Spike timing dependent plasticity promotes synchrony of inhibitory networks in the presence of heterogeneity

Abstract

Recently Haas et al. (J Neurophysiol 96: 3305-3313, 2006), observed a novel form of spike timing dependent plasticity (iSTDP) in GABAergic synaptic couplings in layer II of the entorhinal cortex. Depending on the relative timings of the presynaptic input at time t (pre) and the postsynaptic excitation at time t (post), the synapse is strengthened (Deltat = t(post) - t(pre) > 0) or weakened (Deltat < 0). The temporal dynamic range of the observed STDP rule was found to lie in the higher gamma frequency band (> or =40 Hz), a frequency range important for several vital neuronal tasks. In this paper we study the function of this novel form of iSTDP in the synchronization of the inhibitory neuronal network. In particular we consider a network of two unidirectionally coupled interneurons (UCI) and two mutually coupled interneurons (MCI), in the presence of heterogeneity in the intrinsic firing rates of each coupled neuron. Using the method of spike time response curve (STRC), we show how iSTDP influences the dynamics of the coupled neurons, such that the pair synchronizes under moderately large heterogeneity in the firing rates. Using the general properties of the STRC for a Type-1 neuron model (Ermentrout, Neural Comput 8:979-1001, 1996) and the observed iSTDP we determine conditions on the initial configuration of the UCI network that would result in 1:1 in-phase synchrony between the two coupled neurons. We then demonstrate a similar enhancement of synchrony in the MCI with dynamic synaptic modulation. For the MCI we also consider heterogeneity introduced in the network through the synaptic parameters: the synaptic decay time of mutual inhibition and the self inhibition synaptic strength. We show that the MCI exhibits enhanced synchrony in the presence of all the above mentioned sources of heterogeneity and the mechanism for this enhanced synchrony is similar to the case of the UCI.

Control of neural synchrony using channelrhodopsin-2: a computational study

“…The quantity S(t) denotes the fraction of bound receptors and satisfies the following first order kinetic equation, Talathi et al 2008),…”

“…For all the results presented below, unless otherwise mentioned, I A DC = 0.5 μA/cm 2 , corresponding to intrinsic period T A 0 ≈ 31.05 ms. We will now briefly explain how STRCs can be used to analytically estimate the range of heterogeneity over which the UCI can exhibit 1:1 synchrony (Oprisan and Canavier 2001;Talathi et al 2008). As discussed in Oprisan and Canavier (2001), Talathi et al (2008), our goal is to determine the stability of phase locked state of 1:1 synchrony between the two coupled neurons.…”

“…As discussed in Oprisan and Canavier (2001), Talathi et al (2008), our goal is to determine the stability of phase locked state of 1:1 synchrony between the two coupled neurons. Let t A i (i = 1, 2, · · · ) and t B j ( j = 1, 2, · · · ) represent the spike times for neurons A and B respectively.…”

“…Following earlier works (Oprisan and Canavier 2001;Talathi et al 2008), for the case of UCI network with hyperpolarizing synapse (E R = −75 mV), the stability of δ s can be determined by analyzing the nonlinear map for the evolution of δ n , which is given as:…”

“…These studies lead to the general conclusion that while homogeneous networks of fast spiking interneurons can produce synchrony, the synchrony is very sensitive to heterogeneity in network parameters. Recent work by our group and others have demonstrated that the sensitivity to heterogeneity can be mitigated through a number of biological mechanisms including spike timing dependent plasticity (Zhigulin et al 2003;Talathi et al 2008), signal propagation delays (Crook et al 1997;Talathi et al 2010) and electrical coupling (Bennett and Zukin 2004). While it is clear that a number of different biological mechanisms exist to induce synchrony in brain networks, very few studies have focused on neural stimulation based approaches to induce synchrony in brain networks.…”