How Do Noise Affects Neurons Networks--论文代写范文

人口振荡的频率是更小的,可变性在相似的神经元突触形成，这种状态称为随机同步状态。随机同步发生在强噪声的存在,在最简单的集群状态,所有的神经元会飙升。下面的医学paper代写范文进行研究。

Introduction 
  Of the various patterns of synchronous oscillations that occur in the brain, episodes of activity during which local field potentials display fast oscillations with frequencies in the range 40 to 200 Hz have elicited particular interest. Such episodes have been recorded in vivo in several brain areas, in particular in the rat hippocampus (Buzsaki, Urioste, Hetke, & Wise, 1992; Bragin et al., 1995; Csicsvari, Hirase, Czurko, Mamiya, & Buzsaki, 1999a, ´ 1999b; Siapas & Wilson, 1998; Hormuzdi et al., 2001). During these episodes, single-neuron firing rates are typically much lower than local field potential (LFP) frequencies (Csicsvari et al., 1999a), and single-neuron discharges appear very irregular. 

  Although a detailed analysis of the single-cell firing statistics during these episodes is lacking, this irregularity is consistent with findings of high variability in interspike intervals of cortical neurons in various contexts (see, e.g., Softky & Koch, 1993; Compte et al., 2003), and the observation of large fluctuations in membrane potentials in intracellular recordings in cortex in vivo (see, e.g., Destexhe & Pare 1999; Anderson, ´ Lampl, Gillespie, & Ferster, 2000). Recent theoretical studies have shown that fast synchronous population oscillations in which single-cell firing is highly irregular emerge in networks of strongly interacting inhibitory neurons in the presence of high noise. Brunel and Hakim (1999) investigated analytically the emergence of such oscillations in networks of sparsely connected leaky integrate-and-fire neurons activated by an external noisy input. They showed that the frequency of the population oscillations increases rapidly when the synaptic delay decreases and that it can be much larger than the firing frequency of the neurons. 

  For instance, a network of neurons firing with an average rate of 10 Hz can oscillate at frequencies that can be on the order of 200 Hz when synaptic delays are on the order of 1 to 2 msec (Brunel & Hakim, 1999; Brunel & Wang, 2003). Tiesinga and Jose (2000) found similar collective states in numerical simulations of a fully connected network of inhibitory conductance-based neurons activated with a noisy external input. However, the frequency of the population oscillations in their model was smaller (in the range 20–80 Hz), and the variability of the spike trains was weaker than in the leaky integrate-and-fire (LIF) network for similar synaptic time constants and average firing rates of the neurons. 

  Following the terminology of Tiesinga and Jose (2000), we will call this type of state a stochastic synchronous state. Stochastic synchrony occurs in the presence of strong noise, in contrast to so-called cluster states, which are found when noise and heterogeneities are weak. In the simplest cluster state, all neurons tend to spike together in a narrow window of time; they form one cluster. In such a state, the population oscillation frequency is close to the average frequency of the neurons (Abbott & van Vreeswijk, 1993; Tsodyks, Mit’kov, & Sompolinsky, 1993; Hansel, Mato, & Meunier, 1995; White, Chow, Soto-Trevino, & Kopell, 1998; Golomb & Hansel, 2000; Hansel & Mato, 2003). Clustering in which neurons are divided into two or more groups can also occur (Golomb, Hansel, Shraiman, & Sompolinsky, 1992; Golomb & Rinzel, 1994; Hansel et al., 1995; van Vreeswijk, 1996). Within each of these groups, neurons fire at a similar phase of the population oscillation, but different groups fire at different phases. 

  Thus, the frequency of the population oscillations can be very different from the neuronal firing rate, as in stochastic synchrony. However, in contrast to stochastic synchrony, in cluster states the population frequency is always close to a multiple of the neuronal firing rate. Moreover, single-neuron activity in cluster states is much more regular than in stochastic synchronous states. In this letter, we examine the dynamics of networks of inhibitory neurons in the presence of noisy input. For simplicity, we consider a fully connected network; similarities and differences with more realistic randomly connected networks will be mentioned in the discussion. 

  We consider three classes of models: the LIF model (Lapicque, 1907; Tuckwell, 1988), the exponential integrate-and-fire model (EIF) (Fourcaud-Trocme, Hansel, van ´ Vreeswijk, & Brunel, 2003), and simple conductance-based (CB) models (Hodgkin & Huxley, 1952) with two active currents, a sodium and a potassium current. In these models, we study the instabilities of the asynchronous state. In this state, the population-averaged firing rate becomes constant in the large N limit, and correlations between neurons vanish in this limit. We investigate in particular how the instability responsible for stochastic synchrony relates to other types of instabilities of the asynchronous state. Section 2 is devoted to the LIF model. We fully characterize the spectrum of the instabilities of the asynchronous state and explore in what ways these instabilities depend on the noise amplitude, the average firing rate of the neurons, and the synaptic time constants (latency, rise, and decay time). This can be performed analytically, due to the simplicity of the LIF model and the simplified all-to-all architecture. 

  The LIF neuron has the great advantage of analytical tractability, but it often exhibits nongeneric properties. For instance, the frequency-current relationship that characterizes the response of the neuron to a steady external current exhibits a logarithmic behavior near current threshold, while generic type I neurons have a square root behavior. LIF and standard Hodgkin-Huxley (HH) models may also display substantially different synchronization behaviors in the low-noise regime (Pfeuty, Golomb, Mato, & Hansel, 2003; Pfeuty, Mato, Golomb, & Hansel, 2005). Crucially, LIF neurons respond in a nongeneric way to fast oscillatory external inputs (Fourcaud-Trocme et al., 2003). 

  This motivates an investigation of synchro- ´ nization properties in models with more realistic dynamics. In section 3, we combine analytical calculations with numerical simulations to study a network of EIF neurons. In this model, single-neuron dynamics depend on a voltage-activated current that triggers action potentials. This framework allows us to make predictions regarding the way sodium currents affect the emergence of fast oscillations. In section 4 we simulate several conductance-based network models to compare their behaviors with those of the LIF and the EIF. We conclude that although quantitative aspects of the phenomenology of stochastic synchrony depend on the details of the neuronal dynamics, the occurrence of this type of collective state is a generic feature of large neuronal networks of strongly coupled inhibitory neurons.

 Stability Analysis of the Asynchronous State
  The asynchronous state is stable if any small perturbation from it decays back to zero. To study the instabilities of the asynchronous state, one approach is to diagonalize the linear operator, which describes the dynamics of small perturbations from the asynchronous state (see appendix A). A specific eigenmode, with eigenvalue λ, is stable (resp. unstable) if Re(λ) < 0 (resp. Re(λ) > 0). The frequency at which the mode oscillates is ω/(2π) where ω = Im(λ). The asynchronous state is stable if the real part of the eigenvalue is negative for all the eigenmodes. Here we present an alternative approach that directly provides the equation that determines the critical manifolds in parameter space on which eigenmodes change stability (see also Brunel & Wang, 2003).

 The Spectrum of Instabilities
  Inspection of the qualitative properties of the synaptic and neuronal phase lag helps us to understand how the instabilities of the asynchronous state occur and how they depend on the noise level (see also Fuhrmann, Markram, & Tsodyks, 2002, Brunel & Wang, 2003, for similar considerations).(paper代写)

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