Entropy and its significance in transport of ions through the cell membrane

Abstract

The aim of this paper is to present the concept of entropy in a simple way and to show its key importance in the transport processes of ions through the cell membrane using the latest discoveries in biophysics. Using a real-life example, we show how processes within a system lead to an increase in entropy. We also show how this entropy increase is directly related to the irreversibility of the process, and how it defines the arrow of time (direction of the flow of time). Using an abstract example, we clarify the meaning of the concept of disorder in a system, which is often used in defining entropy by connecting it with the number of microstates that realise a macroscopic state of a system. The importance of entropy in transport processes of ions through the cell membrane is considered. We show that passive transport processes through the cell membrane are the result of an entropy increase in the cell membrane-transported substance system. A model of active ion transport through the cell membrane following Rubi et al. (2017) is presented. The force that transports ions through the channel in the transport protein arises due to the entropy gradient formed along the transport channel, which is a consequence of the funnel shape of the channel. The entropic force is proportional to the ratio of the ion-available cross-sections of the exit and entrance surface of the channel. That means that only a very funnel-shaped channel can produce a sufficiently large force on the ions to overcome the concentration gradient of the substance. We analyse the final result for the force of entropy in the limits of a very wide and very narrow channel and find that the entropic force is proportional to the ratio of the areas of the exit to entrance surfaces of the channel, i.e., when the channel is very wide, while it becomes high as the width of the channel tends to the ion diameter, i.e., when the channel is very narrow. We explicitly explain how the presented model solves several fundamental questions about the active transport of substances: how is energy, a scalar quantity, converted into the directional motion of the ion (a vector quantity), how does energy drive ions considering that the point of release of energy is far from the point of binding of an ion in a transport protein and finally, how does energy, which is released in a very limited space, transport the ions over a very large spatial scale.