[show abstract][hide abstract] ABSTRACT: In this paper we develop a lattice-based computational model focused on bone resorption by osteoclasts in a single cortical basic multicellular unit (BMU). Our model takes into account the interaction of osteoclasts with the bone matrix, the interaction of osteoclasts with each other, the generation of osteoclasts from a growing blood vessel, and the renewal of osteoclast nuclei by cell fusion. All these features are shown to strongly influence the geometrical properties of the developing resorption cavity including its size, shape and progression rate, and are also shown to influence the distribution, resorption pattern and trajectories of individual osteoclasts within the BMU. We demonstrate that for certain parameter combinations, resorption cavity shapes can be recovered from the computational model that closely resemble resorption cavity shapes observed from microCT imaging of human cortical bone.
[show abstract][hide abstract] ABSTRACT: Cell motility is a fundamental process with relevance to embryonic development, immune response, and metastasis. Cells move either spontaneously, in a nondirected fashion, or in response to chemotactic signals, in a directed fashion. Even though they are often studied separately, both forms of motility share many complex processes at the molecular and subcellular scale, e.g., orchestrated cytoskeletal rearrangements and polarization. In addition, at the cellular level both types of motility include persistent runs interspersed with reorientation pauses. Because there is a great range of variability in motility among different cell types, a key challenge in the field is to integrate these multiscale processes into a coherent framework. We analyzed the motility of Dictyostelium cells with bimodal analysis, a method that compares time spent in persistent versus reorientation mode. Unexpectedly, we found that reorientation time is coupled with persistent time in an inverse correlation and, surprisingly, the inverse correlation holds for both nondirected and chemotactic motility, so that the full range of Dictyostelium motility can be described by a single scaling relationship. Additionally, we found an identical scaling relationship for three human cell lines, indicating that the coupling of reorientation and persistence holds across species and making it possible to describe the complexity of cell motility in a surprisingly general and simple manner. With this new perspective, we analyzed the motility of Dictyostelium mutants, and found four in which the coupling between two modes was altered. Our results point to a fundamental underlying principle, described by a simple scaling law, unifying mechanisms of eukaryotic cell motility at several scales.
[show abstract][hide abstract] ABSTRACT: We have developed an off-lattice hybrid discrete-continuum (OLHDC) model of tumor growth and invasion. The continuum part of the OLHDC model describes microenvironmental components such as matrix-degrading enzymes, nutrients or oxygen, and extracellular matrix (ECM) concentrations, whereas the discrete portion represents individual cell behavior such as cell cycle, cell-cell, and cell-ECM interactions and cell motility by the often-used persistent random walk, which can be depicted by the Langevin equation. Using this framework of the OLHDC model, we develop a phenomenologically realistic and bio/physically relevant model that encompasses the experimentally observed superdiffusive behavior (at short times) of mammalian cells. When systemic simulations based on the OLHDC model are performed, tumor growth and its morphology are found to be strongly affected by cell-cell adhesion and haptotaxis. There is a combination of the strength of cell-cell adhesion and haptotaxis in which fingerlike shapes, characteristic of invasive tumor, are observed.
[show abstract][hide abstract] ABSTRACT: Organisms, at scales ranging from unicellular to mammals, have been known to exhibit foraging behavior described by random walks whose segments confirm to Lévy or exponential distributions. For the first time, we present evidence that single cells (mammary epithelial cells) that exist in multi-cellular organisms (humans) follow a bimodal correlated random walk (BCRW).
Cellular tracks of MCF-10A pBabe, neuN and neuT random migration on 2-D plastic substrates, analyzed using bimodal analysis, were found to reveal the BCRW pattern. We find two types of exponentially distributed correlated flights (corresponding to what we refer to as the directional and re-orientation phases) each having its own correlation between move step-lengths within flights. The exponential distribution of flight lengths was confirmed using different analysis methods (logarithmic binning with normalization, survival frequency plots and maximum likelihood estimation).
Because of the presence of non-uniform turn angle distribution of move step-lengths within a flight and two different types of flights, we propose that the epithelial random walk is a BCRW comprising of two alternating modes with varying degree of correlations, rather than a simple persistent random walk. A BCRW model rather than a simple persistent random walk correctly matches the super-diffusivity in the cell migration paths as indicated by simulations based on the BCRW model.
PLoS ONE 01/2010; 5(3):e9636. · 3.73 Impact Factor
[show abstract][hide abstract] ABSTRACT: Cell migration paths of mammary epithelial cells (expressing different versions of the promigratory tyrosine kinase receptor Her2/Neu) were analyzed within a bimodal framework that is a generalization of the run-and-tumble description applicable to bacterial migration. The mammalian cell trajectories were segregated into two types of alternating modes, namely, the "directional mode" (mode I, the more persistent mode, analogous to the bacterial run phase) and the "re-orientation mode" (mode II, the less persistent mode, analogous to the bacterial tumble phase). Higher resolution (more pixel information, relative to cell size) and smaller sampling intervals (time between images) were found to give a better estimate of the deduced single cell dynamics (such as directional-mode time and turn angle distribution) of the various cell types from the bimodal analysis. The bimodal analysis tool permits the deduction of short-time dynamics of cell motion such as the turn angle distributions and turn frequencies during the course of cell migration compared to standard methods of cell migration analysis. We find that the 2-h mammalian cell tracking data do not fall into the diffusive regime implying that the often-used random motility expressions for mammalian cell motion (based on assuming diffusive motion) are invalid over the time steps (fraction of minute) typically used in modeling mammalian cell migration.
Annals of biomedical engineering 12/2008; 37(1):230-45. · 2.41 Impact Factor
[show abstract][hide abstract] ABSTRACT: We report the development of a coarse-grained Langevin dynamics model of a lamellipodium featuring growing F-actin filaments in order to study the effect of stiffness of the F-actin filament, the G-actin monomer concentration, and the number of polymerization sites on lamellipodium protrusion. The virtual lamellipodium is modeled as a low-aspect-ratio doubly capped cylinder formed by triangulated particles on its surface. It is assumed that F-actin filaments are firmly attached to a lamellipodium surface where polymerization sites are located, and actin polymerization takes place by connecting a G-actin particle to a polymerization site and to the first particle of a growing F-actin filament. It is found that there is an optimal number of polymerization sites for rapid lamellipodium protrusion. The maximum speed of lamellipodium protrusion is related to competition between the number of polymerization sites and the number of available G-actin particles, and the degree of pulling and holding of the lamellipodium surface by non-polymerizing actin filaments. The lamellipodium protrusion by actin polymerization displays saltatory motion exhibiting pseudo-thermal equilibrium: the lamellipodium speed distribution is Maxwellian in two dimensions but the lamellipodium motion is biased so that the lamellipodium speed in the direction of the lamellipodium motion is much larger than that normal to the lamellipodium motion.
Journal of Statistical Physics 10/2008; 133(1):79-100. · 1.40 Impact Factor
[show abstract][hide abstract] ABSTRACT: We have developed a necklace model of polyelectrolyte chain in which the necklace structure appears as a result of the counterion condensation on the polyelectrolyte backbone. This necklace structure optimizes the correlation-induced attraction of the condensed counterions and charged monomers and electrostatic repulsion between uncompensated charges. The new feature of this necklace globule is that it can be formed even in good solvent conditions for the polymer backbone. By using the scaling analysis, we have calculated the diagram of state of polyelectrolyte chain as a function of the solvent quality for the polymer backbone and value of the Bjerrum length. To test the predictions of a scaling model, we have performed molecular dynamics simulations of polyelectrolyte chains with the degrees of polymerizations N = 124−304 and fraction of charged monomers f = 1/3 in good, θ, and poor solvent conditions for the polymer backbone. We have identified the range of parameters in which the necklace globule is formed due to correlation-induced attractive interactions in the good solvent conditions for the polymer backbone. The results of the molecular dynamics simulations are in qualitative agreement with the predictions of a scaling model.
[show abstract][hide abstract] ABSTRACT: We have performed molecular dynamics simulations and developed a scaling model of a nanopropulsion engine. The engine consists of a nozzlelike pore with catalytic sites located at the closed end of the nozzle. The nozzle is immersed in a solution of monomers that serves as a ?fuel? for the polymerization reaction. The engine can be thought of as an analogue of the jet propulsion engine that secretes polymers in a solution and utilizes polymer viscoelasticity for its motion. Using scaling analysis, we have established that the nozzle velocity is proportional to the chain's polymerization rate with the proportionality coefficient being determined by the nozzle geometry, the nozzle friction coefficient, and the dynamics of the polymer chains inside the nozzle. The results of the molecular dynamics simulations are in remarkable agreement with the predictions of the scaling model.
[show abstract][hide abstract] ABSTRACT: Complexation between polyelectrolyte and polyampholyte chains in poor solvent conditions for the polyelectrolyte backbone has been studied by molecular dynamics simulations. In a poor solvent a polyelectrolyte forms a necklace-like structure consisting of polymeric globules (beads) connected by strings of monomers. The simulation results can be explained by assuming the existence of two different mechanisms leading to the necklace formation. In the case of weak electrostatic interactions, the necklace formation is driven by optimization of short-range monomer-monomer attraction and electrostatic repulsion between charged monomers on the polymer backbone. In the case of strong electrostatic interactions, the necklace structure appears as a result of counterion condensation. While the short-range attractions between monomers are still important, the correlation-induced attraction between condensed counterions and charged monomers and electrostatic repulsion between uncompensated charges provide significant contribution to optimization of the necklace structure. Upon forming a complex with both random and diblock polyampholytes, a polyelectrolyte chain changes its necklace conformation by forming one huge bead. The collapse of the polyelectrolyte chain occurs due to the neutralization of the polyelectrolyte charge by polyampholytes. In the case of the random polyampholyte, the more positively charged sections of the chain mix with negatively charged polyelectrolyte forming the globular bead while more negatively charged chain sections form loops surrounding the collapsed core of the aggregate. In the case of diblock polyampholyte, the positively charged block, a part of the negatively charged block, and a polyelectrolyte chain form a core of the aggregate with a substantial section of the negatively charged block sticking out from the collapsed core of the aggregate. In both cases the core of the aggregate has a layered structure that is characterized by the variations in the excess of concentration of monomers belonging to polyampholyte and polyelectrolyte chains throughout the core radius. These structures appear as a result of optimization of the net electrostatic energy of the complex and short-range attractive interactions between monomers of the polyelectrolyte chain.
The Journal of Physical Chemistry B 01/2007; 110(48):24652-65. · 3.61 Impact Factor
[show abstract][hide abstract] ABSTRACT: The effect of the strength of electrostatic and short-range interactions on the multilayer assembly of oppositely charged polyelectrolytes at a charged substrate was studied by molecular dynamics simulations. The multilayer buildup was achieved through sequential adsorption of charged polymers in a layer-by-layer fashion from dilute polyelectrolyte solutions. The strong electrostatic attraction between oppositely charged polyelectrolytes at each deposition step is a driving force behind the multilayer growth. Our simulations have shown that a charge reversal after each deposition step is critical for steady multilayer growth and that there is a linear increase in polymer surface coverage after the first few deposition steps. Furthermore, there is substantial intermixing between chains adsorbed during different deposition steps. We show that the polymer surface coverage and multilayer structure are each strongly influenced by the strength of electrostatic and short-range interactions.
[show abstract][hide abstract] ABSTRACT: We performed molecular dynamics simulations of multilayer assemblies of flexible polyelectrolytes and nanoparticles. The film was constructed by sequential adsorption of oppositely charged polymers and nanoparticles in layer-by-layer fashion from dilute solutions. We have studied multilayer films assembled from oppositely charged polyelectrolytes, oppositely charged nanoparticles, and mixed films containing both nanoparticles and polyelectrolytes. For all studied systems, the multilayer assembly proceeds through surface overcharging after completion of each deposition step. There is almost linear growth in the surface coverage and film thickness. The multilayer films assembled from nanoparticles show better layer stratification but at the same time have higher film roughness than those assembled from flexible polyelectrolytes.
[show abstract][hide abstract] ABSTRACT: We performed molecular dynamics simulations of the electrostatic assembly of multilayers of flexible polyelectrolytes at a charged surface. The multilayer build-up was achieved through sequential adsorption of oppositely charged polymers in a layer-by-layer fashion from dilute polyelectrolyte solutions. The steady-state multilayer growth proceeds through a charge reversal of the adsorbed polymeric film which leads to a linear increase in the polymer surface coverage after completion of the first few deposition steps. Moreover, substantial intermixing between chains adsorbed during different deposition steps is observed. This intermixing is consistent with the observed requirement for several deposition steps to transpire for completion of a single layer. However, despite chain intermixing, there are almost perfect periodic oscillations of the density difference between monomers belonging to positively and negatively charged macromolecules in the adsorbed film. Weakly charged chains show higher polymer surface coverage than strongly charged ones.
[show abstract][hide abstract] ABSTRACT: We have studied how the charge distribution along a polyampholyte backbone influences aggregation of polyampholyte and polyelectrolyte chains in dilute and semidilute solutions. Using molecular dynamics (MD) simulations, we have shown that the complexation between polyampholyte and polyelectrolyte chains is due to polarization-induced attractive interactions between molecules. A polyampholyte chain binds to a polyelectrolyte in such a way to maximize the electrostatic attraction between oppositely charged ionic groups and minimize the electrostatic repulsion between similarly charged ones. The charge sequence along the polyampholyte backbone has a profound effect on the complex structure. In dilute solutions, a diblock polyampholyte could form a three-arm starlike complex in which the longest branches of the star are formed either by two sections of the polyelectrolyte chain or by a negatively charged block of the polyampholyte and by a section of the polyelectrolyte chain. There are no such complexes in solutions of random polyampholytes and polyampholytes with short blocky charge sequences. In dilute solutions of moderate polymer concentration polyampholytes with long blocky charge sequences form mixed micellar aggregates containing both polyampholyte and polyelectrolyte chains. In semidilute solutions diblock polyampholytes form a network of micelles spanning the entire system. On the contrary, the structure of multichain aggregates formed by random polyampholytes and polyelectrolytes resembles that of branched polymers with polyampholyte chains cross-linking polyelectrolytes together. The osmotic coefficients of polyampholyte polyelectrolyte mixtures show no dependence on the charge sequence along the polymer backbone, confirming the leading contribution of small ions to osmotic pressure of ionic systems.
[show abstract][hide abstract] ABSTRACT: Nanoscale assembly of protein-polyelectrolyte multilayer thin films on solid surfaces has tremendous potential in areas such as biomaterials, drug delivery and fabrication of biosensing devices. The ability to control nanoscale structure and order of these films is essential for surface patterning and templating. We performed molecular dynamics simulations of the protein-polyelectrolyte layer-by-layer assembly on a solid planar surface formed by hexagonally packed particles. Spherical-shaped model protein was constructed by utilizing the charged residues of lysozyme, which was obtained from the Protein Data Bank, to model protein charge distribution. Multilayer build-up was achieved through sequential adsorption of proteins and flexible polyelectrolytes in a layer-by-layer fashion from dilute solutions. The effect of the three dimensional structural rigidity of proteins, charge distribution and hydrophobicity on the film structure was studied.
[show abstract][hide abstract] ABSTRACT: Molecular dynamics simulations of polyelectrolyte multilayering on a charged spherical particle revealed that the sequential adsorption of oppositely charged flexible polyelectrolytes proceeds with surface charge reversal and highlighted electrostatic interactions as the major driving force of layer deposition. Far from being completely immobilized, multilayers feature a constant surge of chain intermixing during the deposition process, consistent with experimental observations of extensive interlayer mixing in these films. The formation of multilayers as well as the extent of layer intermixing depends on the degree of polymerization of the polyelectrolyte chains and the fraction of charge on its backbone. The presence of ionic pairs between oppositely charged macromolecules forming layers seems to play an important role in stabilizing the multilayer film.
[show abstract][hide abstract] ABSTRACT: Electrostatic assembly of multilayered thin films through sequential adsorption of polyions in layer-by-layer fashion utilizes the strong electrostatic attraction between oppositely charged molecules. We perform molecular dynamics simulations of multilayers of flexible polyelectrolytes around a charged spherical particle. Our simulations establish that the charge reversal after each deposition step is a crucial factor for the steady layer growth. The multilayers appear to be nonequilibrium structures.
[show abstract][hide abstract] ABSTRACT: We present the results of Monte Carlo simulations of complexation between polyampholyte and polyelectrolyte chains. Polymers are modeled as bead-spring chains of charged Lennard-Jones particles each consisting of 32 monomers. Formation of a polyampholyte-polyelectrolyte complex is driven by polarization-induced attractive interactions. The complex is usually formed at the end of the polyelectrolyte with the polyampholyte chain elongated and aligned along the polyelectrolyte backbone. This complex structure between the polarized polyampholyte chain and the polyelectrolyte leads to maximization of the attractive and minimization of the repulsive electrostatic interactions. The size of a polyampholyte in a complex is usually larger than that of an isolated polyampholyte chain. We also observed that initially collapsed polyampholytes undergo a coil-globule transition by forming a complex. The structure of a polyampholyte-polyelectrolyte complex was analyzed by tail and loop distribution functions. We have found that the number of loops increases while their sizes decrease with the strength of the electrostatic interactions. Polyampholytes with random charge sequence form stronger complexes with polyelectrolytes than those with alternating charge sequence. Polyampholytes with long blocky sequences form a double helix with a polyelectrolyte at sufficiently large values of the Bjerrum length.
[show abstract][hide abstract] ABSTRACT: Layer-by-layer self-assembly of charged molecules is a versatile route to structured and robust ultra thin films, which have a variety of applications. Using a simple coarse-grained model of charged polymers, we examine the adsorption of oppositely charged polyelectrolytes on a discretely charged spherical particle using Molecular Dynamics simulations. Effects of the chain degree of polymerization and fraction of charged monomers have been studied. We observed overcharging and subsequent adsorption of the layers, although the layers were subject to competitive polyelectrolyte complexation. The adsorption process has been found to favor longer chains with larger charge fractions. Multilayering appears to be the non-equilibrium kinetically trapped state which after equilibration transforms into bilayer structure. Alternate adsorption of proteins and polyelectrolytes has been simulated and was found to exhibit similar layer structure with an increase in the adsorbed chains. Details of the layer structure have been analyzed using density profiles. Thus, a simple electrostatic model explains the self-assembly.
[show abstract][hide abstract] ABSTRACT: Computer simulations have been performed to study polymeric and biological systems such as protein-polyelectrolyte complexes and bacterial gliding motility. In polymeric systems, we have studied complex formation between proteins (polyampholytes) and polyelectrolyte chains in dilute and semidilute solutions. Using Monte Carlo (MC) and molecular dynamics (MD) simulations we have shown that the complexation between polyampholyte and polyelectrolyte chains is due to polarization induced attractive interactions between molecules. A polyampholyte chain binds to a polyelectrolyte in such a way to maximize the electrostatic attraction between oppositely charged ionic groups and minimize the electrostatic repulsion between similarly charged ones. In dilute solutions, a complex is usually formed by one polyampholyte and one polyelectrolyte chain. The complex structure changes from double helical structure to three-arm star-like complex depending on the strength of electrostatic interaction and the charge sequence along polyampholyte backbone. In dilute solutions of moderate polymer concentration, diblock polyampholytes and polyelectrolytes form micellar aggregates that bind together resulting in a network of micelles spanning the entire system in semidilute solutions. On the contrary, the structure of multichain aggregates formed by random polyampholytes and polyelectrolytes resembles that of branched polymers. In biological systems, we have studied how the slime secretion by Cyanobacteria and Myxobacteria is related to their gliding motility over surfaces. The slime is produced by the nozzle-like pores located on the bacteria surface. To understand the mechanism of gliding motion and its relation to the slime polymerization, we have performed molecular dynamics simulations of a molecular nozzle with growing inside polymer chains. These simulations show that the compression of polymer chains inside the nozzle is a driving force for its motion. There is a linear relationship between the average nozzle velocity and the chain polymerization rate with a proportionality coefficient dependent on the geometric characteristics of the nozzle such as its length and friction coefficient. This minimal model of the molecular engine was used to explain the gliding motion of bacteria over surfaces.
[show abstract][hide abstract] ABSTRACT: We have performed molecular dynamics simulations of multilayer assembly of oppositely charged polyelectrolytes at charged surfaces. The multilayer build-up was achieved through sequential adsorption of charged polymers in a layer-by-layer fashion from dilute polyelectrolyte solutions. The strong electrostatic attraction between oppositely charged polyelectrolytes at each deposition step is a driving force behind the nanometer-scale multilayer growth. Our simulations have shown that a charge reversal after each deposition step is critical for steady multilayer growth and that there is a linear increase in amount of polymer adsorbed after the first few deposition steps. There is substantial intermixing between chains adsorbed during different deposition steps within multilayer film. Despite significant chain intermixing, however, there are almost perfect periodic oscillations in local composition of positively and negatively charged polymers in the adsorbed film. We show that the film thickness, polymer surface coverage exhibit strong correlation with the strength of electrostatic and short-range interactions.