We consider a cell–cell interaction model of competition between cancer cells and immune system cells, first introduced in the framework of the thermostatted kinetic theory, and derive a master equation for the probability of the number of cancer cells and immune system cells for a given activity. Macroscopic deterministic equations for the concentrations and mean activities of cancer cells and immune system cells are deduced from the kinetic equations. The conditions for which the 3Es of immunotherapy (elimination, equilibrium, and escape) are reproduced are discussed. Apparent elimination of cancer followed by a long pseudo-equilibrium phase and the eventual escape of cancer from the control of the immune system are observed in the three descriptions. The macroscopic equations provide an analytical approach to the transition observed in the simulations of both the kinetic equations and the master equation. For efficient control of activity fluctuations, the steady states associated with the elimination of either cancer or immune system disappear and are replaced by a steady state in which cancer is controlled by the immune system.

Titration without separation, e.g. quantification of a target species in living cells, is a challenge of analytical chemistry. We perform the selective detection of a target using the kinetics involved in a photochemical process and develop a correlation method that we illustrate by the titration of a fluorescent photoswitcher and the target of a photoswitching sensor. Correlating an input time series and a well-chosen weighting function associated with a variable characteristic time yields a spectrum of characteristic times. The upper integration limit of the correlation output can be chosen to match the argument of an extremum of the spectrum with a characteristic time of the input time series in order to quantify the target. A similar procedure is followed to optimize the signal-to-noise ratio. Selectivity and signal-to-noise ratio associated with 15 weighting functions are theoretically predicted. The results are applied to the titration of the reversibly photoswitchable fluorescent protein Dronpa-2 and the titration of calcium using a reversibly photoswitchable fluorescent sensor. The performance of the correlation method is favorably compared to the one of other dynamic contrast protocols.

Due to its sensitivity and versatility, fluorescence is widely used to detect specifically labeled biomolecules. However, fluorescence is currently limited by label discrimination, which suffers from the broad full width of the absorption/emission bands and the narrow lifetime distribution of the bright fluorophores. We overcome this limitation by introducing extra kinetic dimensions through illuminations of reversibly photoswitchable fluorophores (RSFs) at different light intensities. In this expanded space, each RSF is characterized by a chromatic aberration-free kinetic fingerprint of photochemical reactivity, which can be recovered with limited hardware, excellent photon budget, and minimal data processing. This fingerprint was used to identify and discriminate up to 20 among 22 spectrally similar reversibly photoswitchable fluorescent proteins (RSFPs) in less than 1s. This strategy opens promising perspectives for expanding the multiplexing capabilities of fluorescence imaging.

We introduce HIGHLIGHT as a simple and general strategy to selectively image a reversibly photoactivatable fluorescent label associated with a given kinetics. The label is submitted to sine-wave illumination of large amplitude, which generates oscillations of its concentration and fluorescence at higher harmonic frequencies. For singularizing a label, HIGHLIGHT uses specific frequencies and mean light intensities associated with resonances of the amplitudes of concentration and fluorescence oscillations at harmonic frequencies. Several non-redundant resonant observables are simultaneously retrieved from a single experiment with phase-sensitive detection. HIGHLIGHT is used for selective imaging of four spectrally similar fluorescent proteins that had not been discriminated so far. Moreover, labels out of targeted locations can be discarded in an inhomogeneous spatial profile of illumination. HIGHLIGHT opens roads for simplified optical setups at reduced cost and easier maintenance.

The Cover Feature shows the principle of HIGHLIGHT, a simple and general strategy to selectively image a reversibly photoactivatable fluorescent label associated with given kinetics. HIGHLIGHT uses specific frequencies and mean light intensities (I1, I2) associated with resonances of the amplitudes of concentration or fluorescence oscillations at harmonic frequencies to generate a set of non-redundant resonant observables (S) that are recovered simultaneously from a single experiment. More information can be found in the Research Article by Annie Lemarchand, Vincent Croquette, Ludovic Jullien, Thomas Le Saux and co-workers.

Classical approximations in chemical kinetics, the quasi-steady-state approximation (QSSA) and the partial-equilibrium approximation (PEA), are used to reduce rate equations for the concentrations and the extents of the reaction steps, respectively. We make precise two conditions on the rate constants necessary and sufficient to eliminate a well-chosen variable in the vicinity of a steady state. The first condition expresses that dynamics admits a small characteristic time associated with a fast variable. The second condition ensures that the fast variable is a concentration for QSSA and an extent for PEA. Both approximations exploit the zeroth order of a singular perturbation method. Eliminating a fast variable does not mean that it has reached a steady state. The fast evolution is considered over and the slow evolution of the eliminated variable is governed by the slow variables. The evolution of the slow variables occurs on a slow manifold in the space of the concentrations or the extents. In some cases the dynamics of the slow variables can be associated with a reduced chemical scheme. QSSA and PEA are applied to three chemical schemes associated with linear and nonlinear dynamics. We find that QSSA cannot be identified with the elimination of a reactive intermediate. The nonlinearities of the rate equations induce a more complex behavior.

Starting from simple examples of chemical schemes for which a concentration or an extent of reaction can be eliminated, we highlight the common features of the quasi-steady-state approximation and the partial-equilibrium approximation. General conditions to apply either of these adiabatic eliminations are mentioned.

Fluorescence imaging has become a powerful tool for observations in biology. Yet it has also encountered limitations to overcome optical interferences of ambient light, autofluorescence, and spectrally interfering fluorophores. In this account, we first examine the current approaches which address these limitations. Then we more specifically report on Out-of-Phase Imaging after Optical Modulation (OPIOM), which has proved attractive for highly selective multiplexed fluorescence imaging even under adverse optical conditions. After exposing the OPIOM principle, we detail the protocols for successful OPIOM implementation.

The competition between cancer cells and immune system cells in inhomogeneous conditions is described at cell scale within the framework of the thermostatted kinetic theory. Cell learning is reproduced by increased cell activity during favorable interactions. The cell activity fluctuations are controlled by a thermostat. The direction of cell velocity is changed according to stochastic rules mimicking a dense fluid. We develop a kinetic Monte Carlo algorithm inspired from the direct simulation Monte Carlo (DSMC) method initially used for dilute gases. The simulations generate stochastic trajectories sampling the kinetic equations for the distributions of the different cell types. The evolution of an initially localized tumor is analyzed. Qualitatively different behaviors are observed as the field regulating activity fluctuations decreases. For high field values, i.e. efficient thermalization, cancer is controlled. For small field values, cancer rapidly and monotonously escapes from immunosurveillance. For the critical field value separating these two domains, the 3E's of immunotherapy are reproduced, with an apparent initial elimination of cancer, a long quasi-equilibrium period followed by large fluctuations, and the final escape of cancer, even for a favored production of immune system cells. For field values slightly smaller than the critical value, more regular oscillations of the number of immune system cells are spontaneously observed in agreement with clinical observations. The antagonistic effects that the stimulation of the immune system may have on oncogenesis are reproduced in the model by activity-weighted rate constants for the autocatalytic productions of immune system cells and cancer cells. Local favorable conditions for the launching of the oscillations are met in the fluctuating inhomogeneous system, able to generate a small cluster of immune system cells with larger activities than those of the surrounding cancer cells.

Fluorescence has become a ubiquitous observable in biology. Yet it encounters limitations, which may originate from optical interferences such as ambient light, autofluorescence, and spectrally interfering fluorophores. In this review, we first report on dynamic contrast which can overcome these limitations. Then we specifically describe out-of-phase imaging after optical modulation, which proved relevant for multiplexed fluorescence imaging even under adverse optical conditions with several optical setups.

A reduced chemical scheme involving a small number of variables is often sufficient to account for the deterministic evolution of the concentration of the main species contributing to a reaction. However, its predictions are questionable in small systems used, for example in fluorescence correlation spectroscopy (FCS) or in explosive systems involving strong nonlinearities such as autocatalytic steps. We make precise dynamical criteria defining the validity domain of the quasi-steady-state approximation and the elimination of a fast concentration in deterministic dynamics. Designing two different three-variable models converging toward the same two-variable model, we show that the variances and covariance of the fluctuations of the slow variables are not correctly predicted using the two-variable model, even in the limit of a large system size. The more striking weaknesses of the reduced scheme are figured out in mesoscaled systems containing a small number of molecules. The results of two stochastic approaches are compared and the shortcomings of the Langevin equations with respect to the master equation are pointed out. We conclude that the description of the fluctuations and their coupling with nonlinearities of deterministic dynamics escape reduced chemical schemes.

A wave front of Fisher and Kolmogorov, Petrovskii, and Piskunov type involving two species A and B with different diffusion coefficients $D_A$ and $D_B$ is studied using a master equation approach in dilute and concentrated solutions. Species A and B are supposed to be engaged in the autocatalytic reaction A+B -> 2A. Contrary to the results of a deterministic description, the front speed deduced from the master equation in the dilute case sensitively depends on the diffusion coefficient of species B. A linear analysis of the deterministic equations with a cutoff in the reactive term cannot explain the decrease of the front speed observed for $D_B > D_A$. In the case of a concentrated solution, the transition rates associated with cross-diffusion are derived from the corresponding diffusion fluxes. The properties of the wave front obtained in the dilute case remain valid but are mitigated by cross-diffusion which reduces the impact of different diffusion coefficients.

Interrogating living cells requires sensitive imaging of a large number of components in real time. The state-of-the-art of multiplexed imaging is usually limited to a few components. This review reports on the promise and the challenges of dynamic contrast to overcome this limitation.

The sensitivity to perturbations of the Fisher and Kolmogorov, Petrovskii, Piskunov front is used to find a quantity revealing perturbations of diffusion in a concentrated solution of two chemical species with different diffusivities. The deterministic dynamics includes cross-diffusion terms due to the deviation from the dilution limit. The behaviors of the front speed, the shift between the concentration profiles of the two species, and the width of the reactive zone are investigated, both analytically and numerically. The shift between the two profiles turns out to be a well-adapted criterion presenting noticeable variations with the deviation from the dilution limit in a wide range of parameter values.

The control of self-organized structures such as Turing patterns is a challenge for chemical engineers. We propose a reaction-diffusion model that includes the reactive role of the solvent and admits Turing patterns of adaptable wavelength. Changing the concentration of the solute is sufficient to tune the wavelength. Particles dynamics simulations are successfully performed, illustrating wavelength control down to the submicrometric scale.

The competition between a cancer and the immune system are modelled at cell scale in the framework of thermostatted kinetic theory. Cell activation and learning are reproduced by the increase of cell activity during interactions. The fluctuations of system activity are controlled by a thermostat which reproduces the regulation of the learning process and memory loss through cell death. An algorithm, including spatial description and inspired from the direct simulation Monte Carlo (DSMC) method, is used to simulate stochastic trajectories for cell numbers and activities. We focus on the decisive role played by the thermostat. For inefficient thermalization, the divergence of the number of cancer cells is obtained in spite of favored production of immune system cells. Conversely, when the activity fluctuations are controlled, the development of cancer is contained even for weakened immune defenses. These results may be correlated to unexpected clinical observations in the case of different cancers, such as carcinoma, lymphoma, and melanoma.

The question of the termination of a periodic spatial structure of Turing-type in a growing system is addressed in a chemical engineering perspective and a biomimetic approach. The effects of the dynamical parameters on the stability and the wavelength of the structure are analytically studied and used to propose experimental conditions for which a Turing pattern stops by itself with a decreasing wavelength. The proposed mechanism is successfully checked by the numerical integration of the equations governing the dynamics of the activator and the inhibitor. We conclude that a local increase of the concentration of the reservoir which controls the injection rate of the inhibitor into the system can be used to achieve the appropriate termination of a Turing pattern.

The wavelength of a periodic spatial structure of Turing type is an intrinsic property of the considered reaction-diffusion dynamics and we address the question of its control at the microscopic scale for given dynamical parameters. The direct simulation Monte Carlo method, initially introduced to simulate particle dynamics in rarefied gases, is adapted to the simulation of concentrated solutions. We perform simulations of a submicrometric Turing pattern with appropriate boundary conditions and show that taking into account the role of the solvent in the chemical mechanism allows us to control the wavelength of the structure. Typically, doubling the concentration of the solute leads to decreasing the wavelength by two. The results could be used to design materials with controlled submicrometric properties in chemical engineering. They could also be considered as a possible interpretation of proportion preservation of embryos in morphogenesis.