scholarly journals Exploring the free energy gain of phase separation via Markov state modeling

2017 ◽  
Vol 147 (3) ◽  
pp. 034107
Author(s):  
Myra Biedermann ◽  
Andreas Heuer
Keyword(s):  
Free Energy ◽  
Phase Separation ◽  
Energy Gain ◽  
Markov State ◽  
Markov State Modeling

scholarly journals Free Energy Landscape and Conformational Kinetics of Hoogsteen Base-Pairing in DNA vs RNA

2020 ◽  
Author(s):  
D. Ray ◽  
I. Andricioaei
Keyword(s):  
Free Energy ◽  
Base Pair ◽  
Nmr Relaxation ◽  
Enhanced Sampling ◽  
Base Pairing ◽  
Naked Dna ◽  
Markov State ◽  
Relaxation Experiments ◽  
Markov State Modeling ◽  
Hoogsteen Base Pairing

ABSTRACTGenetic information is encoded in the DNA double helix which, in its physiological milieu, is characterized by the iconical Watson-Crick nucleobase pairing. Recent NMR relaxation experiments revealed the transient presence of an alternative, Hoogsteen base pairing pattern in naked DNA duplexes and estimated its relative stability and lifetime. In contrast, HG transitions in RNA were not observed. Understanding Hoogsteen (HG) base pairing is important because the underlying "breathing" can modulate significantly DNA/RNA recognition by proteins. However, a detailed mechanistic insight into the transition pathways and kinetics is still missing. We performed enhanced sampling simulation (with combined metadynamics and adaptive force bias method) and Markov State modeling to obtain accurate free energy, kinetics and the intermediates in the transition pathway between WC and HG base pair for both naked B-DNA and A-RNA duplexes. The Markov state model constructed from our unbiased MD simulation data revealed previously unknown complex extra-helical intermediates in this seemingly simple process of base pair conformation switching in B-DNA. Extending our calculation to A-RNA, for which HG base pair is not observed experimentally, resulted in relatively unstable single hydrogen bonded distorted Hoogsteen like base pair. Unlike B-DNA the transition pathway primarily involved base paired and intra-helical intermediates with transition timescales much higher than that of B-DNA. The seemingly obvious flip-over reaction coordinate, i.e., the glycosidic torsion angle is unable to resolve the intermediates; so a multidimensional picture, involving backbone dihedral angles and distance between atoms participating in hydrogen bonds, is required to gain insight into the molecular mechanism.SIGNIFICANCEFormation of unconventional Hoogsteen (HG) base pairing is an important problem in DNA biophysics owing to its key role in facilitating the binding of DNA repairing enzymes, proteins and drugs to damaged DNA. X-ray crystallography and NMR relaxation experiments revealed the presence of HG base pair in naked DNA duplex and protein-DNA complex but no HG base pair was observed in RNA. Molecular dynamics simulations could reproduce the experimental free energy cost of HG base pairing in DNA although a detailed mechanistic insight is still missing. We performed enhanced sampling simulation and Markov state modeling to obtain accurate free energy, kinetics and the intermediates in the transition pathway between WC and HG base pair for both B-DNA and A-RNA.

Phase equilibria in solutions of rod-like particles

1956 ◽  
Vol 234 (1196) ◽  
pp. 73-89 ◽  
Keyword(s):  
Free Energy ◽  
Phase Separation ◽  
Partition Function ◽  
Colloidal Particles ◽  
Double Layers ◽  
Positive Energy ◽  
Isotropic Phase ◽  
Electric Double Layers ◽  
Rigid Rod ◽  
Anisotropic Phase

A partition function for a system of rigid rod-like particles with partial orientation about an axis is derived through the use of a modified lattice model. In the limit of perfect orientation the partition function reduces to the ideal mixing law ; for complete disorientation it corresponds to the polymer mixing law for rigid chains. A general expression is given for the free energy of mixing as a function of the mole numbers, the axis ratio of the solute particles, and a disorientation parameter. This function passes through a minimum followed by a maximum with increase in the disorientation parameter, provided the latter exceeds a critical value which is 2e for the pure solute and which increases with dilution. Assigning this parameter the value which minimizes the free energy, the chemical potentials display discontinuities a t the concentration a t which the minimum first appears. Separation into an isotropic phase and a some what more concentrated anisotropic phase arises because of the discontinuity, in confirmation of the theories of Onsager and Isihara, which treat only the second virial coefficient. Phase separation thus arises as a consequence of particle asymmetry, unassisted by an energy term . Whereas for a large-particle asymmetry both phases in equilibrium are predicted to be fairly dilute when mixing is athermal, a comparatively small positive energy of interaction causes the concentration in the anisotropic phase to increase sharply, while the concentration in the isotropic phase becomes vanishingly small. The theory offers a statistical mechanical basis for interpreting precipitation of rod-like colloidal particles with the formation of fibrillar structures such as are prominent in the fibrous proteins. The asymmetry of tobacco mosaic virus particles (with or without inclusion of their electric double layers) is insufficient alone to explain the well-known phase separation which occurs from their dilute solutions at very low ionic strengths. Higher-order interaction between electric double layers appears to be a major factor in bringing about dilute phase separation for these and other asymmetric colloidal particles bearing large charges, as was pointed out previously by Oster.

scholarly journals Simulation of FUS protein condensates with an adapted coarse-grained model

2020 ◽  
Author(s):  
Zakarya Benayad ◽  
Sören von Bülow ◽  
Lukas S. Stelzl ◽  
Gerhard Hummer
Keyword(s):  
Free Energy ◽  
Phase Separation ◽  
Potential Energy ◽  
Energy Function ◽  
Potential Energy Function ◽  
Scaling Factor ◽  
Coarse Grained ◽  
Disordered Proteins ◽  
General Strategy ◽  
Droplet Shape

AbstractDisordered proteins and nucleic acids can condense into droplets that resemble the membraneless organelles observed in living cells. MD simulations offer a unique tool to characterize the molecular interactions governing the formation of these biomolecular condensates, their physico-chemical properties, and the factors controlling their composition and size. However, biopolymer condensation depends sensitively on the balance between different energetic and entropic contributions. Here, we develop a general strategy to fine-tune the potential energy function for molecular dynamics simulations of biopolymer phase separation. We rebalance protein-protein interactions against solvation and entropic contributions to match the excess free energy of transferring proteins between dilute solution and condensate. We illustrate this formalism by simulating liquid droplet formation of the FUS low complexity domain (LCD) with a rebalanced MARTINI model. By scaling the strength of the nonbonded interactions in the coarse-grained MARTINI potential energy function, we map out a phase diagram in the plane of protein concentration and interaction strength. Above a critical scaling factor of αc ≈ 0.6, FUS LCD condensation is observed, where α = 1 and 0 correspond to full and repulsive interactions in the MARTINI model, respectively. For a scaling factor α = 0.65, we recover the experimental densities of the dilute and dense phases, and thus the excess protein transfer free energy into the droplet and the saturation concentration where FUS LCD condenses. In the region of phase separation, we simulate FUS LCD droplets of four different sizes in stable equilibrium with the dilute phase and slabs of condensed FUS LCD for tens of microseconds, and over one millisecond in aggregate. We determine surface tensions in the range of 0.01 to 0.4mN/m from the fluctuations of the droplet shape and from the capillary-wave-like broadening of the interface between the two phases. From the dynamics of the protein end-to-end distance, we estimate shear viscosities from 0.001 to 0.02Pas for the FUS LCD droplets with scaling factors α in the range of 0.625 to 0.75, where we observe liquid droplets. Significant hydration of the interior of the droplets keeps the proteins mobile and the droplets fluid.

Modeling of Liquid-Liquid Demixing Curve in Lead-Zinc Binary System

2018 ◽  
Vol 18 ◽  
pp. 49-54
Author(s):  
Naceur Amel ◽  
Adjadj Fouzia
Keyword(s):  
Mathematical Model ◽  
Free Energy ◽  
Phase Separation ◽  
Binary System ◽  
Free Energies ◽  
Common Tangent ◽  
Different Temperatures ◽  
Lead Zinc ◽  
The Common ◽  
Zn Alloys

In this work we discussed the modeling of the demixing curve in the liquid state in the Lead – Zinc binary system. We are interested to recalculate the free energies relating on Pb-Zn alloys for several temperatures based on the thermodynamic data collected in the bibliography. This calculation allows us to trace the curve of phase separation from a program after obtaining the mole fractions corresponding to the common tangent to the curve of the free energy with two minima at different temperatures. To do this, we used the Matlab 7.1 as the programming language and the Redlich-Kister polynomial as a mathematical model of development. The results obtained are very satisfactory by comparing them with those of the bibliography.

Physical origin underlying the prenucleation-cluster-mediated nonclassical nucleation pathways for calcium phosphate

2019 ◽  
Vol 21 (27) ◽  
pp. 14530-14540 ◽  
Author(s):  
Xiao Yang ◽  
Mingzhu Wang ◽  
Yang Yang ◽  
Beiliang Cui ◽  
Zhijun Xu ◽  
...  
Keyword(s):  
Free Energy ◽  
Phase Separation ◽  
Calcium Phosphate ◽  
Molecular Mechanism ◽  
Free Energy Calculations ◽  
Nucleation Process ◽  
Physical Origin ◽  
Energy Calculations

We employed free energy calculations to reveal the molecular mechanism underlying the non-classical nucleation process and phase separation for calcium phosphate.

scholarly journals Markov state modeling of sliding friction

2016 ◽  
Vol 94 (5) ◽  
Author(s):  
F. Pellegrini ◽  
François P. Landes ◽  
A. Laio ◽  
S. Prestipino ◽  
E. Tosatti
Keyword(s):  
Sliding Friction ◽  
Markov State ◽  
Markov State Modeling

scholarly journals The National Ignition Facility: the path to a carbon-free energy future

2012 ◽  
Vol 370 (1973) ◽  
pp. 4115-4129 ◽  
Author(s):  
Christopher J. Stolz
Keyword(s):  
Free Energy ◽  
Basic Science ◽  
Lawrence Livermore National Laboratory ◽  
Fusion Energy ◽  
National Laboratory ◽  
Laser System ◽  
Energy Gain ◽  
Laser Fusion ◽  
National Ignition Facility ◽  
Thermonuclear Ignition

The National Ignition Facility (NIF), the world's largest and most energetic laser system, is now operational at Lawrence Livermore National Laboratory. The NIF will enable exploration of scientific problems in national strategic security, basic science and fusion energy. One of the early NIF goals centres on achieving laboratory-scale thermonuclear ignition and energy gain, demonstrating the feasibility of laser fusion as a viable source of clean, carbon-free energy. This talk will discuss the precision technology and engineering challenges of building the NIF and those we must overcome to make fusion energy a commercial reality.

Effects of dynamic vulcanization on the kinetics of isothermal crystallization in a miscible polymeric blend

2015 ◽  
Vol 39 (8) ◽  
pp. 6130-6140 ◽  
Author(s):  
Mohammad Mahdi Abolhasani
Keyword(s):  
Free Energy ◽  
Phase Separation ◽  
Isothermal Crystallization ◽  
The State ◽  
Dynamic Vulcanization ◽  
Kinetics Of ◽  
Polymeric Blend

Is it possible to determine the state of phase separation using the free energy of folding parameter?

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