Atomic charges in the ionizable residues in the protonated/deprotonated states.

<p>Dummy hydrogen atoms with zero charge are added in the deprotonated states.</p

The titration curves of the 9 ionizable groups of EPG as functions of pH values obtained from the VMMS–1 simulations.

<p>The titration curves of the 9 ionizable groups of EPG as functions of pH values obtained from the VMMS–1 simulations.</p

State molar fractions of the heptapeptide, Ace-SDNKTYG-NME, during constant pH VMMS simulations.

<p>pH values are labeled in each panel. All states have an initial molar fraction of 0.125.</p

The molar fractions of deprotonated states during the VMMS–1 simulations of the heptapeptide.

<p>The molar fractions of deprotonated states during the VMMS–1 simulations of the heptapeptide.</p

State equilibrium is represented as a virtual mixture of multiple states (VMMS).

<p>In a solution shown in the center, all states equilibrate with each other and exist by state molar fractions, <i>x</i>₁, <i>x</i>₂,⋯, <i>x</i>_<i>n</i>. In VMMS, every state is explicitly represented by an all-atom subsystem. Each state has its own solvent environment and solvent can be either implicit or explicit. All subsystems form a virtual ideal solution to equilibrate with each other.</p

Energy distributions of the ASP model compound with the GB implicit solvation model in different states.

<p>The solid lines are the protonated state (state 0, black) and deprotonated state (state 1, red). The red dotted lines with filled symbols are in the V₀ (square) state and V₁ (circle) state. The green dotted lines with open symbols are the reweighted results in the V₀ (square) and V₁ (circle) states.</p

Energy distributions of the model HOH solution in the canonical ensemble and in the VMMS ensemble.

<p>The black lines are the LD simulation results for state 0 (solid) and state 1 (dashed). The red lines with squares are the VMMS simulation results for state V₀ (filled) and state V₁ (open). The green lines with circles are the reweighted VMMS simulation results for state V₀ (filled) and state V₁(open).</p

pKa of the ionizable residues in the heptapeptide from the VMMS simulations and other studies.

<p>pKa of the ionizable residues in the heptapeptide from the VMMS simulations and other studies.</p

The pKa of K66 and conformational properties of SNase Δ+PHS/V66K during the VMMS simulation.

<p>The pKa of K66 and conformational properties of SNase Δ+PHS/V66K during the VMMS simulation.</p

The molar fractions of deprotonated states for the 9 ionizable groups of EPG during the VMMS–1 simulations.

<p>The molar fractions of deprotonated states for the 9 ionizable groups of EPG during the VMMS–1 simulations.</p