pyramidal neurons was studied by use of computer simulations to test whether inhibitory interneurons could assist in phaselocking postsynaptic cells. Two models were used: a simplified model, which included only 3 membrane channels, and a detailed 1 l-channel model. 2. The 1 l-channel model included most of the ion channels known to be present in neocortical pyramidal neurons as well as calcium diffusion and other membrane mechanisms. The kinetics for the channels were obtained from voltage-clamp studies in a variety of preparations. The parameters were then adjusted to produce repetitive bursting similar to that seen in some cortical pyramidal cells entrained during visual stimulation. 3. Phase-locking to a train of inhibitory postsynaptic potentials (IPSPs) located on or near the soma was observed in the 3-channel model cell subjected to random synaptic bombardment. In the

This is the second in a series of papers which attempt to recast classical single-neuron biophysics in information theoretical terms. Classical cable theory focuses on analyzing the voltage or current attenuation of a synaptic signal as it propagates from its dendritic input location to the spike initiation zone. On the other hand, we are interested in analyzing the amount of information lost about the signal in this process due to the presence of various noise sources distributed throughout the neuronal membrane. We use a stochastic version of the linear one-dimensional cable equation to derive closedform expressions for the second-order moments of the fluctuations of the membrane potential associated with different membrane current noise sources: thermal noise, noise due to the random opening and closing of sodium and potassium channels and noise due to the presence of "spontaneous" synaptic input. We consider two different scenarios. In the signal estimation paradigm, the time-cour...

Introduction Biological neural networks are large systems of complex elements interacting through a complex array of connections. Individual neurons express a large number of active conductances (Connors et al., 1982; Adams & Gavin, 1986; Llin'as, 1988; McCormick, 1990; Hille, 1992) and exhibit a wide variety of dynamic behaviors on time scales ranging from milliseconds to many minutes (Llin'as, 1988; Harris-Warrick & Marder, 1991; Churchland & Sejnowski, 1992; Turrigiano et al., 1994). Neurons in cortical circuits are typically coupled to thousands of other neurons (Stevens, 1989) and very little is known about the strengths of these synapses (although see Rosenmund et al., 1993; Hessler et al., 1993; Smetters & Nelson, 1993). The complex firing patterns of large neuronal populations are difficult to describe let alone understand. There is little point in accurately modeling each membrane potential in a large neural

this article). Stochastic forcing also broadens the peak of the average subthreshold voltage versus input current curves as in Figure 5b (not shown). In view of this, we have set out to determine (1) whether a subtractive effect is also present with stochastic synaptic input and (2) whether stochastic input produces a divisive regime at lower firing frequencies, as in the compartmental model. For simplicity we considered only the voltage-independent case (# 0) of equation 4.1, since divisiveness was also seen for the S synapses in the compartmental simulations (see Figure 5a). There are a variety of ways in which a stochastic synaptic model with reversal potentials can be approximated by diffusion models (Lansk y & Sato, 1999). Here we let the conductance g in the LIF model be a stochastic quantity by setting g = +#(g)#(t) where g is the mean conductance and #(t) is a stochastic process of standard deviation #( g). To match the smoothness of the conductance fluctuations in the compartmental model, we model #(t) as an Ornstein-Uhlenbeck process (lowpass-filtered gaussian white noise) with correlation time # 75 ms; our results were not qualitatively sensitive to this correlation time. Equation 4.1 thus becomes a stochastic differential equation with multiplicative noise (since the noise term multiplies the state variable Vm ): #t + #( g)#(t) I (4.7 # ) ## #t =- # +#(4.7 ## ) where # is gaussian white noise with zero-mean and unit standard deviation. Numerical simulations produced sigmoidal curves of mean firing rate versus input current I (see Figure 7), as expected. Increases in inhibitory firing rate in the compartmental model were modeled here as increases in mean conductance g; these increases are linearly related, as discussed above...

The availability of efficient and reliable simulation tools is one of the mission-critical technologies in the fast-moving field of computational neuroscience. Research indicates that higher brain functions emerge from large and complex cortical networks and their interactions. The large number of elements (neurons) combined with the high connectivity (synapses) of the biological network and the specific type of interactions impose severe constraints on the explorable system size that previously have been hard to overcome. Here we present a collection of new techniques combined to a coherent simulation tool removing the fundamental obstacle in the computational study of biological neural networks: the enormous number of synaptic contacts per neuron. Distributing an individual simulation over multiple computers enables the investigation of networks orders of magnitude larger than previously possible. The

Abstract not found

Running head: Efficient estimation of detailed single-neuron models

Neuronal function involves the interaction of electrical and chemical signals that are distributed in time and space. ...

ABSTRACT Neurons were acutely dissociated from the CA1 region of hippocampal slices from guinea pigs. Whole-cell recording techniques were used to record and control membrane potential. When the electrode contained KF, the average resting potential was about--40 mV and action potentials in cells at--80 mV (current-clamped) had an amplitude> 100 mV. Cells were voltage-clamped at 22-24 ~ with electrodes containing CsF. Inward currents generated with depolarizing voltage pulses reversed close to the sodium equilibrium potential and could be completely blocked with tetrodotoxin (1 /zM). The amplitude of these sodium currents was maximal at about--20 mV and the amplitude of the tail currents was linear with potential, which indicates that the channels were ohmic. The sodium conductance increased with depolarization in a range from--60 to 0 mV with an average half-maximum at about--40 mV. The decay of the currents was not exponential at potentials more positive than--20 mV. The time to peak and half-decay time of the currents varied with potential and temperature. Half of the channels were inactivated at a potential of--75 mV and inactivation was essentially complete at--40 to--30 mV. Recovery from inactivation was not exponential and the rate varied with potential. At lower temperatures, the amplitude of sodium currents decreased, their time course became longer, and half-maximal inactivation shifted to more negative potentials. In a small fraction of cells studied, sodium currents were much more rapid but the voltage dependence of activation and inactivation was very similar.

ion conductance is attributable to Cl-. At 37°C and pH 7.0, Go averages 2.11 mmho/cm 2 while residual conductance largely due to K + averages 0.34 mmho/cm ~. The resting Go exhibits a biphasic temperature dependence with a Q10 of 1.6 between 6°C and 25°C and a Q10 of nearly 1 between 25°C and 40°C. Decreasing external pH reversibly reduced Go; the apparent pK for groups mediating this decrease is 5.5. Increasing pH up to 10.0 had no effect on Go. Anion conductance sequence and permeability sequence were both determined to be CI-> Br--> I-> CHaSO4-. Lowering the pH below 5.5 reduced the magnitude of the measured conductance to all anions but did not alter the conductance sequence. The permeability sequence was likewise unchanged at low pH. Experiments with varying molar ratios of C1- and I- indicated a marked interaction between these ions in their transmembrane movement. Similar but less striking interaction was seen between CI- and Br-. Current-voltage relationships for Gcl measured at early time-points in the presence of Rb + were linear, but showed marked rectification with longer hyperpolarizing pulses (>50 ms) due to a slow time- and voltage-dependent change in membrane conductance to CI-. This nonlinear behavior appeared to depend on the concentration of CI- present but cannot be attributed to tubular ion accumulation, Tubular disruption with glycerol lowers apparent Go but not GK, suggesting that the transverse tubule (T-tubule) system is permeable to CI- in this species. Quantitative estimates indicate that up to 80 % of Gcl may be associated with the T tubules.