Mechanics and microstructure of blood plasma clots in shear driven rupture.

Intravascular blood clots are subject to hydrodynamic shear and other forces that cause clot deformation and rupture (embolization). A portion of the ruptured clot can block blood flow in downstream vessels. The mechanical stability of blood clots is determined primarily by the 3D polymeric fibrin network that forms a gel. Previous studies have primarily focused on the rupture of blood plasma clots under tensile loading (Mode I), our current study investigates the rupture of fibrin induced by shear loading (Mode II), dominating under physiological conditions induced by blood flow. Using experimental and theoretical approaches, we show that fracture toughness, i.e. the critical energy release rate, is relatively independent of the type of loading and is therefore a fundamental property of the gel. Ultrastructural studies and finite element simulations demonstrate that cracks propagate perpendicular to the direction of maximum stretch at the crack tip. These observations indicate that locally, the mechanism of rupture is predominantly tensile. Knowledge gained from this study will aid in the development of methods for prediction/prevention of thrombotic embolization.

Cracks in tensile-contracting and tensile-dilating poroelastic materials.

Fibrous gels such as cartilage, blood clots, and carbon-nanotube-based sponges with absorbed oils suffer a reduction in volume by the expulsion of liquid under uniaxial tension, and this directly affects crack-tip fields and energy release rates. A continuum model is formulated for isotropic fibrous gels that exhibit a range of behaviors from volume increasing to volume decreasing in uniaxial tension by changing the ratio of two material parameters. The motion of liquid in the pores of such gels is modeled using poroelasticity. The direction of liquid fluxes around cracks is shown to depend on whether the gel locally increases or decreases in volume. The energy release rate for cracks is computed using a surface-independent integral and it is shown to have two contributions - one from the stresses in the solid network, and another from the flow of liquid. The contribution to the integral from liquid permeation tends to be negative when the gel exhibits volume decrease, which effectively is a crack shielding mechanism.

Humidity dependence of fracture toughness of cellulose fibrous networks.

Cellulose-based materials are increasingly finding applications in technology due to their sustainability and biodegradability. The sensitivity of cellulose fiber networks to environmental conditions such as temperature and humidity is well known. Yet, there is an incomplete understanding of the dependence of the fracture toughness of cellulose networks on environmental conditions. In the current study, we assess the effect of moisture content on the out-of-plane (i.e., z-dir.) fracture toughness of a particular cellulose network, specifically Whatman cellulose filter paper. Experimental measurements are performed at 16% RH along the desorption isotherm and 23, 37, 50, 75% RH along the adsorption isotherm using out-of-plane tensile tests and double cantilever beam (DCB) tests. Cohesive zone modeling and finite element simulations are used to extract quantitative properties that describe the crack growth behavior. Overall, the fracture toughness of filter paper decreased with increasing humidity. Additionally, a novel model is developed to capture the high peak and sudden drop in the experimental force measurement caused by the existence of an initiation region. This model is found to be in good agreement with experimental data. The relative effect of each independent cohesive parameter is explored to better understand the cohesive zone-based humidity dependence model. The methods described here may be applied to study rupture of other fiber networks with weak bonds.

Kinetics of self-assembly of inclusions due to lipid membrane thickness interactions.

Self-assembly of proteins on lipid membranes underlies many important processes in cell biology, such as, exo- and endo-cytosis, assembly of viruses, etc. An attractive force that can cause self-assembly is mediated by membrane thickness interactions between proteins. The free energy profile associated with this attractive force is a result of the overlap of thickness deformation fields around the proteins which can be calculated from the solution of a boundary value problem. Yet, the time scales over which two inclusions coalesce has not been explored, even though the evolution of particle concentrations on membranes has been modeled using phase-field approaches. In this paper we compute this time scale as a function of the initial distance between two inclusions by viewing their coalescence as a first passage time problem. The mean first passage time is computed using Langevin dynamics and a partial differential equation, and both methods are found to be in excellent agreement. Inclusions of three different shapes are studied and it is found that for two inclusions separated by about hundred nanometers the time to coalescence is hundreds of milliseconds irrespective of shape. An efficient computation of the interaction energy of inclusions is central to our work. We compute it using a finite difference technique and show that our results are in excellent agreement with those from a previously proposed semi-analytical method based on Fourier-Bessel series. The computational strategies described in this paper could potentially lead to efficient methods to explore the kinetics of self-assembly of proteins on lipid membranes.

Bacterial activity hinders particle sedimentation.

Sedimentation in active fluids has come into focus due to the ubiquity of swimming micro-organisms in natural and industrial processes. Here, we investigate sedimentation dynamics of passive particles in a fluid as a function of bacteria E. coli concentration. Results show that the presence of swimming bacteria significantly reduces the speed of the sedimentation front even in the dilute regime, in which the sedimentation speed is expected to be independent of particle concentration. Furthermore, bacteria increase the dispersion of the passive particles, which determines the width of the sedimentation front. For short times, particle sedimentation speed has a linear dependence on bacterial concentration. Mean square displacement data shows, however, that bacterial activity decays over long experimental (sedimentation) times. An advection-diffusion equation coupled to bacteria population dynamics seems to capture concentration profiles relatively well. A single parameter, the ratio of single particle speed to the bacteria flow speed can be used to predict front sedimentation speed.

Harnessing fluctuation theorems to discover free energy and dissipation potentials from non-equilibrium data.

The Jarzynski relation, as an equality form of the second law of thermodynamics, represents an exact thermodynamic statement that is valid arbitrarily far away from equilibrium. This remarkable relation directly links the equilibrium free energy difference between two states and the probability distribution of the work done along a process that drives the system from one state to the other. Here, we leverage the Jarzynski equality and a local equilibrium assumption, to go beyond the calculation of free energy differences and also extract the dissipation potential from additional measurements of kinematic field variables (strain and velocity fields). The proposed strategy is exemplified over pulling experiments of mass-spring models obeying overdamped Langevin dynamics, which is a prototype for nanorods, fibrous macro-molecules and the Rouse model of polymers. Different interaction potentials, fluid viscosities and bath temperatures are studied, so as to intrinsically control how close or far away the system is from equilibrium. The data-inferred continuum models are then validated against processes governed by different pulling protocols, thereby demonstrating their predictive capability. The methods presented here represent a first step toward full material characterization from non-equilibrium data of macroscopic observables, which could potentially be obtained from experimental observations.

A Semi-Analytic Elastic Rod Model of Pediatric Spinal Deformity.

The mechanism of the scoliotic curve development in healthy adolescents remains unknown in the field of orthopedic surgery. Variations in the sagittal curvature of the spine are believed to be a leading cause of scoliosis in this patient population. Here, we formulate the mechanics of S-shaped slender elastic rods as a model for pediatric spine under physiological loading. Second, applying inverse mechanics to clinical data of the subtypes of scoliotic spines, with characteristic 3D deformity, we determine the undeformed geometry of the spine before the induction of scoliosis. Our result successfully reproduces the clinical data of the deformed spine under varying loads, confirming that the prescoliotic sagittal curvature of the spine impacts the 3D loading that leads to scoliosis.

Biodegradable Piezoelectric Force Sensor.

Measuring vital physiological pressures is important for monitoring health status, preventing the buildup of dangerous internal forces in impaired organs, and enabling novel approaches of using mechanical stimulation for tissue regeneration. Pressure sensors are often required to be implanted and directly integrated with native soft biological systems. Therefore, the devices should be flexible and at the same time biodegradable to avoid invasive removal surgery that can damage directly interfaced tissues. Despite recent achievements in degradable electronic devices, there is still a tremendous need to develop a force sensor which only relies on safe medical materials and requires no complex fabrication process to provide accurate information on important biophysiological forces. Here, we present a strategy for material processing, electromechanical analysis, device fabrication, and assessment of a piezoelectric Poly-l-lactide (PLLA) polymer to create a biodegradable, biocompatible piezoelectric force sensor, which only employs medical materials used commonly in Food and Drug Administration-approved implants, for the monitoring of biological forces. We show the sensor can precisely measure pressures in a wide range of 0-18 kPa and sustain a reliable performance for a period of 4 d in an aqueous environment. We also demonstrate this PLLA piezoelectric sensor can be implanted inside the abdominal cavity of a mouse to monitor the pressure of diaphragmatic contraction. This piezoelectric sensor offers an appealing alternative to present biodegradable electronic devices for the monitoring of intraorgan pressures. The sensor can be integrated with tissues and organs, forming self-sensing bionic systems to enable many exciting applications in regenerative medicine, drug delivery, and medical devices.

Statistical mechanics of a double-stranded rod model for DNA melting and elasticity.

The double-helical topology of DNA molecules observed at room temperature in the absence of any external loads can be disrupted by increasing the bath temperature or by applying tensile forces, leading to spontaneous strand separation known as DNA melting. Here, continuum mechanics of a 2D birod is combined with statistical mechanics to formulate a unified framework for studying both thermal melting and tensile force induced melting of double-stranded molecules: it predicts the variation of melting temperature with tensile load, provides a mechanics-based understanding of the cooperativity observed in melting transitions, and reveals an interplay between solution electrostatics and micromechanical deformations of DNA which manifests itself as an increase in the melting temperature with increasing ion concentration. This novel predictive framework sheds light on the micromechanical aspects of DNA melting and predicts trends that were observed experimentally or extracted phenomenologically using the Clayperon equation.

Extensions of the worm-like-chain model to tethered active filaments under tension.

Intracellular elastic filaments such as microtubules are subject to thermal Brownian noise and active noise generated by molecular motors that convert chemical energy into mechanical work. Similarly, polymers in living fluids such as bacterial suspensions and swarms suffer bending deformations as they interact with single bacteria or with cell clusters. Often, these filaments perform mechanical functions and interact with their networked environment through cross-links or have other similar constraints placed on them. Here, we examine the mechanical properties-under tension-of such constrained active filaments under canonical boundary conditions motivated by experiments. Fluctuations in the filament shape are a consequence of two types of random forces-thermal Brownian forces and activity derived forces with specified time and space correlation functions. We derive force-extension relationships and expressions for the mean square deflections for tethered filaments under various boundary conditions including hinged and clamped constraints. The expressions for hinged-hinged boundary conditions are reminiscent of the worm-like-chain model and feature effective bending moduli and mode-dependent non-thermodynamic effective temperatures controlled by the imposed force and by the activity. Our results provide methods to estimate the activity by measurements of the force-extension relation of the filaments or their mean square deflections, which can be routinely performed using optical traps, tethered particle experiments, or other single molecule techniques.

Combined molecular/continuum modeling reveals the role of friction during fast unfolding of coiled-coil proteins.

Coiled-coils are filamentous proteins that form the basic building block of important force-bearing cellular elements, such as intermediate filaments and myosin motors. In addition to their biological importance, coiled-coil proteins are increasingly used in new biomaterials including fibers, nanotubes, or hydrogels. Coiled-coils undergo a structural transition from an α-helical coil to an unfolded state upon extension, which allows them to sustain large strains and is critical for their biological function. By performing equilibrium and out-of-equilibrium all-atom molecular dynamics (MD) simulations of coiled-coils in explicit solvent, we show that two-state models based on Kramers' or Bell's theories fail to predict the rate of unfolding at high pulling rates. We further show that an atomistically informed continuum rod model accounting for phase transformations and for the hydrodynamic interactions with the solvent can reconcile two-state models with our MD results. Our results show that frictional forces, usually neglected in theories of fibrous protein unfolding, reduce the thermodynamic force acting on the interface, and thus control the dynamics of unfolding at different pulling rates. Our results may help interpret MD simulations at high pulling rates, and could be pertinent to cytoskeletal networks or protein-based artificial materials subjected to shocks or blasts.

Stick-slip kinetics in a bistable bar immersed in a heat bath.

Structural transitions in some rod-like biological macromolecules under tension are known to proceed by the propagation through the length of the molecule of an interface separating two phases. A continuum mechanical description of the motion of this interface, or phase boundary, takes the form of a kinetic law which relates the thermodynamic driving force across it with its velocity in the reference configuration. For biological macromolecules immersed in a heat bath, thermally activated kinetics described by the Arrhenius law is often a good choice. Here we show that 'stick-slip' kinetics, characteristic of friction, can also arise in an overdamped bistable bar immersed in a heat bath. To mimic a rod-like biomolecule we model the bar as a chain of masses and bistable springs moving in a viscous fluid. We conduct Langevin dynamics calculations on the chain and extract a temperature dependent kinetic relation by observing that the dissipation at a phase boundary can be estimated by performing an energy balance. Using this kinetic relation we solve boundary value problems for a bistable bar immersed in a constant temperature bath and show that the resultant force-extension relation matches very well with the Langevin dynamics results. We estimate the force fluctuations at the pulled end of the bar due to thermal kicks from the bath by using a partition function. We also show rate dependence of hysteresis in cyclic loading of the bar arising from the stick-slip kinetics. Our kinetic relation could be applied to rod-like biomolecules, such as, DNA and coiled-coil proteins which exhibit structural transitions that depend on both temperature and loading rate.

Discontinuous growth of DNA plectonemes due to atomic scale friction.

We develop a model to explain discontinuities in the increase of the length of a DNA plectoneme when the DNA filament is continuously twisted under tension. We account for DNA elasticity, electrostatic interactions and entropic effects due to thermal fluctuation. We postulate that a corrugated energy landscape that contains energy barriers is the cause of jumps in the length of the plectoneme as the number of turns is increased. Thus, our model is similar to the Prandtl-Tomlinson model of atomic scale friction. The existence of a corrugated energy landscape can be justified due to the close proximity of the neighboring pieces of DNA in a plectoneme. We assume the corrugated energy landscape to be sinusoidal since the plectoneme has a periodic helical structure and rotation of the bead is a form of periodic motion. We perform calculations with different tensile forces and ionic concentrations, and show that rotation-extension curves manifest stair-step shapes under relatively high ionic concentrations and high forces. We show that the jump in the plectonemic growth is caused by the flattening of the energy barrier in the corrugated landscape.

Dynamic Transition from α-Helices to ß-Sheets in Polypeptide Coiled-Coil Motifs.

We carried out dynamic force manipulations in silico on a variety of coiled-coil protein fragments from myosin, chemotaxis receptor, vimentin, fibrin, and phenylalanine zippers that vary in size and topology of their α-helical packing. When stretched along the superhelical axis, all superhelices show elastic, plastic, and inelastic elongation regimes and undergo a dynamic transition from the α-helices to the ß-sheets, which marks the onset of plastic deformation. Using the Abeyaratne-Knowles formulation of phase transitions, we developed a new theoretical methodology to model mechanical and kinetic properties of protein coiled-coils under mechanical nonequilibrium conditions and to map out their energy landscapes. The theory was successfully validated by comparing the simulated and theoretical force-strain spectra. We derived the scaling laws for the elastic force and the force for α-to-ß transition, which can be used to understand natural proteins' properties as well as to rationally design novel biomaterials of required mechanical strength with desired balance between stiffness and plasticity.

Particle diffusion in active fluids is non-monotonic in size.

We experimentally investigate the effect of particle size on the motion of passive polystyrene spheres in suspensions of Escherichia coli. Using particles covering a range of sizes from 0.6 to 39 microns, we probe particle dynamics at both short and long time scales. In all cases, the particles exhibit super-diffusive ballistic behavior at short times before eventually transitioning to diffusive behavior. Surprisingly, we find a regime in which larger particles can diffuse faster than smaller particles: the particle long-time effective diffusivity exhibits a peak in particle size, which is a deviation from classical thermal diffusion. We also find that the active contribution to particle diffusion is controlled by a dimensionless parameter, the Péclet number. A minimal model qualitatively explains the existence of the effective diffusivity peak and its dependence on bacterial concentration. Our results have broad implications on characterizing active fluids using concepts drawn from classical thermodynamics.

Equilibrium and kinetics of DNA overstretching modeled with a quartic energy landscape.

It is well known that the dsDNA molecule undergoes a phase transition from B-DNA into an overstretched state at high forces. For some time, the structure of the overstretched state remained unknown and highly debated, but recent advances in experimental techniques have presented evidence of more than one possible phase (or even a mixed phase) depending on ionic conditions, temperature, and basepair sequence. Here, we present a theoretical model to study the overstretching transition with the possibility that the overstretched state is a mixture of two phases: a structure with portions of inner strand separation (melted or M-DNA), and an extended phase that retains the basepair structure (S-DNA). We model the double-stranded DNA as a chain composed of n segments of length l, where the transition is studied by means of a Landau quartic potential with statistical fluctuations. The length l is a measure of cooperativity of the transition and is key to characterizing the overstretched phase. By analyzing the different values of l corresponding to a wide spectrum of experiments, we find that for a range of temperatures and ionic conditions, the overstretched form is likely to be a mix of M-DNA and S-DNA. For a transition close to a pure S-DNA state, where the change in extension is close to 1.7 times the original B-DNA length, we find l ? 25 basepairs regardless of temperature and ionic concentration. Our model is fully analytical, yet it accurately reproduces the force-extension curves, as well as the transient kinetic behavior, seen in DNA overstretching experiments.

Biotemplated synthesis of PZT nanowires.

Piezoelectric nanowires are an important class of smart materials for next-generation applications including energy harvesting, robotic actuation, and bioMEMS. Lead zirconate titanate (PZT), in particular, has attracted significant attention, owing to its superior electromechanical conversion performance. Yet, the ability to synthesize crystalline PZT nanowires with well-controlled properties remains a challenge. Applications of common nanosynthesis methods to PZT are hampered by issues such as slow kinetics, lack of suitable catalysts, and harsh reaction conditions. Here we report a versatile biomimetic method, in which biotemplates are used to define PZT nanostructures, allowing for rational control over composition and crystallinity. Specifically, stoichiometric PZT nanowires were synthesized using both polysaccharide (alginate) and bacteriophage templates. The wires possessed measured piezoelectric constants of up to 132 pm/V after poling, among the highest reported for PZT nanomaterials. Further, integrated devices can generate up to 0.820 µW/cm(2) of power. These results suggest that biotemplated piezoelectric nanowires are attractive candidates for stimuli-responsive nanosensors, adaptive nanoactuators, and nanoscale energy harvesters.

A continuum mechanical model of cell motion driven by a biphasic traction stress.

The aim of this paper is to place the cell locomotion problem within the general framework of classical continuum mechanics, and while doing so, to account for the deformation of the actin network in the cytoskeleton; the myosin activity on the lamellum including its effect on depolymerization at the trailing edge; model the stress-dependent driving forces and kinetic laws controlling polymerization at the leading edge, depolymerization at the trailing edge and ATP hydrolysis consistently with the dissipation inequality; and, based on the observations in Gardel et al. (Gardel et al. 2008 J. Cell Biol. 183, 999-1005 (doi:10.1083/jcb.200810060)), include a biphasic velocity-dependent traction stress acting on the actin network. While we chose certain specific models for each of these, in part to allow for an analytical solution, the generality of the framework allows one to readily introduce different constitutive laws to describe these phenomena as might be needed, for example, to study some different type of cells. As described in §5, the predictions of the model compare well with observations such as the magnitude of the very different actin retrograde speeds in the lamellum and lamellipodium including their jump at the interface, the magnitude of the cell speed, and the relative lengths of the lamellipodium and lamellum.

Mechanical fatigue testing in silico: Dynamic evolution of material properties of nanoscale biological particles.

Biological particles have evolved to possess mechanical characteristics necessary to carry out their functions. We developed a computational approach to "fatigue testing in silico", in which constant-amplitude cyclic loading is applied to a particle to explore its mechanobiology. We used this approach to describe dynamic evolution of nanomaterial properties and low-cycle fatigue in the thin spherical encapsulin shell, thick spherical Cowpea Chlorotic Mottle Virus (CCMV) capsid, and thick cylindrical microtubule (MT) fragment over 20 cycles of deformation. Changing structures and force-deformation curves enabled us to describe their damage-dependent biomechanics (strength, deformability, stiffness), thermodynamics (released and dissipated energies, enthalpy, and entropy) and material properties (toughness). Thick CCMV and MT particles experience material fatigue due to slow recovery and damage accumulation over 3-5 loading cycles; thin encapsulin shells show little fatigue due to rapid remodeling and limited damage. The results obtained challenge the existing paradigm: damage in biological particles is partially reversible owing to particle's partial recovery; fatigue crack may or may not grow with each loading cycle and may heal; and particles adapt to deformation amplitude and frequency to minimize the energy dissipated. Using crack size to quantitate damage is problematic as several cracks might form simultaneously in a particle. Dynamic evolution of strength, deformability, and stiffness, can be predicted by analyzing the cycle number (N) dependent damage, [Formula: see text] , where α is a power law and Nf is fatigue life. Fatigue testing in silico can now be used to explore damage-induced changes in the material properties of other biological particles. STATEMENT OF SIGNIFICANCE: Biological particles possess mechanical characteristics necessary to perform their functions. We developed "fatigue testing in silico" approach, which employes Langevin Dynamics simulations of constant-amplitude cyclic loading of nanoscale biological particles, to explore dynamic evolution of the mechanical, energetic, and material properties of the thin and thick spherical particles of encapsulin and Cowpea Chlorotic Mottle Virus, and the microtubule filament fragment. Our study of damage growth and fatigue development challenge the existing paradigm. Damage in biological particles is partially reversible as fatigue crack might heal with each loading cycle. Particles adapt to deformation amplitude and frequency to minimize energy dissipation. The evolution of strength, deformability, and stiffness, can be accurately predicted by analyzing the damage growth in particle structure.

Fracture toughness of fibrin gels as a function of protein volume fraction: Mechanical origins.

The mechanical stability of blood clots necessary for their functions is provided by fibrin, a fibrous gel. Rupture of clots leads to life-threatening thrombotic embolization, which is little understood. Here, we combine experiments and simulations to determine the toughness of plasma clots as a function of fibrin content and correlate toughness with fibrin network structure characterized by confocal and scanning electron microscopy. We develop fibrin constitutive laws that scale with fibrin concentration and capture the force-stretch response of cracked clot specimens using only a few material parameters. Toughness is calculated from the path-independent J* integral that includes dissipative effects due to fluid flow and uses only the constitutive model and overall stretch at crack propagation as input. We show that internal fluid motion, which is not directly measurable, contributes significantly to clot toughness, with its effect increasing as fibrin content increases, because the reduced gel porosity at higher density results in greater expense of energy in fluid motion. Increasing fibrin content (1→10mg/mL) results in a significant increase in clot toughness (3→15 N/m) in accordance with a power law relation reminiscent of cellular solids and elastomeric gels. These results provide a basis for understanding and predicting the tendency for thrombotic embolization. STATEMENT OF SIGNIFICANCE: Fibrin, a naturally occurring biomaterial, is the major determinant of the structural and mechanical integrity of blood clots. We determined that increasing the fibrin content in clots, as in some thrombi and fibrin-based anti-bleeding sealants, results in an increase in clot toughness. Toughness corresponds to the ability to resist rupturing in the presence of a defect. We couple bulk mechanical testing, microstructural measurements, and finite element modeling to capture the force-stretch response of fibrin clots and compute toughness. We show that increased fibrin content in clots reduces porosity and limits fluid motion and that fluid motion drastically alters the clot toughness. These results provide a fundamental understanding of blood clot rupture and could help in rational design of fibrin-containing biomaterials.