稳定的RNA发夹结构及其生物学功能

以UNCG、GNRA、CUUG(N=A、U、C或G,R=G或A)为端环能够形成稳定的、保守的发夹结构。高分辨率的溶液结构、晶体结构和计算机模拟等方法从原子水平上解析了这些发夹特殊的结构特征。在体内,它们发挥着重要的生物学功能:在折叠过程中作为折叠的起始位置帮助组织RNA分子正确折叠;与核酸受体结合参与三级相互作用;与蛋白质发生相互作用;阻止逆转录酶的延伸等等。另外,由于C(UUCG)G发夹极其稳定的特征,在体外RNA分子的实验测定中它还是稳定核酸结构的理想工具。这些稳定的发夹广泛分布于体内rRNA、催化RNA和非编码mRNA中。但在对人类编码区mRNA结构特征的研究当中,却未发现C(UUCG)G发夹。     

Asymptotic Number of Hairpins of Saturated RNA Secondary Structures

In the absence of chaperone molecules, RNA folding is believed to depend on the distribution of kinetic traps in the energy landscape of all secondary structures. Kinetic traps in the Nussinov energy model are precisely those secondary structures that are saturated, meaning that no base pair can be added without introducing either a pseudoknot or base triple. In this paper, we compute the asymptotic expected number of hairpins in saturated structures. For instance, if every hairpin is required to contain at least θ=3 unpaired bases and the probability that any two positions can base-pair is p=3/8, then the asymptotic number of saturated structures is 1.34685?n ^?3/2?1.62178 ⁿ , and the asymptotic expected number of hairpins follows a normal distribution with mean $0.06695640 \cdot n + 0.01909350 \cdot\sqrt{n} \cdot\mathcal{N}$ . Similar results are given for values θ=1,3, and p=1,1/2,3/8; for instance, when θ=1 and p=1, the asymptotic expected number of hairpins in saturated secondary structures is 0.123194?n, a value greater than the asymptotic expected number 0.105573?n of hairpins over all secondary structures. Since RNA binding targets are often found in hairpin regions, it follows that saturated structures present potentially more binding targets than nonsaturated structures, on average. Next, we describe a novel algorithm to compute the hairpin profile of a given RNA sequence: given RNA sequence a ₁,…,a _n , for each integer k, we compute that secondary structure S _k having minimum energy in the Nussinov energy model, taken over all secondary structures having k hairpins. We expect that an extension of our algorithm to the Turner energy model may provide more accurate structure prediction for particular RNAs, such as tRNAs and purine riboswitches, known to have a particular number of hairpins. Mathematica^? computations, C and Python source code, and additional supplementary information are available at the website http://bioinformatics.bc.edu/clotelab/RNAhairpinProfile/.     

New Computational Approach for Peptide Vaccine Design Against SARS-COV-2

International Journal of Peptide Research and Therapeutics - The design for vaccines using in silico analysis of genomic data of different viruses has taken many different paths, but lack of any...     

Predicting Secondary Structural Folding Kinetics for Nucleic Acids

We report a new computational approach to the prediction of RNA secondary structure folding kinetics. In this approach, each elementary kinetic step is represented as the transformation between two secondary structures that differ by a helix. Based on the free energy landscape analysis, we identify three types of dominant pathways and the rate constants for the kinetic steps: 1), formation; 2), disruption of a helix stem; and 3), helix formation with concomitant partial melting of a competing (incompatible) helix. The third pathway, termed the tunneling pathway, is the low-barrier dominant pathway for the conversion between two incompatible helices. Comparisons with experimental data indicate that this new method is quite reliable in predicting the kinetics for RNA secondary structural folding and structural rearrangements. The approach presented here may provide a robust first step for further systematic development of a predictive theory for the folding kinetics for large RNAs.     

A Computational Approach for Deciphering the Organization of Glycosaminoglycans

Background

Increasing evidence has revealed important roles for complex glycans as mediators of normal and pathological processes. Glycosaminoglycans are a class of glycans that bind and regulate the function of a wide array of proteins at the cell-extracellular matrix interface. The specific sequence and chemical organization of these polymers likely define function; however, identification of the structure-function relationships of glycosaminoglycans has been met with challenges associated with the unique level of complexity and the nontemplate-driven biosynthesis of these biopolymers.

Methodology/Principal Findings

To address these challenges, we have devised a computational approach to predict fine structure and patterns of domain organization of the specific glycosaminoglycan, heparan sulfate (HS). Using chemical composition data obtained after complete and partial digestion of mixtures of HS chains with specific degradative enzymes, the computational analysis produces populations of theoretical HS chains with structures that meet both biosynthesis and enzyme degradation rules. The model performs these operations through a modular format consisting of input/output sections and three routines called chainmaker, chainbreaker, and chainsorter. We applied this methodology to analyze HS preparations isolated from pulmonary fibroblasts and epithelial cells. Significant differences in the general organization of these two HS preparations were observed, with HS from epithelial cells having a greater frequency of highly sulfated domains. Epithelial HS also showed a higher density of specific HS domains that have been associated with inhibition of neutrophil elastase. Experimental analysis of elastase inhibition was consistent with the model predictions and demonstrated that HS from epithelial cells had greater inhibitory activity than HS from fibroblasts.

Conclusions/Significance

This model establishes the conceptual framework for a new class of computational tools to use to assess patterns of domain organization within glycosaminoglycans. These tools will provide a means to consider high-level chain organization in deciphering the structure-function relationships of polysaccharides in biology.     

Folding/Unfolding Kinetics of Apomyoglobin

The equilibrium and kinetic folding/unfolding of apomyoglobin (ApoMb) were studied at pH 6.2, 11 °C by recording tryptophan fluorescence. The equilibrium unfolding of ApoMb in the presence of urea was shown to involve accumulation of an intermediate state, which had a higher fluorescence intensity as compared with the native and unfolded states. The folding proceeded through two kinetic phases, a rapid transition from the unfolded to the intermediate state and a slow transition from the intermediate to the native state. The accumulation of the kinetic intermediate state was observed in a wide range of urea concentrations. The intermediate was detected even in the region corresponding to the unfolding limb of the chevron plot. Urea concentration dependence was obtained for the observed folding/unfolding rate. The shape of the dependence was compared with that of two-state proteins characterized by a direct transition from the unfolded to the native state.     

模拟蛋白质折叠过程的新算法研究

蛋白质折叠过程模拟是当前蛋白质研究领域的一个难点问题。针对这一问题,提出了一个描述蛋白质折叠过程的算法-拟蛇算法,并且从分子振荡和分子动力学理论两个方面来证明该算法的核心函数是可行和正确的。经过实验总结出所有蛋白质空间结构都可以通过两种类型函数构造出来,提出了描述蛋白质折叠过程模型。与其它蛋白质折叠过程模拟算法的实验结果比较表明,拟蛇算法所构造的空间结构能量值最小、相似度最好。进而说明拟蛇算法和蛋白质折叠过程模型在描述蛋白质折叠过程方面具有明显优势。     

Folding of branched RNA species

The global structures of branched RNA species are important to their function. Branched RNA species are defined as molecules in which double-helical segments are interrupted by abrupt discontinuities. These include helical junctions of different orders, and base bulges and loops. Common helical junctions are three- and four-way junctions, often interrupted by mispairs or additional nucleotides. There are many interesting examples of functional RNA junctions, including the hammerhead and hairpin ribozymes, and junctions that serve as binding sites for proteins. The junctions display some common structural properties. These include a tendency to undergo pairwise helical stacking and ion-induced conformational transitions. Helical branchpoints can act as key architectural components and as important sites for interactions with proteins. Copyright 1999 John Wiley & Sons, Inc.     

Regulation of Programmed Ribosomal Frameshifting by Co-Translational Refolding RNA Hairpins

RNA structures are unwound for decoding. In the process, they can pause the elongating ribosome for regulation. An example is the stimulation of -1 programmed ribosomal frameshifting, leading to 3′ direction slippage of the reading-frame during elongation, by specific pseudoknot stimulators downstream of the frameshifting site. By investigating a recently identified regulatory element upstream of the SARS coronavirus (SARS-CoV) −1 frameshifting site, it is shown that a minimal functional element with hairpin forming potential is sufficient to down-regulate−1 frameshifting activity. Mutagenesis to disrupt or restore base pairs in the potential hairpin stem reveals that base-pair formation is required for−1 frameshifting attenuation in vitro and in 293T cells. The attenuation efficiency of a hairpin is determined by its stability and proximity to the frameshifting site; however, it is insensitive to E site sequence variation. Additionally, using a dual luciferase assay, it can be shown that a hairpin stimulated +1 frameshifting when placed upstream of a +1 shifty site in yeast. The investigations indicate that the hairpin is indeed a cis-acting programmed reading-frame switch modulator. This result provides insight into mechanisms governing−1 frameshifting stimulation and attenuation. Since the upstream hairpin is unwound (by a marching ribosome) before the downstream stimulator, this study’s findings suggest a new mode of translational regulation that is mediated by the reformed stem of a ribosomal unwound RNA hairpin during elongation.     

Vfold: A Web Server for RNA Structure and Folding Thermodynamics Prediction

Background

The 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.

Results

The 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.

Conclusions

The 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”.     

Design of New and Potent Diethyl Thiobarbiturates as Urease Inhibitors: A Computational Approach

Urease is an important enzyme both in agriculture and medicine research. Strategies based on urease inhibition is critically considered as the first line treatment of infections caused by urease producing bacteria. Since, urease possess agro-chemical and medicinal importance, thus, it is necessary to search for the novel compounds capable of inhibiting this enzyme. Several computational methods were employed to design novel and potent urease inhibitors in this work. First docking simulations of known compounds consists of a set of arylidine barbiturates (termed as reference) were performed on the Bacillus pasteurii (BP) urease. Subsequently, two fold strategies were used to design new compounds against urease. Stage 1 comprised of the energy minimization of enzyme-ligand complexes of reference compounds and the accurate prediction of the molecular mechanics generalized born (MMGB) interaction energies. In the second stage, new urease inhibitors were then designed by the substitution of different groups consecutively in the aryl ring of the thiobarbiturates and N, N-diethyl thiobarbiturates of the reference ligands.. The enzyme-ligand complexes with lowest interaction energies or energies close to the calculated interaction energies of the reference molecules, were selected for the consequent chemical manipulation. This was followed by the substitution of different groups on the 2 and 5 positions of the aryl ring. As a result, several new and potent diethyl thiobarbiturates were predicted as urease inhibitors. This approach reflects a logical progression for early stage drug discovery that can be exploited to successfully identify potential drug candidates.     

Kinetics and Energetics of Biomolecular Folding and Binding

The ability of biomolecules to fold and to bind to other molecules is fundamental to virtually every living process. Advanced experimental techniques can now reveal how single biomolecules fold or bind against mechanical force, with the force serving as both the regulator and the probe of folding and binding transitions. Here, we present analytical expressions suitable for fitting the major experimental outputs from such experiments to enable their analysis and interpretation. The fit yields the key determinants of the folding and binding processes: the intrinsic on-rate and the location and height of the activation barrier.     

TBI Server: A Web Server for Predicting Ion Effects in RNA Folding

Background

Metal ions play a critical role in the stabilization of RNA structures. Therefore, accurate prediction of the ion effects in RNA folding can have a far-reaching impact on our understanding of RNA structure and function. Multivalent ions, especially Mg²⁺, are essential for RNA tertiary structure formation. These ions can possibly become strongly correlated in the close vicinity of RNA surface. Most of the currently available software packages, which have widespread success in predicting ion effects in biomolecular systems, however, do not explicitly account for the ion correlation effect. Therefore, it is important to develop a software package/web server for the prediction of ion electrostatics in RNA folding by including ion correlation effects.

Results

The TBI web server http://rna.physics.missouri.edu/tbi_index.html provides predictions for the total electrostatic free energy, the different free energy components, and the mean number and the most probable distributions of the bound ions. A novel feature of the TBI server is its ability to account for ion correlation and ion distribution fluctuation effects.

Conclusions

By accounting for the ion correlation and fluctuation effects, the TBI server is a unique online tool for computing ion-mediated electrostatic properties for given RNA structures. The results can provide important data for in-depth analysis for ion effects in RNA folding including the ion-dependence of folding stability, ion uptake in the folding process, and the interplay between the different energetic components.     

A New Computational Efficient Approach for Trabecular Bone Analysis using Beam Models Generated with Skeletonized Graph Technique

Micro-finite element (FE) analysis is a well established technique for the evaluation of the elastic properties of trabecular bone, but is limited in its application due to the large number of elements that it requires to represent the complex internal structure of the bone. In this paper, we present an alternative FE approach that makes use of a recently developed 3D-Line Skeleton Graph Analysis (LSGA) technique to represent the complex internal structure of trabecular bone as a network of simple straight beam elements in which the beams are assigned geometrical properties of the trabeculae that they represent. Since an enormous reduction of cputime can be obtained with this beam modeling approach, ranging from approximately 1,200 to 3,600 for the problems investigated here, we think that the FE modeling technique that we introduced could potentially constitute an interesting alternative for the evaluation of the elastic mechanical properties of trabecular bone.     

Kinetics and Energetics of Biomolecular Folding and Binding

The ability of biomolecules to fold and to bind to other molecules is fundamental to virtually every living process. Advanced experimental techniques can now reveal how single biomolecules fold or bind against mechanical force, with the force serving as both the regulator and the probe of folding and binding transitions. Here, we present analytical expressions suitable for fitting the major experimental outputs from such experiments to enable their analysis and interpretation. The fit yields the key determinants of the folding and binding processes: the intrinsic on-rate and the location and height of the activation barrier.Dynamic processes in living cells are regulated through conformational changes in biomolecules—their folding into a particular shape or binding to selected partners. The ability of biomolecules to fold and to bind enables them to act as switches, assembly factors, pumps, or force- and displacement-generating motors (1). Folding and binding transitions are often hindered by a free energy barrier. Overcoming the barrier requires energy-demanding rearrangements such as displacing water from the sites of native contacts and breaking nonnative electrostatic contacts, as well as loss of configurational entropy. Once the barrier is crossed, the folded and bound states are stabilized by short-range interactions: hydrogen bonds, favorable hydrophobic effects, and electrostatic and van der Waals attractions (2).Mechanistic information about folding and binding processes is detailed in the folding and binding trajectories of individual molecules: observing an ensemble of molecules may obscure the inherent heterogeneity of these processes. Single-molecule trajectories can be induced, and monitored, by applying force to unfold/unbind a molecule and then relaxing the force until folding or binding is observed (3–5) (Fig. 1). Varying the force relaxation rate shifts the range of forces at which folding or binding occurs, thus broadening the explorable spectrum of molecular responses to force and revealing conformational changes that are otherwise too fast to detect. The measured force-dependent kinetics elucidates the role of force in physiological processes (6) and provides ways to control the timescales, and even the fate, of these processes. The force-dependent data also provides a route to understanding folding and binding in the absence of force—by extrapolating the data to zero force via a fit to a theory.Open in a separate windowFigure 1Schematic of the output from a force-relaxation experiment. The applied force is continuously relaxed from the initial value F₀ until the biomolecule folds or binds, as signified by a sharp increase in the measured force. From multiple repeats of this experiment, distributions of the folding or binding forces are collected (inset). Fitting the force distributions with the derived analytical expression yields the key parameters that determine the kinetics and energetics of folding or binding.In this letter, we derive an analytical expression for the distribution of transition forces, the major output of force-relaxation experiments that probe folding and binding processes. The expression extracts the key determinants of these processes: the on-rate and activation barrier in the absence of force. The theory is first developed in the context of biomolecular folding, and is then extended to cover the binding of a ligand tethered to a receptor. In contrast to unfolding and unbinding, the reverse processes of folding and binding require a theory that accounts for the compliance of the unfolded state, as well as the effect of the tether, to recover the true kinetic parameters of the biomolecule of interest.In a force-relaxation experiment, an unfolded biomolecule or unbound ligand-receptor complex is subject to a stretching force, which is decreased from the initial value F₀ as the pulling device approaches the sample at speed V until a folding or binding transition is observed (Fig. 1) (3–5). Define S(t) as the probability that the molecule has not yet escaped from the unfolded (implied: or unbound) state at time t. When escape is limited by one dominant barrier, S(t) follows the first-order rate equationS˙(t)≡dS(t)dt=−k←(F(t))S(t),where k_←(F(t)) is the on-rate at force F at time t. Because, prior to the transition, the applied force decreases monotonically with time, the distribution of transition forces, p(F), is related to S(t) through p(F)dF=S˙(t)dt, yieldingp(F)=−k←(F)F˙(F)e−∫F0Fk←(F′)F˙(F′)dF′.(1)Here F˙(F)≡dF(t)/dt<0 is the force relaxation rate. The proper normalization of p(F) is readily confirmed by integrating Eq. 1 from the initial force F₀ to negative infinity, the latter accounting for transitions that do not occur by the end of the experiment. Note that the expression for the distribution of folding/binding forces in Eq. 1 differs from its analog for the unfolding process (7) by the limits of integration and a negative sign, reflecting the property of a relaxation experiment to decrease the survival probability S(t) by decreasing the force. Converting the formal expression in Eq. 1 into a form suitable for fitting experimental data requires establishing functional forms for k_←(F) and F˙(F) and analytically solving the integral. These steps are accomplished below.The on-rate k_←(F) is computed by treating the conformational dynamics of the molecule as a random walk on the combined free energy profile G(x,t) = G₀(x) + G_pull(x,t) along the molecular extension x. Here G₀(x) is the intrinsic molecular potential and G_pull(x,t) is the potential of the pulling device. When G(x,t) features a high barrier on the scale of k_BT (k_B is the Boltzmann constant and T the temperature), the dynamics can be treated as diffusive. The unfolded region of the intrinsic potential for a folding process, unlike that for a barrierless process (8), can be captured by the functionG0(x)=ΔG‡ν1−ν(xx‡)11−ν−ΔG‡ν(xx‡),which has a sharp (if ν = 1/2, Fig. 2, inset) or smooth (if ν = 2/3) barrier of height ΔG^‡ and location x^‡. The potential of a pulling device of stiffness κ_S is G_pull(x,t) = κ_S/2(X₀ – Vt – x)² with an initial minimum at X₀ (corresponding to F₀). Applying Kramers formalism (9) to the combined potential G(x,t), we establish the analytical form of the on-rate at force F(t),k←(F)=k0(1+κSκU(F))1ν−12(1+νFx‡ΔG‡)1ν−1×eβΔG‡[1−(1+κSκU(F))2ν1−ν−1(1+νFx‡ΔG‡)1ν],where k₀ is the intrinsic on-rate, β ≡ (k_BT)⁻¹, andκU(F)=ν(1−ν)2ΔG‡x‡2(1+νFx‡ΔG‡)2−1νis the stiffness of the unfolded biomolecule under force F (see the Supporting Material for details on all derivations). The full nonlinear form of G_pull(x,t) was necessary in the derivation because, in contrast to the typically stiff folded state, the unfolded state may be soft (to be exact, 1/2κ_S x^‡2(F) << k_BT may not be satisfied) and thus easily deformed by the pulling device. Because of this deformation, the folding transition faces an extra contribution (regulated by the ratio κ_S/κ_U(F)) to the barrier height, typically negligible for unfolding, that decreases the on-rate in addition to the applied force F.Open in a separate windowFigure 2Contributions to the free energy profile for folding (inset) and binding (main figure). The derived expression (Eq. 2) extracts the on-rate and the location and height of the activation barrier to folding. When applied to binding data, the expression extracts the parameters of the ligand-tether-receptor (LTR) potential G˜0 (x); the proposed algorithm (Eqs. 3 and 4) removes the contribution of the tether potential G_teth(x) to recover the parameters of the intrinsic ligand-receptor (LR) potential G₀(x).The last piece required for Eq. 1, the loading rate F˙(F), is computed as the time derivative of the force F(t) on the unfolded molecule at its most probable extension at time t:F˙(F)=−κSV1+κS/κU(F).Finally, we realize that the integral in Eq. 1 can be solved analytically exactly, both for ν = 1/2 and ν = 2/3, resulting in the analytical expression for the distribution of folding forces:p(F)=k←(F)|F˙(F)|e−k←(F)β|F˙(F)|x‡(1+κSκU(F))νν−1(1+νFx‡ΔG‡)1−1ν.(2)Equation 2 can be readily applied to (normalized) histograms from force-relaxation experiments to extract the parameters of the intrinsic kinetics and energetics of folding. Being exact for ν = 1/2 and ν = 2/3, Eq. 2 is also an accurate approximation for any ν in the interval 1/2 < ν < 2/3 as long as κ_S ≲ κ_U (F) (see Fig. S1 in the Supporting Material). For simplicity, in Eq. 2 we have omitted the term containing F₀ as negligible if F₀ is large enough to prevent folding events.The solution in Eq. 2 reveals properties of the distribution of folding forces that distinguish it from its unfolding counterpart (7):

• 1.The distribution has a positive skew (Fig. 3), as intuitively expected: the rare folding events occur at high forces when the barrier is still high.Open in a separate windowFigure 3Force histograms from folding (left) and binding (right) simulations at several values of the force-relaxation speed (in nanometers per second, indicated at each histogram). Fitting the histograms with the analytical expression in Eq. 2 (lines) recovers the on-rate and activation barrier for folding or binding (2.Increasing the relaxation speed shifts the distribution to lower forces (Fig. 3): faster force relaxation leaves less time for thermal fluctuations to push the system over a high barrier, causing transitions to occur later (i.e., at lower forces), when the barrier is lower.
• 3.The stiffness κ_S and speed V enter Eq. 2 separately, providing independent routes to control the range of folding forces and thus enhance the robustness of a fit.

The application of the above framework to binding experiments on a ligand and receptor connected by a tether (3) involves an additional step—decoupling the effect of the tether—to reconstruct the parameters of ligand-receptor binding. Indeed, the parameters extracted from a fit of experimental histograms to Eq. 2 characterize the ligand-tether-receptor (LTR) potential (k˜0, x˜‡, ΔG˜‡, ν) (Fig. 2). The parameters of the natural ligand-receptor (LR) potential (k₀, x^‡, ΔG^‡) can be recovered using three characteristics of the tether: contour length L; persistence length p; and extension Δℓ of the tether along the direction of the force in the LTR transition state. The values of L and p can be determined from the force-extension curve of the tether (10); these define the tether potential G_teth(x) (Fig. 2). The value of Δℓ can be found from an unbinding experiment (7) on LTR and the geometry of the tether attachment points (see Fig. S3). Approximating the region of the LR potential between the transition and unbound states as harmonic, with no assumptions about the shape of the potential beyond x^‡, the ligand-receptor barrier parameters are thenx‡=α−1α−2x˜‡,ΔG‡=(α−1)22(α−2)x˜‡Fteth(Δℓ+x˜‡),(3)and the intrinsic unimolecular association rate isk0≈k˜0(βΔG‡)32(βΔG˜‡)1ν−12(x˜‡x‡)2eβ(ΔG˜‡−ΔG‡).(4)Here, the force value Fteth(Δℓ+x˜‡) is extracted from the force-extension curve of the tether at extension Δℓ+x˜‡ andα=2(ΔG˜‡−Gteth(Δℓ)+Gteth(Δℓ+x˜‡))x˜‡Fteth(Δℓ+x˜‡),where G_teth(x) is the wormlike-chain potential (see Eq. S13 in the Supporting Material). Equations 3–4 confirm that a tether decreases the height and width of the barrier (see Fig. 2), thus increasing the on-rate.In Fig. 3, the developed analytical framework is applied to folding and binding force histograms from Brownian dynamics simulations at parameters similar to those in the analogous experimental and computational studies (3,5,11) (for details on simulations and fitting procedure, see the Supporting Material). For the stringency of the test, the simulations account for the wormlike-chain nature of the molecular unfolded and LTR unbound states that is not explicitly accounted for in the theory. With optimized binning (12) of the histograms and a least-squares fit, Eqs. 2–4 recover the on-rate, the location and the height of the activation barrier, and the value of ν that best captures how the kinetics scale with force (

1.Multiple relaxation speeds,

2.Folding/binding events at low forces, and

3.A large number of events at each speed.

Table 1

On-rate and the location and height of the activation barrier from the fit of simulated data to the theory in Eq. 2

A Computational Approach for Simulating Muscle Morphologic Changes in Musculoskeletal Modeling

Digital data characterizing the geometry of anatomic structures (e.g., bones, muscles and tendons) are becoming readily available from Magnetic Resonance Imaging and Computerized Tomography technology. These data can be useful in forward simulations of limb dynamics to study the interaction between tissue morphology and limb dynamics, but only if computational tools are available to manipulate these data to simulate various structural changes. The objective of this project was to develop a computational approach to simulate physiological changes in muscle volume and limb cross-section. A previously reported method for calculating the area and area centroid location of complex shapes was combined with a newly derived algorithm that simulates muscle hypertrophy or atrophy. The new algorithm modifies the cross-sectional areas of specified muscles and the spatial orientation of other muscles, as appropriate, to simulate desired muscle volume changes. An approach of this type is needed to facilitate musculoskeletal modeling and computer simulations of movement designed to address questions related to the interactions between muscle morphology, limb inertial properties and limb dynamics.     

Computational approaches for RNA energy parameter estimation

Methods for efficient and accurate prediction of RNA structure are increasingly valuable, given the current rapid advances in understanding the diverse functions of RNA molecules in the cell. To enhance the accuracy of secondary structure predictions, we developed and refined optimization techniques for the estimation of energy parameters. We build on two previous approaches to RNA free-energy parameter estimation: (1) the Constraint Generation (CG) method, which iteratively generates constraints that enforce known structures to have energies lower than other structures for the same molecule; and (2) the Boltzmann Likelihood (BL) method, which infers a set of RNA free-energy parameters that maximize the conditional likelihood of a set of reference RNA structures. Here, we extend these approaches in two main ways: We propose (1) a max-margin extension of CG, and (2) a novel linear Gaussian Bayesian network that models feature relationships, which effectively makes use of sparse data by sharing statistical strength between parameters. We obtain significant improvements in the accuracy of RNA minimum free-energy pseudoknot-free secondary structure prediction when measured on a comprehensive set of 2518 RNA molecules with reference structures. Our parameters can be used in conjunction with software that predicts RNA secondary structures, RNA hybridization, or ensembles of structures. Our data, software, results, and parameter sets in various formats are freely available at http://www.cs.ubc.ca/labs/beta/Projects/RNA-Params.     

Computational Modeling of Proteins based on Cellular Automata: A Method of HP Folding Approximation

The design of a protein folding approximation algorithm is not straightforward even when a simplified model is used. The folding problem is a combinatorial problem, where approximation and heuristic algorithms are usually used to find near optimal folds of proteins primary structures. Approximation algorithms provide guarantees on the distance to the optimal solution. The folding approximation approach proposed here depends on two-dimensional cellular automata to fold proteins presented in a well-studied simplified model called the hydrophobic–hydrophilic model. Cellular automata are discrete computational models that rely on local rules to produce some overall global behavior. One-third and one-fourth approximation algorithms choose a subset of the hydrophobic amino acids to form H–H contacts. Those algorithms start with finding a point to fold the protein sequence into two sides where one side ignores H’s at even positions and the other side ignores H’s at odd positions. In addition, blocks or groups of amino acids fold the same way according to a predefined normal form. We intend to improve approximation algorithms by considering all hydrophobic amino acids and folding based on the local neighborhood instead of using normal forms. The CA does not assume a fixed folding point. The proposed approach guarantees one half approximation minus the H–H endpoints. This lower bound guaranteed applies to short sequences only. This is proved as the core and the folds of the protein will have two identical sides for all short sequences.