CPHMD

Figure 10-3. Theoretical titration curves for the model compounds of Asp and His obtained from REX-CPHMD simulations [41]. Solid curves are the obtained by fitted the computed deprotonated fraction to the generalized Henderson-Hasselbach equation. The dashed lines indicate the computed pKa values...

An alternative formalism to the acidostat method, continuous constant pH molecular dynamics (CPHMD), has been developed by Brooks and coworkers [42, 58] drawing on the flavor of the early work by Mertz and Pettitt [67], In CPHMD, each titration residue carries a titration coordinate, A j, which is a function of an unbounded variable 0j,... 

The titration coordinates evolve along with the dynamics of the conformational degrees of freedom, r, in simulations with GB implicit solvent models [37, 57], An extended Hamiltonian formalism, in analogy to the A dynamics technique developed for free energy calculations [50], is used to propagate the titration coordinates. The deprotonated and protonated states are those, for which the A value is approximately 1 or 0 (end-point states), respectively. Thus, in contrast to the acidostat method, where A represents the extent of deprotonation, is estimated from the relative occupancy of the states with A 1 (see later discussions). The extended Hamiltonian in the CPHMD method is a sum of the following terms [42],... 

REX-CPHMD simulations have also been applied to understand the mechanism of the formation of protein intermediate states. Recent solution NMR data revealed a sparsely populated intermediate in the villin headpiece domain, in which the N-terminal subdomain is largely random but the C-terminal subdomain adopts a nativelike fold [34], Interestingly, H41 in this intermediate state titrates at a pH value of... 

Figure 10-5. Representative conformations of the (5 amyloid peptide (10-42) under different pH conditions. The conformations were obtained as centroids of the most populated clusters from the replica-exchange CPHMD folding simulations [43, 44]. The N-terminal residues 10-28 are shown in blue the C-terminal residues 29-42 are shown in red. In the most aggregation-prone state (pH 6), the side chains of the central hydrophobic cluster Leu-17, Val-18, Phe-19, Phe-20 and Ala-21 are shown as van der Waals spheres in pink, grey, cyan, purple and green, respectively...

Another interesting application area of PHMD simulations is to investigate electrostatic interactions in the unfolded states of proteins. A traditional view that unfolded proteins adopt random conformational states that are devoid of electrostatic and hydrophobic interactions, are recently challenged by experimental data [20, 69], REX-CPHMD folding simulations of the 35 residue C-terminal subdomain of the villin headpiece domain revealed a significant deviation from the standard pKa values for several titratable residues. Additional simulations, in which a charged group is neutralized confirmed the existence of specific electrostatic interactions in the unfolded states (JK and CLB, manuscript in preparation). 

The development and application of the CPHMD method demonstrate that simulations are capturing physical reality at increasing resolution. With the explosion in computing technologies, we are just at the beginning of a new era, where in silico experimentation becomes an indispensable complement to wet lab experiments in exploring unanswered questions related to a wide variety of biological and chemical processes. 

Continuous protonation state methods Applications of CPHMD... 

This report is mainly concerned with the recent development of a pH-coupled molecular dynamics technique, continuous constant pH molecular dynamics (CPHMD), [12,13] and its applications to first principles pK calculations [14] and pH-coupled biological phenomena [15]. To put this into context, we will also briefly survey other existing methods for pK predictions and pH-coupled conformational dynamics, but we refer interested readers to a recent preliminary review of this area for further details [9]. Finally, we will discuss opportunities for further development of the CPHMD method and our ongoing application studies. 

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