^{1,2}, C. Gosse

^{3}, L. Jullien

^{4}and A. Lemarchand

^{1,2,a)}

### Abstract

Increased focus on kinetic signatures in biology, coupled with the lack of simple tools for chemical dynamics characterization, lead us to develop an efficient method for mechanism identification. A small thermal modulation is used to reveal chemical dynamics, which makes the technique compatible with in cellulo imaging. Then, the detection of concentration oscillations in an appropriate frequency range followed by a judicious analytical treatment of the data is sufficient to determine the number of chemical characteristic times, the reaction mechanism, and the full set of associated rate constants and enthalpies of reaction. To illustrate the scope of the method, dimeric protein folding is chosen as a biologically relevant example of nonlinear mechanism with one or two characteristic times.

This work was supported by the French National Research Agency ANR (T-KiNet grant), the Labex NanoSaclay (T-DropTwo grant), and the Université Pierre et Marie Curie (Convergence program).

INTRODUCTION

DESCRIPTION OF CHEMICAL SYSTEMS

PRINCIPLE OF THE METHOD

ELABORATION OF A TEST

VALIDATION OF THE TEST

DISCUSSION

### Key Topics

- Reaction rate constants
- 23.0
- Reaction enthalphies
- 8.0
- Protein folding
- 7.0
- Relaxation times
- 7.0
- Chemical dynamics
- 6.0

##### C12

## Figures

Protocol to be followed to determine a chemical mechanism from the frequency responses of the considered reactive system submitted to a temperature modulation. This method also provides all the rate constants and enthalpies of reaction without need of fitting.

Protocol to be followed to determine a chemical mechanism from the frequency responses of the considered reactive system submitted to a temperature modulation. This method also provides all the rate constants and enthalpies of reaction without need of fitting.

Frequency behavior of the G(ω) function. The color lines correspond to the responses issued from the various chemical systems described in Table I and modeled by Eq. (1) : the and concentrations have been computed for all possible (a, b, c) triplets and introduced in Eq. (7) . The values for the different kinetic parameters are s−1, s−1, s−1, s−1, ε+1 = 10, ε−1 = 13, ε+2 = 12, and ε−2 = 6. The total concentration N is chosen as a unit reference concentration. The unit of G(ω) and ω is s−1.

Frequency behavior of the G(ω) function. The color lines correspond to the responses issued from the various chemical systems described in Table I and modeled by Eq. (1) : the and concentrations have been computed for all possible (a, b, c) triplets and introduced in Eq. (7) . The values for the different kinetic parameters are s−1, s−1, s−1, s−1, ε+1 = 10, ε−1 = 13, ε+2 = 12, and ε−2 = 6. The total concentration N is chosen as a unit reference concentration. The unit of G(ω) and ω is s−1.

Frequency behavior of the two G i (ω) functions built when the stoichiometry of the mechanism described in Eq. (1) is assumed to obey (a, b, c) = (2, 0, 1). The various color lines correspond to the responses issued from the various chemical systems described in Table I : the , , and concentrations have been computed for all possible (a, b, c) triplets and introduced in Eqs. (20) and (21) . The values for the different kinetic parameters are identical to the ones used in Fig. 2 . The G i (ω) functions have the same unit as and the unit of ω is s−1.

Frequency behavior of the two G i (ω) functions built when the stoichiometry of the mechanism described in Eq. (1) is assumed to obey (a, b, c) = (2, 0, 1). The various color lines correspond to the responses issued from the various chemical systems described in Table I : the , , and concentrations have been computed for all possible (a, b, c) triplets and introduced in Eqs. (20) and (21) . The values for the different kinetic parameters are identical to the ones used in Fig. 2 . The G i (ω) functions have the same unit as and the unit of ω is s−1.

Frequency behavior of the two H i (ω) functions built when the stoichiometry of the mechanism described in Eq. (1) is assumed to obey (a, b, c) = (2, 0, 1). The various color lines correspond to the responses issued from the various chemical systems described in Table I : the , , and concentrations have been computed for all possible (a, b, c) triplets and introduced in Eqs. (22) and (23) . The values for the different kinetic parameters are identical to the ones used in Fig. 2 . The function H i (ω) is dimensionless and the unit of ω is s−1.

Frequency behavior of the two H i (ω) functions built when the stoichiometry of the mechanism described in Eq. (1) is assumed to obey (a, b, c) = (2, 0, 1). The various color lines correspond to the responses issued from the various chemical systems described in Table I : the , , and concentrations have been computed for all possible (a, b, c) triplets and introduced in Eqs. (22) and (23) . The values for the different kinetic parameters are identical to the ones used in Fig. 2 . The function H i (ω) is dimensionless and the unit of ω is s−1.

## Tables

Examples of proteins where folding obeys the various mechanisms that can be depicted by Eq. (1) . Considering a given set of stoichiometric coefficients (a, b, c), the intermediate I is an a-mer and the product P2 is an (ac + b)-mer. The assumed dynamical process used to illustrate our method, (2, 0, 1), is emphasized in bold. We could not find any relevant example for the (1, 1, 1) case.

Examples of proteins where folding obeys the various mechanisms that can be depicted by Eq. (1) . Considering a given set of stoichiometric coefficients (a, b, c), the intermediate I is an a-mer and the product P2 is an (ac + b)-mer. The assumed dynamical process used to illustrate our method, (2, 0, 1), is emphasized in bold. We could not find any relevant example for the (1, 1, 1) case.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content