Can allosteric regulation be predicted from structure?

D the last decade, the classical view of a protein existing in equilibrium between discrete conformational states has undergone a radical transformation. Experimental observations, particularly those obtained from NMRdetected hydrogenydeuterium exchange, indicate that even under native conditions proteins need to be considered as complex statistical ensembles (see for example refs. 1–13). In the view pioneered by Englander and coworkers (1, 2, 4, 7, 8, 14) proteins undergo local unfolding reactions scattered throughout their entire structures. These unfolding reactions occur independently of each other, may involve only a few amino acids, and give rise to a large number of states in which each state is defined by the presence of one or several locally unfolded regions. This collection of states defines the native-state ensemble. The immediate, and perhaps most relevant, consequence of these observations is that the Gibbs energy of stabilization of a protein is not uniformly distributed throughout its three-dimensional structure. There are regions with high stability constants and regions with low stability constants (13, 15). Furthermore, under native conditions cooperativity appears to be local or regional rather than global. The implications of these findings have been mostly discussed in relation to the protein folding problem; however, their biological implications are tremendous because the native state is the functionally relevant state. If cooperativity is local or regional rather than global, how do distal sites communicate with each other? How do regulatory allosteric interactions take place? How are the functional properties of a protein related to the distribution of states within the native ensemble, and how does ligand binding affect this distribution and modulate function? Is the location of stable and unstable regions a random event or it is dictated by functional considerations? How are protein function and stability related? The tools to begin addressing those issues in a systematic way became available with the observation that a structurebased algorithm (COREX) was able to model reasonably well the hydrogen exchange protection data obtained for many proteins (13, 15–19). Within the framework of the COREX algorithm the protein is considered as a statistical ensemble in which each state is characterized by having some region or regions in a nonfolded state. These regions can be as small as four or five amino acids or as large as the entire protein. Depending on the size of the protein the computation is performed either exhaustively or by using a sampling technique (19). The Gibbs energy of all of the resulting states and their respective probabilities are calculated in terms of an empirical structural parameterization of the Gibbs energy (summarized in ref. 20). What the COREX algorithm produces is a list of possible conformations and their respective probabilities, i.e., a probability distribution function. As such it can be used to examine the effects of ligands and other chemical or physical factors on that distribution. Previously (21) it was shown that the incorporation of the ligand linkage equations into the COREX algorithm (CORE_BIND) correctly predicted the propagation of binding effects through the structure of hen egg white lysozyme upon binding of a specific antibody. The paper by Pan et al. (22) in this issue of PNAS explores the linkage between binding sites in Escherichia coli dihydrofolate reductase and makes a convincing case that the coupling between these sites is also mediated by shifts in the probability distribution of the conformational ensemble. The COREX algorithm produces a snapshot of the distribution of states existing under equilibrium conditions. For an ergodic system this distribution is identical to the one that would be obtained if a single protein molecule were observed over a period sufficiently long for thermodynamic averaging. Accordingly, ensemble properties can be mapped into individual molecules. This is illustrated in Fig. 1 for the structural stability of individual residues in a Src homology 3 molecule (18). In the ensemble view, the stability of an individual residue is proportional to the summed probabilities of all of the states in which that residue is in the native state. For an individual molecule, the structural stability of a residue is proportional to the fractional amount of time that the residue spends in the native-state conformation. A highly stable residue will spend most of the time in the native state, whereas a relatively unstable residue will make excursions into different regions of conformational space. These excursions may arise from different processes involving local as well as longer-range fluctuations. For an ergodic system, ensemble and time averages are equivalent. As pointed out by Pan et al. (22) classical linkage theories do not address the mechanism by which different binding sites communicate. The ensemble view created by the COREX algorithm provides an opportunity to examine the longrange effects of ligand binding and allosteric regulation. We can imagine that different conformational states might have different functional properties and that, consequently, a redistribution in the population of states may result in functional changes. A change in the distribution of states is triggered by changes in the Gibbs energy of the states that define the ensemble. States with lower Gibbs energies will be preferentially populated with respect to states with higher Gibbs energies. Therefore, the expression of a specific functional property can be triggered by a decrease in the Gibbs energy of those states that exhibit that property. In biological systems, this is usually accomplished by ligand molecules (activators or inhibitors) that selectively bind to those states that possess the selected property. In the presence of a ligand X, the Gibbs energy of any arbitrary state within the ensemble will be affected by an amount that depends on its binding affinity for the ligand: