Magnetic dimer at a surface: Influence of gravity and external magnetic fields.

The interaction of two dipolar hard spheres near a surface and under the influence of gravity and external perpendicular magnetic fields is investigated theoretically. The full ground-state phase diagram as a function of gravity and magnetic field strengths is established. A dimer (i.e., two touching beads) can only exist when the gravity and magnetic field strengths are simultaneously not too large. Thereby, upon increasing the magnetic field strength, three dimeric states emerge: a lying state (dimer axis parallel to the substrate), an inclined state (intermediate state between the lying and standing ones) and a standing state (dimer axis normal to the substrate). It is found that the orientation angles of the dimer axis and the dipole moment in the newly discovered inclined phase are related by a strikingly simple Snell-Descartes-like law. We argue that our findings can be experimentally verified in colloidal and granular systems.

Helical Superstructure of Intermediate Filaments.

Intermediate filaments are the least explored among the large cytoskeletal elements. We show here that they display conformational anomalies in narrow microfluidic channels. Their unusual behavior can be understood as the consequence of a previously undetected, large-scale helically curved superstructure. Confinement in a channel orders the otherwise soft, strongly fluctuating helical filaments and enhances their structural correlations, giving rise to experimentally detectable, strongly oscillating tangent correlation functions. We propose an explanation for the detected intrinsic curving phenomenon-an elastic shape instability that we call autocoiling. The mechanism involves self-induced filament buckling via a surface stress located at the outside of the cross section. The results agree with ultrastructural findings and rationalize for the commonly observed looped intermediate filament shapes. Beyond curvature, explaining the molecular origin of the detected helical torsion remains an interesting challenge.

How bio-filaments twist membranes.

We study the deformations of a fluid membrane imposed by adhering stiff bio-filaments due to the torques they apply. In the limit of small deformations, we derive a general expression for the energy and the deformation field of the membrane. This expression is specialised to different important cases including closed and helical bio-filaments. In particular, we analyse interface-mediated interactions and membrane wrapping when the filaments apply a local torque distribution on a tubular membrane.

Squeezed helical elastica.

We theoretically study the conformations of a helical semi-flexible filament confined to a flat surface. This squeezed helix exhibits a variety of unexpected shapes resembling circles, waves or spirals depending on the material parameters. We explore the conformation space in detail and show that the shapes can be understood as the mutual elastic interaction of conformational quasi-particles. Our theoretical results are potentially useful to determine the material parameters of such helical filaments in an experimental setting.

Why microtubules run in circles: mechanical hysteresis of the tubulin lattice.

The fate of every eukaryotic cell subtly relies on the exceptional mechanical properties of microtubules. Despite significant efforts, understanding their unusual mechanics remains elusive. One persistent, unresolved mystery is the formation of long-lived arcs and rings, e.g., in kinesin-driven gliding assays. To elucidate their physical origin we develop a model of the inner workings of the microtubule's lattice, based on recent experimental evidence for a conformational switch of the tubulin dimer. We show that the microtubule lattice itself coexists in discrete polymorphic states. Metastable curved states can be induced via a mechanical hysteresis involving torques and forces typical of few molecular motors acting in unison, in agreement with the observations.

A nonequilibrium power balance relation for analyzing dissipative filament dynamics.

Biofilaments like F-actin or microtubules, as well as cilia, flagella, or filament bundles, are often deformed by distributed and time-dependent external forces. It is highly desirable to characterize these filaments' mechanics in an efficient way, either using a single experiment or a high throughput method. We here propose a dynamic power balance approach to study nonequilibrium filament dynamics and exemplify it both experimentally and theoretically by applying it to microtubule gliding assay dynamics. Its usefulness is highlighted by the experimental determination of the lateral friction coefficient for microtubules on kinesins. In contrast to what is usually assumed, friction is anisotropic, in a similar fashion as hydrodynamic friction. We also exemplify, by considering a microtubule buckling event, that if at least one parameter is known in advance, all other parameters can be determined by analyzing a single time-dependent experiment.

Confotronic dynamics of tubular filaments.

Tubular lattices are ubiquitous in nature and technology. Microtubules and nanotubes of all kinds act as important pillars of biological cells and the man-made nano-world. We show that when prestress is introduced in such structures, localized conformational quasiparticles emerge and govern the collective shape dynamics of the lattice. When coupled via cooperative interactions these quasiparticles form larger-scale quasipolymer superstructures exhibiting collective dynamic modes and giving rise to a hallmark behavior radically different from semiflexible beams.

Cooperative lattice dynamics and anomalous fluctuations of microtubules.

Microtubules have been in the focus of biophysical research for several decades. However, the confusing and mutually contradictory results regarding their elasticity and fluctuations have cast doubt on their present understanding. In this paper, we present the empirical evidence for the existence of discrete guanosine diphosphate (GDP)-tubulin fluctuations between a curved and a straight configuration at room temperature as well as for conformational tubulin cooperativity. Guided by a number of experimental findings, we build the case for a novel microtubule model, with the principal result that microtubules can spontaneously form micron-sized cooperative helical states with unique elastic and dynamic features. The polymorphic dynamics of the microtubule lattice resulting from the tubulin bistability quantitatively explains several experimental puzzles, including anomalous scaling of dynamic fluctuations of grafted microtubules, their apparent length-stiffness relation, and their remarkable curved-helical appearance in general. We point out that the multistability and cooperative switching of tubulin dimers could participate in important cellular processes, and could in particular lead to efficient mechanochemical signaling along single microtubules.

Tubulin bistability and polymorphic dynamics of microtubules.

Based on the hypothesis that the GDP-tubulin dimer is a conformationally bistable molecule-rapidly fluctuating between a discrete curved and a straight state-we develop a model for polymorphic dynamics of the microtubule lattice. We show that GDP-tubulin bistability consistently explains unusual dynamic fluctuations, the apparent length-stiffness relation of grafted taxol-stabilized microtubules, and the curved-helical appearance of microtubules in general. When clamped by one end the microtubules undergo an unusual zero energy motion-in its effect reminiscent of a limited rotational hinge. We conclude that microtubules exist in highly cooperative energy-degenerate helical states and discuss possible implications in vivo.

MAP6 is an intraluminal protein that induces neuronal microtubules to coil.

Neuronal activities depend heavily on microtubules, which shape neuronal processes and transport myriad molecules within them. Although constantly remodeled through growth and shrinkage events, neuronal microtubules must be sufficiently stable to maintain nervous system wiring. This stability is somehow maintained by various microtubule-associated proteins (MAPs), but little is known about how these proteins work. Here, we show that MAP6, previously known to confer cold stability to microtubules, promotes growth. More unexpectedly, MAP6 localizes in the lumen of microtubules, induces the microtubules to coil into a left-handed helix, and forms apertures in the lattice, likely to relieve mechanical stress. These features have not been seen in microtubules before and could play roles in maintaining axonal width or providing flexibility in the face of compressive forces during development.

Equation of state of looped DNA.

We derive the equation of state of DNA under tension that features a loop. Such loops occur transiently during DNA condensation in the presence of multivalent ions or permanently through sliding protein linkers such as condensin. The force-extension relation of such looped-DNA modeled as a wormlike chain is calculated via path integration in the semiclassical limit. This allows us to rigorously determine the high stretching asymptotics. Notably the functional form of the force-extension curve resembles that of straight DNA, yet with a strongly renormalized apparent persistence length. We also present analogous results for DNA under tension with several protein-induced kinks and/or loops. That means that the experimentally extracted single-molecule elasticity does not necessarily only reflect the bare DNA stiffness, but can also contain additional contributions that depend on the overall chain conformation and length.

Buckling of stiff polymers: influence of thermal fluctuations.

The buckling of biopolymers is a frequently studied phenomenon The influence of thermal fluctuations on the buckling transition is, however, often ignored and not completely understood. A quantitative theory of the buckling of a wormlike chain based on a semiclassical approximation of the partition function is presented. The contribution of thermal fluctuations to the force-extension relation that allows one to go beyond the classical Euler buckling is derived in the linear and nonlinear regimes as well. It is shown that the thermal fluctuations in the nonlinear buckling regime increase the end-to-end distance of the semiflexible rod if it is confined to two dimensions as opposed to the three-dimensional case. The transition to a buckled state softens at finite temperature. We derive the scaling behavior of the transition shift with increasing ratio of contour length versus persistence length.

Semiflexible Chains at Surfaces: Worm-Like Chains and beyond.

We give an extended review of recent numerical and analytical studies on semiflexible chains near surfaces undertaken at Institut Charles Sadron (sometimes in collaboration) with a focus on static properties. The statistical physics of thin confined layers, strict two-dimensional (2D) layers and adsorption layers (both at equilibrium with the dilute bath and from irreversible chemisorption) are discussed for the well-known worm-like-chain (WLC) model. There is mounting evidence that biofilaments (except stable d-DNA) are not fully described by the WLC model. A number of augmented models, like the (super) helical WLC model, the polymorphic model of microtubules (MT) and a model with (strongly) nonlinear flexural elasticity are presented, and some aspects of their surface behavior are analyzed. In many cases, we use approaches different from those in our previous work, give additional results and try to adopt a more general point of view with the hope to shed some light on this complex field.

Free-energy formalism for particle adsorption.

The equilibrium properties of particle adsorption is investigated theoretically. The model relies on a free-energy formulation which allows us to generalize the Maxwell-Boltzmann description to solutions for which the bulk volume fraction of potentially adsorbed particles is very high. As an application we consider the equilibrium physical adsorption of neutral and charged particles from solution onto two parallel adsorbing surfaces.

Apparent persistence length renormalization of bent DNA.

We derive the single molecule equation of state (force-extension relation) for DNA molecules bearing sliding loops and deflection defects. Analytical results are obtained in the large force limit by employing an analogy with instantons in quantum mechanical tunneling problems. The results reveal a remarkable feature of sliding loops--an apparent strong reduction of the persistence length. We generalize these results to several other experimentally interesting situations ranging from rigid DNA-protein loops to the problem of anchoring deflections in atomic force microscopy stretching of semiflexible polymers. Expressions relating the force-extension measurements to the underlying loop or boundary deflection geometry are provided and applied to the case of the gal repressor dimer protein. The theoretical predictions are complemented and quantitatively confirmed by molecular dynamics simulations.

Solvable model for polymorphic dynamics of biofilaments.

We investigate an analytically tractable toy model for thermally induced polymorphic dynamics of cooperatively rearranging biofilaments-like microtubules. The proposed four-block model, which can be seen as a coarse-grained approximation of the full polymorphic tube model, permits a complete analytical treatment of all thermodynamic properties including correlation functions and angular Fourier mode distributions. Due to its mathematical tractability the model straightforwardly leads to some physical insights in recently discussed phenomena like the "length dependent persistence length." We show that a polymorphic filament can disguise itself as a classical worm-like chain on small and on large scales and yet display distinct anomalous tell-tale features indicating an inner switching dynamics on intermediate length scales.

Interface-mediated interactions: entropic forces of curved membranes.

Particles embedded in a fluctuating interface experience forces and torques mediated by the deformations and by the thermal fluctuations of the medium. Considering a system of two cylinders bound to a fluid membrane, we show that the entropic contribution enhances the curvature-mediated repulsion between the two cylinders. This is contrary to the usual attractive Casimir force in the absence of curvature-mediated interactions. For a large distance between the cylinders, we retrieve the renormalization of the surface tension of a flat membrane due to thermal fluctuations.

Motor driven microtubule shape fluctuations: force from within the lattice.

We develop a general theory of microtubule (MT) deformations by molecular motors generating internal force doublets within the MT lattice. We describe two basic internal excitations, the S and V shape, and compare them with experimental observations from literature. We explain the special role of tubulin vacancies and the dramatic deformation amplifying effect observed for katanin acting at positions of defects. Experimentally observed shapes are used to determine the ratio of MT stretch and shear moduli (approximately 6 x 10(5)) and to estimate the forces induced in the MT lattice by katanin (10's of pN). We conclude that molecular motors if acting cooperatively can "animate" MTs from within the lattice and induce slack even without cross bridging to other structures, a scenario very much reminiscent of the motor driven axoneme.