文章基本信息

标题：The energy conversion in active transport of ions
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作者：Signe Kjelstrup ; Anders Lervik
期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2021
卷号：118
期号：45
DOI：10.1073/pnas.2116586118
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Since their discovery in the middle of the last century ( 1), with the subsequent Nobel prize to Skou in 1997, the family of biological ion pumps ( 2– 4) has posed a challenge to the scientific community at large. The pumps utilize the Gibbs energy of hydrolysis of adenosine triphosphate (ATP) to move ions uphill across a membrane. How do they function? A much-studied case is Ca-ATPase (adenosine triphosphatase), which acts to control the level of the Ca 2 + content in muscle ( Fig. 1 has a schematic representation). When inactive, the pump forms a closed gate in the lipid membrane. The gate opens to the internal side when ATP is supplied to the external side of the membrane. The computational results of Kobayashi et al. ( 5) in PNAS provide support for several critical events. First is the release of calcium ions during opening, following right after a structural change in Ca-ATPase. Next is the rapid protonation of side chains that prevents rebinding of Ca 2 + , combined with interactions between lipid molecules and transmembrane helices that help stabilize the structure. Using rare event molecular dynamics simulations, Kobayashi et al. ( 5) captured the structural changes in great detail and obtained Gibbs energy profiles that demonstrate the importance of a rapid exchange between Ca 2 + ions and protons upon the release of Ca 2 + . Fig. 1 Schematic representation of two of the enzyme states studied by Kobayashi et al. (5): the adenosine diphosphate (ADP)–sensitive phosphoenzyme state, “E1P,” and the low-energy phosphoenzyme state, ”E2p_dp.” The structures were obtained from the supporting information in ref. 5. Here, E1P denotes the state of the enzyme where ADP and Ca 2 + ions (both shown in orange) are bound to it. The ions are bound deeper within the transmembrane helices but are here depicted in front for clarity. E2p_dp denotes the state of the enzyme where the Ca 2 + ions are released to the lumen side of the membrane. The E2P_dp state has the same protonation state as E1P. The enzyme undergoes large structural changes in the transition from the E1P state to the E2p_dp state, and a funnel-like path is opened, widening from the location of the ions inside the enzyme to the lumen side. The transport of ions by the enzyme has been observed and described in great detail in the past by other groups ( 6– 8). The stoichiometry of the pump and its relation to structural changes are known with astounding detail ( 9, 10). The transitions between different states are challenging to investigate by all-atom simulations since the timescale for these transitions (milliseconds or slower) is orders of magnitude larger than achievable by standard brute force atomistic simulations. This does not mean that the actual transition itself is a slow process. In a brute force simulation, most of the computational time is spent exploring the stable state, before the conditions are “just right” to trigger the transition. After initiated, the transition proceeds rapidly. In their work, Kobayashi et al. ( 5) circumvented this timescale problem by focusing directly on the fast, but rare, transition events. Consequently, the authors could use short-timescale simulations to obtain information about the transition event. Nevertheless, the theoretical problem still exists. How do we create a physical–chemical formulation of the molecular mechanism, which involves transforming the scalar chemical energy into a vectorial mass transport on the macroscale? Additionally, can such a description also include the well-documented heat production that follows from the operation of Ca-ATPase ( 11– 14)? The inclusion of such heating effects would allow us to quantify contributions to nonshivering thermogenesis. Answers to these questions are needed to fully understand the pump operation and to provide a physical–chemical description of this operation. While the pump efficiency ( 6, 15) can be computed from black box considerations, a local description is needed to capture molecular events and dissipation during energy conversion. Such a description must localize the energy that is dissipated as heat. A fully general physical–chemical description of the pump function must, therefore, include the temperature as a variable, in addition to a precise formulation of the ion transport and the pump slippage. Only then will we be able to link the local physical–chemical processes to supercellular events. The findings of Kobayashi et al. ( 5) in PNAS for Ca-ATPase are very well suited to bring the discussions of these points to the next level, as we shall comment on below. The Free Energy Landscape with Six Transition States Kobayashi et al. ( 5) presented Gibbs (or free) energy profiles along a path that takes the enzyme from one transition state to another (figure 4E in ref. 5). Knowledge of this energy landscape sets the stage for theoretical considerations. We can measure the degree of advancement along the path in the Gibbs energy landscape by a collective variable γ. In the work of Kobayashi et al. ( 5), the collective variable was based on the coordinates of the C α atoms and carbon atoms of selected side chains in the protein. In previous theoretical work ( 16), we have taken this coordinate to represent the advancement of the ATP hydrolysis. The Gibbs energy profile of the reacting complex (i.e., the reactants and products in a broad sense) can then be denoted μ ( γ ) , where μ is the Gibbs energy of the reacting mixture at any moment in time. The six transition states then correspond to six particular values of γ, and paths in the γ-space describe transitions. A point on a path between states represents an intermediate state (there is no need for a complete conversion into products). With a single collective variable, “shortcuts” between states (i.e., direct connections between two states that are separated by one or more intermediate states) cannot easily be described. Adding such shortcuts would allow theoretical modeling of cases with variable stoichiometry, such as thermogenesis ( 17). For instance, one could include as an additional collective variable γ d , representing the degree of advancement of the diffusing ion in the state space covered by coordinates ( γ , γ d ) . The Gibbs energy landscape will then be a three-dimensional surface in a two-dimensional (2D) collective variable space. In the future, the approach of Kobayashi et al. ( 5) could be used to explore a larger-energy landscape and then, perhaps give more information about additional functions of the enzyme. While the above are wishes for the future, the Gibbs energy profiles by Kobayashi et al. ( 5) can already be used to approximate activation barriers. It is, therefore, next at hand to ask for kinetic information on the processes. In this context, Hill’s cycle diagrams ( 18) [leading to the familiar Post–Albers scheme ( 19)