Goldtzvik, Y. ; Zhang, Z. ; Thirumalai, D. Importance of Hydrodynamic Interactions in the Stepping Kinetics of Kinesin. J Phys Chem B 120, 2071-5.Abstract
Conventional kinesin walks by a hand-over-hand mechanism on the microtubule (MT) by taking ∼8 nm discrete steps and consumes one ATP molecule per step. The time needed to complete a single step is on the order of 20 μs. We show, using simulations of a coarse-grained model of the complex containing the two motor heads, the MT and the coiled coil, that to obtain quantitative agreement with experiments for the stepping kinetics hydrodynamic interactions (HIs) have to be included. In simulations without hydrodynamic interactions, spanning nearly 20 μs, not a single step was completed in one hundred trajectories. In sharp contrast, nearly 14% of the steps reached the target binding site within 6 μs when HIs were included. Somewhat surprisingly, there are qualitative differences in the diffusion pathways in simulations with and without HI. The extent of movement of the trailing head of kinesin on the MT during the diffusion stage of stepping is considerably greater in simulations with HI than in those without HI. It is likely that inclusion of HI is crucial in the accurate description of motility of other motors as well.
Hinczewski, M. ; Thirumalai, D. Noise Control in Gene Regulatory Networks with Negative Feedback. J Phys Chem B 120, 6166-77.Abstract
Genes and proteins regulate cellular functions through complex circuits of biochemical reactions. Fluctuations in the components of these regulatory networks result in noise that invariably corrupts the signal, possibly compromising function. Here, we create a practical formalism based on ideas introduced by Wiener and Kolmogorov (WK) for filtering noise in engineered communications systems to quantitatively assess the extent to which noise can be controlled in biological processes involving negative feedback. Application of the theory, which reproduces the previously proven scaling of the lower bound for noise suppression in terms of the number of signaling events, shows that a tetracycline repressor-based negative-regulatory gene circuit behaves as a WK filter. For the class of Hill-like nonlinear regulatory functions, this type of filter provides the optimal reduction in noise. Our theoretical approach can be readily combined with experimental measurements of response functions in a wide variety of genetic circuits, to elucidate the general principles by which biological networks minimize noise.
Chakrabarti, S. ; Hinczewski, M. ; Thirumalai, D. Phenomenological and microscopic theories for catch bonds. J Struct Biol.Abstract
Lifetimes of bound states of protein complexes or biomolecule folded states typically decrease when subject to mechanical force. However, a plethora of biological systems exhibit the counter-intuitive phenomenon of catch bonding, where non-covalent bonds become stronger under externally applied forces. The quest to understand the origin of catch-bond behavior has led to the development of phenomenological and microscopic theories that can quantitatively recapitulate experimental data. Here, we assess the successes and limitations of such theories in explaining experimental data. The most widely applied approach is a phenomenological two-state model, which fits all of the available data on a variety of complexes: actomyosin, kinetochore-microtubule, selectin-ligand, and cadherin-catenin binding to filamentous actin. With a primary focus on the selectin family of cell-adhesion complexes, we discuss the positives and negatives of phenomenological models and the importance of evaluating the physical relevance of fitting parameters. We describe a microscopic theory for selectins, which provides a structural basis for catch bonds and predicts a crucial allosteric role for residues Asn82-Glu88. We emphasize the need for new theories and simulations that can mimic experimental conditions, given the complex response of cell adhesion complexes to force and their potential role in a variety of biological contexts.
Zhuravlev, P. I. ; Hinczewski, M. ; Chakrabarti, S. ; Marqusee, S. ; Thirumalai, D. Reply to Alberti: Are in vitro folding experiments relevant in vivo?. Proc Natl Acad Sci U S A 113, E3192. reply-to-alberti-are-in-vitro-folding-experiments-relevant-in-vivo.pdf
Hori, N. ; Denesyuk, N. A. ; Thirumalai, D. Salt Effects on the Thermodynamics of a Frameshifting RNA Pseudoknot under Tension. J Mol Biol 428, 2847-59. DOI:10.1016/j.jmb.2016.06.002Abstract

Because of the potential link between -1 programmed ribosomal frameshifting and response of a pseudoknot (PK) RNA to force, a number of single-molecule pulling experiments have been performed on PKs to decipher the mechanism of programmed ribosomal frameshifting. Motivated in part by these experiments, we performed simulations using a coarse-grained model of RNA to describe the response of a PK over a range of mechanical forces (fs) and monovalent salt concentrations (Cs). The coarse-grained simulations quantitatively reproduce the multistep thermal melting observed in experiments, thus validating our model. The free energy changes obtained in simulations are in excellent agreement with experiments. By varying f and C, we calculated the phase diagram that shows a sequence of structural transitions, populating distinct intermediate states. As f and C are changed, the stem-loop tertiary interactions rupture first, followed by unfolding of the 3'-end hairpin (I⇌F). Finally, the 5'-end hairpin unravels, producing an extended state (E⇌I). A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as (logCm)(α) with α=1(0.5) for E⇌I (I⇌F) transition. This relation is used to obtain the preferential ion-RNA interaction coefficient, which can be quantitatively measured in single-molecule experiments, as done previously for DNA hairpins. A by-product of our work is the suggestion that the frameshift efficiency is likely determined by the stability of the 5'-end hairpin that the ribosome first encounters during translation.

Thirumalai, D. 48 Design principles governing the motility of myosin motors. J Biomol Struct Dyn 33 Suppl 1, 33. 48-design-principles-governing-the-motility-of-myosin-motors.pdf
Kang, H. ; Yoon, Y. - G. ; Thirumalai, D. ; Hyeon, C. Confinement-Induced Glassy Dynamics in a Model for Chromosome Organization. Phys Rev Lett 115, 198102.Abstract
Recent experiments showing scaling of the intrachromosomal contact probability, P(s)∼s(-1) with the genomic distance s, are interpreted to mean a self-similar fractal-like chromosome organization. However, scaling of P(s) varies across organisms, requiring an explanation. We illustrate dynamical arrest in a highly confined space as a discriminating marker for genome organization, by modeling chromosomes inside a nucleus as a homopolymer confined to a sphere of varying sizes. Brownian dynamics simulations show that the chain dynamics slows down as the polymer volume fraction (ϕ) inside the confinement approaches a critical value ϕ(c). The universal value of ϕ(c)(∞)≈0.44 for a sufficiently long polymer (N≫1) allows us to discuss genome dynamics using ϕ as the sole parameter. Our study shows that the onset of glassy dynamics is the reason for the segregated chromosome organization in humans (N≈3×10(9), ϕ≳ϕ(c)(∞)), whereas chromosomes of budding yeast (N≈10(8), ϕ<ϕ(c)(∞)) are equilibrated with no clear signature of such organization.
Reddy, G. ; Thirumalai, D. Dissecting Ubiquitin Folding Using the Self-Organized Polymer Model. J Phys Chem B 119, 11358-70.Abstract
Folding of Ubiquitin (Ub), a functionally important protein found in eukaryotic organisms, is investigated at low and neutral pH at different temperatures using simulations of the coarse-grained self-organized-polymer model with side chains (SOP-SC). The melting temperatures (Tm's), identified with the peaks in the heat capacity curves, decrease as pH decreases, in qualitative agreement with experiments. The calculated radius of gyration, showing dramatic variations with pH, is in excellent agreement with scattering experiments. At Tm, Ub folds in a two-state manner at low and neutral pH. Clustering analysis of the conformations sampled in equilibrium folding trajectories at Tm, with multiple transitions between the folded and unfolded states, shows a network of metastable states connecting the native and unfolded states. At low and neutral pH, Ub folds with high probability through a preferred set of conformations resulting in a pH-dependent dominant folding pathway. Folding kinetics reveal that Ub assembly at low pH occurs by multiple pathways involving a combination of nucleation-collapse and diffusion collision mechanism. The mechanism by which Ub folds is dictated by the stability of the key secondary structural elements responsible for establishing long-range contacts and collapse of Ub. Nucleation collapse mechanism holds if the stability of these elements are marginal, as would be the case at elevated temperatures. If the lifetimes associated with these structured microdomains are on the order of hundreds of microseconds, then Ub folding follows the diffusion-collision mechanism with intermediates, many of which coincide with those found in equilibrium. Folding at neutral pH is a sequential process with a populated intermediate resembling that sampled at equilibrium. The transition state structures, obtained using a Pfold analysis, are homogeneous and globular with most of the secondary and tertiary structures being native-like. Many of our findings for both the thermodynamics and kinetics of folding are not only in agreement with experiments but also provide missing details not resolvable in standard experiments. The key prediction that folding mechanism varies dramatically with pH is amenable to experimental tests.
Pincus, D. L. ; Chakrabarti, S. ; Thirumalai, D. Helicase processivity and not the unwinding velocity exhibits universal increase with force. Biophys J 109, 220-30.Abstract
Helicases, involved in a number of cellular functions, are motors that translocate along single-stranded nucleic acid and couple the motion to unwinding double-strands of a duplex nucleic acid. The junction between double- and single-strands creates a barrier to the movement of the helicase, which can be manipulated in vitro by applying mechanical forces directly on the nucleic acid strands. Single-molecule experiments have demonstrated that the unwinding velocities of some helicases increase dramatically with increase in the external force, while others show little response. In contrast, the unwinding processivity always increases when the force increases. The differing responses of the unwinding velocity and processivity to force have lacked explanation. By generalizing a previous model of processive unwinding by helicases, we provide a unified framework for understanding the dependence of velocity and processivity on force and the nucleic acid sequence. We predict that the sensitivity of unwinding processivity to external force is a universal feature that should be observed in all helicases. Our prediction is illustrated using T7 and NS3 helicases as case studies. Interestingly, the increase in unwinding processivity with force depends on whether the helicase forces basepair opening by direct interaction or if such a disruption occurs spontaneously due to thermal fluctuations. Based on the theoretical results, we propose that proteins like single-strand binding proteins associated with helicases in the replisome may have coevolved with helicases to increase the unwinding processivity even if the velocity remains unaffected.
Kang, H. ; Toan, N. M. ; Hyeon, C. ; Thirumalai, D. Unexpected Swelling of Stiff DNA in a Polydisperse Crowded Environment. J Am Chem Soc 137, 10970-8.Abstract
We investigate the conformations of DNA-like stiff chains, characterized by contour length (L) and persistence length (lp), in a variety of crowded environments containing monodisperse soft spherical (SS) and spherocylindrical (SC) particles, a mixture of SS and SC, and a milieu mimicking the composition of proteins in the Escherichia coli cytoplasm. The stiff chain, whose size modestly increases in SS crowders up to ϕ ≈ 0.1, is considerably more compact at low volume fractions (ϕ ≤ 0.2) in monodisperse SC particles than in a medium containing SS particles. A 1:1 mixture of SS and SC crowders induces greater chain compaction than the pure SS or SC crowders at the same ϕ, with the effect being highly nonadditive. We also discover a counterintuitive result that the polydisperse crowding environment, mimicking the composition of a cell lysate, swells the DNA-like polymer, which is in stark contrast to the size reduction of flexible polymers in the same milieu. Trapping of the stiff chain in a fluctuating tube-like environment created by large-sized crowders explains the dramatic increase in size and persistence length of the stiff chain. In the polydisperse medium, mimicking the cellular environment, the size of the DNA (or related RNA) is determined by L/lp. At low L/lp, the size of the polymer is unaffected, whereas there is a dramatic swelling at an intermediate value of L/lp. We use these results to provide insights into recent experiments on crowding effects on RNA and also make testable predictions.
Lin, J. - C. ; Yoon, J. ; Hyeon, C. ; Thirumalai, D. Using simulations and kinetic network models to reveal the dynamics and functions of riboswitches. Methods Enzymol 553, 235-58.Abstract
Riboswitches, RNA elements found in the untranslated region, regulate gene expression by binding to target metaboloites with exquisite specificity. Binding of metabolites to the conserved aptamer domain allosterically alters the conformation in the downstream expression platform. The fate of gene expression is determined by the changes in the downstream RNA sequence. As the metabolite-dependent cotranscriptional folding and unfolding dynamics of riboswitches are the key determinant of gene expression, it is important to investigate both the thermodynamics and kinetics of riboswitches both in the presence and absence of metabolite. Single molecule force experiments that decipher the free energy landscape of riboswitches from their mechanical responses, theoretical and computational studies have recently shed light on the distinct mechanism of folding dynamics in different classes of riboswitches. Here, we first discuss the dynamics of water around riboswitch, highlighting that water dynamics can enhance the fluctuation of nucleic acid structure. To go beyond native state fluctuations, we used the Self-Organized Polymer model to predict the dynamics of add adenine riboswitch under mechanical forces. In addition to quantitatively predicting the folding landscape of add-riboswitch, our simulations also explain the difference in the dynamics between pbuE adenine- and add adenine-riboswitches. In order to probe the function in vivo, we use the folding landscape to propose a system level kinetic network model to quantitatively predict how gene expression is regulated for riboswitches that are under kinetic control.
Kang, H. ; Pincus, P. A. ; Hyeon, C. ; Thirumalai, D. Effects of macromolecular crowding on the collapse of biopolymers. Phys Rev Lett 114, 068303.Abstract

Experiments show that macromolecular crowding modestly reduces the size of intrinsically disordered proteins even at a volume fraction (ϕ) similar to that in the cytosol, whereas DNA undergoes a coil-to-globule transition at very small ϕ. We show using a combination of scaling arguments and simulations that the polymer size R̅(g)(ϕ) depends on x=R̅(g)(0)/D, where D is the ϕ-dependent distance between the crowders. If x≲O(1), there is only a small decrease in R̅(g)(ϕ) as ϕ increases. When x≫O(1), a cooperative coil-to-globule transition is induced. Our theory quantitatively explains a number of experiments.

Qin, M. ; Wang, W. ; Thirumalai, D. Protein folding guides disulfide bond formation. Proc. Natl. Acad. Sci. USA 112, 11241-11246.Abstract

The Anfinsen principle that the protein sequence uniquely determines its structure is based on experiments on oxidative refolding of a protein with disulfide bonds. The problem of how protein folding drives disulfide bond formation is poorly understood. Here, we have solved this long-standing problem by creating a general method for implementing the chemistry of disulfide bond formation and rupture in coarse-grained molecular simulations. As a case study, we investigate the oxidative folding of bovine pancreatic trypsin inhibitor (BPTI). After confirming the experimental findings that the multiple routes to the folded state contain a network of states dominated by native disulfides, we show that the entropically unfavorable native single disulfide [14-38] between Cys14 and Cys38 forms only after polypeptide chain collapse and complete structuring of the central core of the protein containing an antiparallel β-sheet. Subsequent assembly, resulting in native two-disulfide bonds and the folded state, involves substantial unfolding of the protein and transient population of nonnative structures. The rate of [14-38] formation increases as the β-sheet stability increases. The flux to the native state, through a network of kinetically connected native-like intermediates, changes dramatically by altering the redox conditions. Disulfide bond formation between Cys residues not present in the native state are relevant only on the time scale of collapse of BPTI. The finding that formation of specific collapsed native-like structures guides efficient folding is applicable to a broad class of single-domain proteins, including enzyme-catalyzed disulfide proteins.

Denesyuk, N. A. ; Thirumalai, D. How do metal ions direct ribozyme folding?. Nature Chem. 7 793–801. DOI:10.1038/nchem.2330Abstract

Ribozymes, which carry out phosphoryl-transfer reactions, often require Mg2+ ions for catalytic activity. The correct folding of the active site and ribozyme tertiary structure is also regulated by metal ions in a manner that is not fully understood. Here we employ coarse-grained molecular simulations to show that individual structural elements of the group I ribozyme from the bacterium Azoarcus form spontaneously in the unfolded ribozyme even at very low Mg2+ concentrations, and are transiently stabilized by the coordination of Mg2+ ions to specific nucleotides. However, competition for scarce Mg2+ and topological constraints that arise from chain connectivity prevent the complete folding of the ribozyme. A much higher Mg2+ concentration is required for complete folding of the ribozyme and stabilization of the active site. When Mg2+ is replaced by Ca2+ the ribozyme folds, but the active site remains unstable. Our results suggest that group I ribozymes utilize the same interactions with specific metal ligands for both structural stability and chemical activity.

Lin, J. C. ; Yoon, J. ; Hyeon, C. ; Thirumalai, D. Using Simulations and Kinetic Network Models to Reveal the Dynamics and Functions of Riboswitches. In Methods in Enzymology; Academic Press; Vol. 553, pp. 235-258. DOI:10.1016/bs.mie.2014.10.062 lin_me_2015.pdf
Kang, H. ; Pincus, P. A. ; Hyeon, C. ; Thirumalai, D. Effects of Macromolecular Crowding on the Collapse of Biopolymers. Phys. Rev. Lett. 114, 068303. DOI:10.1103/PhysRevLett.114.068303 kang_prl_2015_1.pdf
Lin, J. - C. ; Hyeon, C. ; Thirumalai, D. Sequence-dependent folding landscapes of adenine riboswitch aptamers. Phys Chem Chem Phys 16, 6376-82.Abstract
Expression of a large fraction of genes in bacteria is controlled by riboswitches, which are found in the untranslated region of mRNA. Structurally riboswitches have a conserved aptamer domain to which a metabolite binds, resulting in a conformational change in the downstream expression platform. Prediction of the functions of riboswitches requires a quantitative description of the folding landscape so that the barriers and time scales for the conformational change in the switching region in the aptamer can be estimated. Using a combination of all atom molecular dynamics (MD) and coarse-grained model simulations we studied the response of adenine (A) binding add and pbuE A-riboswitches to mechanical force. The two riboswitches contain a structurally similar three-way junction formed by three paired helices, P1, P2, and P3, but carry out different functions. Using pulling simulations, with structures generated in MD simulations, we show that after P1 rips the dominant unfolding pathway in the add A-riboswitch is the rupture of P2 followed by unraveling of P3. In the pbuE A-riboswitch, after P1 unfolds P3 ruptures ahead of P2. The order of unfolding of the helices, which is in accord with single molecule pulling experiments, is determined by the relative stabilities of the individual helices. Our results show that the stability of isolated helices determines the order of assembly and response to force in these non-coding regions. We use the simulated free energy profile for the pbuE A-riboswitch to estimate the time scale for allosteric switching, which shows that this riboswitch is under kinetic control lending additional support to the conclusion based on single molecule pulling experiments. A consequence of the stability hypothesis is that a single point mutation (U28C) in the P2 helix of the add A-riboswitch, which increases the stability of P2, would make the folding landscapes of the two riboswitches similar. This prediction can be tested in single molecule pulling experiments.
Dominguez, L. ; Meredith, S. C. ; Straub, J. E. ; Thirumalai, D. Transmembrane fragment structures of amyloid precursor protein depend on membrane surface curvature. J Am Chem Soc 136, 854-7.Abstract
The amyloid β (Aβ) peptide associated with Alzheimer's disease results from processing of the amyloid precursor protein (APP) by secretases. Cleavage of APP by β-secretase produces a 99 amino acid C-terminal fragment of APP (C99) consisting of a single transmembrane (TM) helix. Simulations of C99 congeners and structural studies of C99 in surfactant micelles and lipid vesicles have shown that a key peptide structural motif is a prominent "GG kink," centered at two glycines dividing the TM helix. The flexibility of the GG kink is important in the processing of C99 by γ-secretase. We performed multiscale simulations of C99(15-55) in a DPC surfactant micelle and POPC lipid bilayer in order to elucidate the role of membrane surface curvature in modulating the peptide structure. C99(15-55) in a DPC surfactant micelle possesses a "GG kink," in the TM domain near the dynamic hinge located at G37/G38. Such a kink is not observed in C99(15-55) in a POPC lipid bilayer. Intramolecular interaction between the extracellular and TM domains of C99(15-55) is enhanced in the micelle environment, influencing helical stability, TM helix extension, exposure to water, and depth of insertion in the lipophilic region. Our results show that the fluctuations of the structural ensemble of APP are strongly influenced by membrane surface curvature.
Yoon, J. ; Lin, J. - C. ; Hyeon, C. ; Thirumalai, D. Dynamical transition and heterogeneous hydration dynamics in RNA. J Phys Chem B 118, 7910-9.Abstract
Enhanced dynamical fluctuations of RNAs, facilitated by a network of water molecules with strong interactions with RNA, are suspected to be critical in their ability to respond to a variety of cellular signals. Using atomically detailed molecular dynamics simulations at various temperatures of purine (adenine) and preQ1 sensing riboswitch aptamers, which control gene expression by sensing and binding to metabolites, we show that water molecules in the vicinity of RNAs undergo complex dynamics depending on the local structures of the RNAs. The overall lifetimes of hydrogen bonds (HBs) of surface-bound waters are more than at least 1-2 orders of magnitude longer than those of bulk water. Slow hydration dynamics, revealed in the non-Arrhenius behavior of the relaxation time, arises from high activation barriers to break water HBs with a nucleotide and by reduced diffusion of water. The relaxation kinetics at specific locations in the two RNAs show a broad spectrum of time scales reminiscent of glass-like behavior, suggesting that the hydration dynamics is highly heterogeneous. Both RNAs undergo dynamic transition at T = TD ≳ 200 K, as assessed by the mean-square fluctuation of hydrogen atoms ⟨x(2)⟩, which undergoes an abrupt harmonic-to-anharmonic transition at TD. The near-universal value of TD found for these RNAs and previously for tRNA is strongly correlated with changes in hydration dynamics as T is altered. Hierarchical dynamics of waters associated with the RNA surface, revealed in the motions of distinct classes of water with well-separated time scales, reflects the heterogeneous local environment on the molecular surface of RNA. At low temperatures, slow water dynamics predominates over structural transitions. Our study demonstrates that the complex interplay of dynamics between water and the local environment in the RNA structures could be a key determinant of the functional activities of RNA.
Vaitheeswaran, S. ; Thirumalai, D. Entropy and enthalpy of interaction between amino acid side chains in nanopores. J Chem Phys 141, 22D523.Abstract
Understanding the stabilities of proteins in nanopores requires a quantitative description of confinement induced interactions between amino acid side chains. We use molecular dynamics simulations to study the nature of interactions between the side chain pairs ALA-PHE, SER-ASN, and LYS-GLU in bulk water and in water-filled nanopores. The temperature dependence of the bulk solvent potentials of mean force and the interaction free energies in cylindrical and spherical nanopores is used to identify the corresponding entropic and enthalpic components. The entropically stabilized hydrophobic interaction between ALA and PHE in bulk water is enthalpically dominated upon confinement depending on the relative orientations between the side chains. In the case of SER-ASN, hydrogen bonded configurations that are similar in bulk water are thermodynamically distinct in a cylindrical pore, thus making rotamer distributions different from those in the bulk. Remarkably, salt bridge formation between LYS-GLU is stabilized by entropy in contrast to the bulk. Implications of our findings for confinement-induced alterations in protein stability are briefly outlined.