Motor processivity and speed determine structure and dynamics of microtubule-motor assemblies.

Active matter systems can generate highly ordered structures, avoiding equilibrium through the consumption of energy by individual constituents. How the microscopic parameters that characterize the active agents are translated to the observed mesoscopic properties of the assembly has remained an open question. These active systems are prevalent in living matter; for example, in cells, the cytoskeleton is organized into structures such as the mitotic spindle through the coordinated activity of many motor proteins walking along microtubules. Here, we investigate how the microscopic motor-microtubule interactions affect the coherent structures formed in a reconstituted motor-microtubule system. This question is of deeper evolutionary significance as we suspect motor and microtubule type contribute to the shape and size of resulting structures. We explore key parameters experimentally and theoretically, using a variety of motors with different speeds, processivities, and directionalities. We demonstrate that aster size depends on the motor used to create the aster, and develop a model for the distribution of motors and microtubules in steady-state asters that depends on parameters related to motor speed and processivity. Further, we show that network contraction rates scale linearly with the single-motor speed in quasi-one-dimensional contraction experiments. In all, this theoretical and experimental work helps elucidate how microscopic motor properties are translated to the much larger scale of collective motor-microtubule assemblies.

Controlling organization and forces in active matter through optically defined boundaries.

Living systems are capable of locomotion, reconfiguration and replication. To perform these tasks, cells spatiotemporally coordinate the interactions of force-generating, 'active' molecules that create and manipulate non-equilibrium structures and force fields of up to millimetre length scales1-3. Experimental active-matter systems of biological or synthetic molecules are capable of spontaneously organizing into structures4,5 and generating global flows6-9. However, these experimental systems lack the spatiotemporal control found in cells, limiting their utility for studying non-equilibrium phenomena and bioinspired engineering. Here we uncover non-equilibrium phenomena and principles of boundary-mediated control by optically modulating structures and fluid flow in an engineered system of active biomolecules. Our system consists of purified microtubules and light-activatable motor proteins that crosslink and organize the microtubules into distinct structures upon illumination. We develop basic operations-defined as sets of light patterns-to create, move and merge the microtubule structures. By combining these operations, we create microtubule networks that span several hundred micrometres in length and contract at speeds up to an order of magnitude higher than the speed of an individual motor protein. We manipulate these contractile networks to generate and sculpt persistent fluid flows. The principles of boundary-mediated control that we uncover may be used to study emergent cellular structures and forces and to develop programmable active-matter devices.

Connecting the Dots between Mechanosensitive Channel Abundance, Osmotic Shock, and Survival at Single-Cell Resolution.

Rapid changes in extracellular osmolarity are one of many insults microbial cells face on a daily basis. To protect against such shocks, Escherichia coli and other microbes express several types of transmembrane channels that open and close in response to changes in membrane tension. In E. coli, one of the most abundant channels is the mechanosensitive channel of large conductance (MscL). While this channel has been heavily characterized through structural methods, electrophysiology, and theoretical modeling, our understanding of its physiological role in preventing cell death by alleviating high membrane tension remains tenuous. In this work, we examine the contribution of MscL alone to cell survival after osmotic shock at single-cell resolution using quantitative fluorescence microscopy. We conducted these experiments in an E. coli strain which is lacking all mechanosensitive channel genes save for MscL, whose expression was tuned across 3 orders of magnitude through modifications of the Shine-Dalgarno sequence. While theoretical models suggest that only a few MscL channels would be needed to alleviate even large changes in osmotic pressure, we find that between 500 and 700 channels per cell are needed to convey upwards of 80% survival. This number agrees with the average MscL copy number measured in wild-type E. coli cells through proteomic studies and quantitative Western blotting. Furthermore, we observed zero survival events in cells with fewer than ∼100 channels per cell. This work opens new questions concerning the contribution of other mechanosensitive channels to survival, as well as regulation of their activity.IMPORTANCE Mechanosensitive (MS) channels are transmembrane protein complexes which open and close in response to changes in membrane tension as a result of osmotic shock. Despite extensive biophysical characterization, the contribution of these channels to cell survival remains largely unknown. In this work, we used quantitative video microscopy to measure the abundance of a single species of MS channel in single cells, followed by their survival after a large osmotic shock. We observed total death of the population with fewer than ∼100 channels per cell and determined that approximately 500 to 700 channels were needed for 80% survival. The number of channels we found to confer nearly full survival is consistent with the counts of the numbers of channels in wild-type cells in several earlier studies. These results prompt further studies to dissect the contribution of other channel species to survival.

The rate of osmotic downshock determines the survival probability of bacterial mechanosensitive channel mutants.

Mechanosensitive (MS) channels allow cells to sense and respond to environmental changes. In bacteria, these channels are believed to protect against an osmotic shock. The physiological function of these channels has been characterized primarily by a standardized assay, where aliquots of batch-cultured cells are rapidly pipetted into a hypotonic medium. Under this method, it has been inferred many types of MS channels (MscS homologs in Escherichia coli) demonstrate limited effectiveness against shock, typically rescuing less than 10% of the cells when expressed at native levels. We introduce a single-cell-based assay which allows us to control how fast the osmolarity changes, over time scales ranging from a fraction of a second to several minutes. We find that the protection provided by MS channels depends strongly on the rate of osmotic change, revealing that, under a slow enough osmotic drop, MscS homologs can lead to survival rates comparable to those found in wild-type strains. Further, after the osmotic downshift, we observe multiple death phenotypes, which are inconsistent with the prevailing paradigm of how cells lyse. Both of these findings require a reevaluation of our basic understanding of the physiology of MS channels.

Single-cell census of mechanosensitive channels in living bacteria.

Bacteria are subjected to a host of different environmental stresses. One such insult occurs when cells encounter changes in the osmolarity of the surrounding media resulting in an osmotic shock. In recent years, a great deal has been learned about mechanosensitive (MS) channels which are thought to provide osmoprotection in these circumstances by opening emergency release valves in response to membrane tension. However, even the most elementary physiological parameters such as the number of MS channels per cell, how MS channel expression levels influence the physiological response of the cells, and how this mean number of channels varies from cell to cell remain unanswered. In this paper, we make a detailed quantitative study of the expression of the mechanosensitive channel of large conductance (MscL) in different media and at various stages in the growth history of bacterial cultures. Using both quantitative fluorescence microscopy and quantitative Western blots our study complements earlier electrophysiology-based estimates and results in the following key insights: i) the mean number of channels per cell is much higher than previously estimated, ii) measurement of the single-cell distributions of such channels reveals marked variability from cell to cell and iii) the mean number of channels varies under different environmental conditions. The regulation of MscL expression displays rich behaviors that depend strongly on culturing conditions and stress factors, which may give clues to the physiological role of MscL. The number of stress-induced MscL channels and the associated variability have far reaching implications for the in vivo response of the channels and for modeling of this response. As shown by numerous biophysical models, both the number of such channels and their variability can impact many physiological processes including osmoprotection, channel gating probability, and channel clustering.

Comparison and calibration of different reporters for quantitative analysis of gene expression.

Absolute levels of gene expression in bacteria are observed to vary over as much as six orders of magnitude. Thermodynamic models have been proposed as a tool to describe the expression levels of a given transcriptional circuit. In this context, it is essential to understand both the limitations and linear range of the different methods for measuring gene expression and to determine to what extent measurements from different reporters can be directly compared with one aim being the stringent testing of theoretical descriptions of gene expression. In this article, we compare two protein reporters by measuring both the absolute level of expression and fold-change in expression using the fluorescent protein EYFP and the enzymatic reporter ß-galactosidase. We determine their dynamic and linear range and show that they are interchangeable for measuring mean levels of expression over four orders of magnitude. By calibrating these reporters such that they can be interpreted in terms of absolute molecular counts, we establish limits for their applicability: autofluorescence on the lower end of expression for EYFP (at ∼10 molecules per cell) and interference with cellular growth on the high end for ß-galactosidase (at ∼20,000 molecules per cell). These qualities make the reporters complementary and necessary when trying to experimentally verify the predictions from the theoretical models.

Trajectory approach to two-state kinetics of single particles on sculpted energy landscapes.

We study the trajectories of a single colloidal particle as it hops between two energy wells which are sculpted using optical traps. Whereas the dynamical behaviors of such systems are often treated by master-equation methods that focus on particles as actors, we analyze them instead using a trajectory-based variational method called maximum caliber (MaxCal). We show that the MaxCal strategy accurately predicts the full dynamics that we observe in the experiments: From the observed averages, it predicts second and third moments and covariances, with no free parameters. The covariances are the dynamical equivalents of Maxwell-like equilibrium reciprocal relations and Onsager-like dynamical relations.

Membrane shape as a reporter for applied forces.

Recent advances have enabled 3-dimensional reconstructions of biological structures in vivo, ranging in size and complexity from single proteins to multicellular structures. In particular, tomography and confocal microscopy have been exploited to capture detailed 3-dimensional conformations of membranes in cellular processes ranging from viral budding and organelle maintenance to phagocytosis. Despite the wealth of membrane structures available, there is as yet no generic, quantitative method for their interpretation. We propose that by modeling these observed biomembrane shapes as fluid lipid bilayers in mechanical equilibrium, the externally applied forces as well as the pressure, tension, and spontaneous curvature can be computed directly from the shape alone. To illustrate the potential power of this technique, we apply an axial force with optical tweezers to vesicles and explicitly demonstrate that the applied force is equal to the force computed from the membrane conformation.

Engineering cooperativity in biomotor-protein assemblies.

A biosynthetic approach was developed to control and probe cooperativity in multiunit biomotor assemblies by linking molecular motors to artificial protein scaffolds. This approach provides precise control over spatial and elastic coupling between motors. Cooperative interactions between monomeric kinesin-1 motors attached to protein scaffolds enhance hydrolysis activity and microtubule gliding velocity. However, these interactions are not influenced by changes in the elastic properties of the scaffold, distinguishing multimotor transport from that powered by unorganized monomeric motors. These results highlight the role of supramolecular architecture in determining mechanisms of collective transport.

Behavior of complex knots in single DNA molecules.

We used optical tweezers to tie individual DNA molecules in knots. Although these knots become highly localized under tension, they remain surprisingly mobile and undergo thermal diffusion with classical random walk statistics. The diffusion constants of knots with different complexities correlate with theoretical calculations of knot sizes. We show that this correlation can be explained by a simple hydrodynamical model of "self-reptation" of the knot along a polymer.