arXiv subjects

Ana-Sunčana Smith

Publications and source records attributed to Ana-Sunčana Smith.

27 records · Page 2Linked to original sources

arXiv2018

Statistical mechanics of an elastically pinned membrane: Equilibrium dynamics and power spectrum

In biological settings membranes typically interact locally with other membranes or the extracellular matrix in the exterior, as well as with internal cellular structures such as the cytoskeleton. Characterization of the dynamic properties of such interactions presents a difficult task. Significant progress has been achieved through simulations and experiments, yet analytical progress in modelling pinned membranes has been impeded by the complexity of governing equations. Here we circumvent these difficulties by calculating analytically the time-dependent Green's function of the operator governing the dynamics of an elastically pinned membrane in a hydrodynamic surrounding and subject to external forces. This enables us to calculate the equilibrium power spectral density for an overdamped membrane pinned by an elastic, permanently-attached spring subject to thermal excitations. By considering the effects of the finite experimental resolution on the measured spectra, we show that the elasticity of the pinning can be extracted from the experimentally measured spectrum. Membrane fluctuations can thus be used as a tool to probe mechanical properties of the underlying structures. Such a tool may be particularly relevant in the context of cell mechanics, where the elasticity of the membrane's attachment to the cytoskeleton could be measured.

physics.bio-ph↗

arXiv2018

Structural basis for the shielding function of the dynamic trypanosome variant surface glycoprotein coat

The most prominent defence of the unicellular parasite Trypanosoma brucei against the host immune system is a dense coat that comprises a variant surface glycoprotein (VSG). Despite the importance of the VSG family, no complete structure of a VSG has been reported. Making use of high-resolution structures of individual VSG domains, we employed small-angle X-ray scattering to elucidate the first two complete VSG structures. The resulting models imply that the linker regions confer great flexibility between domains, which suggests that VSGs can adopt two main conformations to respond to obstacles and changes of protein density, while maintaining a protective barrier at all times. Single-molecule diffusion measurements of VSG in supported lipid bilayers substantiate this possibility, as two freely diffusing populations could be detected. This translates into a highly flexible overall topology of the surface VSG coat, which displays both lateral movement in the plane of the membrane and variation in the overall thickness of the coat.

physics.bio-ph↗

arXiv2017

Asymptotic expansions of the hypergeometric function with two large parameters $-$ application to the partition function of a lattice gas in a field of traps

The canonical partition function of a two-dimensional lattice gas in a field of randomly placed traps, like many other problems in physics, evaluates to the Gauss hypergeometric function ${}_2F_1(a,b;c;z)$ in the limit when one or more of its parameters become large. This limit is difficult to compute from first principles, and finding the asymptotic expansions of the hypergeometric function is therefore an important task. While some possible cases of the asymptotic expansions of ${}_2F_1(a,b;c;z)$ have been provided in the literature, they are all limited by a narrow domain of validity, either in the complex plane of the variable or in the parameter space. Overcoming this restriction, we provide new asymptotic expansions for the hypergeometric function with two large parameters, which are valid for the entire complex plane of $z$ except for a few specific points. We show that these expansions work well even when we approach the possible singularity of ${}_2F_1(a,b;c;z)$, $|z|=1$, where the current expansions typically fail. Using our results we determine asymptotically the partition function of a lattice gas in a field of traps in the different possible physical limits of few/many particles and few/many traps, illustrating the applicability of the derived asymptotic expansions of the HGF in physics.

math-ph↗

arXiv2016

Effect of body deformability on microswimming

In this work we consider the following question: given a mechanical microswimming mechanism, does increased deformability of the swimmer body hinder or promote the motility of the swimmer? To answer this we study a microswimmer model composed of deformable beads connected with springs. We determine the velocity of the swimmer analytically, starting from the forces driving the motion and assuming that the oscillations in the effective radii of the beads are known and are much smaller than the radii themselves. We find that to the lowest order, only the driving frequency mode of the surface oscillations contributes to the swimming velocity, and that this velocity may both rise and fall with the deformability of the beads depending on the spring constant. To test these results, we run immersed boundary lattice Boltzmann simulations of the swimmer, and show that they reproduce both the velocity-promoting and velocity-hindering effects of bead deformability correctly in the predicted parameter ranges. Our results mean that for a general swimmer, its elasticity determines whether passive deformations of the swimmer body, induced by the fluid flow, aid or oppose the motion.

physics.bio-ph↗

arXiv2016

Setting the pace of microswimmers: when increasing viscosity speeds up self-propulsion

It has long been known that some microswimmers seem to swim counter-intuitively faster when the viscosity of the surrounding fluid is increased, whereas others slow down. This conflicting dependence of the swimming velocity on the viscosity is poorly understood theoretically. Here we explain that any mechanical microswimmer with an elastic degree of freedom in a simple Newtonian fluid can exhibit both kinds of response to an increase in the fluid viscosity for different viscosity ranges, if the driving is weak. The velocity response is controlled by a single parameter $\varGamma$, the ratio of the relaxation time of the elastic component of the swimmer in the viscous fluid and the swimming stroke period. This defines two velocity-viscosity regimes, which we characterize using the bead-spring microswimmer model and analyzing the different forces acting on the parts of this swimmer. The analytical calculations are supported by lattice-Boltzmann simulations, which accurately reproduce the two velocity regimes for the predicted values of $\varGamma$.

cond-mat.soft↗

arXiv2016

Microswimming with inertia

Microswimmers, especially in theoretical treatments, are generally taken to be completely inertia-free, since inertial effects on their motion are typically small and assuming their absence simplifies the problem considerably. Yet in nature there is no discrete break between swimmers for which inertia is negligibly small and for which it is detectable. Here we study a microswimming model for which the effect of inertia is calculated explicitly in the regime of transition between the Stokesian and the non-Stokesian flow limits, which we term the intermediate regime. The model in the inertialess limit is the bead-spring swimmer. We first show that in the intermediate regime a mechanical microswimmer exhibits damped inertial coasting like an underdamped harmonic oscillator. We then calculate analytically the swimmer's velocity by including a mass-acceleration term in the equations of motion which are otherwise based on the Stokes flow. We show that this hybrid treatment combining aspects of underdamped and overdamped dynamics provides an accurate description of the motion in the intermediate regime, as verified here by comparison to simulations using the lattice Boltzmann method, and is a significant improvement over the results from the inertialess theory when either the mass of the swimmer or the forces driving its motion is/are large enough.

cond-mat.soft↗

arXiv2014

Signature of a non-harmonic potential as revealed from a consistent shape and fluctuation analysis of an adherent membrane

The interaction of fluid membranes with a scaffold, which can be a planar surface or a more complex structure, is intrinsic to a number of systems - from artificial supported bilayers and vesicles to cellular membranes. In principle, these interactions can be either discrete and protein mediated, or continuous. In the latter case, they emerge from ubiquitous intrinsic surface interaction potentials as well as nature-designed steric contributions of the fluctuating membrane or from the polymers of the glycocalyx. Despite the fact that these nonspecific potentials are omnipresent, their description has been a major challenge from experimental and theoretical points of view. Here we show that a full understanding of the implications of the continuous interactions can be achieved only by expanding the standard superposition models commonly used to treat these types of systems, beyond the usual harmonic level of description. Supported by this expanded theoretical framework, we present three independent, yet mutually consistent, experimental approaches to measure the interaction potential strength and the membrane tension. Upon explicitly taking into account the nature of shot noise as well as of finite experimental resolution, excellent agreement with the augmented theory is obtained, which finally provides a coherent view of the behavior of the membrane in a vicinity of a scaffold.

cond-mat.soft↗

arXiv2014

Optimal shapes of artificial bead-spring micro-carriers at low Reynolds numbers

Bead-based micro-swimmers are promising systems for payload delivery on the micro-scale. However, the principles underlying their optimal design are not yet fully understood. Here we study a simple device consisting of three arbitrarily-shaped beads connected by two springs. We analytically determine the most favorable kinematic parameters for sinusoidal driving, and show how the swimmer changes from being a pusher to a puller. For cargo carrying ellipsoidal beads, we perform geometric optimization under the constraint of a constant total volume or surface area, with the aim of maximizing the device transport velocity and efficiency. Interestingly, we identify two major transport regimes, which arise from the competition between the elastic and the drag forces faced by the swimmer. We construct a phase diagram that indicates when the fastest swimming emerges because of minimized drag, and when due to heightened interactions among the beads.

physics.flu-dyn↗

arXiv2012

Coexistence of dilute and densely packed domains of ligand-receptor bonds in membrane adhesion

We analyze the stability of micro-domains of ligand-receptor bonds that mediate the adhesion of biological model membranes. After evaluating the effects of membrane fluctuations on the binding affinity of a single bond, we characterize the organization of bonds within the domains by theoretical means. In a large range of parameters, we find the commonly suggested dense packing to be separated by a free energy barrier from a regime in which bonds are sparsely distributed. If bonds are mobile, a coexistence of the two regimes should emerge, which agrees with recent experimental observations.

cond-mat.soft↗