Biomedical subjects

L Mahadevan

Publications and source records attributed to L Mahadevan.

At least 37 records · Page 2Linked to original sources

PubMed2005

Measuring the work of adhesion between a soft confined film and a flexible plate.

We present a theoretical and experimental study of a method for the determination of the adhesion strength between a thin elastomeric film bonded to a rigid substrate and a flexible plate in a geometry common in the peel test. In particular, we characterize the work of adhesion in terms of the length of an equilibrium crack, generated by a spacer of known thickness wedged between the flexible plate and adhesive film, and the elastic and geometric properties of the film and the plate. We treat both the limit of perfect bonding and that of perfect slippage at the interface of the adhesive film and the flexible plate. A series of experiments allow us to verify the theory quantitatively and thus validate our method, which ought to be of value in many technological situations.

Journal Article↗

PubMed2005

Fluid-flow-induced flutter of a flag.

We give an explanation for the onset of fluid-flow-induced flutter in a flag. Our theory accounts for the various physical mechanisms at work: the finite length and the small but finite bending stiffness of the flag, the unsteadiness of the flow, the added mass effect, and vortex shedding from the trailing edge. Our analysis allows us to predict a critical speed for the onset of flapping as well as the frequency of flapping. We find that in a particular limit corresponding to a low-density fluid flowing over a soft high-density flag, the flapping instability is akin to a resonance between the mode of oscillation of a rigid pivoted airfoil in a flow and a hinged-free elastic plate vibrating in its lowest mode.

Journal Article↗

PubMed2005

How the Venus flytrap snaps.

The rapid closure of the Venus flytrap (Dionaea muscipula) leaf in about 100 ms is one of the fastest movements in the plant kingdom. This led Darwin to describe the plant as "one of the most wonderful in the world". The trap closure is initiated by the mechanical stimulation of trigger hairs. Previous studies have focused on the biochemical response of the trigger hairs to stimuli and quantified the propagation of action potentials in the leaves. Here we complement these studies by considering the post-stimulation mechanical aspects of Venus flytrap closure. Using high-speed video imaging, non-invasive microscopy techniques and a simple theoretical model, we show that the fast closure of the trap results from a snap-buckling instability, the onset of which is controlled actively by the plant. Our study identifies an ingenious solution to scaling up movements in non-muscular engines and provides a general framework for understanding nastic motion in plants.

Biomechanical Phenomena↗

PubMed2005

Onset of buckling in drying droplets of colloidal suspensions.

Minute concentrations of suspended particles can dramatically alter the behavior of a drying droplet. After a period of isotropic shrinkage, similar to droplets of a pure liquid, these droplets suddenly buckle like an elastic shell. While linear elasticity is able to describe the morphology of the buckled droplets, it fails to predict the onset of buckling. Instead, we find that buckling is coincident with a stress-induced fluid to solid transition in a shell of particles at a droplet's surface, occurring when attractive capillary forces overcome stabilizing electrostatic forces between particles.

Journal Article↗

PubMed2005

Nested self-similar wrinkling patterns in skins.

Stiff thin films on soft substrates are both ancient and commonplace in nature; for instance, animal skin comprises a stiff epidermis attached to a soft dermis. Although more recent and rare, artificial skins are increasingly used in a broad range of applications, including flexible electronics, tunable diffraction gratings, force spectroscopy in cells, modern metrology methods, and other devices. Here we show that model elastomeric artificial skins wrinkle in a hierarchical pattern consisting of self-similar buckles extending over five orders of magnitude in length scale, ranging from a few nanometres to a few millimetres. We provide a mechanism for the formation of this hierarchical wrinkling pattern, and quantify our experimental findings with both computations and a simple scaling theory. This allows us to harness the substrates for applications. In particular, we show how to use the multigeneration-wrinkled substrate for separating particles based on their size, while simultaneously forming linear chains of monodisperse particles.

Cross-Linking Reagents↗

PubMed2004

Scaling of F-actin network rheology to probe single filament elasticity and dynamics.

The linear and nonlinear viscoelastic response of networks of cross-linked and bundled cytoskeletal filaments demonstrates remarkable scaling with both frequency and applied prestress, which helps elucidate the origins of the viscoelasticity. The frequency dependence of the shear modulus reflects the underlying single-filament relaxation dynamics for 0.1-10 rad/sec. Moreover, the nonlinear strain stiffening of such networks exhibits a universal form as a function of prestress; this is quantitatively explained by the full force-extension relation of single semiflexible filaments.

Actins↗

PubMed2004

Peeling, healing, and bursting in a lubricated elastic sheet.

We consider the dynamics of an elastic sheet lubricated by the flow of a thin layer of fluid that separates it from a rigid wall. By considering long wavelength deformations of the sheet, we derive an evolution equation for its motion, accounting for the effects of elastic bending, viscous lubrication, and body forces. We then analyze various steady and unsteady problems for the sheet, such as peeling, healing, levitating, and bursting, using a combination of numerical simulation and dimensional analysis. On the macroscale, we corroborate our theory with a simple experiment, and, on the microscale, we analyze an oscillatory valve that can transform a continuous stream of fluid into a series of discrete pulses.

Journal Article↗

PubMed2004

Modelling DNA loops using continuum and statistical mechanics.

The classical Kirchhoff elastic-rod model applied to DNA is extended to account for sequence-dependent intrinsic twist and curvature, anisotropic bending rigidity, electrostatic force interactions, and overdamped Brownian motion in a solvent. The zero-temperature equilibrium rod model is then applied to study the structural basis of the function of the lac repressor protein in the lac operon of Escherichia coli. The structure of a DNA loop induced by the clamping of two distant DNA operator sites by lac repressor is investigated and the optimal geometries for the loop of length 76 bp are predicted. Further, the mimicked binding of catabolite gene activator protein (CAP) inside the loop provides solutions that might explain the experimentally observed synergy in DNA binding between the two proteins. Finally, a combined Monte Carlo and Brownian dynamics solver for a worm-like chain model is described and a preliminary analysis of DNA loop-formation kinetics is presented.

Base Sequence↗

PubMed2004

Relating microstructure to rheology of a bundled and cross-linked F-actin network in vitro.

The organization of individual actin filaments into higher-order structures is controlled by actin-binding proteins (ABPs). Although the biological significance of the ABPs is well documented, little is known about how bundling and cross-linking quantitatively affect the microstructure and mechanical properties of actin networks. Here we quantify the effect of the ABP scruin on actin networks by using imaging techniques, cosedimentation assays, multiparticle tracking, and bulk rheology. We show how the structure of the actin network is modified as the scruin concentration is varied, and we correlate these structural changes to variations in the resultant network elasticity.

Actin Cytoskeleton↗

PubMed2004

Soft lubrication.

We consider some basic principles of fluid-induced lubrication at soft interfaces. In particular, we quantify how a soft substrate changes the geometry of and the forces between surfaces sliding past each other. By considering the model problem of a symmetric nonconforming contact moving tangentially to a thin elastic layer, we determine the normal force in the small and large deflection limit, and show that there is an optimal combination of material and geometric properties which maximizes the normal force. Our results can be generalized to a variety of other geometries which show the same qualitative behavior. Thus, they are relevant in the elastohydrodynamic lubrication of soft elastic and poroelastic gels and shells, and in the context of biolubrication in cartilaginous joints.

Cartilage↗

PubMed2004

Elastic behavior of cross-linked and bundled actin networks.

Networks of cross-linked and bundled actin filaments are ubiquitous in the cellular cytoskeleton, but their elasticity remains poorly understood. We show that these networks exhibit exceptional elastic behavior that reflects the mechanical properties of individual filaments. There are two distinct regimes of elasticity, one reflecting bending of single filaments and a second reflecting stretching of entropic fluctuations of filament length. The mechanical stiffness can vary by several decades with small changes in cross-link concentration, and can increase markedly upon application of external stress. We parameterize the full range of behavior in a state diagram and elucidate its origin with a robust model.

Actin Cytoskeleton↗

PubMed2004

Photoinduced deformations of beams, plates, and films.

Photoresponsive solids such as nematic photoelastomers can undergo large deformations induced by light absorbed into rodlike molecules which bend and disrupt liquid crystal order. Significant variation of photoabsorption through the solid leads to nonuniform elastic deformations such as bending of beams and plates and pitting of layers. Such effects are also found in the presence of inhomogeneous thermal or swelling fields in solids or gels. We analyze the small deflection limit of these problems and show that beams made of these materials can have two elastically neutral planes, and that plates of these materials have a typical saddle shape. We also give a scaling analysis of the elasticity of photoinduced mounds and pits and speculate on their applications.

Journal Article↗

PubMed2004

Bending stiffness of a crystalline actin bundle.

The acrosomal process of the sperm of the horseshoe crab (Limulus polyphemus) is a unique crystalline actin bundle, consisting of multiple actin filaments cross-linked by the actin-bundling protein, scruin. For successful fertilization, the acrosomal bundle must penetrate through a 30 microm thick jelly coat surrounding the egg and thus it must be sufficiently stiff. Here, we present two measurements of the bending stiffness of a single crystalline bundle of actin. Results from these measurements indicate that the actin:scruin composite bundle has an average elastic modulus of 2 GPa, which is similar to that of a single actin filament, and a bending stiffness that is more than two orders of magnitude larger than that of a bundle of uncross-linked actin filaments due to stiffening by the scruin matrix.

Acrosome↗

PubMed2004

The elements of draping.

We consider the gravity-induced draping of a 3D object with a naturally flat, isotropic elastic sheet. As the size of the sheet increases, we observe the appearance of new folded structures of increasing complexity that arise because of the competition between elasticity and gravity. We analyze some of the simpler 3D structures by determining their shape and analyzing their response and stability and show that these structures can easily switch between a number of metastable configurations. For more complex draperies, we derive scaling laws for the appearance and disappearance of new length scales. Our results are consistent with commonplace observations of drapes and complement large-scale computations of draping by providing benchmarks. They also yield a qualitative guide to fashion design and virtual reality animation.

Body Constitution↗

PubMed2004

Structural basis for cooperative DNA binding by CAP and lac repressor.

Catabolite gene activator protein (CAP) and lac repressor (LR) are celebrated transcription-regulating proteins that bind to DNA cooperatively forming a ternary complex with the promoter loop. Here we present a multiscale model of the ternary complex derived from crystal structures of the proteins and a continuous structure of the DNA loop built using the theory of elasticity. We predict that the loop is underwound in the binary complex with the LR, whereas in the ternary complex with the LR and CAP, the loop is overwound and extended due to an upstream relocation of a DNA binding hand of LR. The computed relocation distance matches the experimental observations and the energy balance of the system explains the cooperativity effect. Using the multiscale approach, we build an all-atom model of the ternary complex that suggests a series of further experimental investigations.

Binding, Competitive↗

PubMed2003

Biomimetic ratcheting motion of a soft, slender, sessile gel.

Inspired by the locomotion of terrestrial limbless animals, we study the motion of a lubricated rod of a hydrogel on a soft substrate. We show that it is possible to mimic observed biological gaits by vibrating the substrate and by using a variety of mechanisms to break longitudinal and lateral symmetry. Our simple theory and experiments provide a unified view of the creeping, undulating, and inchworming gaits observed in limbless locomotion on land, all of which originate as symmetry-breaking bifurcations of a simple base state associated with periodic longitudinal oscillations of a slender gel. These ideas are therefore also applicable to technological situations that involve moving small, soft solids on substrates.

Animals↗

PubMed2003

Crack street: the cycloidal wake of a cylinder tearing through a thin sheet.

When a cylindrical tool cuts through a thin sheet of a relatively brittle material, it leaves behind a visually arresting crack street in its wake, reminiscent of a vortex street in the wake of a cylinder moving through a fluid. We show that simple geometrical arguments based on the interplay of in-plane stretching and out-of-plane bending suffice to explain the cycloidal morphology of the curved crack. The coupling between geometry and dynamics also allows us to explain the "stick-slip"-like behavior of tearing and suggests that these oscillations should occur generically in the brittle fracture of thin solid films.

Materials Testing↗

PubMed2003

Kinks, rings, and rackets in filamentous structures.

Carbon nanotubes and biological filaments each spontaneously assemble into kinked helices, rings, and "tennis racket" shapes due to competition between elastic and interfacial effects. We show that the slender geometry is a more important determinant of the morphology than any molecular details. Our mesoscopic continuum theory is capable of quantifying observations of these structures and is suggestive of their occurrence in other filamentous assemblies as well.

Acrosome↗