Annie Lemarchand

Temperature Modulation and Quadrature Detection for Selective Titration of Two-State Exchanging Reactants

Biological samples exhibit huge molecular diversity over large concentration ranges. Titrating a given compound in such mixtures is often difficult, and innovative strategies emphasizing selectivity are thus demanded. To overcome limitations inherent to thermodynamics, we here present a generic technique where discrimination relies on the dynamics of interaction between the target of interest and a probe introduced in excess. Considering an ensemble of two-state exchanging reactants submitted to temperature modulation, we first demonstrate that the amplitude of the out-of-phase concentration oscillations is maximum for every compound involved in a reaction whose equilibrium constant is equal to unity and whose relaxation time is equal to the inverse of the excitation angular frequency. Taking advantage of this feature, we next devise a highly specific detection protocol and validate it using a microfabricated resistive heater and an epifluorescence microscope, as well as labeled oligonucleotides to model species displaying various dynamic properties. As expected, quantification of a sought for strand is obtained even if interfering reagents are present in similar amounts. Moreover, our approach does not require any separation and is compatible with imaging. It could then benefit some of the numerous binding assays performed every day in life sciences.

Particle dynamics simulations of Turing patterns

The direct simulation Monte Carlo method is used to reproduce Turing patterns at the microscopic level in reaction-diffusion systems. In order to satisfy the basic condition for the development of such a spatial structure, we propose a model involving a solvent, which allows for disparate diffusivities of individual reactive species. One-dimensional structures are simulated in systems of various lengths. Simulation results agree with the macroscopic predictions obtained by integration of the reaction-diffusion equations. Additional effects due to internal fluctuations are observed, such as temporal transitions between structures of different wavelengths in a confined system. For a structure developing behind a propagating wave front, the fluctuations suppress the induction period and accelerate the formation of the Turing pattern. These results support the ability of reaction-diffusion models to robustly reproduce axial segmentation including the formation of early vertebrae or somites in noisy biological environments.

Reaction-diffusion approach to prevertebrae formation: Effect of a local source of morphogen

Periodic structure formation is an essential feature of embryonic development. Many models of this phenomenon, most of them based on time oscillations, have been proposed. However, temporal oscillations are not always observed during development and how a spatial periodic structure is formed still remains under question. We investigate a reaction-diffusion model, in which a Turing pattern develops without temporal oscillations, to assess its ability to account for the formation of prevertebrae. We propose a correspondence between the species of the reaction scheme and biologically relevant molecules known as morphogens. It is shown that the model satisfactorily reproduces experiments involving grafting of morphogen sources into the embryos. Using a master equation approach and the direct simulation Monte Carlo method, we examine the robustness of the results to internal fluctuations.

Chemical Mechanism Identification from Frequency Response to Small Temperature Modulation

The description of interactions between biochemical species and the elucidation of the corresponding chemical mechanisms encounter an increasing interest both for the comprehension of biological pathways at the molecular scale and for the rationalization of drug design. Relying on powerful experimental tools such as thermal microfluidics and fluorescence detection, we propose a methodology to determine the chemical mechanism of a reaction without fitting parameters. A mechanism consistent with the accessible knowledge is assumed, and the assumption is checked through an iterative protocol. The test is based on the frequency analysis of the response of a targeted reactive species to temperature modulation. We build specific functions of the frequency that are constant for the assumed mechanism and show that the graph of these functions can be drawn from appropriate data analysis. The method is general and can be applied to any complex mechanism. It is here illustrated in detail in the case of single relaxation time mechanisms.

Identification of two-step chemical mechanisms and determination of thermokinetic parameters using frequency responses to small temperature oscillations.

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.

Kinetics of Reactive Modules Adds Discriminative Dimensions for Selective Cell Imaging.

Living cells are chemical mixtures of exceptional interest and significance, whose investigation requires the development of powerful analytical tools fulfilling the demanding constraints resulting from their singular features. In particular, multiplexed observation of a large number of molecular targets with high spatiotemporal resolution appears highly desirable. One attractive road to address this analytical challenge relies on engaging the targets in reactions and exploiting the rich kinetic signature of the resulting reactive module, which originates from its topology and its rate constants. This review explores the various facets of this promising strategy. We first emphasize the singularity of the content of a living cell as a chemical mixture and suggest that its multiplexed observation is significant and timely. Then, we show that exploiting the kinetics of analytical processes is relevant to selectively detect a given analyte: upon perturbing the system, the kinetic window associated to response read-out has to be matched with that of the targeted reactive module. Eventually, we introduce the state-of-the-art of cell imaging exploiting protocols based on reaction kinetics and draw some promising perspectives.

Identification of two-step chemical mechanisms using small temperature oscillations and a single tagged species

In order to identify two-step chemical mechanisms, we propose a method based on a small temperature modulation and on the analysis of the concentration oscillations of a single tagged species involved in the first step. The thermokinetic parameters of the first reaction step are first determined. Then, we build test functions that are constant only if the chemical system actually possesses some assumed two-step mechanism. Next, if the test functions plotted using experimental data are actually even, the mechanism is attributed and the obtained constant values provide the rate constants and enthalpy of reaction of the second step. The advantage of the protocol is to use the first step as a probe reaction to reveal the dynamics of the second step, which can hence be relieved of any tagging. The protocol is anticipated to apply to many mechanisms of biological relevance. As far as ligand binding is considered, our approach can address receptor conformational changes or dimerization as well as competition with or modulation by a second partner. The method can also be used to screen libraries of untagged compounds, relying on a tracer whose concentration can be spectroscopically monitored.

Existence of Solutions of a Partial Integrodifferential Equation with Thermostat and Time Delay

This paper deals with the mathematical analysis of a retarded partial integrodifferential equation that belongs to the class of thermostatted kinetic equations with time delay. Specifically, the paper is devoted to the proof of the existence and uniqueness of mild solutions of the related Cauchy problem. The main result is obtained by employing integration along the characteristic curves and successive approximations sequence arguments. Applications and perspective are also discussed within the paper.

Miming the cancer-immune system competition by kinetic Monte Carlo simulations

In order to mimic the interactions between cancer and the immune system at cell scale, we propose a minimal model of cell interactions that is similar to a chemical mechanism including autocatalytic steps. The cells are supposed to bear a quantity called activity that may increase during the interactions. The fluctuations of cell activity are controlled by a so-called thermostat. We develop a kinetic Monte Carlo algorithm to simulate the cell interactions and thermalization of cell activity. The model is able to reproduce the well-known behavior of tumors treated by immunotherapy: the first apparent elimination of the tumor by the immune system is followed by a long equilibrium period and the final escape of cancer from immunosurveillance.

Temporal cross-correlation asymmetry and departure from equilibrium in a bistable chemical system

This paper aims at determining sustained reaction fluxes in a nonlinear chemical system driven in a nonequilibrium steady state. The method relies on the computation of cross-correlation functions for the internal fluctuations of chemical species concentrations. By employing Langevin-type equations, we derive approximate analytical formulas for the cross-correlation functions associated with nonlinear dynamics. Kinetic Monte Carlo simulations of the chemical master equation are performed in order to check the validity of the Langevin equations for a bistable chemical system. The two approaches are found in excellent agreement, except for critical parameter values where the bifurcation between monostability and bistability occurs. From the theoretical point of view, the results imply that the behavior of cross-correlation functions cannot be exploited to measure sustained reaction fluxes in a specific nonlinear system without the prior knowledge of the associated chemical mechanism and the rate constants.