Load Adaptation of Lamellipodial Actin Networks.

Actin filaments polymerizing against membranes power endocytosis, vesicular traffic, and cell motility. In vitro reconstitution studies suggest that the structure and the dynamics of actin networks respond to mechanical forces. We demonstrate that lamellipodial actin of migrating cells responds to mechanical load when membrane tension is modulated. In a steady state, migrating cell filaments assume the canonical dendritic geometry, defined by Arp2/3-generated 70° branch points. Increased tension triggers a dense network with a broadened range of angles, whereas decreased tension causes a shift to a sparse configuration dominated by filaments growing perpendicularly to the plasma membrane. We show that these responses emerge from the geometry of branched actin: when load per filament decreases, elongation speed increases and perpendicular filaments gradually outcompete others because they polymerize the shortest distance to the membrane, where they are protected from capping. This network-intrinsic geometrical adaptation mechanism tunes protrusive force in response to mechanical load.

The effect of motor-induced shaft dynamics on microtubule stability and length.

Control of microtubule abundance, stability, and length is crucial to regulate intracellular transport as well as cell polarity and division. How microtubule stability depends on tubulin addition or removal at the dynamic ends is well studied. However, microtubule rescue, the event when a microtubule switches from shrinking to growing, occurs at tubulin exchange sites along the shaft. Molecular motors have recently been shown to promote such exchanges. Using a stochastic theoretical description, we study how microtubule stability and length depend on motor-induced tubulin exchange and thus rescue. Our theoretical description matches our in vitro experiments on microtubule dynamics in the presence of kinesin-1 molecular motors. Although the overall dynamics of a population of microtubules can be captured by an effective rescue rate, by assigning rescue to exchange sites, we reveal that the dynamics of individual microtubules within the population differ dramatically. Furthermore, we study in detail a transition from bounded to unbounded microtubule growth. Our results provide novel insights into how molecular motors imprint information of microtubule stability on the microtubule network.

Integer topological defects organize stresses driving tissue morphogenesis.

Tissues acquire function and shape via differentiation and morphogenesis. Both processes are driven by coordinating cellular forces and shapes at the tissue scale, but general principles governing this interplay remain to be discovered. Here we report that self-organization of myoblasts around integer topological defects, namely spirals and asters, suffices to establish complex multicellular architectures. In particular, these arrangements can trigger localized cell differentiation or, alternatively, when differentiation is inhibited, they can drive the growth of swirling protrusions. Both localized differentiation and growth of cellular vortices require specific stress patterns. By analysing the experimental velocity and orientational fields through active gel theory, we show that integer topological defects can generate force gradients that concentrate compressive stresses. We reveal these gradients by assessing spatial changes in nuclear volume and deformations of elastic pillars. We propose integer topological defects as mechanical organizing centres controlling differentiation and morphogenesis.

Calcium storage in multivesicular endo-lysosome.

It is now established that endo-lysosomes, also referred to as late endosomes, serve as intracellular calcium store, in addition to the endoplasmic reticulum. While abundant calcium-binding proteins provide the latter compartment with its calcium storage capacity, essentially nothing is known about the mechanism responsible for calcium storage in endo-lysosomes. In this paper, we propose that the structural organization of endo-lysosomal membranes drives the calcium storage capacity of the compartment. Indeed, endo-lysosomes exhibit a characteristic multivesicular ultrastructure, with intralumenal membranes providing a large amount of additional bilayer surface. We used a theoretical approach to investigate the calcium storage capacity of endosomes, using known calcium binding affinities for bilayers and morphological data on endo-lysosome membrane organization. Finally, we tested our predictions experimentally after Sorting Nexin 3 depletion to decrease the intralumenal membrane content. We conclude that the major negatively-charge lipids and proteins of endo-lysosomes serve as calcium-binding molecules in the acidic calcium stores of mammalian cells, while the large surface area of intralumenal membranes provide the necessary storage capacity.

Selection for Size in Molecular Self-Assembly Drives the De Novo Evolution of a Molecular Machine.

The functioning of machines typically requires a concerted action of their parts. This requirement also holds for molecular motors that drive vital cellular processes and imposes constraints on their conformational changes as well as the rates at which they occur. It remains unclear whether, during evolution, features required for functional molecular machines can emerge simultaneously or require sequential adaptation to different selection pressures. We address this question by theoretically analyzing the evolution of filament treadmilling. This process refers to the self-assembly of linear polymers that grow and shrink at equal rates at their opposite ends. It constitutes a simple biological molecular machine that is involved in bacterial cell division and requires that several conditions are met. In our simulation framework, treadmilling emerges as a consequence of selecting for a target average polymer length. We discuss why other forms of assembly dynamics, which also reach the imposed target length, do not emerge in our simulations. Our work shows that complex molecular functions can evolve de novo under selection for a single physical feature.

Localized States in Active Fluids.

Biological active matter is typically tightly coupled to chemical reaction networks affecting its assembly-disassembly dynamics and stress generation. We show that localized states can emerge spontaneously if assembly of active matter is regulated by chemical species that are advected with flows resulting from gradients in the active stress. The mechanochemical localized patterns form via a subcritical bifurcation and for parameter values for which patterns do not exist in absence of the advective coupling. Our work identifies a generic mechanism underlying localized cellular patterns.

Density-Polarity Coupling in Confined Active Polar Films: Asters, Spirals, and Biphasic Orientational Phases.

Topological defects in active polar fluids can organize spontaneous flows and influence macroscopic density patterns. Both of them play an important role during animal development. Yet the influence of density on active flows is poorly understood. Motivated by experiments on cell monolayers confined to disks, we study the coupling between density and polar order for a compressible active polar fluid in the presence of a +1 topological defect. As in the experiments, we find a density-controlled spiral-to-aster transition. In addition, biphasic orientational phases emerge as a generic outcome of such coupling. Our results highlight the importance of density gradients as a potential mechanism for controlling flow and orientational patterns in biological systems.

Deterministic actin waves as generators of cell polarization cues.

Dendritic cells "patrol" the human body to detect pathogens. In their search, dendritic cells perform a random walk by amoeboid migration. The efficiency of pathogen detection depends on the properties of the random walk. It is not known how the dendritic cells control these properties. Here, we quantify dendritic cell migration under well-defined 2-dimensional confinement and in a 3-dimensional collagen matrix through recording their long-term trajectories. We find 2 different migration states: persistent migration, during which the dendritic cells move along curved paths, and diffusive migration, which is characterized by successive sharp turns. These states exhibit differences in the actin distributions. Our theoretical and experimental analyses indicate that this kind of motion can be generated by spontaneous actin polymerization waves that contribute to dendritic cell polarization and migration. The relative distributions of persistent and diffusive migration can be changed by modification of the molecular actin filament nucleation and assembly rates. Thus, dendritic cells can control their migration patterns and adapt to specific environments. Our study offers an additional perspective on how dendritic cells tune their searches for pathogens.

Quantifying Material Properties of Cell Monolayers by Analyzing Integer Topological Defects.

In developing organisms, internal cellular processes generate mechanical stresses at the tissue scale. The resulting deformations depend on the material properties of the tissue, which can exhibit long-ranged orientational order and topological defects. It remains a challenge to determine these properties on the time scales relevant for developmental processes. Here, we build on the physics of liquid crystals to determine material parameters of cell monolayers. Specifically, we use a hydrodynamic description to characterize the stationary states of compressible active polar fluids around defects. We illustrate our approach by analyzing monolayers of C2C12 cells in small circular confinements, where they form a single topological defect with integer charge. We find that such monolayers exert compressive stresses at the defect centers, where localized cell differentiation and formation of three-dimensional shapes is observed.

FtsZ filaments have the opposite kinetic polarity of microtubules.

FtsZ is the ancestral homolog of tubulin and assembles into the Z ring that organizes the division machinery to drive cell division in most bacteria. In contrast to tubulin that assembles into 13 stranded microtubules that undergo dynamic instability, FtsZ assembles into single-stranded filaments that treadmill to distribute the peptidoglycan synthetic machinery at the septum. Here, using longitudinal interface mutants of FtsZ, we demonstrate that the kinetic polarity of FtsZ filaments is opposite to that of microtubules. A conformational switch accompanying the assembly of FtsZ generates the kinetic polarity of FtsZ filaments, which explains the toxicity of interface mutants that function as a capper and reveals the mechanism of cooperative assembly. This approach can also be employed to determine the kinetic polarity of other filament-forming proteins.

Positional Information Readout in Ca

Living cells respond to spatially confined signals. Intracellular signal transmission often involves the release of second messengers like Ca^{2+}. They eventually trigger a physiological response, for example, by activating kinases that in turn activate target proteins through phosphorylation. Here, we investigate theoretically how positional information can be accurately read out by protein phosphorylation in spite of rapid second messenger diffusion. We find that accuracy is increased by binding of kinases to the cell membrane prior to phosphorylation and by increasing the rate of Ca^{2+} loss from the cell interior. These findings could explain some salient features of the conventional protein kinase Cα.

A calcium optimum for cytotoxic T lymphocyte and natural killer cell cytotoxicity.

KEY POINTS: Cytotoxic T lymphocytes (CTLs) and natural killer (NK) cells are required to eliminate cancer cells. We analysed the Ca2+ dependence of CTL and NK cell cytotoxicity and found that in particular CTLs have a very low optimum of [Ca2+ ]i (between 122 and 334 nm) and [Ca2+ ]o (between 23 and 625 µm) for efficient cancer cell elimination, well below blood plasma Ca2+ levels. As predicted from these results, partial down-regulation of the Ca2+ channel Orai1 in CTLs paradoxically increases perforin-dependent cancer cell killing. Lytic granule release at the immune synapse between CTLs and cancer cells has a Ca2+ optimum compatible with this low Ca2+ optimum for efficient cancer cell killing, whereas the Ca2+ optimum for CTL migration is slightly higher and proliferation increases monotonously with increasing [Ca2+ ]o . We propose that a partial inhibition of Ca2+ signals by specific Orai1 blockers at submaximal concentrations could contribute to tumour elimination. ABSTRACT: Cytotoxic T lymphocytes (CTLs) and natural killer (NK) cells are required to protect the human body against cancer. Ca2+ is a key metabolic factor for lymphocyte function and cancer homeostasis. We analysed the Ca2+ dependence of CTL and NK cell cytotoxicity against cancer cells and found that CTLs have a bell-shaped Ca2+ dependence with an optimum for cancer cell elimination at rather low [Ca2+ ]o (23-625 µm) and [Ca2+ ]i (122-334 nm). This finding predicts that a partial inhibition of Orai1 should increase (rather than decrease) cytotoxicity of CTLs at [Ca2+ ]o higher than 625 µm. We tested this hypothesis in CTLs and indeed found that partial down-regulation of Orai1 by siRNA increases the efficiency of cancer cell killing. We found two mechanisms that may account for the Ca2+ optimum of cancer cell killing: (1) migration velocity and persistence have a moderate optimum between 500 and 1000 µm [Ca2+ ]o in CTLs, and (2) lytic granule release at the immune synapse between CTLs and cancer cells is increased at 146 µm compared to 3 or 800 µm, compatible with the Ca2+ optimum for cancer cell killing. It has been demonstrated in many cancer cell types that Orai1-dependent Ca2+ signals enhance proliferation. We propose that a decrease of [Ca2+ ]o or partial inhibition of Orai1 activity by selective blockers in the tumour microenvironment could efficiently reduce cancer growth by simultaneously increasing CTL and NK cell cytotoxicity and decreasing cancer cell proliferation.

Geometry sensing by self-organized protein patterns.

In the living cell, proteins are able to organize space much larger than their dimensions. In return, changes of intracellular space can influence biochemical reactions, allowing cells to sense their size and shape. Despite the possibility to reconstitute protein self-organization with only a few purified components, we still lack knowledge of how geometrical boundaries affect spatiotemporal protein patterns. Following a minimal systems approach, we used purified proteins and photolithographically patterned membranes to study the influence of spatial confinement on the self-organization of the Min system, a spatial regulator of bacterial cytokinesis, in vitro. We found that the emerging protein pattern responds even to the lateral, two-dimensional geometry of the membrane such that, as in the three-dimensional cell, Min protein waves travel along the longest axis of the membrane patch. This shows that for spatial sensing the Min system does not need to be enclosed in a three-dimensional compartment. Using a computational model we quantitatively analyzed our experimental findings and identified persistent binding of MinE to the membrane as requirement for the Min system to sense geometry. Our results give insight into the interplay between geometrical confinement and biochemical patterns emerging from a nonlinear reaction-diffusion system.

Membrane binding of MinE allows for a comprehensive description of Min-protein pattern formation.

The rod-shaped bacterium Escherichia coli selects the cell center as site of division with the help of the proteins MinC, MinD, and MinE. This protein system collectively oscillates between the two cell poles by alternately binding to the membrane in one of the two cell halves. This dynamic behavior, which emerges from the interaction of the ATPase MinD and its activator MinE on the cell membrane, has become a paradigm for protein self-organization. Recently, it has been found that not only the binding of MinD to the membrane, but also interactions of MinE with the membrane contribute to Min-protein self-organization. Here, we show that by accounting for this finding in a computational model, we can comprehensively describe all observed Min-protein patterns in vivo and in vitro. Furthermore, by varying the system's geometry, our computations predict patterns that have not yet been reported. We confirm these predictions experimentally.

Continuum descriptions of cytoskeletal dynamics.

This tutorial presents an introduction into continuum descriptions of cytoskeletal dynamics. In contrast to discrete models in which each molecule keeps its identity, such descriptions are given in terms of averaged quantities per unit volume like the number density of a certain molecule. Starting with a discrete description for the assembly dynamics of cytoskeletal filaments, we derive the continuity equation, which serves as the basis of many continuum theories. We illustrate the use of this approach with an investigation of spontaneous cytoskeletal polymerization waves. Such waves have by now been observed in various cell types and might help to orchestrate cytoskeletal dynamics during cell spreading and locomotion. Our analysis shows how processes at the scale of single molecules, namely, the nucleation of new filaments and filament treadmilling, can lead to the spontaneous appearance of coherent traveling waves on scales spanning many filament lengths. For readers less familiar with calculus, we include an informal introduction to the Taylor expansion.

Intra- and intercellular fluctuations in Min-protein dynamics decrease with cell length.

Self-organization of proteins in space and time is of crucial importance for the functioning of cellular processes. Often, this organization takes place in the presence of strong random fluctuations due to the small number of molecules involved. We report on stochastic switching of the Min-protein distributions between the two cell halves in short Escherichia coli cells. A computational model provides strong evidence that the macroscopic switching is rooted in microscopic noise on the molecular scale. In longer bacteria, the switching turns into regular oscillations that are required for positioning of the division plane. As the pattern becomes more regular, cell-to-cell variability also lessens, indicating cell length-dependent regulation of Min-protein activity.

The immunological synapse controls local and global calcium signals in T lymphocytes.

Cell polarization is a key feature of T-cell function. The immunological synapse (IS) between T cells and antigen-presenting cells is a beautiful example of how polarization of cells is used to guide cell function. Receptors, signal transducers, the cytoskeleton, and organelles are enriched at or depleted from the IS after its formation, and in many cases these re-localizations have already been linked with certain T-cell functions. One key step for T-cell activation is a rise in the cytoplasmic calcium concentration. Whereas it is undisputed that the IS initiates and controls calcium signals in T cells, very little is known about the role of T-cell polarization for calcium signals and calcium-dependent signal transduction. We briefly summarize the basic commonly agreed principles of IS-dependent calcium signal generation but then focus on the less well understood influence of polarization on calcium signals. The discussion of the role of polarization for calcium signals leads to a model how the IS controls local and global calcium signals and calcium-dependent T-cell functions. We develop a theoretical formalism based on existing spatiotemporal calcium dynamic simulations to better understand the model in the future and allow further predictions which can be tested by fast, high resolution live-cell microscopy.

Phase separation on surfaces in the presence of matter exchange.

We present a field theory to describe the composition of a surface spontaneously exchanging matter with its bulk environment. By only assuming matter conservation in the system, we show with extensive numerical simulations that, depending on the matter exchange rates, a complex patterned composition distribution emerges on the surface. For one-dimensional systems we show analytically and numerically that coarsening is arrested and as a consequence domains have a characteristic length scale. Our results show that the causes of heterogeneous lipid composition in cellular membranes may be justified in simple physical terms.

Length regulation of active biopolymers by molecular motors.

For biopolymers like cytoskeletal actin filaments and microtubules, assembly and disassembly are inherently dissipative processes. Molecular motors can affect the rates of subunit removal at filament ends. We introduce a driven lattice-gas model to study the effects of motor-induced depolymerization on the length of active biopolymers and find that increasing motor activity sharpens unimodal steady-state length distributions. Furthermore, for sufficiently fast moving motors, the relative width of the length distribution is determined only by the attachment rate of motors. Our results show how established molecular processes can be used to robustly regulate the size of cytoskeletal structures like mitotic spindles.