Entropy facilitated active transport

We show how active transport of ions can be interpreted as an entropy facilitated process. In this interpretation, the pore geometry through which substrates are transported can give rise to a driving force. This gives a direct link between the geometry and the changes in Gibbs energy required. Quantifying the size of this effect for several proteins we find that the entropic contribution from the pore geometry is significant and we discuss how the effect can be used to interpret variations in the affinity at the binding site. Active transport is of major importance in biology; meaning transport of a compound against its chemical potential, driven by a chemical reaction. A notable example is the large P-type ATPase protein family which functions as ion or lipid pumps, crucial for a wide range of processes in almost all forms of life [1]. The P-type ATPases share a common topology and their operation can be described using a Post-Albers cycle with four key conformations: E1, E1P, EP2 and E2 [2]. The transitions E1P↔E2P and E2↔E1 in the catalytic cycle are associated with large conformational changes [2] and it is clear ∗[email protected] 1 ar X iv :1 70 1. 02 94 3v 1 [ qbi o. B M ] 1 1 Ja n 20 17 that the energy released by ATP hydrolysis drives the enzyme between these states. One may ask about the meaning of the conformational changes. In particular, the formation of a wide funnel-shaped outlet channel can be observed in several P-type ATPases [3–6] when the enzyme changes from the E1P state to the E2P state. The occluded ion is then eventually exposed to the lumen; but why does the ion leave its binding site when the chemical potential is so much larger in the direction of transport than in the opposite direction? Can this be influenced by the observed pore geometries? How can the change in Gibbs energy by the chemical reaction, which may take place relatively far away from the binding site (see e.g. Ref. [7]), be transferred and used at the ion binding site? These questions, which have been of major interest since the discovery of the pumps, are still not fully answered and this is the topic we discuss here. We shall argue that active transport can be better understood by shifting focus from an energy to an entropy barrier in a specific part of the translocation process. When the outlet channel is formed in the E2P state, the shape of this channel directly facilitates the transport of ions by allowing for an entropy increase, or equivalently, a chemical potential decrease in the E2P state as we will demonstrate. The idea that the actual pore geometry may play a role in active transport, stems from previous studies which have shown how entropic barriers can play a major role for separation purposes [8–10]. To exemplify the impact of the pore geometry, we will take the Ca transporting Ca-ATPase of sarcoplasmic reticulum (SR) but we note that the ideas presented may apply more generally. For the Ca-ATPase, we illustrate the variation of the chemical potential as ions are transported from the cytosol to the lumen of the SR in Fig. 1. It is known that the binding of Ca is fast [11] and at equilibrium, the chemical potential of Ca in the E1 state, μCa2.E1, is equal to the chemical potential in the cytosol, μout. During operation of the pump, there is probably a small difference between μout and μCa2.E1 but the chemical potential in the final state, μin, is clearly larger than μout as depicted in Fig. 1. There is a large uncertainty related to the chemical potential of Ca when the enzyme is in the state E2P, μCa2.E2P. In Fig 1 it is assumed to be close to μin (which is the lower bound resulting in a positive Ca flux), enabling the ion to pass to the lumen. The variation in binding energy inherent in this picture has been attributed to the enthalpic part of the chemical potential, as the enthalpy gives a measure of the bond strength: Repulsive forces can raise the chemical potential μCa2.E2P, which