Size regulation of multiple organelles competing for a limiting subunit pool.

How cells regulate the size of intracellular structures and organelles is a longstanding question. Recent experiments suggest that size control of intracellular structures is achieved through the depletion of a limiting subunit pool in the cytoplasm. While the limiting pool model ensures organelle-to-cell size scaling, it does not provide a mechanism for robust size control of multiple co-existing structures. Here we develop a generalized theory for size-dependent growth of intracellular structures to demonstrate that robust size control of multiple intracellular structures, competing for a limiting subunit pool, is achieved via a negative feedback between the growth rate and the size of the individual structure. This design principle captures size maintenance of a wide variety of subcellular structures, from cytoskeletal filaments to three-dimensional organelles. We identify the feedback motifs for structure size regulation based on known molecular processes, and compare our theory to existing models of size regulation in biological assemblies. Furthermore, we show that positive feedback between structure size and growth rate can lead to bistable size distribution and spontaneous size selection.

Emergence and maintenance of variable-length actin filaments in a limiting pool of building blocks.

Actin is one of the key structural components of the eukaryotic cytoskeleton that regulates cellular architecture and mechanical properties. Dynamic regulation of actin filament length and organization is essential for the control of many physiological processes including cell adhesion, motility and division. While previous studies have mostly focused on the mechanisms controlling the length of single actin filaments, it remains poorly understood how distinct actin filament populations in cells maintain different lengths using the same set of molecular building blocks. Here, we develop a theoretical model for the length regulation of multiple actin filaments by nucleation and growth-rate modulation by actin-binding proteins in a limiting pool of monomers. We first show that spontaneous nucleation of actin filaments naturally leads to heterogeneities in filament length distribution. We then investigate the effects of filament growth inhibition by capping proteins and growth promotion by formin proteins on filament length distribution. We find that filament length heterogeneity can be increased by growth inhibition, whereas growth promoters do not significantly affect length heterogeneity. Interestingly, a competition between filament growth inhibitors and growth promoters can give rise to bimodal filament length distribution as well as a highly heterogeneous length distribution with large statistical dispersion. We quantitatively predict how heterogeneity in actin filament length can be modulated by tuning filamentous actin nucleation and growth rates in order to create distinct filament subpopulations with different lengths.

Growth-induced collective bending and kinetic trapping of cytoskeletal filaments.

Growth and turnover of actin filaments play a crucial role in the construction and maintenance of actin networks within cells. Actin filament growth occurs within limited space and finite subunit resources in the actin cortex. To understand how filament growth shapes the emergent architecture of actin networks, we developed a minimal agent-based model coupling filament mechanics and growth in a limiting subunit pool. We find that rapid filament growth induces kinetic trapping of highly bent actin filaments. Such collective bending patterns are long-lived, organized around nematic defects, and arises from competition between filament polymerization and bending elasticity. The stability of nematic defects and the extent of kinetic trapping are amplified by an increase in the abundance of the actin pool and by crosslinking the network. These findings suggest that kinetic trapping is a robust consequence of growth in crowded environments, providing a route to program shape memory in actin networks.

Growth-induced collective bending and kinetic trapping of cytoskeletal filaments.

Growth and turnover of actin filaments play a crucial role in the construction and maintenance of actin networks within cells. Actin filament growth occurs within limited space and finite subunit resources in the actin cortex. To understand how filament growth shapes the emergent architecture of actin networks, we developed a minimal agent-based model coupling filament mechanics and growth in a limiting subunit pool. We find that rapid filament growth induces kinetic trapping of highly bent actin filaments. Such collective bending patterns are long-lived, organized around nematic defects, and arise from competition between filament polymerization and bending elasticity. The stability of nematic defects and the extent of kinetic trapping are amplified by an increase in the abundance of the actin pool and by crosslinking the network. These findings suggest that kinetic trapping is a robust consequence of growth in crowded environments, providing a route to program shape memory in actin networks.

Interplay of condensate material properties and chromatin heterogeneity governs nuclear condensate ripening.

Biomolecular condensates play pivotal roles in many cellular processes, yet predicting condensate growth dynamics within the complex intracellular environment is challenging. While chromatin mechanics are known to influence condensate coarsening in the nucleus, the effect of condensate properties remains unclear. Our study demonstrates that the interplay between condensate properties and chromatin mechanics dictates condensate growth dynamics. Through chemical dimerization, we induced condensates of various properties in the cell nuclei, revealing distinct growth mechanisms: diffusion-driven or ripening-dominated. To explain experimental observations, we developed a quantitative theory that uncovers the role of chromatin in modulating condensate growth via size-dependent pressure. We find that surface tension is a critical factor in determining whether condensates undergo elastic or Ostwald ripening. Our model predicts that different condensates are affected differently by chromatin heterogeneity, validated by experimentally perturbing chromatin organization. Taken together, our work elucidates how condensate surface tension and chromatin heterogeneity govern nuclear condensate ripening.

Catalytic growth in a shared enzyme pool ensures robust control of centrosome size.

Accurate regulation of centrosome size is essential for ensuring error-free cell division, and dysregulation of centrosome size has been linked to various pathologies, including developmental defects and cancer. While a universally accepted model for centrosome size regulation is lacking, prior theoretical and experimental work suggest a centrosome growth model involving autocatalytic assembly of the pericentriolic material. Here we show that the autocatalytic assembly model fails to explain the attainment of equal centrosome sizes, which is crucial for error-free cell division. Incorporating latest experimental findings into the molecular mechanisms governing centrosome assembly, we introduce a new quantitative theory for centrosome growth involving catalytic assembly within a shared pool of enzymes. Our model successfully achieves robust size equality between maturing centrosome pairs, mirroring cooperative growth dynamics observed in experiments. To validate our theoretical predictions, we compare them with available experimental data and demonstrate the broad applicability of the catalytic growth model across different organisms, which exhibit distinct growth dynamics and size scaling characteristics.

Membrane tension induces F-actin reorganization and flow in a biomimetic model cortex.

The accumulation and transmission of mechanical stresses in the cell cortex and membrane determines the mechanics of cell shape and coordinates essential physical behaviors, from cell polarization to cell migration. However, the extent that the membrane and cytoskeleton each contribute to the transmission of mechanical stresses to coordinate diverse behaviors is unclear. Here, we reconstitute a minimal model of the actomyosin cortex within liposomes that adheres, spreads and ultimately ruptures on a surface. During spreading, accumulated adhesion-induced (passive) stresses within the membrane drive changes in the spatial assembly of actin. By contrast, during rupture, accumulated myosin-induced (active) stresses within the cortex determine the rate of pore opening. Thus, in the same system, devoid of biochemical regulation, the membrane and cortex can each play a passive or active role in the generation and transmission of mechanical stress, and their relative roles drive diverse biomimetic physical behaviors.

Unjamming and emergent nonreciprocity in active ploughing through a compressible viscoelastic fluid.

A dilute suspension of active Brownian particles in a dense compressible viscoelastic fluid, forms a natural setting to study the emergence of nonreciprocity during a dynamical phase transition. At these densities, the transport of active particles is strongly influenced by the passive medium and shows a dynamical jamming transition as a function of activity and medium density. In the process, the compressible medium is actively churned up - for low activity, the active particle gets self-trapped in a cavity of its own making, while for large activity, the active particle ploughs through the medium, either accompanied by a moving anisotropic wake, or leaving a porous trail. A hydrodynamic approach makes it evident that the active particle generates a long-range density wake which breaks fore-aft symmetry, consistent with the simulations. Accounting for the back-reaction of the compressible medium leads to (i) dynamical jamming of the active particle, and (ii) a dynamical non-reciprocal attraction between two active particles moving along the same direction, with the trailing particle catching up with the leading one in finite time. We emphasize that these nonreciprocal effects appear only when the active particles are moving and so manifest in the vicinity of the jamming-unjamming transition.

Size-Regulated Symmetry Breaking in Reaction-Diffusion Models of Developmental Transitions.

The development of multicellular organisms proceeds through a series of morphogenetic and cell-state transitions, transforming homogeneous zygotes into complex adults by a process of self-organisation. Many of these transitions are achieved by spontaneous symmetry breaking mechanisms, allowing cells and tissues to acquire pattern and polarity by virtue of local interactions without an upstream supply of information. The combined work of theory and experiment has elucidated how these systems break symmetry during developmental transitions. Given that such transitions are multiple and their temporal ordering is crucial, an equally important question is how these developmental transitions are coordinated in time. Using a minimal mass-conserved substrate-depletion model for symmetry breaking as our case study, we elucidate mechanisms by which cells and tissues can couple reaction-diffusion-driven symmetry breaking to the timing of developmental transitions, arguing that the dependence of patterning mode on system size may be a generic principle by which developing organisms measure time. By analysing different regimes of our model, simulated on growing domains, we elaborate three distinct behaviours, allowing for clock-, timer- or switch-like dynamics. Relating these behaviours to experimentally documented case studies of developmental timing, we provide a minimal conceptual framework to interrogate how developing organisms coordinate developmental transitions.

Actomyosin pulsation and flows in an active elastomer with turnover and network remodeling.

Tissue remodeling requires cell shape changes associated with pulsation and flow of the actomyosin cytoskeleton. Here we describe the hydrodynamics of actomyosin as a confined active elastomer with turnover of its components. Our treatment is adapted to describe the diversity of contractile dynamical regimes observed in vivo. When myosin-induced contractile stresses are low, the deformations of the active elastomer are affine and exhibit spontaneous oscillations, propagating waves, contractile collapse and spatiotemporal chaos. We study the nucleation, growth and coalescence of actomyosin-dense regions that, beyond a threshold, spontaneously move as a spatially localized traveling front. Large myosin-induced contractile stresses lead to nonaffine deformations due to enhanced actin and crosslinker turnover. This results in a transient actin network that is constantly remodeling and naturally accommodates intranetwork flows of the actomyosin-dense regions. We verify many predictions of our study in Drosophila embryonic epithelial cells undergoing neighbor exchange during germband extension.