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Register a new userThe limits of filopodium stability
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Filopodia are long, finger-like membrane tubes supported by cytoskeletal filaments. Their shape is determined by the stiffness of the actin filament bundles found inside them and by the interplay between the surface tension and bending rigidity of the membrane. Although one might expect the Euler buckling instability to limit the length of filopodia, we show through simple energetic considerations that this is in general not the case. By further analyzing the statics of filaments inside membrane tubes, and through computer simulations that capture membrane and filament fluctuations, we show under which conditions filopodia of arbitrary lengths are stable. We discuss several in vitro experiments where this kind of stability has already been observed. Furthermore, we predict that the filaments in long, stable filopodia adopt a helical shape.
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F1F0 ATP synthase (ATPase) either facilitates the synthesis of ATP in the mitochondrial membranes and bacterial inner membranes in a process driven by the proton moving force (pmf), or uses the energy from ATP hydrolysis to pump protons against the concentration gradient across the membrane. ATPase is composed of two rotary motors, F0 and F1, which generate the opposing rotation and compete for control of their shared central gamma-shaft. Here we present a self-consistent physical model of the F1 motor as a simplified two-state Brownian ratchet based on the asymmetry of torsional elastic energy of the coiled-coil gamma-shaft. This stochastic model unifies the physical description of linear and rotary motors and explains the stepped unidirectional rotation of the $gamma$-shaft, in agreement with the `binding-change ideas of Boyer. Substituting the model parameters, all independently known from recent experiments, our model quantitatively reproduces the ATPase operation, e.g. the `no-load angular velocity is ca. 400~rad/s anticlockwise at 4 mM ATP, in close agreement with experiment. Increasing the pmf torque exerted by F0 can slow, stop and overcome the torque generated by F1, switching from ATP hydrolysis to synthesis at a very low value of `stall torque. We discuss the matters of the motor efficiency, which is very low if calculated from the useful mechanical work it produces - but is quite high when the `useful outcome is measured in the number of H+ pushed against the chemical gradient in the F1 ATP-driven operation.
Vital biological processes such as genome repair require fast and efficient binding of selected proteins to specific target sites on DNA. Here we propose an active target search mechanism based on chromophoresis, the dynamics of DNA-binding proteins up or down gradients in the density of epigenetic marks, or colours (biochemical tags on the genome). We focus on a set of proteins that deposit marks from which they are repelled---a case which is only encountered away from thermodynamic equilibrium. For suitable ranges of kinetic parameter values, chromophoretic proteins can perform unidirectional motion and are optimally redistributed along the genome. Importantly, they can also locally unravel a region of the genome which is collapsed due to self-interactions and dive deep into its core, for a striking enhancement of the efficiency of target search on such an inaccessible substrate. We discuss the potential relevance of chromophoresis for the location of DNA lesions.
Many cellular processes are tightly connected to the dynamics of microtubules (MTs). While in neuronal axons MTs mainly regulate intracellular trafficking, they participate in cytoskeleton reorganization in many other eukaryotic cells, enabling the cell to efficiently adapt to changes in the environment. We show that the functional differences of MTs in different cell types and regions is reflected in the dynamic properties of MT tips. Using plus-end tracking proteins EB1 to monitor growing MT plus-ends, we show that MT dynamics and life cycle in axons of human neurons significantly differ from that of fibroblast cells. The density of plus-ends, as well as the rescue and catastrophe frequencies increase while the growth rate decreases toward the fibroblast cell margin. This results in a rather stable filamentous network structure and maintains the connection between nucleus and membrane. In contrast, plus-ends are uniformly distributed along the axons and exhibit diverse polymerization run times and spatially homogeneous rescue and catastrophe frequencies, leading to MT segments of various lengths. The probability distributions of the excursion length of polymerization and the MT length both follow nearly exponential tails, in agreement with the analytical predictions of a two-state model of MT dynamics.
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 pathway. 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.
Actin cytoskeletal protrusions in crawling cells, or lamellipodia, exhibit various morphological properties such as two characteristic peaks in the distribution of filament orientation with respect to the leading edge. To understand these properties, using the dendritic nucleation model as a basis for cytoskeletal restructuring, a kinetic-population model with orientational-dependent branching (birth) and capping (death) is constructed and analyzed. Optimizing for growth yields a relation between the branch angle and filament orientation that explains the two characteristic peaks. The model also exhibits a subdominant population that allows for more accurate modeling of recent measurements of filamentous actin density along the leading edge of lamellipodia in keratocytes. Finally, we explore the relationship between orientational and spatial organization of filamentous actin in lamellipodia and address recent observations of a prevalence of overlapping filaments to branched filaments---a finding that is claimed to be in contradiction with the dendritic nucleation model.
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