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Active matter systems evade the constraints of thermal equilibrium, leading to the emergence of intriguing collective behavior. A paradigmatic example is given by motor-filament mixtures, where the motion of motor proteins drives alignment and sliding interactions between filaments and their self-organization into macroscopic structures. After defining a microscopic model for these systems, we derive continuum equations, exhibiting the formation of active supramolecular assemblies such as micelles, bilayers, and foams. The transition between these structures is driven by a branching instability, which destabilizes the orientational order within the micelles, leading to the growth of bilayers at high microtubule densities. Additionally, we identify a fingering instability, modulating the shape of the micelle interface at high motor densities. We study the role of various mechanisms in these two instabilities, such as contractility, active splay, and anchoring, allowing for generalization beyond the system considered here.

Biomolecular condensates help organize the cell cytoplasm and nucleoplasm into spatial compartments with different chemical compositions. A key feature of such compositional patterning is the local enrichment of enzymatically active biomolecules which, after transient binding via molecular interactions, catalyze reactions among their substrates. Thereby, biomolecular condensates provide a spatial template for nonuniform concentration profiles of substrates. In turn, the concentration profiles of substrates, and their molecular interactions with enzymes, drive enzyme fluxes which can enable novel nonequilibrium dynamics. To analyze this generic class of systems, with a current focus on self-propelled droplet motion, we here develop a self-consistent sharp interface theory. In our theory, we diverge from the usual bottom-up approach, which involves calculating the dynamics of concentration profiles based on a given chemical potential gradient. Instead, reminiscent of control theory, we take the reverse approach by deriving the chemical potential profile and enzyme fluxes required to maintain a desired condensate form and dynamics. The chemical potential profile and currents of enzymes come with a corresponding power dissipation rate, which allows us to derive a thermodynamic consistency criterion for the passive part of the system (here, reciprocal enzyme-enzyme interactions). As a first-use case of our theory, we study the role of reciprocal interactions, where the transport of substrates due to reactions and diffusion is, in part, compensated by redistribution due to molecular interactions. More generally, our theory applies to mass-conserved active matter systems with moving phase boundaries.

The communication in active systems plays an important role in their self-organization, yet the detail is not fully understood. Here, Ziepke et al. show the formation of complex structures at multiple scales amongst interactive agents that locally process information transmitted by chemical signals.

The subject of the article is a variant of an efficient algorithm for synthesizing a dual discrete model and controller for tracking a given trajectory of a dynamic nonlinear, nonstationary black box object, using standard procedures for diagonalizing the state matrix, which makes it possible to simplify obtaining control values in numerical form and reduce the number of calculations. The current article presents one the possible solutions to the problem of regulator synthesis to ensure stable development of a given trajectory of motion of a nonlinear, non-stationary object of "black box" type using the concept of dual control. The task was set to simplify the previously proposed synthesis algorithm for the adaptive control of dynamic nonlinear, non-stationary objects using the example of first-order object of the "black box" type, using standard procedures for the diagonalization of the state matrix. An extended state matrix is the basis for obtaining a control model and predicting the behavior of a nonlinear non-stationary object, which in turn makes it possible to effectively use the concept of dual control. Methods used in the work are based on concept of dual control, nonlinear dynamic models, matrix theory, difference equations. Obtained results of this work consist of the development of a version of a dual nonparametric controller of nonstationary nonlinear processes, which has adaptive properties, does not require knowledge of the physics of functioning of the control object, is presented in the form of a simple algebraic formula that does not contain coefficients that require adjustment. Conclusion. Scientific novelty lies in the application of each interval matrix operator control for the diagonalization of the state submatrix. This operator is used for subsequent calculation of the control action. This approach enables the use of a standard diagonalization procedure using mathematical applications. The results are presented in the form of a final formula that does not require use of matrix operations during control, which makes it possible to simplify the synthesis of the controller using standard mathematical procedures.

The generation of new hybrid varieties of tomato (Solanum lycopersicum L.) is the most widely used breeding method for this species and requires at least seven self-fertilization cycles to generate stable parent lines. The development of doubled haploids aims at obtaining completely homozygous lines in a single generation, although, to date, routine commercial application has not been possible in this species. In contrast, obtaining doubled haploid lines via gynogenesis has been successfully implemented in recalcitrant crops such as melon, cucumber, pumpkin, loquat and walnut. This review provides an overview of the requirements and advantages of gynogenesis as an inducer of haploidy in different agricultural crops, with the purpose of assessing the potential for its application in tomato breeding. Successful cases of gynogenesis variants involving in vitro culture of unfertilized ovules, use of 60Co-irradiated pollen, in vivo haploid inducers and wide hybridization are presented, suggesting that these methodologies could be implemented in tomato breeding programs to obtain doubled haploids.