Kinetic and thermodynamic modeling of a voltage-gated sodium channel

Macromolecular rate theory explains the temperature dependence of membrane conductance kinetics

The factor Q10 is used in neuroscience to adjust reaction rates of voltage-activated membrane conductances to different temperatures and is widely assumed to be constant. By performing an analysis of published data of the reaction rates of sodium, potassium, and calcium membrane conductances, we demonstrate that 1) Q10 is temperature dependent, 2) this relationship is similar across conductances, and 3) there is a strong effect at low temperatures (<15°C). We show that macromolecular rate theory (MMRT) explains this temperature dependency. MMRT predicts the existence of optimal temperatures at which reaction rates decrease as temperature increases, a phenomenon that we also found in the published data sets. We tested the consequences of using MMRT-adjusted reaction rates in the Hodgkin-Huxley model of the squid's giant axon. The MMRT-adjusted model reproduces the temperature dependence of the rising and falling times of the action potential. Furthermore, the model also reproduces these properties for different squid species that live in different climates. In a second example, we compare spiking patterns of biophysical models based on human pyramidal neurons from the Allen Cell Types database at room and physiological temperatures. The original models, calibrated at 34°C, failed to generate realistic spikes at room temperature in more than half of the tested models, while the MMRT produces realistic spiking in all conditions. In another example, we show that using the MMRT correction in hippocampal pyramidal cell models results in 100% differences in voltage responses. Finally, we show that the shape of the Q10 function results in systematic errors in predicting reaction rates. We propose that the optimal temperature could be a thermodynamical barrier to avoid over excitation in neurons. While this study is centered on membrane conductances, our results have important consequences for all biochemical reactions involved in cell signaling.