Loop Free Energy Research Articles

ZN symmetry in SU(N) gauge theories

In this paper, we study [Formula: see text] symmetry of [Formula: see text] gauge group, in one-dimensional gauged chain. The action can be obtained by considering the terms of a [Formula: see text]-dimensional Euclidean lattice action of a [Formula: see text] gauge theory that break the [Formula: see text] symmetry explicitly. The matter fields in the resulting partition function can be integrated out exactly, for a given background of link variables, to calculate the Polyakov loop free energy. To keep the temperature fixed, the lattice spacing is scaled appropriately as the number of “temporal” sites is varied. In the case of Higgs as matter field, the Polyakov loop free energy exhibits the [Formula: see text] symmetry in the limit of large number of temporal sites. For fermions, the strength of [Formula: see text] explicit breaking decreases for finer lattices, but approaches a nonzero value in the same limit. We discuss the possible implications of these results to [Formula: see text] gauge theories in [Formula: see text] dimensions.

First Principles Calculation of Protein-Protein Dimer Affinities of ALS-Associated SOD1 Mutants.

Cu,Zn superoxide dismutase (SOD1) is a 32 kDa homodimer that converts toxic oxygen radicals in neurons to less harmful species. The dimerization of SOD1 is essential to the stability of the protein. Monomerization increases the likelihood of SOD1 misfolding into conformations associated with aggregation, cellular toxicity, and neuronal death in familial amyotrophic lateral sclerosis (fALS). The ubiquity of disease-associated mutations throughout the primary sequence of SOD1 suggests an important role of physicochemical processes, including monomerization of SOD1, in the pathology of the disease. Herein, we use a first-principles statistical mechanics method to systematically calculate the free energy of dimer binding for SOD1 using molecular dynamics, which involves sequentially computing conformational, orientational, and separation distance contributions to the binding free energy. We consider the effects of two ALS-associated mutations in SOD1 protein on dimer stability, A4V and D101N, as well as the role of metal binding and disulfide bond formation. We find that the penalty for dimer formation arising from the conformational entropy of disordered loops in SOD1 is significantly larger than that for other protein–protein interactions previously considered. In the case of the disulfide-reduced protein, this leads to a bound complex whose formation is energetically disfavored. Somewhat surprisingly, the loop free energy penalty upon dimerization is still significant for the holoprotein, despite the increased structural order induced by the bound metal cations. This resulted in a surprisingly modest increase in dimer binding free energy of only about 1.5 kcal/mol upon metalation of the protein, suggesting that the most significant stabilizing effects of metalation are on folding stability rather than dimer binding stability. The mutant A4V has an unstable dimer due to weakened monomer-monomer interactions, which are manifested in the calculation by a separation free energy surface with a lower barrier. The mutant D101N has a stable dimer partially due to an unusually rigid β-barrel in the free monomer. D101N also exhibits anticooperativity in loop folding upon dimerization. These computational calculations are, to our knowledge, the most quantitatively accurate calculations of dimer binding stability in SOD1 to date.

VfoldMCPX: predicting multistrand RNA complexes.

Multistrand RNA complexes play a critical role in RNA-related biological processes. The understanding of RNA functions and the rational design of RNA nanostructures require accurate prediction of the structure and folding stability of the complexes, including those containing pseudoknots. Here, we present VfoldMCPX, a new model for predicting two-dimensional (2D) structures and folding stabilities of multistrand RNA complexes. Based on a partition function-based algorithm combined with physical loop free energy parameters, the VfoldMCPX model predicts not only the native structure but also the folding stability of the complex. An important advantage of the model is the ability to treat pseudoknotted structures. Extensive tests on structure predictions show the VfoldMCPX model provides improved accuracy for multistranded RNA complexes, especially for RNA complexes with three or more strands and/or containing pseudoknots. We have developed a freely accessible VfoldMCPX web server at http://rna.physics.missouri.edu/vfoldMCPX2.

Predicting Selective RNA Processing and Stabilization Operons in Clostridium spp.

In selective RNA processing and stabilization (SRPS) operons, stem–loops (SLs) located at the 3′-UTR region of selected genes can control the stability of the corresponding transcripts and determine the stoichiometry of the operon. Here, for such operons, we developed a computational approach named SLOFE (stem–loop free energy) that identifies the SRPS operons and predicts their transcript- and protein-level stoichiometry at the whole-genome scale using only the genome sequence via the minimum free energy (ΔG) of specific SLs in the intergenic regions within operons. As validated by the experimental approach of differential RNA-Seq, SLOFE identifies genome-wide SRPS operons in Clostridium cellulolyticum with 80% accuracy and reveals that the SRPS mechanism contributes to diverse cellular activities. Moreover, in the identified SRPS operons, SLOFE predicts the transcript- and protein-level stoichiometry, including those encoding cellulosome complexes, ATP synthases, ABC transporter family proteins, and ribosomal proteins. Its accuracy exceeds those of existing in silico approaches in C. cellulolyticum, Clostridium acetobutylicum, Clostridium thermocellum, and Bacillus subtilis. The ability to identify genome-wide SRPS operons and predict their stoichiometry via DNA sequence in silico should facilitate studying the function and evolution of SRPS operons in bacteria.

One-loop tests of the supersymmetric higher spin AdS4/CFT3 correspondence

We compute one loop free energy for D=4 Vasiliev higher spin gravities based on Konstein-Vasiliev algebras hu(m;n|4), ho(m;n|4) or husp(m;n|4) and subject to higher spin preserving boundary conditions, which are conjectured to be dual to the U(N), O(N) or USp(N) singlet sectors, respectively, of free CFTs on the boundary of $AdS_4$. Ordinary supersymmetric higher spin theories appear as special cases of Konstein-Vasiliev theories, when the corresponding higher spin algebra contains $OSp({\cal N}|4)$ as subalgebra. In $AdS_4$ with $S^3$ boundary, we use a modified spectral zeta function method, which avoids the ambiguity arising from summing over infinite number of spins. We find that the contribution of the infinite tower of bulk fermions vanishes. As a result, the free energy is the sum of those which arise in type A and type B models with internal symmetries, the known mismatch between the bulk and boundary free energies for type B model persists, and ordinary supersymmetric higher spin theories exhibit the mismatch as well. The only models that have a match are type A models with internal symmetries, corresponding to $n=0$. The matching requires identification of the inverse Newton's constant $G_N^{-1}$ with $N$ plus a proper integer as was found previously for special cases. In $AdS_4$ with $S^1\times S^2$ boundary, the bulk one loop free energies match those of the dual free CFTs for arbitrary $m$ and $n$. We also show that a supersymmetric double-trace deformation of free CFT based on OSp(1|4) does not contribute to the ${\cal O}(N^0)$ free energy, as expected from the bulk.

Predicting RNA Structure with Vfold.

In order to carry out biological functions, RNA molecules must fold into specific three-dimensional (3D) structures. Current experimental methods to determine RNA 3D structures are expensive and time consuming. With the recent advances in computational biology, RNA structure prediction is becoming increasingly reliable. This chapter describes a recently developed RNA structure prediction software, Vfold, a virtual bond-based RNA folding model. The main features of Vfold are the physics-based loop free energy calculations for various RNA structure motifs and a template-based assembly method for RNA 3D structure prediction. For illustration, we use the yybP-ykoY Orphan riboswitch as an example to show the implementation of the Vfold model in RNA structure prediction from the sequence.

Coarse-Grained Prediction of RNA Loop Structures

One of the key issues in the theoretical prediction of RNA folding is the prediction of loop structure from the sequence. RNA loop free energies are dependent on the loop sequence content. However, most current models account only for the loop length-dependence. The previously developed “Vfold” model (a coarse-grained RNA folding model) provides an effective method to generate the complete ensemble of coarse-grained RNA loop and junction conformations. However, due to the lack of sequence-dependent scoring parameters, the method is unable to identify the native and near-native structures from the sequence. In this study, using a previously developed iterative method for extracting the knowledge-based potential parameters from the known structures, we derive a set of dinucleotide-based statistical potentials for RNA loops and junctions. A unique advantage of the approach is its ability to go beyond the the (known) native structures by accounting for the full free energy landscape, including all the nonnative folds. The benchmark tests indicate that for given loop/junction sequences, the statistical potentials enable successful predictions for the coarse-grained 3D structures from the complete conformational ensemble generated by the Vfold model. The predicted coarse-grained structures can provide useful initial folds for further detailed structural refinement.

A Multiscale Approach to RNA 3D Structure Prediction

One of the key issues in the theoretical prediction of RNA stability and structure is how to predict the loop free energy. Experimental results have shown strong sequence-dependence of the loop free energy. However, most currently available models only account for the loop length-dependence of the loop free energy. We recently developed a three-bead coarse-grained model to generate the three-dimensional conformations for RNA hairpin loops. Based on the pseudo-torsion angles for the coarse-grained structures, we can extract a set of pseudo-torsion angle-based statistical potential parameters from the known structures. The statistical potential parameters enable folding predictions of the low-energy coarse-grained 3D structures from the sequence. Further molecular dynamics computations for an ensemble of decoy conformations about the predicted coarse-grained structures lead to the final all-atom structures. A notable advantage of the approach is the use of the statistical potential for evaluating the loop free energies and guiding the search for the low-energy coarse-grained structures from the sequence.

Free Energy Density for Gauge Background Fields at Finite Temperature

The effective action and background field method have been applied to investigate free energy density for non-Abelian gauge theory at finite temperature, in which quantum corrections are included and certain symmetries of generating functional are restored. Renormalization is also considered for the gauge field. We give result for the one loop free energy density of gauge theory at high temperature and non-zero chemical potential, correcting a result previously at zero temperature and density. Some results are extended up to two loops

RNA Internal Loops with Tandem AG Pairs: The Structure of the 5′GAGU/3′UGAG Loop Can Be Dramatically Different from Others, Including 5′AAGU/3′UGAA

Thermodynamic stabilities of 2 × 2 nucleotide tandem AG internal loops in RNA range from −1.3 to +3.4 kcal/mol at 37 °C and are not predicted well with a hydrogen-bonding model. To provide structural information to facilitate development of more sophisticated models for the sequence dependence of stability, we report the NMR solution structures of five RNA duplexes: (rGACGAGCGUCA)2, (rGACUAGAGUCA)2, (rGACAAGUGUCA)2, (rGGUAGGCCA)2, and (rGACGAGUGUCA)2. The structures of these duplexes are compared to that of the previously solved (rGGCAGGCC)2 (Wu, M., SantaLucia, J., Jr., and Turner, D. H. (1997) Biochemistry 36, 4449−4460). For loops bounded by Watson−Crick pairs, the AG and Watson−Crick pairs are all head-to-head imino-paired (cis Watson−Crick/Watson−Crick). The structures suggest that the sequence-dependent stability may reflect non-hydrogen-bonding interactions. Of the two loops bounded by G-U pairs, only the 5′UAGG/3′GGAU loop adopts canonical UG wobble pairing (cis Watson−Crick/Watson−Crick), with AG pairs that are only weakly imino-paired. Strikingly, the 5′GAGU/3′UGAG loop has two distinct duplex conformations, the major of which has both guanosine residues (G4 and G6 in (rGACGAGUGUCA)2) in a syn glycosidic bond conformation and forming a sheared GG pair (G4-G6*, GG trans Watson−Crick/Hoogsteen), both uracils (U7 and U7*) flipped out of the helix, and an AA pair (A5-A5*) in a dynamic or stacked conformation. These structures provide benchmarks for computational investigations into interactions responsible for the unexpected differences in loop free energies and structure.

A two-length-scale polymer theory for RNA loop free energies and helix stacking

The reliability of RNA secondary structure predictions is subject to the accuracy of the underlying free energy model. Mfold and other RNA folding algorithms are based on the Turner model, whose weakest part is its formulation of loop free energies, particularly for multibranch loops. RNA loops contain single-strand and helix-crossing segments, so we develop an enhanced two-length freely jointed chain theory and revise it for self-avoidance. Our resulting universal formula for RNA loop entropy has fewer parameters than the Turner/Mfold model, and yet simulations show that the standard errors for multibranch loop free energies are reduced by an order of magnitude. We further note that coaxial stacking decreases the effective length of multibranch loops and provides, surprisingly, an entropic stabilization of the ordered configuration in addition to the enthalpic contribution of helix stacking. Our formula is in good agreement with measured hairpin free energies. We find that it also improves the accuracy of folding predictions.

Salt Dependence of Nucleic Acid Hairpin Stability

Single-stranded junctions/loops are frequently occurring structural motifs in nucleic acid structures. Due to the polyanionic nature of the nucleic acid backbone, metal ions play a crucial role in the loop stability. Here we use the tightly bound ion theory, which can account for the possible ion correlation and ensemble (fluctuation) effects, to predict the ion-dependence of loop and stem-loop (hairpin) free energies. The predicted loop free energy is a function of the loop length, the loop end-to-end distance, and the ion (Na + and Mg 2+ in this study) concentrations. Based on the statistical mechanical calculations, we derive a set of empirical formulas for the loop thermodynamic parameters as functions of Na + and Mg 2+ concentrations. For three specific types of loops, namely, hairpin, bulge, and internal loops, the predicted free energies agree with the experimental data. Further applications of these empirical formulas to RNA and DNA hairpin stability lead to good agreements with the available experimental data. Our results indicate that the ion-dependent loop stability makes significant contribution to the overall ion-dependence of the hairpin stability.

RNA Folding: Conformational Statistics, Folding Kinetics, and Ion Electrostatics

RNA folding is a remarkably complex problem that involves ion-mediated electrostatic interaction, conformational entropy, base pairing and stacking, and noncanonical interactions. During the past decade, results from a variety of experimental and theoretical studies pointed to (a) the potential ion correlation effect in Mg2+-RNA interactions, (b) the rugged energy landscapes and multistate RNA folding kinetics even for small RNA systems such as hairpins and pseudoknots, (c) the intraloop interactions and sequence-dependent loop free energy, and (d) the strong nonadditivity of chain entropy in RNA pseudoknot and other tertiary folds. Several related issues, which have not been thoroughly resolved, require combined approaches with thermodynamic and kinetic experiments, statistical mechanical modeling, and all-atom computer simulations.

Thermodynamic stability of DNA tandem mismatches.

The thermodynamics of nine hairpin DNAs were evaluated using UV-monitored melting curves and differential scanning calorimetry (DSC). Each DNA has the same five-base loop and a stem with 8-10 base pairs. Five of the DNAs have a tandem mismatch in the stem, while four have all base pairs. The tandem mismatches examined (ga/ga, aa/gc, ca/gc, ta/ac, and tc/tc) spanned the range of stability observed for this motif in a previous study of 28 tandem mismatches. UV-monitored melting curves were obtained in 1.0 M Na(+), 0.1 M Na(+), and 0.1 M Na(+) with 5 mM Mg(2+). DSC studies were conducted in 0.1 M Na(+). Transition T(m) values were unchanged over a 50-fold range of strand concentration. Model-independent enthalpy changes (DeltaH degrees ) evaluated by DSC were in good agreement (+/-8%) with enthalpy values determined by van't Hoff analyses of the melting curves in 0.1 M Na(+). The average heat capacity change (DeltaC(p)) associated with the hairpin to single strands transitions was estimated from plots of DeltaH degrees and DeltaS degrees with T(m) and ln T(m), respectively, and from profiles of DSC curves. The average DeltaC(p) values (113 +/- 9 and 42 +/- 27 cal x K(-1) x mol(-1) of bp), were in the range of values reported in previous studies. Consideration of DeltaC(p) produced large changes in DeltaH degrees and DeltaS degrees extrapolated from the transition region to 37 degrees C and smaller but significant changes to free energies. The loop free energy of the five tandem mismatches at 37 degrees C varied over a range of approximately 4 kcal x mol(-1) for each solvent.

Thermodynamic behavior of IIA string theory on a pp-wave

We obtain the thermal one loop free energy and the Hagedorn temperature of IIA superstring theory on the pp-wave geometry which comes from the circle compactification of the maximally supersymmetric eleven dimensional one. We use both operator and path integral methods and find the complete agreement between them in the free energy expression. In particular, the free energy in the $\mu \to \infty$ limit is shown to be identical with that of IIB string theory on maximally supersymmetric pp-wave, which indicates the universal thermal behavior of strings in the large class of pp-wave backgrounds. We show that the zero point energy and the modular properties of the free energy are naturally incorporated into the path integral formalism.

Boundary states for AdS2 branes in AdS3

We construct boundary states for the AdS 2 D-branes in AdS 3. We show that, in the semi-classical limit, the boundary states correctly reproduce geometric configurations of these branes. We use the boundary states to compute the one loop free energy of open string stretched between the branes. The result agrees precisely with the open string computation in hep-th/0106129.

Selective pressures on RNA hairpins in vivo and in vitro.

Comparison of the most stable potential hairpins in the sequences of natural ribozymes with those in the randomized sequences has revealed that the hairpin loop energies are lower than expected by chance. Although these hairpins are not necessarily parts of functional structures, there is a selective pressure to diminish the destabilizing free energies of the hairpin loops. In contrast, no significant bias is observed in the stacking values of the most stable stems. In the ribozymes isolated in vitro the loops of potential hairpins are closer to random values, which can result in less efficient folding rates. Furthermore, the effects of kinetic traps seem to be more significant in the folding pathways of the in vitro isolates due to a potential to form stable stacks incompatible with the functional folds. Similarly to natural ribozyme sequences, the untranslated regions of viral RNAs also form hairpins with relatively low loop free energies. These evolutionary trends suggest ways for efficient engineering of improved RNA constructs on the basis of analysis of in vitro isolates and approaches for the search of regions coding for functional RNA structures in large genome sequences.

Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure

An improved dynamic programming algorithm is reported for RNA secondary structure prediction by free energy minimization. Thermodynamic parameters for the stabilities of secondary structure motifs are revised to include expanded sequence dependence as revealed by recent experiments. Additional algorithmic improvements include reduced search time and storage for multibranch loop free energies and improved imposition of folding constraints. An extended database of 151,503 nt in 955 structures? determined by comparative sequence analysis was assembled to allow optimization of parameters not based on experiments and to test the accuracy of the algorithm. On average, the predicted lowest free energy structure contains 73 % of known base-pairs when domains of fewer than 700 nt are folded; this compares with 64 % accuracy for previous versions of the algorithm and parameters. For a given sequence, a set of 750 generated structures contains one structure that, on average, has 86 % of known base-pairs. Experimental constraints, derived from enzymatic and flavin mononucleotide cleavage, improve the accuracy of structure predictions.

Melting of a self-complementary DNA minicircle: Comparison of optical melting theory with exchange broadening of the nuclear magnetic resonance spectrum

Melting curves are calculated for the 16-base-pair duplex DNA sequence 5′ GTATCCGTACGGATAC 3′ linked on the ends by TTTT single-strand loops. The equilibrium statistical thermodynamic theory of DNA melting is modified to include effects of end-loops on the melting transition. An excellent fit of the experimental melting curve in 0.2 m-NaCl is obtained using two adjustable parameters, one for end-loop formation and the other for formation of the complete 40-base single-strand loop. The best-fit calculated melting curve permits evaluation of these parameters. The free energy to close a TTTT end-loop is 2.12 kcal/mol (1 cal = 4.184 J). A TTTT end-loop or hairpin loop is significantly more stable than an internal loop of comparable size sandwiched between two helical regions, even after allowing for the different stacking contributions. Reasons for this increased stability are presented. The loop free energy of the 40-base single-strand open minicircle is evaluated to be +1.27 kcal/mol, thus favoring the melting of two end-loops into the large open minicircle. The present results are compared with those of others for d(T-A) oligomers. The sequence TTTT forms a more stable end-loop, or hairpin, than TATA by about 2.0 kcal/mol. Theoretical rate constants for the proton-transfer step in the standard hydrogen-exchange model are calculated by extending the theory of diffusion-controlled reactions to take account of the electrostatic potential of the DNA. The predicted ratios of rate constants for different pairs of catalysts exchanging an A · T proton agree satisfactorily with the available experimental data for a 14-base-pair linear duplex, which confirms the diffusion-control of the proton-transfer step. Data presented here for the 16 base-pair duplex of the minicircle are consistent with catalysis-limited exchange in which the proton-transfer step is likewise diffusion-controlled. Under catalysis-limited conditions, the imino proton exchange rates are predicted from the catalytic rate constants, prevailing buffer catalyst concentrations, and the equilibrium constants to form the unstacked open state of optical melting theory. The observed exchange rates of the A · T base-pairs show no sign of the strong predicted end-melting trend, and exceed the predicted values by factors of 10 to 400. Moreover, the succession of “melting” in the nuclear magnetic resonance line-broadening deviates from that predicted by optical melting theory. In particular, the central base-pairs (T · A(8) and A · T(9) are out of order by 25 deg.C. These and other considerations indicate that the solvent-accessible open state of the standard model for imino proton exchange is most probably not identical with the unstacked open state of optical melting theory. Considerations concerning the recently reported exchange in the absence of added catalyst (AAC) indicate that the structures and kinetics of the solvent-accessible open states may differ for A · T base-pairs in certain locales, as well as A · T pairs in different duplex DNAs. AAC exchange is inferred to be much less important for many DNAs, including ours, than for others, and to be much more important in poly[d(A-T)] · poly[d(A-T)].