Coarse-grained Network Research Articles

Modeling global changes induced by local perturbations to the HIV-1 capsid

The HIV-1 capsid is a conical protein shell made up of hexamers and pentamers of the capsid protein. The capsid houses the viral genome and replication machinery, and its opening, or uncoating, within the host cell marks a critical step in the HIV-1 lifecycle. Binding of host factors such as TRIM5α and cyclophilin A (CypA) can alter the capsid’s stability, accelerating or delaying the onset of uncoating and disrupting infectivity. We employ coarse-grained computational modeling to investigate the effects of point mutations and host factor binding on HIV-1 capsid stability. We find that the largest fluctuations occur in the low-curvature regions of the capsid, and that its structural dynamics are affected by perturbations at the inter-hexamer interfaces and near the CypA binding loop, suggesting roles for these features in capsid stability. Our models show that linking capsid proteins across hexamers attenuates vibration in the low-curvature regions of the capsid, but that linking within hexamers does not. These results indicate a possible mechanism through which CypA binding alters capsid stability and highlight the utility of coarse-grained network modeling for understanding capsid mechanics.

Simulation of Deformation and Aggregation of Two Red Blood Cells in a Stenosed Microvessel by Dissipative Particle Dynamics.

The motion of two red blood cells in a stenosed microvessel was simulated using dissipative particle dynamics. The effects of intercellular interaction, red blood cell deformability and the initial cell orientation on the deformation and aggregation of the RBCs and on the flow resistance were investigated. The red blood cell membrane was treated as a three-dimensional coarse-grained network model and the intercellular interaction was modeled by the Morse potential based on a depletion-mediated assumption. It is shown that the flow resistance increases dramatically when the red blood cells enter into the stenosis and decreases rapidly as RBCs move away from the stenosis. Particularly, for a pair of stiffer red blood cells with the initial inclination angle of 90°, the maximum value of the flow resistance is larger; while a higher flow resistance can also come from a stronger aggregation. For a pair of stiffer red blood cells moving parallel to the main flow, when their positions are closer to the vessel wall at the upstream of the stenosis, the flow resistance increases due to the migration to the vessel center at the stenosis. In addition, for a pair of red blood cells with the initial inclination angle of 0°, the flow resistance from the aggregate formed by a pair of red blood cells with a larger deformation is higher.

Approach to the unfolding and folding dynamics of add A-riboswitch upon adenine dissociation using a coarse-grained elastic network model.

Riboswitches are noncoding mRNA segments that can regulate the gene expression via altering their structures in response to specific metabolite binding. We proposed a coarse-grained Gaussian network model (GNM) to examine the unfolding and folding dynamics of adenosine deaminase (add) A-riboswitch upon the adenine dissociation, in which the RNA is modeled by a nucleotide chain with interaction networks formed by connecting adjoining atomic contacts. It was shown that the adenine binding is critical to the folding of the add A-riboswitch while the removal of the ligand can result in drastic increase of the thermodynamic fluctuations especially in the junction regions between helix domains. Under the assumption that the native contacts with the highest thermodynamic fluctuations break first, the iterative GNM simulations showed that the unfolding process of the adenine-free add A-riboswitch starts with the denature of the terminal helix stem, followed by the loops and junctions involving ligand binding pocket, and then the central helix domains. Despite the simplified coarse-grained modeling, the unfolding dynamics and pathways are shown in close agreement with the results from atomic-level MD simulations and the NMR and single-molecule force spectroscopy experiments. Overall, the study demonstrates a new avenue to investigate the binding and folding dynamics of add A-riboswitch molecule which can be readily extended for other RNA molecules.

Influence of crosslinking functionality, temperature and conversion on heterogeneities in polymer networks

Crosslinked polymer formation commonly occurs when two or more multi-functional precursors react to form a three-dimensional network. The resulting networks may contain a significant number of topological imperfections such as loops or dangling ends when formed using crosslinkers with high functionality or when crosslinking at high temperatures. We employ molecular dynamics simulations to analyze these topological imperfections in coarse-grained networks generated from precursors consisting of ‘chain extenders’ composed of two beads (dimers) and a crosslinker of functionality f = 3 or 6 for a wide range of crosslinking temperatures and final conversions. It is shown that these imperfections result in networks in which the number of elastically active chains, the cycle rank and the number of elastically active junctions is smaller than predicted by the Miller–Macosko theory. Such defects must adversely affect the mechanical properties, resistance to solvent swelling and, possibly, the long-term protective properties of polymer networks.

Symmetry-based coarse-graining of evolved dynamical networks

Networks with a prescribed power-law scaling in the spectrum of the graph Laplacian can be generated by evolutionary optimization. The Laplacian spectrum encodes the dynamical behavior of many important processes. Here, the networks are evolved to exhibit subdiffusive dynamics. Under the additional constraint of degree-regularity, the evolved networks display an abundance of symmetric motifs arranged into loops and long linear segments. Exploiting results from algebraic graph theory on symmetric networks, we find the underlying backbone structures and how they contribute to the spectrum. The resulting coarse-grained networks provide an intuitive view of how the anomalous diffusive properties can be realized in the evolved structures.

Monte Carlo tests of small-world architecture for coarse-grained networks of the United States railroad and highway transportation systems

Several studies have shown that human transportation networks exhibit small-world structure, meaning they have high local clustering and are easily traversed. However, some have concluded this without statistical evaluations, and others have compared observed structure to globally random rather than planar models. Here, we use Monte Carlo randomizations to test US transportation infrastructure data for small-worldness. Coarse-grained network models were generated from GIS data wherein nodes represent the 3105 contiguous US counties and weighted edges represent the number of highway or railroad links between counties; thus, we focus on linkage topologies and not geodesic distances. We compared railroad and highway transportation networks with a simple planar network based on county edge-sharing, and with networks that were globally randomized and those that were randomized while preserving their planarity. We conclude that terrestrial transportation networks have small-world architecture, as it is classically defined relative to global randomizations. However, this topological structure is sufficiently explained by the planarity of the graphs, and in fact the topological patterns established by the transportation links actually serve to reduce the amount of small-world structure.

The phenotype of cancer cell invasion controlled by fibril diameter and pore size of 3D collagen networks

The behavior of cancer cells is strongly influenced by the properties of extracellular microenvironments, including topology, mechanics and composition. As topological and mechanical properties of the extracellular matrix are hard to access and control for in-depth studies of underlying mechanisms in vivo, defined biomimetic in vitro models are needed. Herein we show, how pore size and fibril diameter of collagen I networks distinctively regulate cancer cell morphology and invasion. Three-dimensional collagen I matrices with a tight control of pore size, fibril diameter and stiffness were reconstituted by adjustment of concentration and pH value during matrix reconstitution. At first, a detailed analysis of topology and mechanics of matrices using confocal laser scanning microscopy, image analysis tools and force spectroscopy indicate pore size and not fibril diameter as the major determinant of matrix elasticity. Secondly, by using two different breast cancer cell lines (MDA-MB-231 and MCF-7), we demonstrate collagen fibril diameter – and not pore size – to primarily regulate cell morphology, cluster formation and invasion. Invasiveness increased and clustering decreased with increasing fibril diameter for both, the highly invasive MDA-MB-231 cells with mesenchymal migratory phenotype and the MCF-7 cells with amoeboid migratory phenotype. As this behavior was independent of overall pore size, matrix elasticity is shown to be not the major determinant of the cell characteristics. Our work emphasizes the complex relationship between structural-mechanical properties of the extracellular matrix and invasive behavior of cancer cells. It suggests a correlation of migratory and invasive phenotype of cancer cells in dependence on topological and mechanical features of the length scale of single fibrils and not on coarse-grained network properties.

Dynamic moduli of magneto-sensitive elastomers: a coarse-grained network model.

The viscoelastic properties of magneto-sensitive elastomers (MSEs) in a low-frequency regime are studied using a coarse-grained network model. The proposed model takes into account the mechanical coupling between magnetic particles included in a whole network structure and magnetic interactions between them. We show that the application of a constant uniform magnetic field leads to the splitting of the relaxation spectrum into two branches for the motions of the particles parallel and perpendicular to the field. The shear dynamic moduli G' and G'' of MSEs are calculated as a function of frequency. The values of G' and G'' are shown to depend on the direction of the shear deformation with respect to the magnetic field. For instance, both G' and G'' decrease if the magnetic field is applied parallel to the shear velocity (D-geometry) and increase if it is applied along the shear gradient (G-geometry). The latter prediction is in a qualitative agreement with existing experimental data. The theory allows us to analyse experimental data and to extract the structural characteristics of MSEs.

Thermal Properties and Topology of Epoxy Networks: A Multiscale Simulation Methodology

We present a novel hierarchical multiscale methodology aimed at generating the atomistic structure of epoxy networks and predicting their properties and topology. Our approach combines several computational techniques and consists of four separate procedures: (1) mapping of the polymerizing monomers onto a coarse-grained representation using the method of neural-gas networks, (2) cross-linking the coarse-grained monomers at mesoscale by applying dissipative particle dynamics and a probabilistic reaction scheme, (3) reverse mapping of the coarse-grained polymer network to a fully atomistic representation, and (4) simulation of the atomistic model by means of molecular dynamics technique. As a case study, we simulate DGEBA + DETDA epoxy network formation and analyze the thermal properties and the network topology. It was found that the parameters used for generating the atomistic structures (degree of coarse graining in our case) can significantly influence the network topology and properties. Moreover, we ...

Combining Theory and Experiments to Understand Sugar Regulation in Bacteria

In this review we discuss the interaction between experiments and theory in understanding regulatory systems in bacterial cells, using the galactose network of E. coli as a model system to illustrate this. Initially, experiments led to a coarse-grained network view of this system, which revealed the structure of entangled negative and positive feedback loops that regulates galactose metabolism. A dynamical model, based on this network picture and in vitro experiments, indicated that one of the main regulators would have little role to play in any steady-state scenarios. The dynamical experiments this result suggested revealed the intricate timing sequence of gene expression in situations of rapidly decreasing galactose. All this information is slowly coming together to form a picture of how the different elements of the galactose regulatory system work together to regulate metabolism in the presence of fluctuating and changing food sources.

Assessing the effect of dynamics on the closed-loop protein-folding hypothesis

The closed-loop (loop-n-lock) hypothesis of protein folding suggests that loops of about 25 residues, closed through interactions between the loop ends (locks), play an important role in protein structure. Coarse-grain elastic network simulations, and examination of loop lengths in a diverse set of proteins, each supports a bias towards loops of close to 25 residues in length between residues of high stability. Previous studies have established a correlation between total contact distance (TCD), a metric of sequence distances between contacting residues (cf. contact order), and the log-folding rate of a protein. In a set of 43 proteins, we identify an improved correlation (r2 = 0.76), when the metric is restricted to residues contacting the locks, compared to the equivalent result when all residues are considered (r2 = 0.65). This provides qualified support for the hypothesis, albeit with an increased emphasis upon the importance of a much larger set of residues surrounding the locks. Evidence of a similar-sized protein core/extended nucleus (with significant overlap) was obtained from TCD calculations in which residues were successively eliminated according to their hydrophobicity and connectivity, and from molecular dynamics simulations. Our results suggest that while folding is determined by a subset of residues that can be predicted by application of the closed-loop hypothesis, the original hypothesis is too simplistic; efficient protein folding is dependent on a considerably larger subset of residues than those involved in lock formation.

Relaxation spectrum of a polymer network with included particles: A regular cubic network model with mutual friction

A theory of the viscoelastic properties of crosslinked polymers with included particles is developed. The model of a regular cubic coarse-grain network, which suggests the viscoelastic interaction of the particles with the crosslink sites, is used. The particles are assumed to be close to isotropic, and their mobility is described via the introduction of a friction coefficient that is directly proportional to the particle radii. In the framework of this model, the spectrum of relaxation times of the network with included particles consists of two branches: One corresponds to the local displacements of the particles relative to the crosslink sites; the other describes the large-scale collective mobility of the particles along with the network fragments. At all values of the viscoelastic parameters of the model, the relative width of the relaxation-time spectrum for the network with included particles is higher than that for the initial network without included particles. This theoretical result qualitatively explains the experimental data on the mechanical and dielectric relaxations of crosslinked composites, which verify the broadening of the frequency dependences of the elasticity modulus, loss modulus, and dielectric-loss factor for the filled crosslinked polymers relative to these dependences for the initial (unfilled) polymer networks.

Milestoning Simulation Reveals Mechanism of Helix-Breaking

Milestoning Simulation Reveals Mechanism of Helix-Breaking

Coarse-Grained Computational Characterization of RNA Nanocube Flexibility Correlates with Experiments

The emerging field of RNA-based nanotechnology can benefit from the development of new computational methods capable of helping in the design and characterization of nano-scale particles, leading to the development of qualitatively new structures and novel therapeutics. We have approached the computer-aided design process by creating a pipeline of tools, starting with a database of n-way junctions and kissing-loops called RNAJunction. This database provides building blocks for our programs, such as NanoTiler and RNA2D3D, which use them to design 3D models of RNA nanostructures. First, the building blocks are treated as rigid objects. Then, just as the natural RNA is shaped (deformed) by the larger structural contexts, our programs allow for deformations to be applied in order to produce fully assembled models. To assess the realistic limits of these deformations, we consider flexibility data available as alternative structures in databases as well as results of Molecular Dynamics (MD) simulations at the atomic resolution level and coarse-grained computational methods. Here we present an example of the modeling process including RNA flexibility information for three nanocube model variants and a novel application of a coarse-grained Anisotropic Network Model (ANM) to the RNA nanostructure characterization. The predictions of different efficiency of assembly for three nanocube variants, based on the exploratory modeling, were confirmed in in vitro experiments. The ANM simulations showed that the dynamics of the full nanostructure has to be considered in order to explain the differences between the size of the initial static models and that of the experimentally measured nanoparticles, thus bringing the computational and the experimental results into agreement. The ANM simulations also offered an additional insight into the assembly yields and the difference in the melting temperatures of the cube variants.Funded in part by HHSN261200800001E

Network Topologies and Dynamics Leading to Endotoxin Tolerance and Priming in Innate Immune Cells

The innate immune system, acting as the first line of host defense, senses and adapts to foreign challenges through complex intracellular and intercellular signaling networks. Endotoxin tolerance and priming elicited by macrophages are classic examples of the complex adaptation of innate immune cells. Upon repetitive exposures to different doses of bacterial endotoxin (lipopolysaccharide) or other stimulants, macrophages show either suppressed or augmented inflammatory responses compared to a single exposure to the stimulant. Endotoxin tolerance and priming are critically involved in both immune homeostasis and the pathogenesis of diverse inflammatory diseases. However, the underlying molecular mechanisms are not well understood. By means of a computational search through the parameter space of a coarse-grained three-node network with a two-stage Metropolis sampling approach, we enumerated all the network topologies that can generate priming or tolerance. We discovered three major mechanisms for priming (pathway synergy, suppressor deactivation, activator induction) and one for tolerance (inhibitor persistence). These results not only explain existing experimental observations, but also reveal intriguing test scenarios for future experimental studies to clarify mechanisms of endotoxin priming and tolerance.

Network Topologies and Dynamics Leading to Endotoxin Tolerance and Priming in Innate Immune Cells

The innate immune system, acting as the first line of host defense, senses and adapts to foreign challenges through complex intracellular and intercellular signaling networks. Endotoxin tolerance and priming elicited by macrophages are classic examples of the complex adaptation of innate immune cells. Upon repetitive exposures to different doses of bacterial endotoxin (lipopolysaccharide) or other stimulants, macrophages show either suppressed or augmented inflammatory responses compared to a single exposure to the stimulant. Endotoxin tolerance and priming are critically involved in both immune homeostasis and the pathogenesis of diverse inflammatory diseases. However, the underlying molecular mechanisms are not well understood. By means of a computational search through the parameter space of a coarse-grained three-node network with a two-stage Metropolis sampling approach, we enumerated all the network topologies that can generate priming or tolerance. We discovered three major mechanisms for priming (pathway synergy, suppressor deactivation, activator induction) and one for tolerance (inhibitor persistence). These results not only explain existing experimental observations, but also reveal intriguing test scenarios for future experimental studies to clarify mechanisms of endotoxin priming and tolerance.

Transition Pathways of Proteins Explored by Combining Molecular Dynamics Simulations and Monte Carlo Sampling of Collective Modes

The conformational transition of proteins is explored using a molecular dynamics (MD) simulation protocol which is guided by the normal modes derived from coarse-grained anisotropic network model (ANM). The methodology applies to the cases where the passage from one substate to another (e.g., the open and closed forms of an enzyme, or outward-facing and inward-facing states of a transporter) within a global energy minimum (native state) involves relatively low energy barriers, based on the assumption that low energy barriers may be surmounted/overlooked by adopting a coarse-grained description of the structure and energetics, which smoothes out the energy landscape. The basic approach is to deform the structure along ANM modes, similar to the adaptive ANM (aANM) procedure adopted in our previous work,(Yang et al., 2009) but with the major improvement that the intermediate structures are selected from the complete pool of all accessible ANM modes of motion using a Monte Carlo/Metrolopis algorithm. Application to two proteins with different functional mechanisms, Escherichia coli adenylate kinase (AK) and dopamine transporter, shows that the transition between the two alternative forms does not necessarily obey the same pathway(s). For example, in the case of AK, the open-to-closed (O->C) and closed-to-open (C->O) transitions of AK proceed via distinct intermediate conformers: the ATP-binding (LID) domain closing (opening) takes place faster than the nucleotide monophosphate-binding (NMP) domain closing (opening) in the O->C (C->O) transition.Yang, Z., Majek, P., and Bahar, I. (2009). Allosteric transitions of supramolecular systems explored by network models: application to chaperonin GroEL. PLoS Comput. Biol. 5, e1000360.

Structure-based, biophysical annotation of molecular coevolution of acetylcholinesterase

Acetylcholinesterase (AChE) is an important enzyme in the nervous system. It terminates signal transmission at chemical synapses by degrading the neurotransmitter acetylcholine and was found to play a role in plaque formation in Alzheimer's disease. Several functional parts of its structure have been identified in the past. Here, we use a coarse-grained anisotropic network model approach based on structure data to analyze protein mechanics of AChE. Single contacts in the protein are "switched off" and the change in the intrinsic dynamics is measured. We correlate the gained insight with information about coevolution within the molecule derived from multiple sequence alignments. More than 300 AChE sequences were aligned and the mutual information of the positions was calculated. From these structural, biophysical, and evolutionary data we could reveal sites of coevolutionary signatures in AChE, annotate them by the selective pressure induced for biophysical reasons, and further pave the way for a more detailed understanding of evolutionary boundary conditions for AChE.

Coarse graining for synchronization in directed networks

Coarse-graining model is a promising way to analyze and visualize large-scale networks. The coarse-grained networks are required to preserve statistical properties as well as the dynamic behaviors of the initial networks. Some methods have been proposed and found effective in undirected networks, while the study on coarse-graining directed networks lacks of consideration. In this paper we proposed a path-based coarse-graining (PCG) method to coarse grain the directed networks. Performing the linear stability analysis of synchronization and numerical simulation of the Kuramoto model on four kinds of directed networks, including tree networks and variants of Barabási-Albert networks, Watts-Strogatz networks, and Erdös-Rényi networks, we find our method can effectively preserve the network synchronizability.

A Fine-Grained Embedded-Software-Network Detection Method

The continuous development of embedded technology has emerged an increasing demand of internet-based embedded software. The current existing tools only offer coarse-grained network detection, in other words, they don’t satisfy the refining detection standard for the convenience of developers. This paper begins with analysis into defects of the current network detection methods and tools with deep insight from the Netfilter of Linux kernel and protocol stack for packet processing technology, it then proposes a fine-grained network detection method, with which we build up an embedded-software-network detection tool for digital-home-appliances. The built tool can operate real-time and fine-grained monitoring. An experiment has been performed in the final section of the paper to prove the accuracy of the method.