Ming S. Liu

Kinetics and chemomechanical properties of the F1-ATPase molecular motor

F1-ATPase hydrolyzes ATP into ADP and Pi and converts chemical energy into mechanical rotation with exceptionally high efficiency. This energy-transducing molecular motor increasingly attracts interest for its unique cellular functions and promising application in nanobiotechnology. To better understand the chemomechanics of rotation and loading dynamics of F1-ATPase, we propose a computational model based on enzyme kinetics and Langevin dynamics. We show that the torsional energy and stepwise rotation can be regulated by a series of near-equilibrium reactions when nucleotides bind or unbind, as well as characterized by an effective “ratchet” drag coefficient and a fitting chemomechanic coefficient. For the case of driving an actin filament, the theoretical load-rotation profile is analyzed and comparison with experimental data indicates reasonable agreement. The chemomechanics described in this work is of fundamental importance to all ATP-fueled motor proteins.

Coarse‐grained dynamics of the receiver domain of NtrC: Fluctuations, correlations and implications for allosteric cooperativity

Receiver domains are key molecular switches in bacterial signaling. Structural studies have shown that the receiver domain of the nitrogen regulatory protein C (NtrC) exists in a conformational equilibrium encompassing both inactive and active states, with phosphorylation of Asp54 allosterically shifting the equilibrium towards the active state. To analyze dynamical fluctuations and correlations in NtrC as it undergoes activation, we have applied a coarse‐grained dynamics algorithm using elastic network models. Normal mode analysis reveals possible dynamical pathways for the transition of NtrC from the inactive state to the active state. The diagonalized correlation between the inactive and the active (phosphorylated) state shows that most correlated motions occur around the active site of Asp54 and in the region Thr82 to Tyr101. This indicates a coupled correlation of dynamics in the “Thr82‐Tyr101” motion. With phosphorylation inducing significant flexibility changes around the active site and α3 and α4 helices, we find that this activation makes the active‐site region and the loops of α3/β4 and α4/β5 more stable. This means that phosphorylation entropically favors the receiver domain in its active state, and the induced conformational changes occur in an allosteric manner. Analyses of the local flexibility and long‐range correlated motion also suggest a dynamics criterion for determining the allosteric cooperativity of NtrC, and may be applicable to other proteins. Proteins 2008.

Dynamics of the SPRY domain–containing SOCS box protein 2: Flexibility of key functional loops

The SPRY domain was identified originally as a sequence repeat in the dual‐specificity kinase splA and ryanodine receptors and subsequently found in many other distinct proteins, including more than 70 encoded in the human genome. It is a subdomain of the B30.2/SPRY domain and is believed to function as a protein–protein interaction module. Three‐dimensional structures of several B30.2/SPRY domain–containing proteins have been reported recently: murine SSB‐2 in solution by NMR spectroscopy, a Drosophila SSB (GUSTAVUS), and human PRYSPRY protein by X‐ray crystallography. The three structures share a core of two antiparallel β‐sheets for the B30.2/SPRY domain but show differences located mainly at one end of the β‐sandwich. Analysis of SSB‐2 residues required for interactions with its intracellular ligands has provided insights into B30.2/SPRY binding specificity and identified loop residues critical for the function of this domain. We have investigated the backbone dynamics of SSB‐2 by means of Modelfree analysis of its backbone 15N relaxation parameters and carried out coarse‐grained dynamics simulation of B30.2/SPRY domain–containing proteins using normal mode analysis. Translational self‐diffusion coefficients of SSB‐2 measured using pulsed field gradient NMR were used to confirm the monomeric state of SSB‐2 in solution. These results, together with previously reported amide exchange data, highlight the underlying flexibility of the loop regions of B30.2/SPRY domain–containing proteins that have been shown to be important for protein–protein interactions. The underlying flexibility of certain regions of the B30.2/SPRY domain–containing proteins may also contribute to some apparent structural differences observed between GUSTAVUS or PRYSPRY and SSB‐2.

Allosteric Conformational Transition in Adenylate Kinase: Dynamic Correlations and Implication for Allostery

An essential aspect of protein science is to determine the deductive relationship between structure, dynamics, and various sets of functions. The role of dynamics is currently challenging our understanding of protein functions, both experimentally and theoretically. To verify the internal fluctuations and dynamics correlations in an enzyme protein undergoing conformational transitions, we have applied a coarse-grained dynamics algorithm using the elastic network model for adenylate kinase. Normal mode analysis reveals possible dynamical and allosteric pathways for the transition between the open and the closed states of adenylate kinase. As the ligands binding induces significant flexibility changes of the nucleotides monophosphate (NMP) domain and adenosine triphosphate (ATP) domain, the diagonalized correlation between different structural transition states shows that most correlated motions occur between the NMP domain and the helices surrounding the ATP domain. The simultaneous existence of positive and negative correlations indicates that the conformational changes of adenylate kinase take place in an allosteric manner. Analyses of the cumulated normal mode overlap coefficients and long-range correlated motion provide new insights of operating mechanisms and dynamics of adenylate kinase. They also suggest a quantitative dynamics criterion for determining the allosteric cooperativity, which may be applicable to other proteins.

Mg2+ coordinating dynamics in Mg:ATP fueled motor proteins

The coordination of Mg(2+) with the triphosphate group of adenosine triphosphate (ATP) in motor proteins is investigated using data mining and molecular dynamics. The possible coordination structures available from crystal data for actin, myosin, RNA polymerase, DNA polymerase, DNA helicase, and F1-ATPase are verified and investigated further by molecular dynamics. Coordination states are evaluated using structural analysis and quantified by radial distribution functions, coordination numbers, and pair interaction energy calculations. The results reveal a diverse range of both transitory and stable coordination arrangements between Mg(2+) and ATP. The two most stable coordinating states occur when Mg(2+) coordinates two or three oxygens from the triphosphate group of ATP. Evidence for five-site coordination is also reported involving water in addition to the triphosphate group. The stable states correspond to a pair interaction energy of either ∼-2750 kJ/mol or -3500 kJ/mol. The role of water molecules in the hydration shell surrounding Mg(2+) is also reported.

Conformational dynamics of ATP/Mg:ATP in motor proteins via data mining and molecular simulation.

The conformational diversity of ATP/Mg:ATP in motor proteins was investigated using molecular dynamics and data mining. Adenosine triphosphate (ATP) conformations were found to be constrained mostly by inter cavity motifs in the motor proteins. It is demonstrated that ATP favors extended conformations in the tight pockets of motor proteins such as F(1)-ATPase and actin whereas compact structures are favored in motor proteins such as RNA polymerase and DNA helicase. The incorporation of Mg(2+) leads to increased flexibility of ATP molecules. The differences in the conformational dynamics of ATP/Mg:ATP in various motor proteins was quantified by the radius of gyration. The relationship between the simulation results and those obtained by data mining of motor proteins available in the protein data bank is analyzed. The data mining analysis of motor proteins supports the conformational diversity of the phosphate group of ATP obtained computationally.

A mechanochemical theory for the ATP-fuelled biomolecular motors

Biomolecular motors are normally single or complex biomolecules exerting mechanical forces over molecular and cellular scales. The ATP-fuelled biomolecular motors can transduce the chemical energy from ATP hydrolysis into forces and motions in cells. In biomolecular motors, transport reactions are both stoichiometric and enzymatic. We outline a mechanochemical theoretical framework for biomolecular motors to understand their enzymatic kinetics and continuous dynamics. The theory is validated by describing the operating mechanism and dynamics of several ATP-fuelled molecular motors driving various loads.

Mechanochemical theory for the ATP-fuelled biomolecular motors

Biomolecular motors are normally single or complex biomolecules exerting mechanical forces across molecular and cellular scales. The ATP-fuelled biomolecular motors can transduce the chemical energy from ATP hydrolysis into forces and motions in cells. In biomolecular motors, transport reactions are both stoichiometric and enzymatic. We set up a mechanochemical theory for biomolecular motors to understand its enzymatic kinetics and continuous dynamics. This theory is validated by modeling the operating mechanism and dynamics of several ATP-fuelled molecular motors driving various loads