Dynamical Renormalization Group for Mode-Coupling Field Theories with Solenoidal Constraint

The recent inflow of empirical data about the collective behaviour of strongly correlated biological systems has brought field theory and the renormalization group into the biophysical arena. Experiments on bird flocks and insect swarms show that social forces act on the particles’ velocity through the generator of its rotations, namely the spin, indicating that mode-coupling field theories are necessary to reproduce the correct dynamical behaviour. Unfortunately, a theory for three coupled fields—density, velocity and spin—has a prohibitive degree of intricacy. A simplifying path consists in getting rid of density fluctuations by studying incompressible systems. This requires imposing a solenoidal constraint on the primary field, an unsolved problem even for equilibrium mode-coupling theories. Here, we perform an equilibrium dynamic renormalization group analysis of a mode-coupling field theory subject to a solenoidal constraint; using the classification of Halperin and Hohenberg, we can dub this case as a solenoidal Model G. We demonstrate that the constraint produces a new vertex that mixes static and dynamical coupling constants, and that this vertex is essential to grant the closure of the renormalization group structure and the consistency of dynamics with statics. Interestingly, although the solenoidal constraint leads to a modification of the static universality class, we find that it does not change the dynamical universality class, a result that seems to represent an exception to the general rule that dynamical universality classes are narrower than static ones. Our results constitute a solid stepping stone in the admittedly large chasm towards developing an off-equilibrium mode-coupling theory of biological groups.

Changing Cross-Reactivity for Different Immunoassays Using the Same Antibodies: Theoretical Description and Experimental Confirmation

Many applications of immunoassays involve the possible presence of structurally similar compounds that bind with antibodies, but with different affinities. In this regard, an important characteristic of an immunoassay is its cross-reactivity: the possibility of detecting various compounds in comparison with a certain standard. Based on cross-reactivity, analytical systems are assessed as either high-selective (responding strictly to a specific compound) or low-selective (responding to a number of similar compounds). The present study demonstrates that cross-reactivity is not an intrinsic characteristic of antibodies but can vary for different formats of competitive immunoassays using the same antibodies. Assays with sensitive detection of markers and, accordingly, implementation at low concentrations of antibodies and modified (competing) antigens are characterized by lower cross-reactivities and are, thus, more specific than assays requiring high concentrations of markers and interacting reagents. This effect was confirmed by both mathematical modeling and experimental comparison of an enzyme immunoassay and a fluorescence polarization immunoassay of sulfonamides and fluoroquinolones. Thus, shifting to lower concentrations of reagents decreases cross-reactivities by up to five-fold. Moreover, the cross-reactivities are changed even in the same assay format by varying the ratio of immunoreactants’ concentrations and shifting from the kinetic or equilibrium mode of the antigen-antibody reaction. The described patterns demonstrate the possibility of modulating immunodetection selectivity without searching for new binding reactants.

Influence of random effects on the equilibrium modes in the population dynamics model

In the paper, we study a dynamic model of interacting populations of the type “predator-two prey”. A detailed parametric analysis of the equilibrium modes arising in the system is carried out. In zones of the bifurcation parameter, where the coexistence of several equilibrium regimes is found, separable surfaces are constructed. Those surfaces are the boundaries of the attraction basins of different equilibria. It is shown that the effect of an external random disturbance can destroy the equilibrium mode of coexistence of three populations and lead to a qualitatively different mode of coexistence. Such qualitative changes lead to the extinction of one or two of the three populations. Using the technique of stochastic sensitivity function and the method of confidence domains, the probabilistic mechanisms of destruction of equilibrium modes are demonstrated. A parametric analysis of the probabilities of extinction of populations for two types is carried out. The range of the bifurcation parameter and the level of noise intensity, that are the most favorable for the coexistence of three populations, are discussed.

The effect of solvent relaxation time constants on free energy gap law for ultrafast charge recombination following photoinduced charge separation

Ultrafast low exergonic charge recombination following photoinduced charge separation proceeds in a non-equilibrium mode and its rate constant is nearly independent of the free energy gap.