Free energy of conformational transition paths in biomolecules: The string method and its application to myosin VI

Ovchinnikov, Victor; Karplus, Martin; Vanden‐Eijnden, Eric

doi:10.1063/1.3544209

Cited by 125 publications

(213 citation statements)

References 77 publications

(136 reference statements)

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“…Once the optimized string has been obtained, thermodynamic and kinetic information can be extracted from milestoning simulations. Recent successes (31,32) in applying the string method to study transition events prompted us to incorporate this concept in our TPT analysis of the MSM for Src kinase activation. Here we adopt the following prescription to generate path strings connecting the reactant and the product based on a steepest descent/ascent type of strategy to the net flux.…”

Section: Resultsmentioning

confidence: 99%

Transition path theory analysis of c-Src kinase activation

Meng

Shukla

Pande

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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Nonreceptor tyrosine kinases of the Src family are large multidomain allosteric proteins that are crucial to cellular signaling pathways. In a previous study, we generated a Markov state model (MSM) to simulate the activation of c-Src catalytic domain, used as a prototypical tyrosine kinase. The long-time kinetics of transition predicted by the MSM was in agreement with experimental observations. In the present study, we apply the framework of transition path theory (TPT) to the previously constructed MSM to characterize the main features of the activation pathway. The analysis indicates that the activating transition, in which the activation loop first opens up followed by an inward rotation of the αC-helix, takes place via a dense set of intermediate microstates distributed within a fairly broad "transition tube" in a multidimensional conformational subspace connecting the two end-point conformations. Multiple microstates with negligible equilibrium probabilities carry a large transition flux associated with the activating transition, which explains why extensive conformational sampling is necessary to accurately determine the kinetics of activation. Our results suggest that the combination of MSM with TPT provides an effective framework to represent conformational transitions in complex biomolecular systems.transition path theory | conformational transition | Markov state models P roteins, rather than being static molecular structures, often exhibit large-scale collective motions that are biologically essential for their function (1, 2). Dynamics and flexibility form the foundation of both the conformational selection and induced-fit mechanisms of protein-protein or protein-ligand binding (3). An energy landscape theory was proposed in the early 1990s to conceptualize protein dynamics (4) and was extensively used to characterize the protein folding problem (5) and allostery (6). According to the energy landscape theory, the complex topography of the landscape that underlies the dynamics can give rise to multiple and significantly populated conformational states (metastable states). The study of protein dynamics is not only interested in obtaining the thermodynamic properties of those metastable states but also pays significant attention to the transition pathways linking them and the kinetic information. A noteworthy example of biological significance is presented by the nonreceptor tyrosine kinases of the Src family. A well-characterized prototypical tyrosine kinase is c-Src, which plays vital roles in cellular signaling pathways (7); overactivation is key to tumorgenesis and metastasis and obesity (8). Although the configurations of the regulatory domains are important in controlling kinase activity, the conformational changes occurring within the catalytic domain itself (Fig.1A and SI Methods for more details) is of special interest. Intramolecular motions, both at short and large length scales, control the activation of c-Src. Therefore, a better understanding of the internal motions displayed within the ...

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Section: Resultsmentioning

confidence: 99%

Transition path theory analysis of c-Src kinase activation

Meng

Shukla

Pande

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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“…A recent application of the string method to a conformational transition in myosin V indicates that the minimum energy path and the minimum free energy path are very similar, though the main barrier is lowered significantly by the entropic contributions along the latter (47).…”

Section: Methodsmentioning

confidence: 99%

Unsuspected pathway of the allosteric transition in hemoglobin

Fischer

Olsen

Nam

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

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Large conformational transitions play an essential role in the function of many proteins, but experiments do not provide the atomic details of the path followed in going from one end structure to the other. For the hemoglobin tetramer, the transition path between the unliganded (T) and tetraoxygenated (R) structures is not known, which limits our understanding of the cooperative mechanism in this classic allosteric system, where both tertiary and quaternary changes are involved. The conjugate peak refinement algorithm is used to compute an unbiased minimum energy path at atomic detail between the two end states. Although the results confirm some of the proposals of Perutz [Perutz MF (1970) Stereochemistry of cooperative effects in haemoglobin. Nature 228:726-734], the subunit motions do not follow the textbook description of a simple rotation of one αβ-dimer relative to the other. Instead, the path consists of two sequential quaternary rotations, each involving different subdomains and axes. The quaternary transitions are preceded and followed by phases of tertiary structural changes. The results explain the recent photodissociation measurements, which suggest that the quaternary transition has a fast (2 μs) as well as a slow (20 μs) component and provide a testable model for single molecule FRET experiments.conformational change | cooperativity | domain motion | protein hinges M any proteins undergo large conformational transitions that are essential for their functions (1-3). The transitions can occur in monomers such as the myosin molecular motor (4-6), in multisubunit complexes such as the chaperone GroEL (7), and in systems such as the flagellar motor of bacteria, which is composed of several hundred proteins (8). Probably the most studied example is the T (tense) to R (relaxed) transition in the vertebrate hemoglobin tetramer (Hb) (9-11), for which the conformational transition increases the efficiency of oxygen transport. Hemoglobin, which is composed of two identical α-and two identical β-subunits, is the paradigm for the development of models of cooperativity and allosteric regulation in proteins (9-13). Phenomenologically, the positive cooperativity involves the increase in the affinity for oxygen of unliganded subunits upon the successive binding of oxygen to other subunits. This is achieved by structural changes within subunits (tertiary changes) and between subunits (quaternary changes). Based on the superposition of the crystallographic structures for the deoxy unliganded T state and the fully liganded R state of the protein, the quaternary T → R transition has been described as involving primarily an approximately 15°rotation of one "dimer" (α 1 β 1 ) relative to the other (α 2 β 2 ) around a virtual axis (Fig. 1A) (9, 14). Together with a small relative translation of the αβ-dimers, this reduces the central cavity between the dimers (a channel along the C2 axis of symmetry), where the heterotropic effector 2,3-bisphosphoglycerate is bound in the T state. An important aspect of these structural ch...

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“…14 Recently, simulations in non-overlapping Voronoi cells 15,16 have become a more common implementation of the method. When the principal curve 15 in this method is sufficiently straight, the confinement in a Voronoi cell is similar to applying a flat 1D potential that rises to infinity at the two boundaries.…”

Section: Discussionmentioning

confidence: 99%

“…As mentioned earlier, the finite temperature string method could be implemented in simulations in which the coarse coordinates X  are constrained at hyperplanes 14 or confined in Voronoi cells with reflective boundaries 15,16 . Alternatively, similar to some previous studies, 18 we recently adopted an implementation 19 based on the umbrella sampling with Hamiltonian replica exchange 20 to calculate ) (α G .…”

Section: Umbrella Sampling Along a Curvementioning

confidence: 99%

“…If some of the unrepresented degrees of freedom involve infrequent transitions between multiple states, they may suffer poor sampling within the simulation time, thus resulting in hysteresis. 29,30 Therefore, it would be preferable to select a relatively large number of coarse coordinates, as in 8 many applications of the string methods [12][13][14][15][16] , to reduce the risk of ignoring slow and relevant degrees of freedom.…”

Section: Coarse Coordinates and Configuration Spacementioning

confidence: 99%

See 1 more Smart Citation

Finite Temperature String Method with Umbrella Sampling: Application on a Side Chain Flipping in Mhp1 Transporter

Song

Zhu

2016

J. Phys. Chem. B

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Protein conformational change is of central importance in molecular biology. Here we demonstrate a computational approach to characterize the transition between two metastable conformations in all-atom simulations. Our approach is based on the finite temperature string method, and the implementation is essentially a generalization of umbrella sampling simulations with Hamiltonian replica exchange. We represent the transition pathway by a curve in the conformational space, with the curve parameter taken as the reaction coordinate. Our approach can efficiently refine a transition pathway and compute a one-dimensional free energy as a function of the reaction coordinate. A diffusion model can then be used to calculate the forward and backward transition rates, the major kinetic quantities for the transition. We applied the

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Free energy of conformational transition paths in biomolecules: The string method and its application to myosin VI

Cited by 125 publications

References 77 publications

Transition path theory analysis of c-Src kinase activation

Transition path theory analysis of c-Src kinase activation

Unsuspected pathway of the allosteric transition in hemoglobin

Finite Temperature String Method with Umbrella Sampling: Application on a Side Chain Flipping in Mhp1 Transporter

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