The problem of finding the optimal combination of parameters of the Peyard – Bishop-Dauxois model is considered using one of the new reparametrizations proposed by N. Theodorakopoulos. The relationship between the parameters of the inter-site potential of the model and the entropy gain in large open regions of DNA is analyzed. The direct transfer of the properties of long DNAs to short chains is shown to be unacceptable due to different contributions of the loop entropy during melting. The erroneousness of taking into account the finite nature of stacking interactions “directly” through a radical change in the parameters of the inter-site potential of the Peyard – Bishop – Dauxois model is demonstrated.

Interconnection of irreversible port Hamiltonian systems

Structural and thermodynamic consequences of the G31U and U5C mutations in the SARS-CoV-2 s2m

Pseudoknotted RNA molecules play important biological roles that depend on their folded structure. To understand the underlying principles that determine their thermodynamics and folding/unfolding mechanisms, we carried out a study on a variant of the mouse mammary tumor virus pseudoknotted RNA (VPK), a widely studied model system for RNA pseudoknots. Our method is based on a coarse-grained discrete-state model and the algorithm of PK3D (pseudoknot structure predictor in three-dimensional space), with RNA loops explicitly constructed and their conformational entropic effects incorporated. Our loop entropy calculations are validated by accurately capturing previously measured melting temperatures of RNA hairpins with varying loop lengths. For each of the hairpins that constitutes the VPK, we identified alternative conformations that are more stable than the hairpin structures at low temperatures and predicted their populations at different temperatures. Our predictions were validated by thermodynamic experiments on these hairpins. We further computed the heat capacity profiles of VPK, which are in excellent agreement with available experimental data. Notably, our model provides detailed information on the unfolding mechanisms of pseudoknotted RNA. Analysis of the distribution of base-pairing probability of VPK reveals a cooperative unfolding mechanism instead of a simple sequential unfolding of first one stem and then the other. Specifically, we find a simultaneous "loosening" of both stems as the temperature is raised, whereby both stems become partially melted and co-exist during the unfolding process.

Protein conformational switches are widely used in functional regulation and biosensing to visualize biological substances in vitro and in vivo. A major challenge in protein switch design strategies is coupling the target recognition domain to an output domain to produce a change in fluorescence wavelength or intensity. To overcome this challenge, we tested a rational design strategy that exploits two key protein engineering principles (1) loop entropy, by which long insertions into a loop of a host protein destabilizes the host due to an entropic cost associated with loop closure unless the inserted sequence adopts a folded structure; (2) alternate frame folding (AFF), which allows a protein (GFP variants, in this case) to switch between two mutually exclusive folds. For proof-of-concept, we chose an unfolded, circularly permuted FK506-binding protein (cpFKBP) as the input recognition domain, and inserted it in one of the two mutually exclusive folds of the GFP-AFF fusion protein. Upon addition of ligand, cpFKBP folding effects a conformational change in which the 10th beta strand of GFP exchanges, replacing Thr203 (green state) with Tyr203 (yellow state). Single point mutations and insertions were introduced to thermodynamically balance the protein switch for response within a reasonable timescale. We observe a shift in emission wavelength within an hour in response to ligand in vitro and in cellulo with a yellow:green color change of ~2.5-fold. This protein switch design has the advantages of genetic encodability, potential modularity and a ratiometric response. The design strategy further provides insight into protein engineering principles for application in molecular diagnostics, cellular biosensors and activatable proteins.

In the theory of cluster algebras, a mutation loop induces discrete dynamical systems via its actions on the cluster \({\mathcal {A}}\)- and \({\mathcal {X}}\)-varieties. In this paper, we introduce a property of mutation loops, called the sign stability, with a focus on the asymptotic behavior of the iteration of the tropical \({\mathcal {X}}\)-transformation. The sign stability can be thought of as a cluster algebraic analogue of the pseudo-Anosov property of a mapping class on a surface. A sign-stable mutation loop has a numerical invariant which we call the cluster stretch factor, in analogy with the stretch factor of a pseudo-Anosov mapping class on a marked surface. We compute the algebraic entropies of the cluster \({\mathcal {A}}\)- and \({\mathcal {X}}\)-transformations induced by a sign-stable mutation loop, and conclude that these two coincide with the logarithm of the cluster stretch factor. This gives a cluster algebraic analogue of the classical theorem which relates the topological entropy of a pseudo-Anosov mapping class with its stretch factor.

The critical behavior of ribonucleic acid (RNA) secondary structures with quenched sequence randomness is studied by means of the constrained annealing method. A thermodynamic phase transition is induced by including the conformational weight of loop structures. In addition to the expected melting at high temperature, a cold-melting transition appears when the disorder strength induces competition between favorable and unfavorable base pairs. Our results suggest that the cold denaturation of RNA found experimentally might be triggered by quenched sequence disorder. We calculate hot- and cold-melting critical temperatures for competing favorable and unfavorable base-pair energies and present a folding phase diagram as a function of the loop exponent and temperature.

A Polymer Physics Framework for the Entropy of Arbitrary Pseudoknots

SummaryAgonist binding in the extracellular region of the G protein-coupled adenosine A2A receptor increases its affinity to the G proteins in the intracellular region, and vice versa. The structural basis for this effect is not evident from the crystal structures of A2AR in various conformational states since it stems from the receptor dynamics. Using atomistic molecular dynamics simulations on four different conformational states of the adenosine A2A receptor, we observed that the agonists show decreased ligand mobility, lower entropy of the extracellular loops in the active-intermediate state compared with the inactive state. In contrast, the entropy of the intracellular region increases to prime the receptor for coupling the G protein. Coupling of the G protein to A2AR shrinks the agonist binding site, making tighter receptor agonist contacts with an increase in the strength of allosteric communication compared with the active-intermediate state. These insights provide a strong basis for structure-based ligand design studies.

A conspicuous feature of the amyotrophic lateral sclerosis (ALS)-associated protein SOD1 is that its maturation into a functional enzyme relies on local folding of two disordered loops into a catalytic subdomain. To drive the disorder-to-order transition, the protein employs a single Zn2+ ion. The question is then if the entropic penalty of maintaining such disordered loops in the immature apoSOD1 monomer is large enough to explain its unusually low stability, slow folding, and pathological aggregation in ALS. To find out, we determined the effects of systematically altering the SOD1-loop lengths by protein redesign. The results show that the loops destabilize the apoSOD1 monomer by ∼3 kcal/mol, rendering the protein marginally stable and accounting for its aggregation behavior. Yet the effect on the global folding kinetics remains much smaller with a transition-state destabilization of <1 kcal/mol. Notably, this 1/3 transition-state to folded-state stability ratio provides a clear-cut example of the enigmatic disagreement between the Leffler α value from loop-length alterations (typically 1/3) and the "standard" reaction coordinates based on solvent perturbations (typically >2/3). Reconciling the issue, we demonstrate that the disagreement disappears when accounting for the progressive loop shortening that occurs along the folding pathway. The approach assumes a consistent Flory loop entropy scaling factor of c = 1.48 for both equilibrium and kinetic data and has the added benefit of verifying the tertiary interactions of the folding nucleus as determined by phi-value analysis. Thus, SOD1 not only represents a case where evolution of key catalytic function has come with the drawback of a destabilized apo state but also stands out as a well-suited model system for exploring the physicochemical details of protein self-organization.

Within gauge/gravity duality, we consider the AdS-Schwarzschild metric in arbitrary dimensions. We obtain analytical closed-form results for the two-point function, Wilson loop and entanglement entropy for strip geometries in the finite-temperature field-theory dual. According to the duality, these are given by the area of minimal surfaces of different dimension in the gravity background. Our analytical results involve generalised hypergeometric functions. We show that they reproduce known numerical results to great accuracy. Our results allow to identify new physical behaviour: for instance, we consider the entanglement density, i.e. the difference of entanglement entropies at finite and vanishing temperature divided by the volume of the entangling region. For field theories of dimension seven or higher, we find that the entanglement density displays non-monotonic behaviour as function of ℓ · T , with ℓ the strip width and T the temperature. This implies that the area theorem, proven for RG flows in general dimensions, does not apply here. This may signal the emergence of new degrees of freedom for AdS Schwarzschild black holes in eight or more dimensions.

We investigate the temperature and magnetic field dependence of the Polyakov loop and heavy quark entropy in a bottom-up Einstein-Maxwell-dilaton (EMD) holographic model for the strongly coupled quark-gluon plasma (QGP) that quantitatively matches lattice data for the $(2+1)$-flavor QCD equation of state at finite magnetic field and physical quark masses. We compare the holographic EMD model results for the Polyakov loop at zero and nonzero magnetic fields and the heavy quark entropy at vanishing magnetic field with the latest lattice data available for these observables and find good agreement for temperatures $T\gtrsim 150$ MeV and magnetic fields $eB\lesssim 1$ GeV$^2$. Predictions for the behavior of the heavy quark entropy at nonzero magnetic fields are made that could be readily tested on the lattice.

RNA-RNA interactions are essential for genomic RNA dimerization, mRNA splicing, and many RNA-related gene expression and regulation processes. The prediction of the structure and folding stability of RNA-RNA complexes is a problem of significant biological importance and receives substantial interest in the biological community. The VfoldCPX server provides a new web interface to predict the two-dimensional (2D) structures of RNA-RNA complexes from the nucleotide sequences. The VfoldCPX server has several novel advantages including the ability to treat RNAs with tertiary contacts (crossing base pairs) such as loop-loop kissing interactions and the use of physical loop entropy parameters. Based on a partition function-based algorithm, the server enables prediction for structure with and without tertiary contacts. Furthermore, the server outputs a set of energetically stable structures, ranked by their stabilities. The results allow users to gain extensive physical insights into RNA-RNA interactions and their roles in RNA function. The web server is freely accessible at “http://rna.physics.missouri.edu/vfoldCPX”.

From the viewpoint of holography, the phase structure of a 5-dimensional Reissner-Nordström-AdS black hole is probed by the two-point correlation function, Wilson loop, and entanglement entropy. As the case of thermal entropy, we find for all the probes that the black hole undergoes a Hawking-Page phase transition, a first-order phase transition, and a second-order phase transition successively before it reaches a stable phase. In addition, for these probes, we find that the equal area law for the first-order phase transition is valid always and the critical exponent of the heat capacity for the second-order phase transition coincides with that of the mean field theory regardless of the size of the boundary region.

Two Pathways Mediate Inter-Domain Allosteric Regulation in Pin1

The ever increasing discoveries of noncoding RNA functions draw a strong demand for RNA structure determination from the sequence. In recently years, computational studies for RNA structures, at both the two-dimensional and the three-dimensional levels, led to several highly promising new developments. In this chapter, we describe a recently developed RNA structure prediction method based on the virtual bond-based coarse-grained folding model (Vfold). The main emphasis in the Vfold method is placed on the loop entropy calculations, the treatment of noncanonical (mismatch) interactions and the 3D structure assembly from motif-based template library. As case studies, we use the glycine riboswitch and the G310-U376 domain of MLV RNA to illustrate the Vfold-based prediction of RNA 3D structures from the sequences.

Two Pathways Mediate Interdomain Allosteric Regulation in Pin1

To investigate the effects of added molecular heterogeneity on the hysteretic features of liquid-glass-liquid transition, we studied acetaminophen, sulfathiazole, and three of their mixtures by calorimetry, and determined the T(g) and the fictive temperature, T(f), from changes in the enthalpy and entropy on the cooling and heating paths, as well as the non-exponential parameter, β(cal). We find that, (i) T(f) for cooling is within 1-3 K of T(f) for heating and both are close to T(g), (ii) the closed loop entropy change in the liquid-glass-liquid range is negligibly small, (iii) T(g) and T(f) increase on increasing sulfathiazole in the mixture, (iv) β(cal) first slightly increases when the second component is added and then decreases, and (v) ageing causes deviations from a non-exponential, nonlinear behavior of the glass. In terms of fluctuations in a potential energy landscape, adding a solute heterogeneity would shift the state point to another part of the landscape with a different distribution of barrier heights and a different number of minima accessible to the state point. Part of the change in β(cal) is attributed to hydrogen-bond formation between the two components. Ageing changes the relaxation times distribution, more at short relaxation times than at long relaxation times, and multiplicity of relaxation modes implied by β(cal) < 1 indicates that each mode contributing to the enthalpy has its own T(g) or T(f). β(cal) differs from β(age) determined from isothermal ageing, and the distribution parameter of α-relaxation times would differ from both β(cal) and β(age).

BackgroundThe ever increasing discovery of non-coding RNAs leads to unprecedented demand for the accurate modeling of RNA folding, including the predictions of two-dimensional (base pair) and three-dimensional all-atom structures and folding stabilities. Accurate modeling of RNA structure and stability has far-reaching impact on our understanding of RNA functions in human health and our ability to design RNA-based therapeutic strategies.ResultsThe Vfold server offers a web interface to predict (a) RNA two-dimensional structure from the nucleotide sequence, (b) three-dimensional structure from the two-dimensional structure and the sequence, and (c) folding thermodynamics (heat capacity melting curve) from the sequence. To predict the two-dimensional structure (base pairs), the server generates an ensemble of structures, including loop structures with the different intra-loop mismatches, and evaluates the free energies using the experimental parameters for the base stacks and the loop entropy parameters given by a coarse-grained RNA folding model (the Vfold model) for the loops. To predict the three-dimensional structure, the server assembles the motif scaffolds using structure templates extracted from the known PDB structures and refines the structure using all-atom energy minimization.ConclusionsThe Vfold-based web server provides a user friendly tool for the prediction of RNA structure and stability. The web server and the source codes are freely accessible for public use at “http://rna.physics.missouri.edu”.

The denaturation transition of circular DNA is studied within a Poland-Scheraga-type approach, generalized to account for the fact that the total linking number (LK), which measures the number of windings of one strand around the other, is conserved. In the model the LK conservation is maintained by invoking both overtwisting and writhing (supercoiling) mechanisms. This generalizes previous studies, which considered each mechanism separately. The phase diagram of the model is analyzed as a function of the temperature and the elastic constant κ associated with the overtwisting energy for any given loop entropy exponent c. As in the case where the two mechanisms apply separately, the model exhibits no denaturation transition for c ≤ 2. For c > 2 and κ = 0 we find that the model exhibits a first-order transition. The transition becomes of higher order for any κ > 0. We also calculate the contribution of the two mechanisms separately in maintaining the conservation of the linking number and find that it is weakly dependent on the loop exponent c.