Cellular structures are established and maintained through a dynamic interplay between assembly and regulatory processes. Self-organization of molecular components provides a variety of possible spatial structures: the regulatory machinery chooses the most appropriate to express a given cellular function. Here we study the extent and the characteristics of self-organization using microtubules and molecular motors as a model system. These components are known to participate in the formation of many cellular structures, such as the dynamic asters found in mitotic and meiotic spindles. Purified motors and microtubules have previously been observed to form asters in vitro. We have reproduced this result with a simple system consisting solely of multi-headed constructs of the motor protein kinesin and stabilized microtubules. We show that dynamic asters can also be obtained from a homogeneous solution of tubulin and motors. By varying the relative concentrations of the components, we obtain a variety of self-organized structures. Further, by studying this process in a constrained geometry of micro-fabricated glass chambers, we demonstrate that the same final structure can be reached through different assembly 'pathways.

Single actin filaments undergoing brownian movement in two dimensions were observed at 20 degrees C in fluorescence optical video microscopy. The persistence length (Lp) was derived from the analysis of either the cosine correlation function or the average transverse fluctuations of a series of recorded shapes of filaments assembled from rhodamine-action. Phalloidin-stabilized filaments had a persistence length of 18 +/- 1 micron, in agreement with recent observations. In the absence of phalloidin, rhodamine-labeled filaments could be observed under a variety of solution conditions once diluted in free unlabeled G-actin at the appropriate critical concentration. Such nonstabilized F-ADP-actin filaments had the same Lp of 9 +/- 0.5 microns, whether they had been assembled from ATP-G-actin or from ADP-G-actin, and independently of the tightly bound divalent metal ion. In the presence of BeF3-, which mimics the gamma-phosphate of ATP, F-ADP-BeF3-actin was appreciably more rigid, with Lp = 13.5 microns. Hence, newly formed F-ADP-Pi-actin filaments are more rigid than "old" F-ADP-actin filaments, a fact which has implications in actin-based motility processes. In the presence of skeletal tropomyosin and troponin, filaments were rigid (Lp = 20 +/- 1 micron) in the off state (-Ca2+), and flexible (Lp = 12 microns) in the on state (+Ca2+), consistent with the steric blocking model. In agreement with x-ray diffraction data, no appreciable difference was recorded between the off and on states using smooth muscle tropomyosin and caldesmon (Lp = 20 +/- 1 micron). In conclusion, this method allows accurate measurement of small (< or = 15%) changes in mechanical properties of actin filaments in correlation with their biological functions.

We use magnetic tweezers to study local viscoelastic response in filamentous actin networks. The choice of magnetic, colloidal particles of varying size allows us to explore properties on the relevant micron and submicron scales. At these scales the mechanical response is determined by the bending properties of individual filaments and described by an anomalous power-law behavior. In the absence of external forces the particles exhibit a subdiffusive motion. [S0031-9007(96)01627-4] Complex molecular systems, such as polymer solutions, polymer melts, gels, (micro)emulsions, and foams, often display a combination of the elastic properties of solids and the viscous properties of fluids. Using classical rheological methods [1], the viscoelastic properties of such materials have been described at scales much larger than the molecular dimensions, and the systems under study have mostly been treated as homogeneous media. In many situations, however, local mechanical properties are of critical importance. For instance, the shape and motility of living cells, as well as cytoplasmic transport, are strongly influenced by the mechanical properties of cytoskeleton networks [2] at submicron and micron scales.Actin filaments ( f-actin), formed upon polymerization of globular actin proteins, are major components of the cytoskeleton and are involved in both transport and motility [3]. Easily purified and polymerized in vitro, actin is a model system for the study of the mechanics and assembly of biopolymers [4,5]. In this paper we show, using the example of actin filaments, how micromechanical measurements can provide information about local viscoelastic properties of the medium.f-actin is a rigid polymer with a persistence length L p of the order of 15 mm [6]. At high enough concentrations, in the so-called semidilute regime, the polymers form a three-dimensional network with a mesh size L. L is typically of the order of a micron and thus much smaller than L p . Viscoelastic properties of this inhomogeneous medium can be locally studied by inserting colloidal magnetic beads and perturbing them with external magnetic forces. In fact, such simple methods have been used for many years to explore the cytoplasm [7]. For beads with diameter, d, much larger than L, the mechanical perturbation is macroscopic. On the other hand, if d is much smaller than the mesh size, the bead is expected to probe only the solvent viscosity and geometrical constraints introduced by polymers. Therefore, the regime that is relevant for exploring the local network mechanics is one for which d is comparable to L. In this case, the bead is moving inside a "cage" of typical linear size L. To move further, it has to perturb the polymers of the cage, either through the influence of an external force or via thermal fluctuations. In both cases, one can study the viscoelastic properties on micron scales by observing the motion of individual beads. We show below that this approach can be made quantitative, and that local mechanical properties of the network can be...

We describe the dynamic behavior of semidilute solutions of actin filaments (a semiflexible polymer), pointing out some of the rheological regimes present in this biologically important system. We deduce the macroscopic storage modulus and show that over a certain frequency range semiflexible polymers show a novel variation in the shear modulus; the mechanism should be distinguished from Rouse behavior in solutions of flexible polymers.

We study first-order quantum phase transitions in models where the mean-field traitment is exact, and the exponentially fast closure of the energy gap with the system size at the transition. We consider exactly solvable ferromagnetic models, and show that they reduce to the Grover problem in a particular limit. We compute the coefficient in the exponential closure of the gap using an instantonic approach, and discuss the (dire) consequences for quantum annealing.