View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Biophysical Journal Volume 108 June 2015 2771–2774 2771 Biophysical Letter Dynamically Driven Protein Allostery Exhibits Disparate Responses for Fast and Slow Motions Jingjing Guo1,2 and Huan-Xiang Zhou1,* 1Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida; and 2School of Pharmacy, State Key Laboratory of Applied Organic Chemistry and Department of Chemistry, Lanzhou University, Lanzhou, China ABSTRACT There is considerable interest in the dynamic aspect of allosteric action, and in a growing list of proteins allostery has been characterized as being mediated predominantly by a change in dynamics, not a transition in conformation. For consid- ering conformational dynamics, a protein molecule can be simplified into a number of relatively rigid microdomains connected by joints, corresponding to, e.g., communities and edges from a community network analysis. Binding of an allosteric activator strengthens intermicrodomain coupling, thereby quenching fast (e.g., picosecond to nanosecond) local motions but initiating slow (e.g., microsecond to millisecond), cross-microdomain correlated motions that are potentially of functional importance. This scenario explains allosteric effects observed in many unrelated proteins. Received for publication 20 March 2015 and in final form 24 April 2015. *Correspondence: [email protected] Allostery, whereby ligand binding at a distal site affects Our simple model, inspired by community analysis on binding affinity or catalytic activity at the active site, is Pin1 (12), represents three main microdomains of Pin1 as traditionally considered as mediated through conforma- springs for describing local motions (Fig. 1). In apo Pin1, tional transition (1). In 1951, Wyman and Allen (2) intermicrodomain coupling is weak. We extremitize this described a scenario of cooperative oxygen binding to he- situation by assuming that the three springs are totally un- moglobin in terms of conformational entropy. Later it was coupled. The potential energy of the model is then proposed that an allosteric ligand may produce changes in X 3 2 U0ðx1; x2; x3Þ¼ ðki=2Þx ; (1) protein dynamics within a given conformational state i ¼ 1 i without a switch in conformational states (3). A growing list of proteins has been characterized as exemplars of where xi denote the internal coordinates for the local mo- such dynamically driven allostery (4–12). Our molecular- tions and ki denote the spring constants. Upon binding to dynamics (MD) simulations (12) along with the NMR the WW domain, a phosphopeptide with sequence FFpSPR data of Namanja et al. (7) suggest that a main consequence acts as a bridge between microdomains 1 and 3 via direct of substrate binding to the WW domain of Pin1 is rigidifica- physical contact. In addition, the coupling between the other tion of the loops around the catalytic site of the PPIase two pairs of microdomains is also strengthened. Represent- domain. Previous theoretical work of dynamically driven ing the intermicrodomain coupling by harmonic potentials, allostery has focused on free energy, not dynamics per se, we obtain the total potential energy and indeed this type of allostery has been referred to as X X 3 2 3 2 entropic allostery (3,13,14). Here we examine generic fea- Uðx1; x2; x3Þ¼ ðki=2Þx þ ðJi=2Þðxiþ1 À xiÞ ; i ¼ 1 i i ¼ 1 tures of dynamics in dynamically driven allostery. (2) For the purpose of considering conformational dynamics, we may simplify a protein molecule into a number of rela- J tively rigid microdomains connected by joints. For example, where i denote the strengths of intermicrodomain coupling, x h x allosteric network methods use data from MD simulations and 4 1 (for the circular coupling pattern). We are inter- J > k to partition proteins into communities and edges between ested in the strong coupling regime, where i i. them (8,10,12). Our premise is that the binding of an allo- We assume that the motions are diffusive in nature. In apo steric activator adds physical coupling between nearby Pin1, the local motions are uncoupled and each internal co- d microdomains and strengthens other intermicrodomain ordinate is assigned its own diffusion coefficient i. Each coupling. The stronger coupling, as illustrated on a simple model, leads to disparate responses for fast and slow Editor: Nathan Baker. motions, which are actually observed in Pin1 and many Ó 2015 by the Biophysical Society other proteins. http://dx.doi.org/10.1016/j.bpj.2015.04.035 2772 Biophysical Letters FIGURE 1 Dynamic model of protein allo- stery. The community analysis results for (A) apo and (B) FFpSPR-bound Pin1 from Guo et al. (12) are shown as motivation for the dynamic model. The communities are shown in different colors as cartoon structures (left) or as circles (middle). Inter- community connections are shown as lines, with width proportional to the cumulative betweenness of intercommunity edges (middle). The three largest communities are represented in the dynamic model, each by a spring (right). The springs are weakly coupled in the apo form but are strongly coupled in the FFpSPR-bound form. Motions of the internal coordinates are assumed to be diffusive. To see this figure in color, go online. coordinate then undergoes diffusion in a harmonic well. The first exponential has a relaxation time ts ¼ kBT/kD that This situation is similar to the diffusion-in-a-cone model is orders-of-magnitude longer than those (ti ¼ kBT/kidi) for for bond vector internal (e.g., picosecond to nanosecond) local motions in the apo protein. Compared to the first expo- motions in interpreting NMR relaxation data (15). For the nential, the second exponential has a much shorter relaxation diffusion in a harmonic well, the time correlation function time tf ¼ kBT/(k þ 3J)D as well as a much smaller amplitude 2 is a single exponential: hxi(t)xi(0)i¼hxi iexp(–t/ti), where (note that J > k). The normalized cross correlation, hxixji/ 2 2 2 1/2 hxi i¼kBT/ki, with kB denoting Boltzmann’s constant, (hxi ihxj i) ,isJ/(k þ J) and approaches 1, indicating highly T denoting the absolute temperature, and relaxation time synchronous motions of the internal coordinates. So the bind- ti ¼ kBT/kidi. ing of the allosteric ligand strengthens intermicrodomain When the microdomains become strongly coupled as oc- coupling, and consequently quenches fast, asynchronous mo- curs upon FFpSPR-WW binding, a major consequence on tions but initiates slow, synchronous motions. the dynamics is that the effective diffusion coefficient, D, These predicted dynamic consequences are precisely for the coupled motions is orders-of-magnitude smaller what had been found by Namanja et al. Their side-chain 2 than the diffusion coefficients, di, for the local motions. Intu- methyl D relaxation data indicated quenched picosecond- itively, one certainly expects D/di < 1, but there is also direct to-nanosecond dynamics upon FFpSPR binding (7). On experimental support. By measuring residue-residue contact the other hand, microsecond-to-millisecond exchange dy- formation rates in unstructured peptides, it was found that namics, as captured by the product of the longitudinal and relative diffusion of two residues in a peptide chain is an or- transverse relaxation rates of side-chain methyl 13C, was der-of-magnitude slower than the relative diffusion of free enhanced (18). In our MD simulations, the allosteric action amino acids (16). Even more dramatically, the intramolecu- of FFpSPR-WW binding is manifested by rigidification of lar diffusion coefficient in unfolded protein L was found to the catalytic-site loops (12). To further dissect the allosteric decrease 2–3 orders of magnitude as the concentration of mechanism, we investigated whether the effects of FFpSPR- the denaturant GdnHCl was reduced from 6 to 0 M (17). WW binding could be mimicked by artificially enhancing Removing the denaturant had the effect of increasing intra- intra- or intermicrodomain coupling in the form of confor- molecular coupling, but still the diffusion studied was in mational restraints in MD simulations. Artificial enhance- the unfolded (though compact) protein. Because di describe ment of coupling within microdomain 1 or 2 or between local motions of essentially free amino acids whereas D de- microdomains 2 and 3 was ineffective, but artificial scribes coupled motions within a folded protein, it would coupling of microdomains 1–3 together produced the not be surprising if the values of D/di are even smaller than same allosteric action as FFpSPR-WW binding. This obser- implicated by these experiments. vation provides support to our modeling of allosteric bind- The problem of diffusion in the potential of Eq. 2 can be ing as strengthening intermicrodomain coupling. solved analytically. When all the spring constants ki are iden- Our model predicts that allosteric action reduces with tical (¼ k) and all the coupling constants Ji are identical (¼ J), weakening of ligand-induced intermicrodomain coupling. the time correlation functions of all the coordinates are hxi(t) Namanja et al. (7,18,19) found that a second phosphopep- xi(0)i¼(kBT/3k)exp(–t/ts) þ (2kBT/3(k þ 3J)) exp(–t/tf). tide, from the mitotic phosphatase Cdc25C, produced less Biophysical Journal 108(12) 2771–2774 Biophysical Letters 2773 prominent effects on both picosecond-to-nanosecond and minimally affected. On the other hand, correlated micro- microsecond-to-millisecond dynamics than FFpSPR did. second-to-millisecond motions are initiated throughout the To see whether the reduced allosteric action is mediated whole dimer while picosecond-to-nanosecond motions of by weakened intermicrodomain coupling, here we carried some residues are dampened, consistent with our model pre- out an MD simulation of Pin1 with the Cdc25C peptide diction. Further support of the dynamic model is provided bound at the WW site.