α-Actinin links extracellular matrix rigidity-sensing contractile units with periodic cell-edge retractions.

During spreading and migration, the leading edges of cells undergo periodic protrusion-retraction cycles. The functional purpose of these cycles is unclear. Here, using submicrometer polydimethylsiloxane pillars as substrates for cell spreading, we show that periodic edge retractions coincide with peak forces produced by local contractile units (CUs) that assemble and disassemble along the cell edge to test matrix rigidity. We find that, whereas actin rearward flow produces a relatively constant force inward, the peak of local contractile forces by CUs scales with rigidity. The cytoskeletal protein α-actinin is shared between these two force-producing systems. It initially localizes to the CUs and subsequently moves inward with the actin flow. Knockdown of α-actinin causes aberrant rigidity sensing, loss of CUs, loss of protrusion-retraction cycles, and, surprisingly, enables the cells to proliferate on soft matrices. We present a model based on these results in which local CUs drive rigidity sensing and adhesion formation.

Tropomyosin controls sarcomere-like contractions for rigidity sensing and suppressing growth on soft matrices.

Cells test the rigidity of the extracellular matrix by applying forces to it through integrin adhesions. Recent measurements show that these forces are applied by local micrometre-scale contractions, but how contraction force is regulated by rigidity is unknown. Here we performed high temporal- and spatial-resolution tracking of contractile forces by plating cells on sub-micrometre elastomeric pillars. We found that actomyosin-based sarcomere-like contractile units (CUs) simultaneously moved opposing pillars in net steps of ∼2.5 nm, independent of rigidity. What correlated with rigidity was the number of steps taken to reach a force level that activated recruitment of α-actinin to the CUs. When we removed actomyosin restriction by depleting tropomyosin 2.1, we observed larger steps and higher forces that resulted in aberrant rigidity sensing and growth of non-transformed cells on soft matrices. Thus, we conclude that tropomyosin 2.1 acts as a suppressor of growth on soft matrices by supporting proper rigidity sensing.

Cells test substrate rigidity by local contractions on submicrometer pillars.

Cell growth and differentiation are critically dependent upon matrix rigidity, yet many aspects of the cellular rigidity-sensing mechanism are not understood. Here, we analyze matrix forces after initial cell-matrix contact, when early rigidity-sensing events occur, using a series of elastomeric pillar arrays with dimensions extending to the submicron scale (2, 1, and 0.5 µm in diameter covering a range of stiffnesses). We observe that the cellular response is fundamentally different on micron-scale and submicron pillars. On 2-µm diameter pillars, adhesions form at the pillar periphery, forces are directed toward the center of the cell, and a constant maximum force is applied independent of stiffness. On 0.5-µm diameter pillars, adhesions form on the pillar tops, and local contractions between neighboring pillars are observed with a maximum displacement of ∼60 nm, independent of stiffness. Because mutants in rigidity sensing show no detectable displacement on 0.5-µm diameter pillars, there is a correlation between local contractions to 60 nm and rigidity sensing. Localization of myosin between submicron pillars demonstrates that submicron scale myosin filaments can cause these local contractions. Finally, submicron pillars can capture many details of cellular force generation that are missed on larger pillars and more closely mimic continuous surfaces.

Dynamics of the bacterial flagellar motor: the effects of stator compliance, back steps, temperature, and rotational asymmetry.

The rotation of a bacterial flagellar motor (BFM) is driven by multiple stators tethered to the cell wall. Here, we extend a recently proposed power-stroke model to study the BFM dynamics under different biophysical conditions. Our model explains several key experimental observations and reveals their underlying mechanisms. 1), The observed independence of the speed at low load on the number of stators is explained by a force-dependent stepping mechanism that is independent of the strength of the stator tethering spring. Conversely, without force-dependent stepping, an unrealistically weak stator spring is required. 2), Our model with back-stepping naturally explains the observed absence of a barrier to backward rotation. Using the same set of parameters, it also explains BFM behaviors in the high-speed negative-torque regime. 3), From the measured temperature dependence of the maximum speed, our model shows that stator-stepping is a thermally activated process with an energy barrier. 4), The recently observed asymmetry in the torque-speed curve between counterclockwise- and clockwise-rotating BFMs can be quantitatively explained by the asymmetry in the stator-rotor interaction potentials, i.e., a quasilinear form for the counterclockwise motor and a quadratic form for the clockwise motor.

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.

Dynamics of the bacterial flagellar motor with multiple stators.

The bacterial flagellar motor drives the rotation of flagellar filaments and enables many species of bacteria to swim. Torque is generated by interaction of stator units, anchored to the peptidoglycan cell wall, with the rotor. Recent experiments [Yuan J, Berg HC (2008) Proc Natl Acad Sci USA 105:1182-1185] show that at near-zero load the speed of the motor is independent of the number of stators. Here, we introduce a mathematical model of the motor dynamics that explains this behavior based on a general assumption that the stepping rate of a stator depends on the torque exerted by the stator on the rotor. We find that the motor dynamics can be characterized by two timescales: the moving-time interval for the mechanical rotation of the rotor and the waiting-time interval determined by the chemical transitions of the stators. We show that these two timescales depend differently on the load, and that their cross-over provides the microscopic explanation for the existence of two regimes in the torque-speed curves observed experimentally. We also analyze the speed fluctuation for a single motor by using our model. We show that the motion is smoothed by having more stator units. However, the mechanism for such fluctuation reduction is different depending on the load. We predict that the speed fluctuation is determined by the number of steps per revolution only at low load and is controlled by external noise for high load. Our model can be generalized to study other molecular motor systems with multiple power-generating units.

Min-oscillations in Escherichia coli induced by interactions of membrane-bound proteins.

During division it is of primary importance for a cell to correctly determine the site of cleavage. The bacterium Escherichia coli divides in the center, producing two daughter cells of equal size. Selection of the center as the correct division site is in part achieved by the Min-proteins. They oscillate between the two cell poles and thereby prevent division at these locations. Here, a phenomenological description of these oscillations is presented, where lateral interactions between proteins on the cell membrane play a key role. Solutions to the dynamic equations are compared to experimental findings. In particular, the temporal period of the oscillations is measured as a function of the cell length and found to be compatible with the theoretical prediction.