Gaussian Chain Model Research Articles

Physical Education Teaching Quality Assessment Model Based on Gaussian Process Machine Learning Algorithm

Physical education is an integral component of academic curricula focused on promoting overall health and well-being through physical activity and exercise. It encompasses a range of activities designed to enhance students' physical fitness, motor skills, and knowledge of healthy lifestyle habits. In addition to fostering physical development, physical education contributes to the development of social skills, teamwork, and discipline. Students engage in various sports, fitness routines, and educational modules that encourage a lifelong commitment to an active and healthy lifestyle. This demand for improvement in the teaching quality assessment of physical education among the students. Hence, this paper proposed a novel Gaussian Hidden Chain Probabilistic Machine Learning (GHCP-ML). The proposed GHCP-ML model estimates the features for the teaching quality assessment using the Gaussian Hidden Chain model. With the proposed GHCP-ML model features related to the teaching assessment of the physical education are computed. The proposed GHCP-ML model uses the machine learning model for the assessment and computation of the factors related to the teaching quality of students in physical education. With the Gaussian Chain model, the factors related to physical education are evaluated for the classification of the relationship between physical education and teaching quality assessment. Simulation analysis demonstrated that with the proposed GHCP-ML model physical education is improved significantly with teaching quality by ~12% than the conventional techniques. The student physical education performance is improved by more than 80% with the proposed GHCP-ML model compared with the conventional techniques.

Simulating Stress-Strain Behavior by Using Individual Chains: Uniaxial Deformation of Amorphous Cis- and Trans-1,4-Polybutadiene.

This work develops a probability-based numerical method for quantifying mechanical properties of non-Gaussian chains subject to uniaxial deformation, with the intention of being able to incorporate polymer-polymer and polymer-filler interactions. The numerical method arises from a probabilistic approach for evaluating the elastic free energy change of chain end-to-end vectors under deformation. The elastic free energy change, force, and stress computed by applying the numerical method to uniaxial deformation of an ensemble of Gaussian chains were in excellent agreement with analytical solutions that were obtained with a Gaussian chain model. Next, the method was applied to configurations of cis- and trans-1,4-polybutadiene chains of various molecular weights that were generated under unperturbed conditions over a range of temperatures with a Rotational Isomeric State (RIS) approach in previous work (Polymer2015, 62, 129-138). Forces and stresses increased with deformation, and further dependences on chain molecular weight and temperature were confirmed. Compression forces normal to the imposed deformation were much larger than tension forces on chains. Smaller molecular weight chains represent the equivalent of a much more tightly cross-linked network, resulting in greater moduli than larger chains. Young's moduli computed from the coarse-grained numerical model were in good agreement with experimental results.

Accounting for the ultraviolet divergence in field-theoretic simulations of block copolymer melts.

This study examines the ultraviolet (UV) divergence in field-theoretic simulations (FTSs) of block copolymer melts, which causes an unphysical dependence on the grid resolution, Δ, used to represent the fields. Our FTSs use the discrete Gaussian-chain model and a partial saddle-point approximation to enforce incompressibility. Previous work has demonstrated that the UV divergence can be accounted for by defining an effective interaction parameter, χ=z∞χb+c2χb 2+c3χb 3+⋯, in terms of the bare interaction parameter, χb, used in the FTSs, where the coefficients of the expansion are determined by a Morse calibration. However, the need to use different grid resolutions for different ordered phases generally restricts the calibration to the linear approximation, χ ≈ z∞χb, and prevents the calculation of order-order transitions. Here, we resolve these two issues by showing how the nonlinear calibration can be translated between different grids and how the UV divergence can be removed from free energy calculations. By doing so, we confirm previous observations from particle-based simulations. In particular, we show that the free energy closely matches self-consistent field theory (SCFT) predictions, even in the region where fluctuations disorder the periodic morphologies, and similarly, the periods of the ordered phases match SCFT predictions, provided the SCFT is evaluated with the nonlinear χ.

A Review of Polymer Physics and Potential Applications to Radiation Biophysics and Neurodegenerative Disorders

Polymers are an essential aspect of molecular biology and biochemistry. The most significant of macromolecules involved in biological processes and phenomena are polymers. In this article, we provide a comprehensive summary of the proposed physical models for the configuration of polymers. Such physical models include the freely-jointed chain, freely-rotating chain, worm-like chain, and the Gaussian chain model. We then connect these models to the existing models regarding the radiation biophysics of DNA damage, as well as to the damage of RNA molecules, and provide an insight into future areas of research in the subject areas. The conclusion is that polymer physics and the Linear-Quadratic model can be used for future biophysical research in cancer and neurological disorders. Through such connections, we hope to provide a potential future insight with regards to biophysical research in cancer and neurodegenerative disorders.

Polymer physics-based mathematical models for the correlation of DNA and mRNA in a eukaryotic cell

<abstract><p>DNA and mRNA are essential aspects of cells. They are responsible for much of the genomic activity that takes place in a cell, and are significant macromolecules for research in cell and molecular biology. DNA and mRNA are polymers, molecules that are composed of repeating subunits known as monomers. In the past, a number of theoretical models that elucidate the physical properties of polymers have been proposed to the scientific community. These models include the Freely-Jointed Chain, Freely-Rotating Chain, Worm-Like Chain, and Gaussian Chain Models. In this paper, I make use of such theoretical models in polymer physics, and derive a number of theoretical models that correlate DNA, its respective pre-mRNA strand, and the corresponding post-mRNA strand in a eukaryotic cell. Furthermore, graphical representations of some of the mathematical models derived in the paper are also rendered. Based on this, the theoretical models formulated in this paper can be applied to research in the fields of mathematical biology, biophysics, biochemistry, and cell/molecular biology.</p></abstract>

Fluctuation correction for the order-disorder transition of diblock copolymer melts.

The order-disorder transition (ODT) of diblock copolymer melts is evaluated for an invariant polymerization index of N¯=104, using field-theoretic simulations (FTS) supplemented by a partial saddle-point approximation for incompressibility. For computational efficiency, the FTS are performed using the discrete Gaussian-chain model, and results are then mapped onto the continuous model using a linear approximation for the Flory-Huggins χ parameter. Particular attention is paid to the complex phase window. Results are found to be consistent with the well-established understanding that the gyroid phase extends down to the ODT. Furthermore, our simulations are the first to predict that the Fddd phase survives fluctuation effects, consistent with experiments.

Single Chain Mean-Field Theory Study on Responsive Behavior of Semiflexible Polymer Brush.

The application of single chain mean-field theory (SCMFT) on semiflexible chain brushes is reviewed. The worm-like chain (WLC) model is the best mode of semiflexible chain that can continuously recover to the rigid rod model and Gaussian chain (GC) model in rigid and flexible limits, respectively. Compared with the commonly used GC model, SCMFT is more applicable to the WLC model because the algorithmic complexity of the WLC model is much higher than that of the GC model in self-consistent field theory (SCFT). On the contrary, the algorithmic complexity of both models in SCMFT are comparable. In SCMFT, the ensemble average of quantities is obtained by sampling the conformations of a single chain or multi-chains in the external auxiliary field instead of solving the modified diffuse equation (MDE) in SCFT. The precision of this calculation is controlled by the number of bonds used to discretize the chain contour length L and the number of conformations M used in the ensemble average. The latter factor can be well controlled by metropolis Monte Carlo simulation. This approach can be easily generalized to solve problems with complex boundary conditions or in high-dimensional systems, which were once nightmares when solving MDEs in SCFT. Moreover, the calculations in SCMFT mainly relate to the assemble averages of chain conformations, for which a portion of conformations can be performed parallel on different computing cores using a message-passing interface (MPI).

Effects of Asymmetric Molecular Architecture on Chain Stretching and Dynamics in Miktoarm Star Copolymers

We use broad-band dielectric spectroscopy (BDS) and small-angle X-ray scattering (SAXS) to investigate the impact of architectural asymmetry in the miktoarm star copolymer on the dielectric polymer relaxations. The miktoarm copolymers studied contain one or two polystyrene (PS) chains of constant molecular weight and two identical poly(cis-1,4-isoprene) (PI) chains with varied molecular weights. Using the chains in the PI block as dielectric probes, we find that the architecturally asymmetric miktoarm star copolymer systems (PSPI2) feature distributions in chain relaxation times and dielectric relaxation strengths that are not dependent on molecular weight or morphology, in stark contrast to the effects of morphological confinement observed for symmetric diblock systems (PS-b-PI or PS2PI2). Along with evidence from the SAXS measurements regarding phase separation, these results are attributed to influences from chain stretching within the framework of the Gaussian chain model for block copolymer systems. As such, the molecular architecture in block copolymers happens to be a versatile handle to control polymer chain dynamics and, ultimately, the macroscopic physicochemical properties in architecturally complex polymers.

Revisiting the Θ Point

Using the first-order perturbation theory, we compute the osmotic second and third virial coefficients, the mean-square end-to-end distance ⟨Re2⟩, and the mean-square radius of gyration ⟨Rg2⟩ of a polymer near the Θ point. Our model is based on the discrete Gaussian chain model and includes a square-gradient term accounting for the finite-range interaction (characterized by κ), in addition to the usual monomer second and third virial coefficients (characterized by v and w, respectively). The use of the discrete model avoids the divergence problems encountered in previous studies using the continuous model. Our study identifies four special temperatures in the Θ regime: the temperature ΘN where the osmotic second virial coefficient vanishes, the critical temperature ΘNcr for phase separation, and two compensation temperatures ΘN(e) and ΘN(g) at which ⟨Re2⟩ and ⟨Rg2⟩ reach their respective ideal values. In the infinite chain-length limit N → ∞, all of these four temperatures approach Θ∞, the Θ temperature for the infinitely long chain. These temperatures differ from each other by terms of order N–1/2. In general, these temperatures follow the order ΘN > ΘNcr and ΘN > ΘN(e) > ΘN(g). Furthermore, ΘN > Θ∞, in agreement with the result obtained by Khokhlov some time ago. On the other hand, depending on the ratio w/κb, Θ∞ can be higher than ΘN(e) (for w/κb < 9.45), lower than ΘN(g) (for w/κb > 11.63), or in between ΘN(e) and ΘN(g) (for 9.45 < w/κb < 11.63). ΘNcr can be either higher or lower than Θ∞ depending on whether w/b6 is larger or smaller than 0.574. From the order of these temperatures, we conclude that the chain is mostly expanded relative to the ideal chain at its ΘN. However, at Θ∞, the chain can be either expanded or contracted, depending on the relative position of Θ∞ with respect to ΘN(e) and ΘN(g) and depending on whether the chain dimension is measured by ⟨Re2⟩ or ⟨Rg2⟩.

Coarse-Grained Lattice Modeling and Monte Carlo Simulations of Stress Relaxation in Strain-Induced Crystallization of Rubbers.

Two-dimensional triangulated surface models for membranes and their three-dimensional (3D) extensions are proposed and studied to understand the strain-induced crystallization (SIC) of rubbers. It is well known that SIC is an origin of stress relaxation, which appears as a plateau in the intermediate strain region of stress–strain curves. However, this SIC is very hard to implement in models because SIC is directly connected to a solid state, which is mechanically very different from the amorphous state. In this paper, we show that the crystalline state can be quite simply implemented in the Gaussian elastic bond model, which is a straightforward extension of the Gaussian chain model for polymers, by replacing bonds with rigid bodies or eliminating bonds. We find that the results of Monte Carlo simulations for stress–strain curves are in good agreement with the reported experimental data of large strains of up to 1200%. This approach allows us to intuitively understand the stress relaxation caused by SIC.

Field theoretic approach for block polymer melts: SCFT and FTS.

This perspective addresses the development of polymer field theory for predicting the equilibrium phase behavior of block polymer melts. The approach is tailored to the high-molecular-weight limit, where universality reduces all systems to the standard Gaussian chain model, an incompressible melt of elastic threads interacting by contact forces. Using mathematical identities, this particle-based version of the model is converted to an equivalent field-based version that depends on fields rather than particle coordinates. The statistical mechanics of the field-based model is typically solved using the saddle-point approximation of self-consistent field theory (SCFT), which equates to mean field theory, but it can also be evaluated using field theoretic simulations (FTS). While SCFT has matured into one of the most successful theories in soft condensed matter, FTS are still in its infancy. The two main obstacles of FTS are the high computational cost and the occurrence of an ultraviolet divergence, but fortunately there has been recent groundbreaking progress on both fronts. As such, FTS are now well poised to become the method of choice for predicting fluctuation corrections to mean field theory.

Calibration of a lattice model for high-molecular-weight block copolymer melts.

The Morse calibration is applied to a lattice model designed for efficient simulations of two-component polymer melts of high molecular weight. The model allows multiple occupancy per site, which results in high invariant polymerization indices, and interactions are limited to monomers within the same site, which enhances the computational speed. The calibration maps the interaction parameter of the lattice model, α, onto the Flory-Huggins χ parameter of the standard Gaussian-chain model, by matching the disordered-state structure function, S(k), of symmetric diblock copolymers to renormalized one-loop predictions. The quantitative accuracy of the calibration is tested by comparing the order-disorder transition of symmetric diblock copolymer melts to the universal prediction obtained from previous simulations. The model is then used to confirm the universality of fluctuation corrections to the critical point of symmetric binary homopolymer blends.

Calibration of the Flory-Huggins interaction parameter in field-theoretic simulations.

Field-theoretic simulations (FTS) offer a versatile method of dealing with complicated block copolymer systems, but unfortunately they struggle to cope with the level of fluctuations typical of experiments. Although the main obstacle, an ultraviolet divergence, can be removed by renormalizing the Flory-Huggins χ parameter, this only works for unrealistically large invariant polymerization indexes, N¯. Here, we circumvent the problem by applying the Morse calibration, where a nonlinear relationship between the bare χb used in FTS and the effective χ corresponding to the standard Gaussian-chain model is obtained by matching the disordered-state structure function, S(k), of symmetric diblock copolymers to renormalized one-loop predictions. This calibration brings the order-disorder transition obtained from FTS into agreement with the universal results of particle-based simulations for values of N¯ characteristic of the experiment. In the limit of weak interactions, the calibration reduces to a linear approximation, χ ≈ z∞χb, consistent with the previous renormalization of χ for large N¯.

Shear deformation of low-density polymer brushes in a good solvent

Self-consistent field approach is used to model a single end-tethered polymer chain on a substrate subject to various forces in three dimensions. Starting from a continuous Gaussian chain model, the following perturbations are considered: (i) hydrodynamic interaction with an externally imposed shear flow for which a new theoretical framework is formulated; (ii) excluded volume effect in a good solvent, treated in a mean field approximation; (iii) monomer-substrate repulsion. While the chain stretches along the flow, the change of the density profile perpendicular to the substrate is negligible for any reasonable simulation parameters. This null effect is in agreement with multiple neutron scattering studies.

Three-Color Single-Molecule FRET and Fluorescence Lifetime Analysis of Fast Protein Folding.

We describe the theory, experiment, and analysis of three-color Förster resonance energy transfer (FRET) spectroscopy for probing conformational dynamics of a fast-folding protein, α3D. In three-color FRET, site-specific labeling of fluorophores is required to avoid ambiguity resulting from various species with different combinations of labeling positions. To this end, we first attached two dyes to a cysteine residue and an unnatural amino acid and then appended a cysteine residue to the C-terminus of the protein by the sortase-mediated ligation for attaching the third dye. To determine all three FRET efficiencies, we used alternating excitation of the donor and acceptor 1 with two picosecond-pulsed lasers. Since the folded and unfolded states are not distinguishable in binned fluorescence trajectories due to fast-folding on a millisecond time scale, we used a maximum likelihood method that analyzes photon trajectories without binning the data. The extracted kinetic parameters agree very well with the previously measured parameters for the same protein with two-color FRET, suggesting that the addition of the third fluorophore does not affect the folding dynamics of the protein. From the extracted fractions of acceptor photon counts, the FRET efficiencies for all three dye pairs were calculated after various corrections. They were compared with the FRET efficiencies obtained from the global analysis of two-color segments collected in the same experiment. The FRET efficiencies of the folded state from the three-color segments agree with those from the two-color segments, whereas the three-color and two-color FRET efficiencies of the unfolded state are different. This happens because fluctuations of all three interdye distances contribute to the FRET efficiency measured in three-color FRET. We show that this difference can be accounted for by using the Gaussian chain model for the unfolded state with the parameters obtained from the analysis of two-color segments. This result shows that three-color FRET provides additional information on the flexibility of molecules that cannot be obtained from a combination of two-color FRET experiments with three dye pairs. Using the delay times of photons from the laser pulse, fluorescence lifetimes were determined using the maximum likelihood analysis. The correlation between FRET efficiencies and lifetimes of the donor, acceptor 1, and acceptor 2 was visualized in two-dimensional FRET efficiency-lifetime histograms. These histograms can be used to demonstrate the presence of conformational dynamics in a protein.

Applications of worm-like chain model in polymer physics

Saito, Takahashi and Yunoki developed the continuous version of worm-like chain (WLC) model that is very suitable for description of the polymer conformational properties affected by chain rigidity. By adjusting persistence length directly, the WLC model can depict the extensive range of chain conformations from flexible chains to rigid chains. It is widely accepted that more physical properties of real polymer can be obtained by utilizing coarse-grained model than Gaussian chain (GSC). This paper reviews the applications of the WLC model in the framework based on self-consistent field theory, which is an efficient method of theoretical exploration of phase separation in polymer system. It is noticed that the development of numerical schemes is in favor of solving modified diffusion equation that adjusts the probability distribution of polymers. In addition, we conclude the recent applications of the self-consistent field theory based on the WLC model as the following three points: phase transitions of liquid crystal polymer; the influences of surface curvature on polymer system that involves the chain orientation effects; self-assembly of worm-like block copolymer. These researches have been out of the range of the self-consistent field theory based on GSC model that has been used in a large number of theoretical studies. Finally, we present ideas of theoretical development in field theory simulations based on the WLC model in the future. It is universally acknowledged that chain rigidity is a key factor that influences the properties of structural stabilities in the meso-scale in articles. Theoretical researches determine the key physical mechanisms that play crucial roles in many experimental systems with attractively promising applications in practice, for systems such as liquid crystalline polymers and organic solar cell based on the conjugated polymers.

Conformational properties and the entropic barrier in the "head-on" adsorption of a single polymer chain towards a flat surface.

This work investigates the change in conformations and the entropic free energy barrier in the "head-on" adsorption process of a flexible polymer chain towards a flat surface in the framework of the Gaussian chain model. Analytical expressions are reported for the distribution of chain end, the mean square end-to-end distance, the entropic free energy barrier and the adsorption equilibrium constant at low surface coverage (the "mushroom" regime). Theoretical results are discussed in the context of polyoxyethylene-phosphonate-type polymer dispersants, possessing a non-adsorbing polyoxyethylene chain and an adsorbing head-group.

Tuning the Flexibility of Glycine-Serine Linkers To Allow Rational Design of Multidomain Proteins.

Flexible polypeptide linkers composed of glycine and serine are important components of engineered multidomain proteins. We have previously shown that the conformational properties of Gly-Gly-Ser repeat linkers can be quantitatively understood by comparing experimentally determined Förster resonance energy transfer (FRET) efficiencies of ECFP-linker-EYFP proteins to theoretical FRET efficiencies calculated using wormlike chain and Gaussian chain models. Here we extend this analysis to include linkers with different glycine contents. We determined the FRET efficiencies of ECFP-linker-EYFP proteins with linkers ranging in length from 25 to 73 amino acids and with glycine contents of 33.3% (GSSGSS), 16.7% (GSSSSSS), and 0% (SSSSSSS). The FRET efficiency decreased with an increasing linker length and was overall lower for linkers with less glycine. Modeling the linkers using the WLC model revealed that the experimentally observed FRET efficiencies were consistent with persistence lengths of 4.5, 4.8, and 6.2 Å for the GSSGSS, GSSSSS, and SSSSSS linkers, respectively. The observed increase in linker stiffness with reduced glycine content is much less pronounced than that predicted by a classical model developed by Flory and co-workers. We discuss possible reasons for this discrepancy as well as implications for using the stiffer linkers to control the effective concentrations of connected domains in engineered multidomain proteins.

Jump transition observed in translocation time for ideal poly-X proteinogenic chains as a result of competing folding and anchoraging contributions.

In this work we analyze the translocation of homopolymer chains poly-X, where X represents any of the 20 naturally occurring amino acid residues, in terms of size N and single-helical propensity ω. We provide an analytical framework to calculate both the free energy F of translocation and the translocation time τ as a function of chain size N, energies U and ε of the unfolded and folded states, respectively. Our results show that free energy F has a characteristic bell-shaped barrier as function of the percentage of monomers translocated. Inclusion of single-helical propensity ω associated to monomer X and chain's native energy ε in the translocation model increases the energy barrier ΔF up to one order of magnitude as compared with the well-known Gaussian chain model. Computation of the mean first-passage time as function of chain size N shows that the translocation time τ exhibits a significant jump of several orders of magnitude at a critical chain size N. This jump markedly slows down translocation of chains larger than N. Existence of the transition jump of τ has been observed experimentally at least in poly(ethylene oxide) chains [R. P. Choudhury, P. Galvosas, and M. Schönhoff, J. Phys. Chem. B 112, 13245 (2008)]JPCBFK1520-610610.1021/jp804680q. Our results suggest the transition jump of τ as a function of N may be a very well spread feature throughout translocation of poly-X chains.

A pH-dependent computational approach to the effect of mutations on protein stability.

This article describes a novel software implementation for high-throughput scanning mutagenesis with a focus on protein stability. The approach combines molecular mechanics calculations with calculations of protein ionization and a Gaussian-chain model of electrostatic interactions in unfolded state. Comprehensive testing demonstrates a state-of-the-art accuracy for predicted free energy differences on single, double, and triple mutations with a correlation coefficient R above 0.7, which takes about 1.5 min per mutation on a single CPU. Unlike most of existing in silico methods for fast mutagenesis, the stability changes are reported as a continuous function of solution pH for wide pH intervals. We also propose a novel in silico strategy for searching stabilized protein variants that is based on combinatorial scanning mutagenesis using representative amino acid types. Our in silico predictions are in excellent agreement with the hyper-stabilized variants of mesophilic cold shock protein found using the Proside method of direct evolution. © 2016 Wiley Periodicals, Inc.