Globular Protein Folding In Vitro and In Vivo

In vitro, computational, and theoretical studies of protein folding have converged to paint a rich and complex energy landscape. This landscape is sensitively modulated by environmental conditions and subject to evolutionary pressure on protein function. Of these environments, none is more complex than the cell itself, where proteins function in the cytosol, in membranes, and in different compartments. A wide variety of kinetic and thermodynamics experiments, ranging from single-molecule studies to jump kinetics and from nuclear magnetic resonance to imaging on the microscope, have elucidated how protein energy landscapes facilitate folding and how they are subject to evolutionary constraints and environmental perturbation. Here we review some recent developments in the field and refer the reader to some original work and additional reviews that cover this broad topic in protein science.

Microscale Testing and Modelling of Cement Paste as Basis for Multi-Scale Modelling

This work aims to provide a method for numerically and experimentally investigating the fracture mechanism of cement paste at the microscale. For this purpose, a new procedure was proposed to prepare micro cement paste cubes (100 × 100 × 100 µm³) and beams with a square cross section of 400 × 400 µm². By loading the cubes to failure with a Berkovich indenter, the global mechanical properties of cement paste were obtained with the aid of a nano-indenter. Simultaneously the 3D images of cement paste with a resolution of 2 µm³/voxel were generated by applying X-ray microcomputed tomography to a micro beam. After image segmentation, a cubic volume with the same size as the experimental tested specimen was extracted from the segmented images and used as input in the lattice model to simulate the fracture process of this heterogeneous microstructure under indenter loading. The input parameters for lattice elements are local mechanical properties of different phases. These properties were calibrated from experimental measured load displacement diagrams and failure modes in which the same boundary condition as in simulation were applied. Finally, the modified lattice model was applied to predict the global performance of this microcube under uniaxial tension. The simulated Young’s modulus agrees well with the experimental data. With the method presented in this paper the framework for fitting and validation of the modelling at microscale was created, which forms a basis for multi-scale analysis of concrete.

Diffusion-limited phase separation in eukaryotic chemotaxis

The ability of cells to sense spatial gradients of chemoattractant factors governs the development of complex eukaryotic organisms. Cells exposed to shallow chemoattractant gradients respond with strong accumulation of the enzyme phosphatidylinositol 3-kinase (PI3K) and its D3-phosphoinositide product (PIP(3)) on the plasma membrane side exposed to the highest chemoattractant concentration, whereas PIP(3)-degrading enzyme PTEN and its product PIP(2) localize in a complementary pattern. Such an early symmetry-breaking event is a mandatory step for directed cell movement elicited by chemoattractants, but its physical origin is still mysterious. Here, we propose that directional sensing is the consequence of a phase-ordering process mediated by phosphoinositide diffusion and driven by the distribution of chemotactic signal. By studying a realistic reaction-diffusion lattice model that describes PI3K and PTEN enzymatic activity, recruitment to the plasma membrane, and diffusion of their phosphoinositide products, we show that the effective enzyme-enzyme interaction induced by catalysis and diffusion introduces an instability of the system toward phase separation for realistic values of physical parameters. In this framework, large reversible amplification of shallow chemotactic gradients, selective localization of chemical factors, macroscopic response timescales, and spontaneous polarization arise naturally. The model is robust with respect to order-of-magnitude variations of the parameters.

A simple approach to polymer mixture miscibility

Polymeric mixtures are important materials, but the control and understanding of mixing behaviour poses problems. The original Flory-Huggins theoretical approach, using a lattice model to compute the statistical thermodynamics, provides the basic understanding of the thermodynamic processes involved but is deficient in describing most real systems, and has little or no predictive capability. We have developed an approach using a lattice integral equation theory, and in this paper we demonstrate that this not only describes well the literature data on polymer mixtures but allows new insights into the behaviour of polymers and their mixtures. The characteristic parameters obtained by fitting the data have been successfully shown to be transferable from one dataset to another, to be able to correctly predict behaviour outside the experimental range of the original data and to allow meaningful comparisons to be made between different polymer mixtures.

A 3D Lattice Modelling Study of Drying Shrinkage Damage in Concrete Repair Systems

Differential shrinkage between repair material and concrete substrate is considered to be the main cause of premature failure of repair systems. The magnitude of induced stresses depends on many factors, for example the degree of restraint, moisture gradients caused by curing and drying conditions, type of repair material, etc. Numerical simulations combined with experimental observations can be of great use when determining the influence of these parameters on the performance of repair systems. In this work, a lattice type model was used to simulate first the moisture transport inside a repair system and then the resulting damage as a function of time. 3D simulations were performed, and damage patterns were qualitatively verified with experimental results and cracking tendencies in different brittle and ductile materials. The influence of substrate surface preparation, bond strength between the two materials, and thickness of the repair material were investigated. Benefits of using a specially tailored fibre reinforced material, namely strain hardening cementitious composite (SHCC), for controlling the damage development due to drying shrinkage in concrete repairs was also examined.

Specificity in molecular design: a physical framework for probing the determinants of binding specificity and promiscuity in a biological environment

Binding specificity is an important consideration in drug design. An effective drug molecule often must bind with high specificity to its intended target in the body; lower specificity implies the possibility of significant binding to unintended partners, which could instigate deleterious side effects. However, if the target is a rapidly mutating agent, a drug that is too specific will quickly lose its efficacy by not binding well to functional mutants. Therefore, in molecular design, it is crucial to tailor the binding specificity of a drug to the problem at hand. In practice, specificity is often studied on a case-by-case basis, and it is difficult to create general understanding of the determinants of specificity from the union of such available cases. In this work, we undertook a comprehensive, general study of molecular binding with emphasis on understanding the determinants of specificity from a physical standpoint. By extending a theoretical framework grounded in continuum electrostatics and creating an abstracted lattice model that captures key physical aspects of binding interactions, we systematically explored the relationship between a molecule's physical characteristics and its binding specificity toward potential partners. The theory and simulated binding interactions suggested that charged molecules are more specific binders than their hydrophobic counterparts for several reasons. First, the biological spectrum of possible binding characteristics includes more partners that bind equally well to hydrophobic ligands than to charged ligands. Also, charged ligands, whose electrostatic potentials have strong orientational dependence, are more sensitive to shape complementarity than their hydrophobic counterparts. Ligand conformational and orientational flexibility can further influence a charged molecule's ability to bind specifically. Interestingly, we found that conformational flexibility can increase the specificity of polar and charged ligands, by allowing them to greatly lower the binding free energy to a select few partners relative to others. Additionally, factors such as a molecule's size and the ionic strength of the solution were found to predictably affect binding specificity. Taken together, these results, all of which stem from a unified theoretical framework, provide valuable physical insight into the general determinants of binding specificity and promiscuity in a biological environment. The general principles discussed here could prove useful in the design of molecules with tailored specificities, leading to more effective therapeutics.

Yb3+/Ho3+ Co-Doped Apatite Upconversion Nanoparticles to Distinguish Implanted Material from Bone Tissue

The exploration of bone reconstruction with time requires the combination of a biological method and a chemical technique. Lanthanide Yb³⁺ and Ho³⁺ co-doped fluorapatite (FA:Yb³⁺/Ho³⁺) and hydroxyapatite (HA:Yb³⁺/Ho³⁺) particles with varying dopant concentrations were prepared by hydrothermal synthesis and thermal activation. Controllable green and red upconversion emissions were generated under 980 nm near-infrared excitation; the FA:Yb³⁺/Ho³⁺ particles resulted in superior green luminescence, while HA:Yb³⁺/Ho³⁺ dominated in red emission. The difference in the green and red emission behavior was dependent on the lattice structure and composition. Two possible lattice models were proposed for Yb³⁺/Ho³⁺ co-doped HA and FA along the hydroxyl channel and fluorine channel of the apatite crystal structure. We first reported the use of the upconversion apatite particles to clearly distinguish implanted material from bone tissue on stained histological sections of harvested in vivo samples. The superposition of the tissue image and material image is a creative method to show the material-tissue distribution and interrelation. The upconversion apatite particles and image superposition method provide a novel strategy for long-term discriminable fluorescence tracking of implanted material or scaffold during bone regeneration.

Upscaling Cement Paste Microstructure to Obtain the Fracture, Shear, and Elastic Concrete Mechanical LDPM Parameters

Modeling the complex behavior of concrete for a specific mixture is a challenging task, as it requires bridging the cement scale and the concrete scale. We describe a multiscale analysis procedure for the modeling of concrete structures, in which material properties at the macro scale are evaluated based on lower scales. Concrete may be viewed over a range of scale sizes, from the atomic scale (10-10 m), which is characterized by the behavior of crystalline particles of hydrated Portland cement, to the macroscopic scale (10 m). The proposed multiscale framework is based on several models, including chemical analysis at the cement paste scale, a mechanical lattice model at the cement and mortar scales, geometrical aggregate distribution models at the mortar scale, and the Lattice Discrete Particle Model (LDPM) at the concrete scale. The analysis procedure starts from a known chemical and mechanical set of parameters of the cement paste, which are then used to evaluate the mechanical properties of the LDPM concrete parameters for the fracture, shear, and elastic responses of the concrete. Although a macroscopic validation study of this procedure is presented, future research should include a comparison to additional experiments in each scale.

Modelling Filler Dispersion in Elastomers: Relating Filler Morphology to Interface Free Energies via SAXS and TEM Simulation Studies

The properties of rubber are strongly influenced by the distribution of filler within the polymer matrix. Here, we introduce a Monte Carlo-based morphology generator. The basic elements of our model are cubic cells, which, in the current version, can be either silica filler particles or rubber volume elements in adjustable proportion. The model allows the assignment of surface free energies to the particles according to whether a surface represents, for instance, ‘naked’ silica or silanised silica. The amount of silanisation is variable. We use a nearest-neighbour site-exchange Monte Carlo algorithm to generate filler morphologies, mimicking flocculation. Transmission electron micrographs (TEM) as well as small angle scattering (SAS) intensities can be calculated along the Monte Carlo trajectory. In this work, we demonstrate the application of our morphology generator in terms of selected examples. We illustrate its potential as a tool for screening studies, relating interface tensions between the components to filler network structure as characterised by TEM and SAS.

Slow Dynamics of Ring Polymer Melts by Asymmetric Interaction of Threading Configuration: Monte Carlo Study of a Dynamically Constrained Lattice Model

Abnormally slower diffusional processes than its internal structure relaxation have been observed in ring polymeric melt systems recently. A key structural feature in ring polymer melts is topological constraints which allow rings to assume a threading configuration in the melt phase. In this work, we constructed a lattice model under the assumption of asymmetric diffusivity between two threading rings, and investigated a link between the structural correlation and its dynamic behavior via Monte Carlo simulations. We discovered that the hierarchical threading configurations render the whole system to exhibit abnormally slow dynamics. By analyzing statistical distributions of timescales of threading configurations, we found that the decoupling between internal structure relaxation and diffusion is crucial to understand the threading effects on the dynamics of a ring melt. In particular, in the limit of small but threaded rings, scaling exponents of the diffusion coefficient D and timescale τ diff with respect to the degree of polymerization N agree well with that of the annealed tree model as well as our mean-field analysis. As N increases, however, the ring diffusion abruptly slows down to the glassy behavior, which is supported by a breakdown of the Stokes⁻Einstein relation.

Splitting fracture in bovine bone using a porosity-based spring network model

We examine the specific role of the structure of the network of pores in plexiform bone in its fracture behaviour under compression. Computed tomography scan images of the sample pre- and post-compressive failure show the existence of weak planes formed by aligned thin long pores extending through the length. We show that the physics of the fracture process is captured by a two-dimensional random spring network model that reproduces well the macroscopic response and qualitative features of fracture paths obtained experimentally, as well as avalanche statistics seen in recent experiments on porcine bone.

SuSMoST: Surface Science Modeling and Simulation Toolkit

We present to the scientific community the Surface Science Modeling and Simulation Toolkit (SuSMoST), which includes a number of utilities and implementations of statistical physics algorithms and models. With SuSMoST it is possible to predict or explain the structure and thermodynamic properties of adsorption layers. SuSMoST automatically builds formal graph and tensor-network models based on atomic description of adsorption complexes and helps to do ab initio calculations of interactions between adsorbed species. Using methods of various nature SuSMoST generates representative samples of adsorption layers and computes its thermodynamic quantities such as mean energy, coverage, density, and heat capacity. From these data one can plot phase diagrams of adsorption systems, assess thermal stability of self-assembled structures, simulate thermal desorption spectra, and so forth.

Investigating the thermal dissociation of viral capsid by lattice model

The dissociation of icosahedral viral capsids was investigated by a homogeneous and a heterogeneous lattice model. In thermal dissociation experiments with cowpea chlorotic mottle virus and probed by small-angle neutron scattering, we observed a slight shrinkage of viral capsids, which can be related to the strengthening of the hydrophobic interaction between subunits at increasing temperature. By considering the temperature dependence of hydrophobic interaction in the homogeneous lattice model, we were able to give a better estimate of the effective charge. In the heterogeneous lattice model, two sets of lattice sites represented different capsid subunits with asymmetric interaction strengths. In that case, the dissociation of capsids was found to shift from a sharp one-step transition to a gradual two-step transition by weakening the hydrophobic interaction between AB and CC subunits. We anticipate that such lattice models will shed further light on the statistical mechanics underlying virus assembly and disassembly.

Asymmetric Finite Size of Ions and Orientational Ordering of Water in Electric Double Layer Theory Within Lattice Model

In the present review, a brief historical survey of the mean-field theoretical description of Electric Double Layer (EDL) is presented. Special attention is devoted to asymmetric finite size of ions and orientational ordering of water dipoles. A model of Wicke and Eigen, who were first to explicitly derive the ion distribution functions for finite size of ions, is discussed. Arguments are given in favour of changing the recently adopted name of the mean-field EDL model for finite size of ions from Bikerman model to Bikerman-Wicke-Eigen model. Theoretically predicted asymmetric and symmetric camel-like shape of the voltage dependence of the differential capacitance is also discussed.

Confined Polymers as Self-Avoiding Random Walks on Restricted Lattices

Polymers in highly confined geometries can display complex morphologies including ordered phases. A basic component of a theoretical analysis of their phase behavior in confined geometries is the knowledge of the number of possible single-chain conformations compatible with the geometrical restrictions and the established crystalline morphology. While the statistical properties of unrestricted self-avoiding random walks (SAWs) both on and off-lattice are very well known, the same is not true for SAWs in confined geometries. The purpose of this contribution is (a) to enumerate the number of SAWs on the simple cubic (SC) and face-centered cubic (FCC) lattices under confinement for moderate SAW lengths, and (b) to obtain an approximate expression for their behavior as a function of chain length, type of lattice, and degree of confinement. This information is an essential requirement for the understanding and prediction of entropy-driven phase transitions of model polymer chains under confinement. In addition, a simple geometric argument is presented that explains, to first order, the dependence of the number of restricted SAWs on the type of SAW origin.

A Computational Approach to Studying Protein Folding Problems Considering the Crucial Role of the Intracellular Environment

Intracellular protein folding (PF) is performed in a highly inhomogeneous, crowded, and correlated environment. Due to this inherent complexity, the study and understanding of PF phenomena is a fundamental issue in the field of computational systems biology. In particular, it is important to use a modeled medium that accurately reflects PF in natural systems. In the current study, we present a simulation wherein PF is carried out within an inhomogeneous modeled medium. Simulation resources included a two-dimensional hydrophobic-polar (HP) model, evolutionary algorithms, and the dual site-bond model. The dual site-bond model was used to develop an environment where HP beads could be folded. Our modeled medium included correlation lengths and fractal-like behavior, which were selected according to HP sequence lengths to induce folding in a crowded environment. Analysis of three benchmark HP sequences showed that the modeled inhomogeneous space played an important role in deeper energy folding and obtained better performance and convergence compared with homogeneous environments. Our computational approach also demonstrated that our correlated network provided a better space for PF. Thus, our approach represents a major advancement in PF simulations, not only for folding but also for understanding functional chemical structure and physicochemical properties of proteins in crowded molecular systems, which normally occur in nature.

A Probabilistic Graphical Model for Ab Initio Folding

Despite significant progress in recent years, ab initio folding is still one of the most challenging problems in structural biology. This paper presents a probabilistic graphical model for ab initio folding, which employs Conditional Random Fields (CRFs) and directional statistics to model the relationship between the primary sequence of a protein and its three-dimensional structure. Different from the widely-used fragment assembly method and the lattice model for protein folding, our graphical model can explore protein conformations in a continuous space according to their probability. The probability of a protein conformation reflects its stability and is estimated from PSI-BLAST sequence profile and predicted secondary structure. Experimental results indicate that this new method compares favorably with the fragment assembly method and the lattice model.

A Lattice Model for Elastic Particulate Composites

In the present article, a version of the lattice or spring network method is proposed to model the mechanical response of elastic particulate composites with a high volume fraction of spherical particles and with a much weaker matrix compared to the stiffness of the particles. The main subject of the article is the determination of the axial stiffnesses of the springs of the cell. A comparison of the mechanical response of a three-dimensional particulate composite cube obtained using the finite element method and the proposed methodology showed that the efficiency of the proposed methodology increases with an increasing volume fraction of the particles.

Pattern selection by material aging: Modeling chemical gardens in two and three dimensions

Chemical gardens are complex, often macroscopic, structures formed by precipitation reactions. Their thin walls compartmentalize the system and adjust in size and shape if the volume of the interior reactant solution is increased by osmosis or active injection. Spatial confinement to a thin layer is known to result in various patterns including self-extending filaments and flower-like patterns organized around a continuous, expanding front. Here, we describe a cellular automaton model for this type of self-organization, in which each lattice site is occupied by one of the two reactants or the precipitate. Reactant injection causes the random replacement of precipitate and generates an expanding near-circular precipitate front. If this process includes an age bias favoring the replacement of fresh precipitate, thin-walled filaments arise and grow-like in the experiments-at the leading tip. In addition, the inclusion of a buoyancy effect allows the model to capture various branched and unbranched chemical garden shapes in two and three dimensions. Our results provide a model of chemical garden structures and highlight the importance of temporal changes in the self-healing membrane material.

Effect of Surface Roughness on Aggregation of Polypeptide Chains: A Monte Carlo Study

The self-assembly of amyloidogenic peptides and proteins into fibrillar structures has been intensively studied for several decades, because it seems to be associated with a number of neurodegenerative diseases, such as Alzheimer’s and Parkinson’s disease. Therefore, understanding the molecular mechanisms of this phenomenon is important for identifying an effective therapy for the corresponding diseases. Protein aggregation in living organisms very often takes place on surfaces like membranes and the impact of a surface on this process depends not only on the surface chemistry but also on its topology. Our goal was to develop a simple lattice model for studying the role of surface roughness in the aggregation kinetics of polypeptide chains and the morphology of aggregates. We showed that, consistent with the experiment, an increase in roughness slows down the fibril formation, and this process becomes inhibited at a very highly level of roughness. We predicted a subtle catalytic effect that a slightly rough surface promotes the self-assembly of polypeptide chains but does not delay it. This effect occurs when the interaction between the surface and polypeptide chains is moderate and can be explained by taking into account the competition between energy and entropy factors.

Mixed Mode Crack Propagation in Polymers Using a Discrete Lattice Method

The fracture behavior of polymeric materials has been widely studied in recent years, both experimentally and numerically. Different numerical approaches have been considered in the study of crack propagation processes, from continuum-based numerical formulations to discrete models, many of the latter being limited in the selection of the Poisson's coefficient of the considered material. In this work, we present a numerical and experimental analysis of the crack propagation process of polymethylmethacrylate beams with central and eccentric notches subjected to quasi-static three-point bending tests. The developed discrete numerical model consists of a regular triangular lattice model based on axial and normal interaction springs, accounting for nearest-neighbor interactions. The proposed model allows solving the above mentioned limitation in the selection of Poisson's coefficient, incorporating a fracture criterion defined by a bilinear law with softening that includes the fracture energy in the formulation and allows considering a progressive damage. One of the main objectives of this work is to show the capacity of this lattice to simulate quasi-static fracture problems. The obtained results show that the proposed lattice model is capable of providing results close to the experimental ones in terms of crack pattern, peak load and initial stiffening.

The Regulatory Roles of Intrinsically Disordered Linker in VRN1-DNA Phase Separation

Biomacromolecules often form condensates to function in cells. VRN1 is a transcriptional repressor that plays a key role in plant vernalization. Containing two DNA-binding domains connected by an intrinsically disordered linker (IDL), VRN1 was shown to undergo liquid-like phase separation with DNA, and the length and charge pattern of IDL play major regulatory roles. However, the underlying mechanism remains elusive. Using a polymer chain model and lattice-based Monte-Carlo simulations, we comprehensively investigated how the IDL regulates VRN1 and DNA phase separation. Using a worm-like chain model, we showed that the IDL controls the binding affinity of VRN1 to DNA, by modulating the effective local concentration of the VRN1 DNA-binding domains. The predicted binding affinities, under different IDL lengths, were in good agreement with previously reported experimental results. Our simulation of the phase diagrams of the VRN1 variants with neutral IDLs and DNA revealed that the ability of phase separation first increased and then decreased, along with the increase in the linker length. The strongest phase separation ability was achieved when the linker length was between 40 and 80 residues long. Adding charged patches to the IDL resulted in robust phase separation that changed little with IDL length variations. Our study provides mechanism insights on how IDL regulates VRN1 and DNA phase separation, and why naturally occurring VRN1-like proteins evolve to contain the charge segregated IDL sequences, which may also shed light on the molecular mechanisms of other IDL-regulated phase separation processes in living cells.

Structure of Strongly Adsorbed Polymer Systems: A Computer Simulation Study

The structure of very thin polymer films formed by strongly adsorbed macromolecules was studied by computer simulation. A coarse-grained model of strictly two-dimensional polymer systems was built, and its properties determined by an efficient Monte Carlo simulation algorithm. Properties of the model system were determined by means of Monte Carlo simulations with a sampling algorithm that combines Verdier-Stockmayer, pivot and reputation moves. The effects of temperature, chain length and polymer concentration on the macromolecular structure were investigated. It was shown that at low temperatures, the chain size increases with the concentration, that is, inversely with high temperatures. This behavior should be explained by the influence of inter-chain interactions.

Simulation Studies of Dynamical Heterogeneity in a Dense Two-Dimensional Dimer-Solvent System with Obstacles

A coarse-grained model of a two-dimensional colloidal suspension was designed. The model was athermal and, in addition, a lattice approximation was introduced. It consisted of solvent (monomer) molecules, dimer molecules, and immobile impenetrable obstacles that introduced additional heterogeneity into the system. Dynamic properties were determined by a Monte Carlo simulation using the dynamic lattice liquid simulation algorithm. It is shown that there is a range of obstacle concentrations in which different diffusion characteristics were observed for dimers and solvents. In the system studied, it is possible to define the ranges of concentrations of individual components (solvent, dimers, and obstacles), in which the nature of the movement of dimers and solvents is different (normal diffusion vs. subdiffusion). The ratio of diffusion coefficients of solvent molecules and dimers for short times does not depend on the concentration of obstacles, while for long times, the ratio increases but remains independent of the concentration of the dimer.

The Longitudinal Superdiffusive Motion of Block Copolymer in a Tight Nanopore

The structure and dynamic properties of polymer chains in a confined environment were studied by means of the Monte Carlo method. The studied chains were represented by coarse-grained models and embedded into a simple 3D cubic lattice. The chains stood for two-block linear copolymers of different energy of bead-bead interactions. Their behavior was studied in a nanotube formed by four impenetrable surfaces. The long-time unidirectional motion of the chain in the tight nanopore was found to be correlated with the orientation of both parts of the copolymer along the length of the nanopore. A possible mechanism of the anomalous diffusion was proposed on the basis of thermodynamics of the system, more precisely on the free energy barrier of the swapping of positions of both parts of the chain and the impulse of temporary forces induced by variation of the chain conformation. The mean bead and the mass center autocorrelation functions were examined. While the former function behaves classically, the latter indicates the period of time of superdiffusive motion similar to the ballistic motion with the autocorrelation function scaling with the exponent t^5/3. A distribution of periods of time of chain diffusion between swapping events was found and discussed. The influence of the nanotube width and the chain length on the polymer diffusivity was studied.