(a) Movement of a zinc ion (smaller circle) through randomly distributed CA molecules (larger circles) and binding to a CA molecule. The paths of CA molecules are not shown. (b) Various variables used in simulations that are obtained from the current particle positions.
Reaction data obtained from the mobile trap algorithm with a of 0.9. The numbers and diffusion coefficients of particles of types and are 6 and 12 and and , respectively. Reaction data were fitted with an analytical solution with of and uncertainty of 54%.
Survival time vs concentration of CA with a rectangular hyperbola curve fit [per Eq. (19)] for three different values, 0.05, 0.01, and 0.005. Simulation times shown are average values for 100 realizations of each case.
Average reaction rate (1/survival time) vs concentration of CA with a straight-line curve fit [per Eq. (19)] for three different values, 0.05, 0.01, and 0.005. Simulation times shown are average values for 100 realizations of each case.
A straight line passing through vs data allows interpolation for a particular value corresponding to a particular value.
A typical plot of the number of free CA molecules as a function of time, obtained from selective CA dissociation simulations, with 12 complex CA molecules, and and of 0.0055 and , respectively. The time duration between two successive CA selections for dissociation was ; the total simulated duration was . For this case, the value is , which is very close to the experimental value of .
Comparison between reaction data obtained from our implementation of Gillespie’s algorithm and the mobile trap simulations. The numbers of CA and zinc particles were 12 each, and the simulated duration was . Data represent average values for ten realizations for each case.
Number of complex CA-Zn molecules as a function of time when 20 zinc molecules react with a hypothetical variant of CA having a of 0.055 via the forward CA-Zn reaction. The number of CA molecules is 200. Reaction curves are shown for stationary (solid) and mobile (dotted) CA molecules. Cases shown are for fast zinc ions reacting with CA molecules (a) and slow zinc ions reacting with CA molecules (b).
Number of complex CA-Zn molecules as a function of time when 200 zinc ions react with 20 CA molecules in the reversible reaction. The reaction curves are for stationary CA (solid curve) as well as mobile CA (dotted curve) molecules. The value was 0.055 and the value was . Cases shown are for fast zinc ions reacting with CA molecules (a) and slow zinc ions reacting with CA molecules (b).
The point of time (deviation time) at which the reaction data from the mobile trap and the static trap methodology deviate from each other, plotted as a function of relative zinc mobility, the probability of association and dissociation; (a) normalized time of deviation as a function of relative zinc mobility, (b) reciprocal of deviation time as a function of the probability of association, and (c) deviation time as a function of the probability of dissociation.
Prior work in measurement of intracellular zinc concentration.
Experimentally determined and values for various variants of human carbonic anhydrase. Asterisks indicate unreported values.
values of CA-Zn reaction obtained using the straight lines as well the rectangular hyperbola method. Asterisks indicate unreported values.
values for various initial numbers of CA and zinc particles. These data were obtained from the mobile trap implementation and the selective CA dissociation simulations.
Average numbers of CA-Zn association events and complex CA dissociation events from ten mobile trap and Gillespie-type simulations. For the mobile trap simulations, and values were 0.0055 and , respectively. For Gillespie’s algorithm simulations, and values were and , respectively.
The on rate constant values for CA-Zn reactions involving (a) fast zinc ions reacting with mobile and stationary CA molecules and (b) slow zinc ions reacting with mobile and stationary CA molecules. The probability of association is 0.055 in each case.
On rate and off rate constants for CA-Zn reactions involving fast and slow zinc ions reacting with mobile and stationary CA molecules.
The values of constants obtained from curve fitting Eq. (22) in Figs. 8(b), 9(a), and 9(b) data. These values show that the reaction data from the static trap and the mobile trap methodologies are characterized by different exponents and the saturation points.
The values of parameters used to simulate Zn-CA association-dissociation reactions using the static trap and the mobile trap approaches. The values of the deviation times were obtained using simulations.
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