Thermal Impact on Spiking Properties in Hodgkin-Huxley Neuron with Synaptic Stimulus

The effect of environmental temperature on neuronal spiking behaviours is investigated by numerically simulating the temperature dependence of spiking threshold of the Hodgkin-Huxley neuron subject to synaptic stimulus. We find that the spiking threshold exhibits a global minimum in a “comfortable temperature” range where spike initiation needs weakest synaptic strength, indicating the occurrence of optimal use of synaptic transmission in neural system. We further explore the biophysical origin of this phenomenon in ion channel gating kinetics and also discuss its possible biological relevance in information processing in neural systems. PACS numbers: 87.17.Aa, 87.19.La, 87.10.+e Thermal Impact on Spiking Properties in Hodgkin-Huxley Neuron with Synaptic Stimulus2 Neuronal spiking is the basis of communication and coding in nervous systems and has been studied for decades [1, 2, 3]. Spiking behaviours of a neuron come from the activation and inactivation of various ion channels, which may vary due to the influences of environmental factors [4, 5]. Temperature is one of the most important regulators to neuronal activities [6, 7, 8, 9]. Electrophysiological experiments on neural spiking activities are mostly conducted either at room temperature in vitro or at body temperature in vivo, thus our knowledge about how a neuron behaves in a continuously changing temperature environment is usually fragmental. Variation in temperature leads to two main impacts in the spiking dynamics of excitable neurons: one is on the maximum ion channel conductances [10, 11] and the other is on ion channel gating kinetics [12, 13, 14], hence altering the shape and amplitude of action potentials [15] and the generation [16, 17] and propagation [18] of spikes. Neuronal spiking activities can be described by means of firing properties, such as firing rates [19], the precise timing of spikes [20, 21, 22], or the spiking threshold behaviors [23, 24, 25, 26]. The temperature dependence of spiking threshold of squid giant axons under current injection has been investigated experimentally [23, 24, 27] and numerically [28, 29]. More realistically, in fact, neurons communicate with each other via synaptic connections and respond to synaptic stimuli by firing spikes, so as to detect, transmit, and process neural information. It is an interesting question how the environmental temperature affects the spiking properties of a neuron stimulated by realistic synaptic input. This study is to approach the above topic by examining the temperature dependence of spiking threshold of a neuron subject to synaptic stimulus, based on widely-accepted Hodgkin-Huxley (HH) neuron model, as an example, which was originally proposed to account for the excitable properties of giant squid axons [12] and is now regarded to be an useful paradigm that accounts naturally for the spiking behaviors of real neurons. Our results reveal that there is an environmental temperature range where the spiking threshold shows a global minimum, implying that the optimal use of synaptic transmission occurs in neural systems. The biophysical origin of this interesting phenomenon together with its biological relevance is also investigated and discussed. The dynamics of the HH model with synaptic stimulus is described by the following coupled differential equations: dV/dt = (Isyn − Iion)/C, dm/dt = [m∞(V )−m]/τm(V, T ), dh/dt = [h∞(V )− h]/τh(V, T ), dn/dt = [n∞(V )− n]/τn(V, T ), (1) with V being the membrane potential, C the membrane capacity, n the activation variable of potassium channel, and m and h the activation and inactivation variables of sodium channel, respectively. m∞, h∞, n∞ and τm, τh, τn represent the saturated values and the time constants of the gating variables, respectively. The τ ’s in Eqs. (1) depend on the environmental temperature T , usually by being divided by a Q10 factor of a, Q10(T, a) = a (T−T0)/10 with the a value being usually chosen as a = 3 (suggested in Ref. [4]) and T0 = 6.3 ◦C denoting the experimental temperature for the original model Thermal Impact on Spiking Properties in Hodgkin-Huxley Neuron with Synaptic Stimulus3 construction [12] . The ionic current Iion includes the usual sodium, potassium, and leak currents: Iion = GNa(T )m h(V − VNa) +GK(T )n (V − VK) +GL(T )(V − VL), (2) where VNa, VK , VL are the reversal potentials for the channel currents. The maximum channel conductances GNa, GK , and GL are regulated by environmental temperature with a Q10 factor of a = 1 − 1.5 (see Ref. [4]). The synaptic input is modeled by Isyn = gsyn(t)(V − Vsyn) with Vsyn being the synaptic reversal potential and gsyn(t) being the time-dependent post-synaptic conductance, gsyn(t) = Gsynα(t − t0), where t0 represents the onset time of the synapse, Gsyn determines the peak of synaptic conductance and α(t) = (t/τsyn) exp(1 − t/τsyn), t > 0, with τsyn determining the characteristic time of the synaptic interaction. In this study we choose τsyn = 2ms, and Vsyn = 0mV to mimic excitatory synapse input in neural system [25, 30]. The other values of parameters can be found in Ref. [12]. The spiking threshold here is characterized as the critical value of Gsyn, by which the membrane potential of the stimulated neuron exceeds a voltage threshold Vth (chosen as Vth = −20mV here). Our investigation begins with the question how environmental temperature affects the spiking threshold of HH neuron stimulated by synaptic input. In figure 1, one may find that the spiking threshold undergoes a U-shaped dependence on the environmental temperature, i.e., there is a global minimum spiking threshold in a temperature range. We refer to this temperature range as “comfortable temperature” one for the neuron. In the comfortable temperature range the neuron needs weakest synaptic stimulus to fire spikes; from the engineering perspective this facilitates the extraction, transmission and processing of information in neural systems. Our result suggests that environmental temperature can make the neurons communicate easier with each other by maximizing the utility of synaptic transmitters. The optimal use of synaptic stimulus in nervous system is of great biological significance for real neurons. Theoretically, a U-shaped dependence of a physical quantity characteristic may result from the competition of (at least) two contrary factors/aspects. In a neural system, environmental temperature influences the maximum ion conductances and the channel gating rates, as demonstrated by experimental observations [4] and explicitly included in our model simulation. To find out what factors account for this Ushaped dependence phenomenon, we make a comparative examination. The effects of temperature regulation on spiking threshold through the maximum ion conductances and through the gating time constants of channel variables (see figure 2) are investigated respectively. If only the influence of temperature on the maximum ion conductances is considered, the spiking threshold increases monotonously with temperature. In direct contrast, the sole temperature effect via gating kinetics of ion channels gives rise to a temperature dependence of spiking threshold that almost resemble the control result in figure 1. Thus one can reach the conclusion that it is the dominant role of temperature on the gating kinetics of ion channels that yields the phenomenon of optimal use of synapse transmission in neural system, though changes in maximum channel conductances Thermal Impact on Spiking Properties in Hodgkin-Huxley Neuron with Synaptic Stimulus4 simultaneously contribute slightly to the elevation of spiking threshold with increasing environmental temperature. So far we have been aware of that the occurrence of optimal use of synaptic transmission attributes mainly to the thermal impacts on the gating kinetics of ion channels, the direct link lacks between these two: why does a monotonous dependence of gating time constants on temperature result in a non-monotonous temperature dependence of spiking threshold in neural systems? As well known, the activation of sodium ion channel depolarizes the membrane potential and forms the rise phase of an action potential; on the contrary, the activation of potassium ion channel along with the inactivation of sodium ion channel forms the decay phase of an action potential. Is it the competition of the gating behaviours between these two types of channels that yields the U-shaped temperature dependence of spiking threshold? The answer to this question is unfortunately negative (simulation results are not shown here). Thus we divide the three gating variables of ion channels into two categories: one is the sodium ion channel activation variable m, which is beneficial for a neuron to initiate spikes, and the other includes the sodium ion channel inactivation variable h and the potassium ion channel activation variable n, which serve to terminate action potentials. We speculate that it is the interaction between these two contrary (competitive) aspects that lead to the temperature dependence of the neuron’s spiking threshold. To confirm our interpretation, we design further comparative explorations. In figure 3 one can find contrasting dependencies of spiking threshold on environmental temperature between the thermal impact via activation kinetic of sodium ion channel alone and that via the inactivation of sodium ion channel together with the activation kinetic of potassium ion channel. These results are in good agreement with our speculation. In the above simulation results for the temperature dependence of spiking threshold are obtained by choosing the specific Q10 factors of a = 3 for time constants of channel gating variables and a = 1.25 for the maximum ion conductances. Although other Q10 factors might also be used for the neural system [4, 31], they are not expected to yield essential difference and the U-shaped temperature dependence still occurs. Examples for the HH neuron are shown in figure 4, where one can see that temperature dependencies of spiking threshold are very similar to the control case (see figure 1). The characteristic time τsyn of synaptic interaction may also vary with environmental temperature, but again it does not lead to any essentially different result against our conclusions. In fact, the elegance of optimal use of synaptic transmission in a range of environmental temperature in squid giant axons can be further generalized to other nervous systems, such as the cochlear nucleus neuron in auditory system [32]. Presumably, this subcellular mechanism of thermal impacts on the neuronal spiking via ion channel kinetic behaviours can serve as the base for the psychophysical evidence that various animals live optimally in a specific range of environmental temperature. In summary, we have investigated the effects of environmental temperature on the spiking behaviours of a neuron subject to synaptic stimulus. Our results reveal that the spiking threshold shows a global minimum in the so-called comfortable temperature Thermal Impact on Spiking Properties in Hodgkin-Huxley Neuron with Synaptic Stimulus5 range, implying the occurrence of optimal use of synaptic transmission in neural system. We further illustrate that the emergence of this phenomenon attributes mainly to the combined competition of the temperature-dependent gating kinetics of ion channel activation/inactivation variables. The optimal use of synaptic transmission in neural system can, from an engineer’s perspective, largely facilitate the extraction, processing and transmission of neural information in neurons.