Uniporter substrate binding and transport: reformulating mechanistic questions

Transporters are involved in material transport, signaling, and energy input in all living cells. One of the fundamental questions about transporters is concerned with the precise role of their substrate in driving the transport process. This is particularly important for uniporters, which must utilize the chemical potential of substrate as the only energy source driving the transport. Thus, uniporters present an excellent model for the understanding of how the difference in substrate concentration across the membrane is used as a driving force. Local conformational changes induced by substrate binding are widely considered as the main mechanism to drive the functional cycle of a transporter; in addition, reducing the energy barrier of the transition state has also been proposed to drive the transporter. However, both points of view require modification to allow consolidation with fundamental thermodynamic principles. Here, we discuss the relationship between thermodynamics and kinetics of uniporters. Substrate binding-induced reduction of the transition-state energy barrier accelerates the transport process in kinetic terms, while the chemical potential of the substrate drives the process thermodynamically.

conformation (C in ); and in 2010, the structure of FucP from the same superfamily was reported in the outwardfacing conformation (C out ) (Abramson et al. 2003;Huang et al. 2003;Dang et al. 2010). More recently, crystal structures of GLUT uniporters from the MFS family have also been reported in both the C in and C out states (Deng et al. 2014;Deng et al. 2015;Nomura et al. 2015) (Fig. 1). These structural studies illustrate the impressive accuracy of the alternating-access model, which is specifically termed as a ''rocker-switch'' model for MFS transporters. From a theoretical point of view, the Jardetzky model is a typical example of the so-called two-state model in physics, which has found broad applications in biology (Phillips et al. 2009). While there are claims that a twostate model is too simple to describe the complex properties of uniporters, such as trans-acceleration and asymmetric transport (Carruthers et al. 2009;Naftalin and De Felice 2012), we believe that this model can provide mechanistic explanations to these seemingly complicated phenomena. There are more complicated cases in which the transport process of a uniporter may deviate from the two-state model, for example being allosterically regulated or containing loops in addition to the major reaction cycle. However, in most cases, the two-state model would be a good starting point to dissect the transport mechanism.

TWO-STATE MODEL FOR A TRANSPORT CYCLE
In the two-state model, each of the two conformations, C in and C out , of a given uniporter may have two sub-states, i.e., being either occupied or unoccupied by the substrate. Thus, a transport cycle of the uniporter can be presented with a two-state, four-step King-Altman plot (Fig. 2). In thermodynamic terms, such a cycle can be described by just three independent parameters, which can be chosen from f(0), f(?), [S] in /K d,in , [S] out /K d,out , DG E , or DG D . These parameters are introduced in the next three paragraphs, followed by examples of GLUT transporters.
The partition function f([S]) (: ([C out ] ? [C out S])/ ([C in ] ? [C in S])) describes the ratio of C out to C in as a function of substrate concentration, and f(0) and f(?) are the corresponding values at zero and saturated substrate concentration, respectively . The curve of f([S]) vs [S] can be measured experimentally, using techniques such as single-molecule Fö rster resonance energy transfer (smFRET) or double electron-electron resonance (DEER) (Smirnova et al. 2007;Akyuz et al. 2015;Heng et al. 2015).
Among the above-mentioned parameters, those favored by biochemists are perhaps the dissociation constants K d,in and K d,out in the C in and C out states, respectively (see Appendix 1). These parameters can be calculated from f([S]), provided that f(0) = f(?) . Most substrate-binding assays used in studying transporters, such as surface plasma resonance (SPR), isothermal titration calorimetry (ITC), or scintillation proximity assay (SPA), provide an apparent dissociation constant, K d,app , which is neither K d,in nor K d,out , but is a weighted average value of both . In addition, a possibility that the ''transition'' state can be stabilized by substrate in the in vitro assay may further complicate interpretations of the results from such a K d measurement.
Free-energy terms DG E and DG D are the most important parameters in the two-state physics model (Phillips et al. 2009). DG E 1 is the free-energy difference between C in and C out in the absence of the substrate. The corresponding conformational change is referred to as transition-0 (Figs. 2, 3). DG E (:-RTln(f(0))) is directly related to the concentration ratio of the two conformations at zero substrate concentration, and a negative value would indicate that C out represents a more stable state than C in . Furthermore, the differential binding energy, DG D , is defined as RTln(K d,in /K d,out ). On the one hand, DG D is an intrinsic property of the transporter in a sense that its value is independent of the substrate concentration. The concept of DG D has been implied in the Jardetzky's (2) free energy of releasing (R), DG R (:RTln([S] in /K d,in )); and (3) the differential binding energy DG D . For a given Dl S determined by the experimental condition, a favorable change in DG D (e.g., by a mutation in the transporter) is necessarily accompanied by unfavorable changes in DG L and/ or DG R , in terms of facilitating the transport process. In addition, the combined term DG D -DG E (i.e., -RTln(f(?))) is the free-energy change associated with the substrate-carrying conformational change, transition-1. Thus, in principle, all of the above thermodynamic parameters can be calculated solely from values of the partition function f([S]) measured at three or more substrate concentrations. These parameters are sufficient to describe the thermodynamic cycle of a two-state model, which may serve as the basis for more sophisticated mathematic models for transporters.
Based on previously reported data at 0°C, DG E and DG D of human GLUT1 are estimated to be ?2.8 RT and ?0.2 RT, respectively (Lowe and Walmsley 1986). The small value of DG D suggests that K d,in and K d,out are nearly identical and that differential binding energy contributes almost zero to the driving force for GLUT1. Thus, what actually drives the transport process in this case can only originate from the DG L and DG R terms, by favoring the forward movement and/or preventing the backward movement (Zhang and Han 2016). In addition, in both the absence and presence of substrate, GLUT1 stays predominantly in the C in state (with f(0) = 0.06 and f(?) = 0.07), which is in agreement with the above-mentioned positive value of DG E . A recently reported 1.5-Å crystal structure of GLUT3 (PDB ID: 4ZW9) (Deng et al. 2015) revealed that a substrate glucose molecule forms multiple hydrogen bonds with amino acid residues from the central cavity of the transporter, and the binding site is relatively narrow. The hydrogen bonds (i.e., the enthalpy term in DG L or DG R ) contribute favorably to both substrate affinity and selectivity. However, while the narrow binding site contributes positively to the substrate selectivity, it negatively affects the affinity because of a decrease in Outside Inside Transition-1 Transition-0 Inϐlux transport Efϐlux transport S S Fig. 2 Two-state four-step model. The top-left panel is a schematic presentation of the two-state model, and the remaining are its King-Altman diagrams in different types of transport. In each type of transport, dominant paths are shown in solid lines, and the rate-limiting step (for GLUT1) is underlined Schematics of the free-energy landscape of influx transport by GLUT1. A free-energy landscape plot describes the thermodynamic relationship between different states. The plot must satisfy the First and Second Laws of thermodynamics. Horizontal lines represent states. Tilted lines represent transitions between states.
Red arrows are associated with the chemical potential of the substrate. Subscripts ''L,'' ''R,'' ''D,'' and ''E'' stand for energy terms associated with loading, releasing, differential binding, and empty carrier, respectively. The starting and ending states are identical, only being differed by the release of heat (Q) during one transport cycle. Experimental raw data from Lowe and Walmsley (1986) are reflected in the relative scales of the free-energy terms, but derived values of energy barriers of transition-1 (T-1) and transition-0 (T-0) are significantly reduced in the current plot (see Appendix 5). Note that for each and every ten-fold change in either population (such as life time or concentration) or kinetic rate, the corresponding free-energy change is 2.3 RT (i.e., RTln (10)). In addition, since DG D & 0, for the substrate bindinginduced reductions of the energy barrier DDG OI à & DDG IO à (denoted as DDG à ). Assuming that a hydrogen bond contributes 2 RT (*5 kJ/mol) free energy, the 5 RT reduction in DG à is equivalent to 2-3 hydrogen bonds entropy (see Appendix 1). Then, how these thermodynamic parameters are related to the kinetic properties of a uniporter remains to be discussed.

KINETICS
Apart from considering thermodynamic parameters, understanding the precise mechanisms of substrate transport of a uniporter requires further kinetic information, i.e., the parameters k 1 0 , k -1 , and so on as shown in the King-Altman plot (Fig. 2). However, not all of these kinetic parameters act independently from each other; on the contrary, they are related via thermodynamic parameters (e.g., DG E = RTln(k -4 /k 4 )). One major obstacle in studying kinetics of transport is that the precise measurement of kinetic parameters presents a far more daunting technical challenge than measuring thermodynamic parameters.
A free-energy landscape plot (Fig. 3) is a useful tool to visually represent the transport process, for instance whether a step is thermodynamically favorable Zhang and Han 2016). While the vertical dimension of the plot represents Gibbs free energy, the horizontal dimension can be considered as an alternative expression of the King-Altman plot. Depending on the depth (or focus) of the analysis, multiple steps in a free-energy landscape may be merged as a single one. In addition, every step in the free-energy landscape plot may be further divided into more sub-steps (see Appendix 1 for an example). In particular, each (nondiffusion limiting) step in a free-energy landscape may contain a local transition state which is related to the kinetics of the given step (see Appendix 2). Such transition states are schematically shown in Fig. 3 for both transition-1 and transition-0. A general procedure to construct a free-energy landscape plot of the two-state model, in order to comprehend relationships between functions of a uniporter and both its thermodynamic and kinetic properties, is outlined in Appendix 3.
For an influx transport process, the transport cycle runs in the clockwise direction in Fig. 2; and for an efflux transport, the cycle runs in the counter-clockwise direction. In the discussion below, we will use the kinetic parameters to name the associated ''reaction'' steps whenever appropriate. For example, the k 2 step denotes the substrate-carrying, C out -to-C in transition-1, and the associated free-energy barrier is denoted as DG z 2 : Since all steps in the transport cycle are mutually exclusive, the minimum time required by the influx (efflux) cycle is denoted as s influx,min (s efflux,min ).
where s 1 , s 2 , and so on are the minimum time spent by the transporter at each step. Therefore, the maximum rate of influx transport (e.g., under so-called zero-trans conditions (Krupka and Deves 1981)), simply denoted as V influx , satisfies the following relationship: Similarly, the maximum rate of efflux transport, V efflux , satisfies the following relationship: For a uniporter of molecular weight C50 kDa, its major conformation changes are most likely to be slower than the diffusion-dominated substrate loading and releasing. In other words, the substrate loading (k 0 1 and k 0 À3 ) and releasing (k -1 and k 3 ) steps are usually much faster than those of the transition-0 (k 4 and k -4 ) and transition-1 (k 2 and k -2 ) steps, as long as the substrate concentration on the loading side is sufficiently high ()K d,L ) and that on the releasing side is low ((K d,R , implicating relatively large k -1 and/or k 3 ). Thus, the terms corresponding to steps k 0 1 , k À1 , k 3 , and k 0 À3 in the above equations can be omitted. In other words, depending on the experimental setup as well as properties of the transporter, the ratelimiting step(s) is very likely to be at either transition-0 or transition-1 (or sometimes both).
As an example, it has been shown that for a full cycle of glucose uptake by GLUT1, the energy barrier of the substrate-free transition-0 is higher than that of the substrate-carrying transition-1 (Lowe and Walmsley 1986). Thus, in a zero-trans influx (efflux) assay (i.e., under the condition of [S] L ) K M and [S] R & 0) the transport rate is dominated by the kinetic parameter, k 4 (k -4 ), at transition-0. Therefore, the following is true: Shown in the free-energy landscape plot (Fig. 3), the above results may be interpreted in such a way that transport in the direction of a lower energy barrier at the rate-limiting step is running faster than transport in the opposite direction. This phenomenon is called asymmetric transport. The logic presented here to interpret asymmetric transport, which was also employed in earlier work by others (Lowe and Walmsley 1986), is conceptually more straight forward than a model proposed recently (Zhang and Han 2016). For GLUT1, it was estimated that at 0°C V efflux is more than 10 times faster than V influx (Lowe and Walmsley 1986). In addition, the inward-facing conformation is thermodynamically favored in the absence of substrates (f(0) = 0.06), strongly indicating that C in represents the resting state. These observations are consistent with the function of rapid glucose efflux of GLUT1, e.g., in erythrocytes delivering glucose to places of high energy demand such as the brain, though the tendency to transport asymmetrically may become less pronounced at physiological temperatures (Lowe andWalmsley 1986, Carruthers et al. 2009). Under the condition that transition-0 is the rate-limiting step, the ratio of V influx to V efflux is determined by DG E (or f(0)), which in turn is influenced by interactions between the transporter and the membrane (e.g., by electric charges carried by the transporter and the electrostatic membrane potential). In general, if a uniporter is adapted to mainly transport substrates in one direction, such transporter is likely to have a value of DG E compatible with such a function.
Moreover, equilibrium exchange studies on GLUT1, where influx of radiolabeled glucose was coupled with efflux of non-labeled glucose, showed that the influx rate of the radiolabeled glucose (V ee ) is *100 times faster than V influx (i.e., in the absence of a coupled efflux) (Lowe and Walmsley 1986). Similar to Eq. 3, the following holds true for V ee : Equation 6 reflects the fact that, for equilibrium exchange, transition-0 is no longer the rate-limiting step (Fig. 2). In addition, it was estimated that k 2 / k -2 & 10 (i.e., f(?) = 0.07) (Lowe and Walmsley 1986). Thus, the rate-limiting step of the equilibrium exchange is the efflux of the non-labeled glucose, and V ee & k -2 . Since the rate constant of a reaction step is reciprocally related to the forward energy barrier of its local transition state by the Arrhenius equation (Appendix 2), the V ee /V influx (&k -2 /k 4 ) ratio of 100 suggests that the energy barrier of substrate-carrying transition-1 (in particular DG -2 à ) is *5 RT (i.e., RTln(100)) lower than that of substrate-free transition-0 (DG 4 à ). This point will be discussed further in the last section.
Trans-acceleration is a phenomenon that uptake of radiolabeled substrate is enhanced by the existence of (other types of) non-radiolabeled substrates at the opposite side of the membrane. While GLUT1 and GLUT3 display characteristics of trans-acceleration, GLUT4 and GLUT2 lack such trait (Nishimura et al. 1993). Similar to the above discussion, transacceleration in GLUT1 can be explained by the fact that k -2 ) k 4 , given the argument that, once the second substrate is added on the trans-side, the rate-limiting step switches from the k 4 step to the k -2 step in the King-Altman plot. In contrast, absence of transacceleration suggests that GLUT4 has an energy barrier for the substrate-carrying transition-1 (the k -2 step) comparable with transition-0 (the k 4 step), such that the V ee /V influx (&k -2 /k 4 ) ratio becomes close to 1 (assuming the remaining profile of thermodynamic parameters of GLUT4 are the same as that of GLUT1). Consistent with its trans-acceleration property, GLUT1 also shows asymmetry in zero-trans influx/efflux assays as mentioned above; in contrast, GLUT4 displays kinetic symmetry (Taylor and Holman 1981). In particular, for GLUT1, the rate-limiting steps for zerotrans influx and efflux are k 4 and k -4 , respectively, and thus V influx /V efflux (&k 4 /k -4 , Eq. 5) equals to *1/10, indicating asymmetry. In contrast, because of equal heights for both transition-0 and -1 in GLUT4, its ratio of V influx /V efflux (&k 4 /k -2 ) becomes close to 1, indicating symmetry. Interestingly, studies with chimeric constructs showed that transmembrane helix 6 (TM6) of GLUT4 is responsible for a lowering of the energy barrier at transition-0 compared with that of GLUT1 (Vollers and Carruthers 2012). It is noted that an MFS transporter contains two domains, N-and C-domain, which are related by a pseudo two-fold symmetry (Fig. 1). TM6 is located on the surface of the N-domain, directly contacting with the lipid bilayer. However, it is not involved in the inter-domain interface where substrates are bound and conformational changes occur. As a certain degree of intra-domain flexibility is required by the function of an MFS transporter (Quistgaard et al. 2016), in GLUT4 the interface between TM6 and other TM helices within the Ndomain may be more frictionless, rendering the transition-0 state more flexible and thus less strained during the conformational change.
Therefore, both its thermodynamic and kinetic properties are essential for proper functioning of a uniporter. It is important to understand how external free energy, including electrochemical potential of the substrate, drives the thermodynamic process of the transporter, and how the substrate binding affects the kinetic property of the transporter. The simple, twostate, four-step model described here should provide meaningful interpretations in both aspects, at least qualitatively.

REDUCTION OF THE ENERGY BARRIER OF THE TRANSITION STATE
On the cell surface, various potential substrates/ligands may exist in the surroundings of a uniporter, and they compete for the uniporter or cooperate with each other for utilizing the transporter. For instance, both glucose and lactate (a product of glycolysis) compete for transport by GLUT1 (Simpson et al. 2007). In general, these substances may be divided into three classes: those (1) whose binding increases the transition rate relative to transition-0; (2) whose binding has no effect on the transition rate; and (3) whose binding reduces the transition rate. Borrowing terminology from receptor-mediated signaling , in terms of promoting the conformational transition of the uniporter, these three types of ligands may be considered as agonists, antagonists, and (partial) inverse agonists. While glucose transported by GLUT1 belongs to the first type of ligands, glucose transported by GLUT4 seems to belong to the second (Nishimura et al. 1993). In addition, aspartic acid (and Na ? ) transported by Glt Ph seems to belong to the third type (Akyuz et al. 2015). Clearly, not all ligands of the third type are necessarily inhibitors. In addition, it is hypothetically feasible to imagine another type of inhibitors, namely one that overstabilizes a transition state in a manner that the transition state simply becomes a deep energy valley, mimicking a classical transition-state analog inhibitor that traps the enzyme at the transition state (sometimes by forming a covalent bond). The affinity of such an inhibitor must be so strong that it would over-compensate DG à . Nevertheless, such inhibitors for transporters remain to be discovered. Therefore, whether a given ligand is a good substrate for a transporter may not only depend on its affinity strength in the loading step, but also on how it affects the energy barrier of the transition state.
Proper functioning of a uniporter depends on the balance between efficient transport and prevention of potential leakage of non-specific ligands. Substrate binding-induced reduction of the energy barrier results in such a balance, thus making biological sense (Klingenberg 2007). This is especially true for those transporters that are more or less constitutively expressed at the cell surface (such as GLUT1). It may be of less importance, however, for transporters that are dynamically regulated by other mechanisms, for example for insulin-induced cell surface expression of GLUT4 (James et al. 1989). On the one hand, transition-0 is more likely to be the rate-limiting step, so that the transporter would not switch freely between the C out and C in states, thus limiting incidental leakage. On the other hand, in order for the transport cycle to proceed, the energy barrier of transition-0 (which is part of the transport cycle of the uniporter) must be reasonably low, in order to render the barrier accessible to thermal motion. An ''ideal'' substrate of a given uniporter could be defined as a ligand that decreases the energy barrier of transition-1 relative to transition-0, thus (1) increasing the rate of conformational transition as well as the transport cycle and (2) competing more effectively with other potential substances in utilizing the transporter.
Hypothetically, there may be numerous ways for a substrate to affect the energy barrier (DG à ). Lowering DG à of a uniporter does not consume extra energy input, including the chemical potential of the substrate. Instead, substrate binding per se plays a role in reducing DG à . The substrate binding-induced reduction of DG à was termed as intrinsic binding energy (Klingenberg 2006). We would like to emphasize that this ''driving'' energy is gained from substrate binding in the first half of the transition but is immediately released in the second half of the same transition. Since the transition rate is mainly determined by the forward kinetic rate, the overall effect of the DG à reduction at the ratelimiting step is acceleration of transport. It is well known that substrate binding may induce so-called occluded conformations, which have been captured in a number of reported crystal structures (Deng et al. 2015). Thus, the occluded conformations are likely to have higher affinity towards substrates than the C in and C out states (Quistgaard et al. 2016), at least under the in vitro conditions. In lipid bilayers where both mechanical membrane tension and electrostatic membrane potential may be present, such an occluded conformation may or may not be thermodynamically stable. However, as long as it is not over-stabilized relatively to the following substrate-releasing state, an occluded state would not prevent proceeding of the transport. The two-state model remains valid should the transient occluded state be merged with neighboring sub-steps of the transition. Furthermore, the transition-state functions as a mechanism for strong substrate selectivity. Analogously, stabilization of the transition state of an enzyme-substrate complex is a common mechanism in enzyme catalysis as well as selectivity. For transporters, such a mechanism has been specifically termed as induced transition fit (Klingenberg 2007). It should be stressed that reduction of DG à is not driven by the chemical potential of the substrate, because during the transition-1 the substrate has already bound to the transporter thus being irrelevant to the external concentration(s) of the substrate. Detailed structure studies of uniporters may provide information on the mechanism of substrate binding-mediated reduction of DG à , as exemplified in mechanistic discussion on GLUT1 crystal structure (Deng et al. 2014). Similar mechanisms may