Schematic of how BXD works with a reaction coordinate, ρ, split into m boxes.
Schematic of the procedure for deriving arbitrarily high-resolution kinetic data from BXD simulations. The procedure relies on introducing a new box c between boxes a and b, and then expressing the new rate coefficients in terms of k ab and k ba .
log10(k inst ) as a function of log10(1<![CDATA[/]] >t) for four different peptides. The left-hand panels show the results of BXD calculations (dotted red line) compared with a 1<![CDATA[/]] >t α power law, with α = 1 (black line) and α = 0.93 (blue dashed line). The red squares indicate the timescales over which the BXD results are reliable, as described in the text. The right-hand panels show each peptide's free energy (or potential of mean force) as function of its extension. The position of the “absorbing boundary” where the loop formation is assumed to be irreversible (i.e., the border between the boxes 0 and 1) is indicated by the black arrow.
BXD results obtained from 10-ALA. Panel A shows the free energy as a function of extension coordinate. Panel B shows log10(k inst ) as a function of log10(1<![CDATA[/]] >t) using the strongly non-equilibrium initial conditions in Eq. (8) , and how increasing the number of boxes with Eqs. (7) extends the timescale over which power law kinetics are observed. Panel C shows the same results as B, but with a 225 × 225 kinetic matrix. It also shows the overlap between the BXD results and unbiased MD results as described in the text. Panel D shows log10(k inst ) as a function of log10(1<![CDATA[/]] >t) using equilibrium initial conditions. The final two panels show the eigenvalues of the kinetic matrix M weighted with their coefficients F(k) in Eq. (11) for (E) non-equilibrium and (F) equilibrium initial conditions.
Routes selected randomly on a landscape. At time t 2 the hikers who took the route t 3 are still walking but the hikers on the short route t 1 have already returned. Therefore at the moment t 2 the instantaneous rate constant of return is equal to 1<![CDATA[/]] >t 2. If the start and end-point of all routes are close then there is a large number of short routes, which is not the case when start and end point are distant from each other.
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