Encyclopedia of Computational Neuroscience

Living Edition
| Editors: Dieter Jaeger, Ranu Jung

Balanced State

  • Lars SchwabeEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4614-7320-6_573-1

Keywords

Balance State Synaptic Conductance Awake Animal Lower Absolute Number Dendritic Input 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Synonyms

Definition

The balanced state of neurons is characterized by a high value of the total membrane conductance caused by synaptic inputs. It is the state of cortical neurons in vivo in awake animals, and it is due to massive excitatory and inhibitory inputs that almost cancel out. In this state, the responses are driven by fluctuations (possible also due to coincident events) in the input, and due to a greatly reduced effective membrane time constant, the neuron responds rapidly.

Detailed Description

The notion of high-conductance states, and the fact that neurons could integrate differently in such states, was first proposed by modeling studies. A meanwhile classical dichotomy distinguished between two operating modes of neurons: the integrator mode and the coincidence detection mode. In the integrator mode, the postsynaptic neuron is emitting spikes, because it integrates over time the excitatory presynaptic inputs. In the coincidence detection mode, it fires spikes, because many presynaptic excitatory neurons synchronize their excitatory inputs. By changing the time constant of the postsynaptic neuron, one could switch between these two modes: Coincidence detection calls for a short time constant, where the neuron quickly “forgets” previous inputs and needs coincident spikes so that the membrane potential is elevated enough to emit a postsynaptic spike; in the integration mode, the time constant should be longer to allow for summing inputs over time. Cortical neurons in vivo are likely to operate in the latter mode, because due to massive excitatory and balanced inhibitory inputs, the effective time constant is very small. This has various consequences for cortical computations at both the single-neuron and network levels, which are now addressed in greater detail, aver the observation of a “high-conductance state” in recapitulated.

Empirical Evidence for a “High-Conductance State”

It is well known to physiologists that neurons in anesthetized animals often appear during intracellular recordings as if they operate in two distinct states, namely a so-called “up” state and a “down” state. In the “up” state, the neurons are depolarized and can fire action potentials, which are irregular as observed in extracellular recordings in awake animals. In the “down” state the neurons are hyperpolarized and emit no spikes. How do these two states emerge? The detailed mechanisms are still under investigation, but experiments revealed that the “down” state can be much more easily manipulated via current injections than the “up” state. The lack of strong effects in the “up” state is consistent with a very high membrane conductance. A plausible explanation of this approximately 2–3 times increase of conductance relative to the resting leak conductance is to assume it as due to synaptic inputs.

Consequences for Single-Neuron Computations

In 1994 Shadlen and Newsome explored the idea that excitatory and inhibitory synaptic inputs might be balanced and keep the membrane potential close to, but below, the firing threshold (Shadlen and Newsome 1994). In this scenario the neuron can still respond, because fluctuations can push the membrane potential above a threshold. Simulation studies showed that in this regime, the neural responses are much more irregular compared to a non-balanced scenario with little or no inhibition, i.e., when strong excitation drives the responses. For neuronal models this means that neurons in a balanced state are best described with stochastic formalisms (Tuckwell 1988).

Given that neurons in the balanced state are sensitive to fluctuations in the inputs, they could also detect changes in such fluctuations. Of particular interest have been those brought about by changing correlations between presynaptic excitatory, inhibitory, or between excitatory and inhibitory spikes (Salinas and Sejnowski 2000). Interestingly, such correlations could change without affecting the average of the inputs. For neuronal modeling this is important, because it calls for stochastic models beyond simplistic rate-base descriptions. The fluctuations of balanced inputs have been implicated in changing the gain of neurons. Such gain modulations have been described as a physiological signature of attentional top-down modulations. Chance et al. (2002) have shown the feasibility of this mechanism using modeling and dynamic-clamp (Sharp et al. 1992), but in vivo tests of this hypothesis remain technically too challenging.

Another consequence of the balanced state is that responses to inputs can be very rapid as pointed out already in 1975 by Barrett (1975). This can be demonstrated using the simple RC circuit model of the subthreshold membrane potential dynamics: Let us consider a leaky integrator, modeled as an RC circuit, with a time constant τ = RC = C/g, where R is the membrane resistance (and g = 1/R the conductance) and C is the membrane capacitance. The dynamics of membrane potential V are given by
$$ C\frac{ dV}{ dt}=- gV+{g}_{\mathrm{AMPA}}(t)\left({E}_{\mathrm{AMPA}}-V\right)+{g}_{\mathrm{GABA}}(t)\left({E}_{\mathrm{GABA}}-V\right) $$
where g AMPA(t) and g GABA(t) are the excitatory and inhibitory synaptic conductances (with reversal potentials E AMPA and E GABA) due to approximately balanced presynaptic inputs, i.e., the resulting currents cancel each other at a certain subthreshold voltage. These synaptic conductances are time dependent due to the different arrivals of spikes at the synapses and the kinetics of synaptic transmission. Averaging these conductances over time yields g AMPA and g GABA. Setting \( \frac{ dV}{ dt}=0 \) and solving for the effective time constant τ eff shows that
$$ {\tau}_{\mathrm{eff}}=\frac{C}{g+{g}_{\mathrm{AMPA}}+{g}_{\mathrm{GABA}}}<\frac{C}{g}\kern0.5em . $$

Thus, with increasing synaptic conductance, the neuron responds faster. This may be of particular relevance in sensory systems with high-frequency inputs, because in a non-balanced state, the neuron could not lock to such inputs.

Such a high-conductance state also affects the integration of dendritic signals. In line with Rall’s classical works (Rall 1964), Barrett also suggests a location-dependence of the impact of dendritic inputs onto the somatic membrane potential. He emphasized the role of synaptic background activity, which would decrease the resistance and further reduce the impact of distal dendritic inputs. Experiments showed, however, that the dendritic inputs are approximately location-independent (Magee 2000). This observation could be a natural consequence of the massive synaptic inputs onto active excitable dendrites in the balanced state, i.e., dendrites that support the local initiation of spikes (London and Häusser 2005). Rudolph and Destexhe have shown in simulation studies (Rudolph and Destexhe 2003) that the decreased impact with increasing distance from the soma predicted by Rall and Barrett could be balanced by an increased likelihood of evoking a dendritic spike as the input resistance increases with distance from the soma.

Consequences for Network-Based Computations

While single-neuron modeling studies usually assume background inputs with certain properties such as balanced inputs, network models need to explicitly account for them. In 1996 van Vreeswijk and Sompolinsky (1996) showed that sparsely connected recurrent networks with strong but balanced excitation and inhibition naturally lead to the temporally irregular spiking patterns observed in awake animals. One may wonder how such a tight balance between excitation and inhibition required by network models could be realized in cortical networks, given that local inhibitory interneurons are far less numerous than the excitatory neurons. Despite their lower absolute number, inhibitory neurons are often reported to have higher firing rates. Moreover, their synapses onto postsynaptic targets show much less short-term depression than excitatory synapses. In combination, this could make the recurrent inhibition much stronger than evident by their lower absolute number.

It is known that blocking inhibition causes the cortex to become epileptic (Dichter and Ayala 1987), and already in 1975 Sillito showed that reducing inhibition lets sensory neurons (in primary visual cortex, V1) lose their orientation selectivity (Sillito 1975). This further supports the notion that the balanced state is the natural cortical state of awake animals. Experimental studies later investigated in greater detail the potential network mechanisms underlying the spike responses in vivo using paired recordings. For example, Okun and Lampl showed in 2008 via simultaneous intracellular recordings of pairs of nearby neurons in rat somatosensory cortex (Okun and Lampl 2008) that the excitatory and inhibitory inputs covary in strength and time. They found this covariation during both the spontaneous “resting-state” activity and during sensory stimulation. Marino et al. (2005) performed intracellular recordings in vivo in V1 and showed that such a covariation in space could explain the experimentally observed invariance of the orientation tuning with location in the orientation map of V1. The balanced state as observed in single neurons may also have large-scale macroscopic correlates, namely, the spontaneously occurring states reported during resting-state activity in V1 (Kenet et al. 2003). From a modeling perspective, it is worth mentioning that such macroscopic phenomena can be simulated and analyzed using rate model (Blumenfeld et al. 2006).

Discussion and Future Directions

Meanwhile, the balanced state is accepted in the community as the state that characterizes cortical neurons in vivo. Many studies have investigated how it affects single-neuron computations. Other studies have developed self-consistent network models that reproduce the balanced state. Experimental tests of model predictions appeared in the literature with quite some delay relative to the modeling studies. This is not a surprise, because direct empirical evidence for the balanced state is technically very hard to obtain, as it calls for intracellular multiunit recordings of connected neurons in vivo. Future modeling studies should respect this and aim at specific predictions for easier to access macroscopic observables. Future modeling studies could also investigate how adaptation at various timescales affects the balance between excitation and inhibition. Given that cortical networks seem to be exquisitely balanced, even small perturbations could have major impacts. The role of inhibitory plasticity in maintaining the balanced state has been addressed in first modeling studies (Vogels et al. 2012). Exploring how a certain adaptation or learning mechanism behaves in the balanced state in vivo is now becoming a necessity for all modeling studies of adaptation, learning, and cortical computation. Finally, one may need to address explicitly the energetic costs of the balanced state. Are the potential benefits, from a normative point of view, really worth all the energy the brain is investing into maintaining this mode of operation? It could be that the most fascinating properties of the balanced state that warrant this investment are still to be discovered.

References

  1. Barrett JN (1975) Motoneuron dendrites: role in synaptic integration. Fed Proc 34:1398–1407PubMedGoogle Scholar
  2. Blumenfeld B, Bibitchkov D, Tsodyks M (2006) Neural network model of the primary visual cortex: from functional architecture to lateral connectivity and back. J Comp Neurosci 20(2):214–241CrossRefGoogle Scholar
  3. Chance FS, Abbott LF, Reyes AD (2002) Gain modulation from background synaptic input. Neuron 35:773–782PubMedCrossRefGoogle Scholar
  4. Dichter MA, Ayala GF (1987) Cellular mechanisms of epilepsy: a status report. Science 237:157–164PubMedCrossRefGoogle Scholar
  5. Kenet T, Bibitchkov D, Tsodyks M, Grinvald A, Arieli A (2003) Spontaneously emerging cortical representations of visual attributes. Nature 425(6961):954–956PubMedCrossRefGoogle Scholar
  6. London M, Häusser M (2005) Dendritic computation. Ann Rev Neurosci 28:503–532PubMedCrossRefGoogle Scholar
  7. Magee JC (2000) Dendritic integration of excitatory synaptic input. Nat Rev Neurosci 1(3):181–190PubMedCrossRefGoogle Scholar
  8. Mariño J, Schummers J, Lyon DC, Schwabe L, Beck O, Wiesing P, Obermayer K, Sur M (2005) Invariant computations in local cortical networks with balanced excitation and inhibition. Nat Neurosci 8(2):194–201PubMedCrossRefGoogle Scholar
  9. Okun M, Lampl I (2008) Instantaneous correlation of excitation and inhibition during ongoing and sensory-evoked activities. Nat Neurosci 11:535–537PubMedCrossRefGoogle Scholar
  10. Rall W (1964) Theoretical significance of dendritic trees for neuronal input-output relations. In: Reiss R, Alto P (eds) Neural theory and modeling. Stanford University Press, StanfordGoogle Scholar
  11. Rudolph M, Destexhe A (2003) A fast-conducting, stochastic integrative mode for neocortical neurons in vivo. J Neurosci 23:2466–2476PubMedGoogle Scholar
  12. Salinas E, Sejnowski TJ (2000) Impact of correlated synaptic input on output firing rate and variability in simple neuronal models. J Neurosci 20:6193–6209PubMedGoogle Scholar
  13. Shadlen MN, Newsome WT (1994) Noise, neural codes and cortical organization. Curr Opin Neurobiol 4:569–579PubMedCrossRefGoogle Scholar
  14. Sharp AA, Abbott LF, Marder E (1992) Artificial electrical synapses in oscillatory networks. J Neurophysiol 67:1691–1694PubMedGoogle Scholar
  15. Sillito AM (1975) The contribution of inhibitory mechanisms to the receptive field properties of neurones in the striate cortex of the cat. J Physiol 250:305–329PubMedCentralPubMedGoogle Scholar
  16. Tuckwell HC (1988) Introduction to theoretical neurobiology. Cambridge University Press, Cambridge, UKCrossRefGoogle Scholar
  17. van Vreeswijk CA, Sompolinsky H (1996) Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science 274:1724–1726PubMedCrossRefGoogle Scholar
  18. Vogels TP, Sprekeler H, Zenke F, Clopath C, Gerstner W (2012) Inhibitory plasticity balances excitation and inhibition in sensory pathways and memory networks. Science 336(6083):802Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Computer Science and Electrical Engineering, Adaptive and Regenerative Software SystemsUniversität RostockRostockGermany