Biomolecular condensates in cells are often rich in catalytically-active enzymes. This is particularly true in the case of the large enzymatic complexes known as metabolons, which contain different enzymes that participate in the same catalytic pathw
ay. One possible explanation for this self-organization is the combination of the catalytic activity of the enzymes and a chemotactic response to gradients of their substrate, which leads to a substrate-mediated effective interaction between enzymes. These interactions constitute a purely non-equilibrium effect and show exotic features such as non-reciprocity. Here, we analytically study a model describing the phase separation of a mixture of such catalytically-active particles. We show that a Michaelis-Menten-like dependence of the particles activities manifests itself as a screening of the interactions, and that a mixture of two differently-sized active species can exhibit phase separation with transient oscillations. We also derive a rich stability phase diagram for a mixture of two species with both concentration-dependent activity and size dispersity. This work highlights the variety of possible phase separation behaviours in mixtures of chemically-active particles, which provides an alternative pathway to the passive interactions more commonly associated with phase separation in cells. Our results highlight non-equilibrium organizing principles that can be important for biologically relevant liquid-liquid phase separation.
Understanding how electrolyte solutions behave out of thermal equilibrium is a long-standing endeavor in many areas of chemistry and biology. Although mean-field theories are widely used to model the dynamics of electrolytes, it is also important to
characterize the effects of fluctuations in these systems. In a previous work, we showed that the dynamics of the ions in a strong electrolyte that is driven by an external electric field can generate long-ranged correlations manifestly different from the equilibrium screened correlations; in the nonequilibrium steady state, these correlations give rise to a novel long-range fluctuation-induced force (FIF). Here, we extend these results by considering the dynamics of the strong electrolyte after it is quenched from thermal equilibrium upon the application of a constant electric field. We show that the asymptotic long-distance limit of both charge and density correlations is generally diffusive in time. These correlations give rise to long-ranged FIFs acting on the neutral confining plates with long-time regimes that are governed by power-law temporal decays toward the steady-state value of the force amplitude. These findings show that nonequilibrium fluctuations have nontrivial implications on the dynamics of objects immersed in a driven electrolyte, and they could be useful for exploring new ways of controlling long-distance forces in charged solutions.
Chemotaxis of enzymes in response to gradients in the concentration of their substrate has been widely reported in recent experiments, but a basic understanding of the process is still lacking. Here, we develop a microscopic theory for chemotaxis, va
lid for enzymes and other small molecules. Our theory includes both non-specific interactions between enzyme and substrate, as well as complex formation through specific binding between the enzyme and the substrate. We find that two distinct mechanisms contribute to enzyme chemotaxis: a diffusiophoretic mechanism due to the non-specific interactions, and a new type of mechanism due to binding-induced changes in the diffusion coefficient of the enzyme. The latter chemotactic mechanism points towards lower substrate concentration if the substrate enhances enzyme diffusion, and towards higher substrate concentration if the substrate inhibits enzyme diffusion. For a typical enzyme, attractive phoresis and binding-induced enhanced diffusion will compete against each other. We find that phoresis dominates above a critical substrate concentration, whereas binding-induced enhanced diffusion dominates for low substrate concentration. Our results resolve an apparent contradiction regarding the direction of urease chemotaxis observed in experiments, and in general clarify the relation between enhanced diffusion and chemotaxis of enzymes. Finally, we show that the competition between the two distinct chemotactic mechanisms may be used to engineer nanomachines that move towards or away from regions with a specific substrate concentration.
We study the stochastic dynamics of an electrolyte driven by a uniform external electric field and show that it exhibits generic scale invariance despite the presence of Debye screening. The resulting long-range correlations give rise to a Casimir-li
ke fluctuation-induced force between neutral boundaries that confine the ions; this force is controlled by the external electric field, and it can be both attractive and repulsive with similar boundary conditions, unlike other long-range fluctuation-induced forces. This work highlights the importance of nonequilibrium correlations in electrolytes and shows how they can be used to tune interactions between uncharged biological or synthetic structures at large separations.
Pair interactions between active particles need not follow Newtons third law. In this work we propose a continuum model of pattern formation due to non-reciprocal interaction between multiple species of scalar active matter. The classical Cahn-Hillia
rd model is minimally modified by supplementing the equilibrium Ginzburg-Landau dynamics with particle number conserving currents which cannot be derived from a free energy, reflecting the microscopic departure from action-reaction symmetry. The strength of the asymmetry in the interaction determines whether the steady state exhibits a macroscopic phase separation or a traveling density wave displaying global polar order. The latter structure, which is equivalent to an active self-propelled smectic phase, coarsens via annihilation of defects, whereas the former structure undergoes Ostwald ripening. The emergence of traveling density waves, which is a clear signature of broken time-reversal symmetry in this active system, is a generic feature of any multi-component mixture with microscopic non-reciprocal interactions.
Many functional units in biology, such as enzymes or molecular motors, are composed of several subunits that can reversibly assemble and disassemble. This includes oligomeric proteins composed of several smaller monomers, as well as protein complexes
assembled from a few proteins. By studying the generic spatial transport properties of such proteins, we investigate here whether their ability to reversibly associate and dissociate may confer them a functional advantage with respect to non-dissociating proteins. In uniform environments with position-independent association-dissociation, we find that enhanced diffusion in the monomeric state coupled to reassociation into the functional oligomeric form leads to enhanced reactivity with distant targets. In non-uniform environments with position-dependent association-dissociation, caused e.g. by spatial gradients of an inhibiting chemical, we find that dissociating proteins generically tend to accumulate in regions where they are most stable, a process that we term stabilitaxis.
Many experiments in recent years have reported that, when exposed to their corresponding substrate, catalytic enzymes undergo enhanced diffusion as well as chemotaxis (biased motion in the direction of a substrate gradient). Among other possible mech
anisms, in a number of recent works we have explored several passive mechanisms for enhanced diffusion and chemotaxis, in the sense that they require only binding and unbinding of the enzyme to the substrate rather than the catalytic reaction itself. These mechanisms rely on conformational changes of the enzyme due to binding, as well as on phoresis due to non-contact interactions between enzyme and substrate. Here, after reviewing and generalizing our previous findings, we extend them in two different ways. In the case of enhanced diffusion, we show that an exact result for the long-time diffusion coefficient of the enzyme can be obtained using generalized Taylor dispersion theory, which results in much simpler and transparent analytical expressions for the diffusion enhancement. In the case of chemotaxis, we show that the competition between phoresis and binding-induced changes in diffusion results in non-trivial steady state distributions for the enzyme, which can either accumulate in or be depleted from regions with a specific substrate concentration.
An interacting pair of chemotactic (anti-chemotactic) active colloids, that can rotate their axes of self-propulsion to align {parallel (anti-parallel)} to a chemical gradient, shows dynamical behaviour that varies from bound states to scattering. Th
e underlying two-body interactions are purely dynamical, non-central, non-reciprocal, and controlled by changing the catalytic activity and phoretic mobility. Mutually chemotactic colloids trap each other in a final state of fixed separation; the resulting `active dimer translates. A second type of bound state is observed where the polar axes undergo periodic cycles leading to phase-synchronised circular motion around a common point. These bound states are formed depending on initial conditions and can unbind on increasing the speed of self propulsion. Mutually anti-chemotactic swimmers always scatter apart. We also classify the fixed points underlying the bound states, and the bifurcations leading to transitions from one type of bound state to another, for the case of a single swimmer in the presence of a localised source of solute.
A number of microorganisms leave persistent trails while moving along surfaces. For single-cell organisms, the trail-mediated self-interaction will influence its dynamics. It has been discussed recently [Kranz textit{et al.} Phys. Rev. Lett. textbf{1
17}, 8101 (2016)] that the self-interaction may localize the organism above a critical coupling $chi_c$ to the trail. Here we will derive a generalized active particle model capturing the key features of the self-interaction and analyze its behavior for smaller couplings $chi < chi_c$. We find that fluctuations in propulsion speed shift the localization transition to stronger couplings.
