Active Control of Cellular Orientation through In-Situ Stress in the Substrate

We investigate the orientation of cells on substrates to find possible methods for controlling the cellular orientation. The force dipole model is employed in our modelling and simulation. The elastic interaction between cells as well as the elastic interaction between the cell and in-situ stress field in the substrate are found to be the two main physical mechanisms to control the cellular orientation. The former interaction dominates the cellular orientation when the in-situ stress is small, while the later dominates when the in-situ stress is large enough. Two cells tend to align perpendicularly on a free substrate, but the cellular orientation varies with the increasing in-situ stress. Two cells tendto align in parallel when the normal stress is large enough. Their direction is perpendicular to the extension stress direction or parallel to the compression stress direction. When the positive in-situ shear stress is large enough, the two cells tend to align at -45°. Based on this theoretical simulation, it is believed that the cellular orientation on substrates can be controlled by thein-situ stresses.     

Radial distribution function of rod-like polyelectrolytes

We study the effect of electrostatic interactions on the distribution function of the end-to-end distance of a single polyelectrolyte chain in the rod-like limit. The extent to which the radial distribution function of a polyelectrolyte is reproduced by that of a wormlike chain with an adjusted effective persistence length is investigated. Strong evidence is found for a universal scaling formula connecting the effective persistence length of a polyelectrolyte with the strength of the electrostatic interaction and the Debye screening length. Received 4 March 2002 and Received in final form 1 July 2002 RID="a" ID="a"e-mail: jrudnick@physics.ucla.edu     

Colloidal dipolar interactions in 2D smectic-C films

We use a two-dimensional (2D) elastic free energy to calculate the effective interaction between two circular disks immersed in smectic-C films. For strong homeotropic anchoring, the distortion of the director field caused by the disks generates topological defects that induce an effective interaction between the disks. We use finite elements, with adaptive meshing, to minimize the 2D elastic free energy. The method is shown to be accurate and efficient for inhomogeneities on the length scales set by the disks and the defects, that differ by up to 3 orders of magnitude. We compute the effective interaction between two disk-defect pairs in a simple (linear) configuration. For large disk separations, D, the elastic free energy scales as ∼D ^-2, confirming the dipolar character of the long-range effective interaction. For small D the energy exhibits a pronounced minimum. The lowest energy corresponds to a symmetrical configuration of the disk-defect pairs, with the inner defect at the mid-point between the disks. The disks are separated by a distance that is twice the distance of the outer defect from the nearest disk. The latter is identical to the equilibrium distance of a defect nucleated by an isolated disk. Received 26 October 2001 and Received in final form 14 December 2001     

Molecular Dynamics Simulation on Charge Transfer Relaxation between Myoglobin and Water

Dynamical processes of myoglobin after photon-excited charge transfer between Fe ion and surrounding water anion are simulated by a molecular dynamics model. The roles of Coulomb interaction effect and water effect in the relaxation process are discussed. It is found that the relaxations before and after charge transfer are similar. Strong Coulomb interactions and less water mobility decrease Coulomb energy fluctuations. An extra transferred charge of Fe ion has impact on water packing with a distance up to 0.86nm.     

Variational theory for a single polyelectrolyte chain

Variational methods are applied to a single polyelectrolyte chain. The polymer is modeled as a Gaussian chain with screened electrostatic repulsion between all monomers. As a variational Hamiltonian, the most general Gaussian kernel, including the possibility of a classical or mean polymer path, is employed. The resulting self-consistent equations are systematically solved both for large and small monomer-monomer separations along the chain. In the absence of screening, the polymer is stretched on average. It is described by a straight classical path with Gaussian fluctuations around it. If the electrostatic repulsion is screened, the polymer is isotropically swollen for large separations, and for small separations the polymer correlation function is calculated as an analytic expansion in terms of the monomer-monomer separation along the chain. The electrostatic persistence length and the electrostatic blobsize are inferred from the crossover between distinct scaling ranges. We perform a global analysis of the scaling behavior as a function of the screening length and electrostatic interaction strength , where is the Bjerrum length and A is the distance of charges along the polymer chain. We find three different scaling regimes. i) A Gaussian-persistent regime with Gaussian behavior at small, persistent behavior at intermediate, and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and only for intermediate values of the screening length. The electrostatic persistence length is defined as the crossover length between the persistent and the asymptotically swollen behavior and is given by and thus disagrees with previous (restricted) variational treatments which predict a linear dependence on the screening length .ii) A Gaussian regime with Gaussian behavior at small and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and/or strong screening, and the electrostatic repulsion between monomers only leads to subfluent corrections to Gaussian scaling at small separations. The concept of a persistence length is without meaning in this regime. iii) A persistent regime , where the chain resembles a stretched rod on intermediate and small scales. Here the persistence length is given by the original Odijk prediction, , if the overstretching of the chain is avoided. We also investigate the effects of a finite polymer length and of an additional excluded-volume interaction, which modify the resultant scaling behavior. Applications to experiments and computer simulations are discussed. Received 24 December 1997     

A study of Barstar folding events using boundary value simulations

From extensive biophysical studies of protein folding, two competing mechanisms emerged: hydrophobic collapse and the framework model. Our protein of choice is Barstar—a barnase inhibitor. The approximation algorithm we used to study Barstar folding trajectories is called SDEL—stochastic difference equation in length. Using the native structure as the final boundary value and a collection of unfolded structures as the varying initial boundary value, SDEL calculates an ensemble of least action pathways between these boundaries. The results are atomically detailed folding pathways, with as many intermediate structures as you request in the input. We generated 12 pathways, starting from a structurally wide selection of unfolded conformations. Using the protein's radius of gyration as our primary reaction coordinate, we tracked H-bonds, dihedral angles, native and non-native contacts, and energy along the folding pathways. This paper will follow our findings, with special emphasis on pinpointing hydrophobic collapse as a more appropriate mechanism for Barstar. Comparison with pathway predictions for Barstar using experimental techniques will also be discussed.     

Using 3D fluid-structure interaction model to analyse the biomechanical properties of erythrocyte

This Letter presents a newly developed three-dimensional fluid-structure interaction model of the red blood cell (RBC). The model consists of a deformable liquid capsule modelled as Newtonian fluid enclosed by a hyperelastic membrane with viscoelastic property. Numerical results show that viscosity in the cytoplasm affects the deformed shape of RBC under loading. This observation is contrary to the earlier belief that viscosity of the cytoplasm can be neglected. Numerical simulations carried out to investigate large deformation induced on the RBC model using direct tensile forces show significant improvement in terms of correlation with experimental results. The membrane shear modulus estimated from the model ranges between 3.7 to compares well with results obtained from micropipette aspiration experiments.     

Percolation in a network with long-range connections: Implications for cytoskeletal structure and function

Cell shape, signaling, and integrity depend on cytoskeletal organization. In this study we describe the cytoskeleton as a simple network of filamentary proteins (links) anchored by complex protein structures (nodes). The structure of this network is regulated by a distance-dependent probability of link formation as P=p/d^s, where p regulates the network density and s controls how fast the probability for link formation decays with node distance (d). It was previously shown that the regulation of the link lengths is crucial for the mechanical behavior of the cells. Here we examined the ability of the two-dimensional network to percolate (i.e. to have end-to-end connectivity), and found that the percolation threshold depends strongly on s. The system undergoes a transition around s=2. The percolation threshold of networks with s<2 decreases with increasing system size L, while the percolation threshold for networks with s>2 converges to a finite value. We speculate that s<2 may represent a condition in which cells can accommodate deformation while still preserving their mechanical integrity. Additionally, we measured the length distribution of F-actin filaments from publicly available images of a variety of cell types. In agreement with model predictions, cells originating from more deformable tissues show longer F-actin cytoskeletal filaments.     

Electrostatic theory of viral self-assembly

Viruses self-assemble from identical capsid proteins and their genome consisting, for example, of a long single stranded (ss) RNA. For a big class of T=3 viruses, capsid proteins have long positive N-terminal tails. We explore the role played by the Coulomb interaction between the brush of positive N-terminal tails rooted at the inner surface of the capsid and the negative ss RNA molecule. We show that viruses are most stable when the total contour length of ss RNA is close to the total length of the tails. For such a structure the absolute value of the total RNA charge is approximately twice as large as the charge of the capsid. This conclusion agrees with structural data.     

Lie Symmetries and Conserved Quantities for Super-Long Elastic Slender Rod

DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. We study the Lie symmetries of a super-long elastic slender rod by using the methods of infinitesimal transformation. Based on Kirchhoff＇s analogue, generalized Hamilton canonical equations are analysed. The infinitesimal transformations with respect to the radian coordinate, the generalized coordinate, and the quasimomentum of the model are introduced. The Lie symmetries and conserved quantities of the model are presented.     

Elastic rod model of a supercoiled DNA molecule

We study the elastic behaviour of a supercoiled DNA molecule. The simplest model is that of a rod-like chain, involving two elastic constants, the bending and the twist rigidities. Writing this model in terms of Euler angles, we show that the corresponding Hamiltonian is singular and needs a small distance cut-off, which is a natural length scale giving the limit of validity of the model, of the order of the double-helix pitch. The rod-like chain in the presence of the cut-off is able to reproduce quantitatively the experimentally observed effects of supercoiling on the elongation-force characteristics, in the small supercoiling regime. An exact solution of the model, using both transfer matrix techniques and its mapping to a quantum mechanics problem, allows to extract, from the experimental data, the value of the twist rigidity. We also analyse the variation of the torque and the writhe-to-twist ratio versus supercoiling, showing analytically the existence of a rather sharp crossover regime which can be related to the excitation of plectoneme-like structures. Finally we study the extension fluctuations of a stretched and supercoiled DNA molecule, both at fixed torque and at fixed supercoiling angle, and we compare the theoretical predictions to some preliminary experimental data. Received 1 April 1999 and Received in final form 4 January 2000     

Elastic charge density representation of the interaction via the nematic director field

The interaction between particle-like sources of the nematic director distortions (e.g., colloids, point defects, macromolecules in nematic emulsions) allows for a useful analogy with the electrostatic multipole interaction between charged bodies. In this paper we develop this analogy to the level corresponding to the charge density and consider the general status of the pairwise approach to the nematic emulsions with finite-size colloids. It is shown that the elastic analog of the surface electric charge density is represented by the two transverse director components on the surface imposing the director distortions. The elastic multipoles of a particle are expressed as integrals over the charge density distribution on this surface. Because of the difference between the scalar electrostatics and vector nematostatics, the number of elastic multipoles of each order is doubled compared to that in the electrostatics: there are two elastic charges, two vectors of dipole moments, two quadrupolar tensors, and so on. The two-component elastic charge is expressed via the vector of external mechanical torque applied on the particle. As a result, the elastic Coulomb-like coupling between two particles is found to be proportional to the scalar product of the two external torques and does not directly depend on the particles' form and anchoring. The real-space Green function method is used to develop the pairwise approach to nematic emulsions and determine its form and restrictions. The pairwise potentials are obtained in the familiar form, but, in contrast to the electrostatics, they describe the interaction between pairs (dyads) of the elastic multipole moments. The multipole moments are shown to be uniquely determined by the single-particle director field, unperturbed by other particles. The pairwise approximation is applicable only in the leading order in the small ratio particle size-to-interparticle distance as the next order contains irreducible three-body terms.     

Simulation of proliferation and differentiation of cells in a stem-cell niche

Stem-cell niches represent microscopic compartments formed of environmental cells that nurture stem cells and enable them to maintain tissue homeostasis. The spatio-temporal kinetics of proliferation and differentiation of cells in such niches depend on the specifics of the niche structure and on adhesion and communication between cells and may also be influenced by spatial constraints on cell division. We propose a generic lattice model, taking all these factors into account, and systematically illustrate their role. The model is motivated by the experimental data available for the niches located in the subventricular zone of adult mammalian brain. The general conclusions drawn from our Monte Carlo simulations are applicable to other niches as well. One of our main findings is that the kinetics under consideration are highly stochastic due to a relatively small number of cells proliferating and differentiating in a niche and the autocatalytic character of the symmetric cell division. In particular, the kinetics exhibit huge stochastic bursts especially if the adhesion between cells is taken into account. In addition, the results obtained show that despite the small number of cells present in stem-cell niches, their arrangement can be predetermined to appreciable extent provided that the adhesion of different cells is different so that they tend to segregate.     

Communicability betweenness in complex networks

Betweenness measures provide quantitative tools to pick out fine details from the massive amount of interaction data that is available from large complex networks. They allow us to study the extent to which a node takes part when information is passed around the network. Nodes with high betweenness may be regarded as key players that have a highly active role. At one extreme, betweenness has been defined by considering information passing only through the shortest paths between pairs of nodes. At the other extreme, an alternative type of betweenness has been defined by considering all possible walks of any length. In this work, we propose a betweenness measure that lies between these two opposing viewpoints. We allow information to pass through all possible routes, but introduce a scaling so that longer walks carry less importance. This new definition shares a similar philosophy to that of communicability for pairs of nodes in a network, which was introduced by Estrada and Hatano [E. Estrada, N. Hatano, Phys. Rev. E 77 (2008) 036111]. Having defined this new communicability betweenness measure, we show that it can be characterized neatly in terms of the exponential of the adjacency matrix. We also show that this measure is closely related to a Fréchet derivative of the matrix exponential. This allows us to conclude that it also describes network sensitivity when the edges of a given node are subject to infinitesimally small perturbations. Using illustrative synthetic and real life networks, we show that the new betweenness measure behaves differently to existing versions, and in particular we show that it recovers meaningful biological information from a protein-protein interaction network.     

Signal propagation in stem-cell niches

Stem cells, maintaining tissue homeostasis, are nurtured in microscopic niches formed of so-called environmental cells. The kinetics of proliferation and differentiation of stem cells in such niches depend on their interaction with the messenger proteins secreted by environmental cells. We propose a generic mean-field kinetic model of the propagation of such signals. To motivate our study, we briefly describe a stem-cell niche in the Drosophila ovary. Our model is however applicable to other niches as well. In particular, it helps one to understand the necessary conditions for the niche function. For example, the model predicts that in the case of the Drosophila ovary each germline stem cell should have in the external membrane at least 700 receptors interacting with the signaling Dpp and Gpp proteins emanating from the cap cells.     

Elasticity theory of a twisted stack of plates

We present an elastic model of B-form DNA as a stack of thin, rigid plates or base pairs that are not permitted to deform. The symmetry of DNA and the constraint of plate rigidity limit the number of bulk elastic constants contributing to a macroscopic elasticity theory of DNA to four. We derive an effective twist-stretch energy in terms of the macroscopic stretch along and relative excess twist about the DNA molecular axis. In addition to the bulk stretch and twist moduli found previously, we obtain a twist-stretch modulus with the following remarkable properties: 1) it vanishes when the radius of the helical curve following the geometric center of each plate is zero, 2) it vanishes with the elastic constant K₂₃ that couples compression normal to the plates to a shear strain, if the plates are perpendicular to the molecular axis, and 3) it is nonzero if the plates are tilted relative to the molecular axis. This implies that a laminated helical structure carved out of an isotropic elastic medium will not twist in response to a stretching force, but an isotropic material will twist if it is bent into the shape of a helix. Received: 4 July 1997 / Received in final form: 16 October 1997 / Accepted: 21 October 1997     

The influence of process parameters on deposition characteristics of a soft/hard composite coating in kinetic spray process

In kinetic spray processes, the non-uniformity of resultant composite coatings is generally caused by the difference in critical velocity and deposition efficiency between the components of a mixed feedstock. In the present paper, the effects of process parameters, such as feed rate, spray distance, and particle velocity, on the compositional variation between the mixed feedstock and resultant composite coating have been investigated. The results showed that the high diamond fraction in the coating can be achieved using a low feed rate, intermediate spray distance, and high impact particle velocity. The possibility of impact between hard brittle diamond particles is the main factor affecting the diamond fraction in the coating. Although the deposition efficiency, diamond fraction, and bond strength of the coating increase with particle velocity, a slight decrease of cohesive strength between diamond particle and bronze base was also observed.     

Elastic rods in life- and material-sciences: A general integrable model

The study of elastic deformations in thin rods has recently seen renewed interest due to the close connection between these systems and coarse-grained models of widespread application in life- and material-sciences. Until now, the analysis has been restricted to the solution of equilibrium equations for continuous models characterized by constant bending and twisting elastic moduli and/or by isotropic rod section. However, more realistic models often require more general conditions: indeed this is the case whenever microscopic information issuing from atomistic simulations is to be transferred to analytic or semi-analytic coarse-grained or macroscopic models. In this paper we will show that integrable, indeed solvable, equations are obtained under quite general conditions and that regular (e.g. circular helical) solutions emerge from reasonable choices of elastic stiffnesses.