Information processing and energy efficiency of temperature-sensitive Morris-Lecar neuron

Abstract

In biological organisms, the temperature is an important factor, which affects the motion of micro-particles and biochemical reaction. In current work, we investigate the effect of temperature on the capacity of information processing and the energy efficiency of the Hodgkin’s three basic classes of neurons. Increasing the temperature, both of the total entropy and information rate would maintain nearly as constant, and then decrease rapidly and fall to zero. Moreover, energy consumption is reduced as the temperature increases. However, the energy consumption of the class 1 neuron is remarkably greater than that of class 2 and 3 neurons with the same temperature. It is also interesting that the class 3 neuron consumes less energy than that of class 1 and 2 neurons, but generates the same value of total entropy and information rate for the same condition.

Introduction

During the process of information coding and encoding in the nervous system, neurons consumed enormous energy. Studies have shown that the mammalian brain consumes about 20% of the body’s metabolic energy, although it only accounts for about 2% of the total body weight (Attwell and Laughlin, 2001). Such huge energy consumption indicates that our brain must run energy efficiently, and the brain should process as much information as possible at the lowest energy cost (Laughlin et al., 1998). It is also believed that energy efficiency is one of the key principles for the evolution of the nervous system under selective pressure (Attwell and Laughlin, 2001, Niven and Laughlin, 2008). The energy supply, in the nervous system, mainly includes synaptic signal transmission, resting state maintenance, action potentials (APs) production, and other necessary metabolism (Sengupta et al., 2010). It is reported that the energy consumed by the APs accounts for half of the total energy supply in the nervous system (Attwell and Laughlin, 2001, Howarth et al., 2012). Many studies also have revealed that there are lots of factors associated with energy efficient, including ion channel dynamics (Alle et al., 2009, Schmidt-Hieber and Bischofberger, 2010), the number of channels on a single neuron, the level of neurotransmitters in synapses (Levy and Baxter, 2002, Harris et al., 2012), the number of neurons in a neuronal network (Schreiber et al., 2002, Yu and Liu, 2014) and the number of spikes representing (or coding) the same information (Yu et al., 2014, Olshausen and Field, 2004, Lörincz et al., 2012).

In addition, the temperature is a crucial factor to affect many kinds of life activities, such as the catalytic reactions of biological enzymes and the hydrolysis of ATP (Raison, 1973). In experiments, the temperature is more effective than chemical substances to block the conduction of signals in axons. Early experiments have observed that low temperatures could decrease the firing frequency and induce the failure of the neuronal signals conduction in myelinated and unmyelinated axons (Franz and Iggo, 1968). That cool temperatures block the propagation of high-frequency information (electrical signals) along axons is a useful method to prevent abnormally high electrical level signals in the nervous system (Ackermann et al., 2010). However, at high temperatures, such as fever-like temperatures, the amplitude of the APs in unmyelinated axons decreases, causing a loss of information (Pekala et al., 2016). Considering the relationship of synaptic noise and temperature, Erichsen obtained temperature–capacity and capacity–activity phase diagrams and reveal the importance of temperature on the mutual information in neural network (Bollé et al., 2004). Burek et al. have also found that increases in temperatures will shorten the period-doubling cascade and chaotic transition between tonic and bursting regimes for cold receptor neurons (Burek et al., 2019). The results of experimental and theoretical studies have been shown that temperature affects the ion channel gating kinetics (Collins and Rojas, 1982, Fohlmeister et al., 2010). Yu et al. have found that warmer body temperatures facilitate energy efficiency allowing the brain to utilize an energy efficient neural code (Yu et al., 2012). Therefore, temperature is an important factor that constrains the energy efficiency of the nervous system.

In 1952, Hodgkin identified three basic classes of neurons based on the neuronal electrophysiological characteristics: class 1 neurons generate APs with a continuous frequency–current (f–I) relationship; Class II neurons show a discontinuous f–I relationship; class 3 neurons fail to spike repetitively, and typically spike only one time at the onset of stimulation (Prescott et al., 2008, Gu et al., 2013). Such classification reveals the distinct dynamical mechanisms of action potential initiation and has been proven very useful in distinguishing neurons with different coding properties (St-Hilaire and Longtin, 2004, Tateno et al., 2004). Injected with a time-varying stimulus, the three classes of neurons display complicated phase-locking behaviors (Wang et al., 2011). These three classes of neurons are ubiquitous in the biological nervous system. Such neurons have been observed in biological experiments. For example, hippocampus CA1 pyramidal neurons participate in various brain rhythms in vivo, and these pyramidal neurons are class 1 neurons (Wang et al., 2013). While interneurons in the neocortical and entorhinal cortex are class 2 neurons (Tikidji-Hamburyan et al., 2015).