhibitory synaptic inputs is much wider, suggesting that in awake animals the E/I balance is profoundly skewed towards inhibition (Haider et al., 2013). However in the auditory cortex of awake mice excitation and inhibition have similar magnitude and frequency tuning (Zhou et al., 2014), in agreement with previous results in anesthetized animals. Finally, a study of ongoing activity in the barrel cortex of anesthetized rats found that a switch to lighter anesthesia induces a profound shift toward excitation, probably due to depression of inhibitory synapses in the regime of higher activity under light anesthesia (Taub et al., 2013). At the present time it is not clear whether the differences between these studies are due to differences between brain areas, special connectivity subserving sensory tuning or other factors.

In addition to differences between awake and anesthetized conditions, the effects of transition between quiet wakefulness and locomotion were recently studied. Locomotion was found to have a differential effect on primary visual and auditory cortices, increasing the firing and shifting the balance towards excitation in the former (Bennett et al., 2013), while suppressing firing and equally scaling down both excitation and inhibition in the latter (Zhou et al., 2014). Hence, the impact of locomotion on brain-state and in particular on E/I balance is not uniform across the sensory cortices.

#### Interneuron classes and the E/I balance

In spite of constituting a minority, inhibitory interneurons in the cortex are vastly more diverse than the excitatory cells, with large variety of dendritic and axonal arborization patterns (Ramon Y Cajal, 1911; Jones 1975). Histochemical and other methods revealed that GABAergic neurons in the cortex are subdivided into at least 4 almost non-overlapping classes (Kawaguchi and Kubota 1997; Harris and Mrsic-Flogel 2013): Parvalbumin (PV) expressing cells, somatostatin (Sst) expressing cells, vasoactive intestinal peptide (VIP) expressing cells and neurogliaform cells (NGs). Anatomical evidence and recordings in brain-slices suggest that these classes have different roles in the E/I balance and may have different functional roles across cortical layers. Current studies use molecular genetics and imaging methods to understand the role and function of each subtype.

Several converging lines of evidence indicate that PV cells constitute the major source of inhibitory current in principal cells for both spontaneous activity and sensory evoked responses. It follows that the sensory tuning of inhibitory synaptic inputs of pyramidal cells is expected to be the same or wider than the sensory tuning of the individual PV cells. For example, for orientation tuning in the mouse visual cortex, the tuning curves of PV cells were found to be much wider than of the principal cells, explaining the wide tuning of inhibitory inputs of pyramidal neurons (Atallah et al., 2012). In the auditory cortex the PV cells were found to be tuned for frequency, again consistent with inhibitory inputs to pyramidal cells originating in the neighboring PV neurons (Moore and Wehr 2013; Li et al., 2014).

The role of the other classes of inhibitory interneurons is currently investigated in many labs, in particular using the powerful new optogenetic tools. Optogenetic stimulation was recently used to examine the effect of PV and Sst cells on orientation tuning (Atallah et al. 2012; Lee et al., 2012; Wilson et al., 2012). (Atallah et al. 2012) and (Wilson et al., 2012) suggest that PV cells do not alter the tuning of principal cells. (Wilson et al., 2012) furthermore attribute to Sst cells the ability to sharpen orientation selectivity of principal cells by a subtraction effect. In contrast, (Lee et al., 2012) report that activation of PV cells was found to sharpen the orientation tuning of principal cells. Whether the contradiction between the studies is real or only at the level of data interpretation is not entirely clear (Lee et al., 2014; Atallah et al., 2014).

## 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 (Isaacson and Scanziani, 2011). Furthermore, the excitatory and inhibitory synaptic inputs appear to be individually matched in each pyramidal cell (Xue et al., 2014) with a high temporal precision of just a few milliseconds. Yet, whether excitation and inhibition share the same sensory tuning seems to depend on various factors, including animal species, the sensory modality and brain-state.

The E/I balance was studied most extensively in the cortex, however 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), prefrontal cortex (Yizhar et al., 2011) and others, not covered here in detail. This entry also did not describe E/I balance development and plasticity, e.g., (Froemke et al., 2007; Dorrn et al., 2010; Sun et al., 2010; Li et al. 2012). 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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