Biology subjects

Thirumalai, D.

Publications and source records attributed to Thirumalai, D..

At least 109 records · Page 6Linked to original sources

bioRxiv2018

Processivity, velocity and universal characteristics of nucleic acidunwinding by helicases

Helicases that act as motors and unwind double stranded nucleic acids are broadly classified as either active or passive, depending on whether or not they directly destabilize the double strand. By using this description in a mathematical framework, we derive analytic expressions for the velocity and run-length of a general model of finitely processive helicases. We show that, in contrast to the helicase unwinding velocity, the processivity exhibits a universal increase in response to external force. We use our results to analyze velocity and processivity data from single molecule experiments on the superfamily-4 ring helicase T7, and establish quantitatively that T7 is a weakly active helicase. We predict that compared to single-strand translocation, there is almost a two orders-of-magnitude increase in the back-stepping probability of T7 while unwinding double-stranded DNA. Our quantitative analysis of T7 suggests that the tendency of helicases to take frequent back-steps may be more common than previously anticipated, as was recently shown for the XPD helicase. Finally, our results suggest the intriguing possibility of a single underlying physical principle governing the experimentally observed increase in unwinding efficiencies of helicases in the presence of force, oligomerization or partner proteins like single strand binding proteins. The clear implication is that helicases may have evolved to maximize processivity rather than speed.

biophysics↗

bioRxiv2018

Molecular simulations of the monovalent-ion dependent Folding Thermodynamics of RNA

How ions affect RNA folding thermodynamics and kinetics is an important but a vexing problem that remains unsolved. Experiments have shown that the free energy change, {Delta}G(c), of RNA upon folding varies with the salt concentration (c) as, {Delta}G(c) = kc ln c + const, where the coefficient kc is proportional to the difference in the uptake of ions (ion preferential coefficient), {Delta}{Gamma}, between the folded and unfolded states. We performed simulations of a coarse-grained model, by modeling electrostatic interactions implicitly and with explicit representation of ions, to elucidate the molecular underpinnings of the relationship between folding free energy and ion preferential coefficient. Without any input from experiments, the simulations quantitatively reproduce the heat capacity for the -1 frame shifting pseudoknot (PK) from Beet Western Yellow Virus, thus validating the model. We show that {Delta}G(c) calculated directly from {Delta}{Gamma} varies linearly with ln c (c < 0.2M), for a hairpin and the PK, thus demonstrating a molecular link between the two quantities for RNA molecules that undergo substantial conformational changes during folding. Explicit ion simulations also show the linear dependence of {Delta}G(c) on ln c at all c with kc = 2kBT, except that {Delta}G(c) values are shifted by about 2 kcal/mol higher than experiments at all salt concentrations. The discrepancy is due to an underestimate the {Gamma} values for both the folded and unfolded states, while giving accurate values for {Delta}{Gamma}. The predictions for the salt dependence of {Delta}{Gamma} are amenable to test using single molecule pulling experiments. Our simulations, representing a significant advance in quantitatively describing ion effects in RNA, show that the framework provided here can be used to obtain accurate thermodynamics of RNA folding.

biophysics↗

bioRxiv2018

Interface residues that drive allosteric transitions also control the assembly of L-lactate dehydrogenase

The allosteric enzyme, L-lactate dehydrogenase (LDH), is activated by fructose 1,6-metaphosphate (FBP) to reduce pyruvate to lactate. The molecular details of the FBP-driven transition between the low affinity T-state to the high affinity R-state in LDH, a tetramer composed of identical subunits, are not known. The dynamics of theT[->]R allosteric transition, investigated using Brownian dynamics (BD) simulations of the Self-Organized Polymer (SOP) model, revealed that coordinated rotations of the subunits drive the T[->]R transition. We used the structural perturbation method (SPM), which requires only the static structure, to identify the allostery wiring diagram (AWD), a network of residues that transmits signals across the tetramer, as LDH undergoes the T[->]R transition. Interestingly, the residues that play a major role in the dynamics, which are predominantly localized at the interfaces, coincide with the AWD identified using the SPM. The conformational changes in the T[->]R transition start from the region near the active site, comprising of helix C, helix 1/2G, helix 3G and helix 2F, and proceed to other structural units, thus completing the global motion. Brownian dynamics simulations of the tetramer assembly, triggered by a temperature quench from the fully disrupted conformations, show that the bottleneck for assembly is the formation of the correct orientation between the subunits, requiring contacts between the interface residues. Surprisingly, these residues are part of the AWD, which was identified using the SPM. Taken together, our results show that LDH, and perhaps other multi-domain proteins, may have evolved to stabilize distinct states of allosteric enzymes using precisely the same AWD that also controls the functionally relevant allosteric transitions.

biophysics↗

bioRxiv2018

Dynamics of Allosteric Transitions in Dynein

1Cytoplasmic Dynein, a motor with an unusual architecture made up of a motor domain belonging to the AAA+ family, walks on microtubule towards the minus end. Prompted by the availability of structures in different nucleotide states, we performed simulations based on a new coarse-grained model to illustrate the molecular details of the dynamics of allosteric transitions in the motor. The simulations show that binding of ATP results in the closure of the cleft between the AAA1 and AAA2, which in turn triggers conformational changes in the rest of the motor domain, thus poising dynein in the pre-power stroke state. Interactions with the microtubule, which are modeled implicitly, substantially enhances the rate of ADP release, and formation of the post-power stroke state. The dynamics associated with the key mechanical element, the linker (LN) domain, which changes from a straight to a bent state and vice versa, are highly heterogeneous suggestive of multiple routes in the pre power stroke to post power stroke transition. We show that persistent interactions between the LN and the insert loops in the AAA2 domain prevent the formation of pre-power stroke state when ATP is bound to AAA3, thus locking dynein in a non-functional repressed state. Motility in such a state may be rescued by applying mechanical force to the LN domain. Taken together, these results show how the intricate signaling dynamics within the motor domain facilitate the stepping of dynein.

biophysics↗

bioRxiv2018

Charge fluctuation effects on the shape of flexible polyampholytes with applications to Intrinsically disordered proteins

Random polyampholytes (PAs) contain positively and negatively charged monomers that are distributed randomly along the polymer chain. The interaction between charges is assumed to be given by the Debye-Huckel potential. We show that the size of the PA is determined by an interplay between electrostatic interactions, giving rise to the polyelectrolyte (PE) effect due to net charge per monomer ({sigma}), and an effective attractive PA interaction due to charge fluctuations,{delta}{sigma} . The interplay between these terms gives rise to non-monotonic dependence of the radius of gyration, Rg on the inverse Debye length,{kappa} when PA effects are important [Formula]. In the opposite limit, Rg decreases monotonically with increasing{kappa} . Simulations of PA chains, using a charged bead-spring model, further corroborates our theoretical predictions. The simulations unambiguously show that conformational heterogeneity manifests itself among sequences that have identical PA parameters. A clear implication is that the phases of PA sequences, and by inference IDPs, cannot be determined using only the bare PA parameters ({sigma} and{delta}{sigma} ).The theory is used to calculate the changes in Rg on N, the number of residues for a set of Intrinsically Disordered Proteins (IDPs). For a certain class of IDPs, with N between 24 to 441, the size grows as Rg ~ N0.6, which agrees with data from Small Angle X-ray Scattering (SAXS) experiments.

biophysics↗

bioRxiv2018

Share, but unequally: A mechanism for emergence and maintenance of intratumor heterogeneity

Intratumor heterogeneity (ITH), referring to coexistence of different cell subpopulations in a single tumor, has been a major puzzle in cancer research for almost half a century. The lack of understanding of the underlying mechanism of ITH hinders progress in developing effective therapies for cancers. Based on the findings in a recent quantitative experiment on pancreatic cancer we developed a general evolutionary model, accounting for interactions between different cell populations through paracrine or juxtacrine factors. We show that the emergence of a stable heterogeneous state in a tumor requires an unequal allocation of paracrine growth factors (\"public goods\") between cells that produce them and those that merely consume them. Our model provides a quantitative explanation of recent in vitro experimental studies in pancreatic cancer in which insulin growth factor (IGF-II) plays the role of public goods. The calculated phase diagrams as a function of exogenous resources and fraction of growth factor producing cells show ITH persists only in a narrow range of concentration of exogenous IGF-II. Remarkably, maintenance of ITH requires cooperation among tumor cell subpopulations in harsh conditions, specified by lack of exogenous IGF-II, whereas surplus exogenous IGF-II elicits competition. The theory also quantitatively accounts for measured in vivo tumor growth in glioblastoma multiforme (GBM). The predictions for GBM tumor growth as a function of the fraction of tumor cells are amenable to experimental tests. The mechanism for ITH also provides hints for devising efficacious therapies.

cancer biology↗

bioRxiv2018

Structure of APP-C991-99 and Implications for Role of Extra-Membrane Domains in Function and Oligomerization

The 99 amino acid C-terminal fragment of Amyloid Precursor Protein APP-C99 (C99) is cleaved by {gamma}-secretase to form A{beta} peptide, which plays a critical role in the etiology of Alzheimers Disease (AD). The structure of C99 consists of a single transmembrane domain flanked by intra and intercellular domains. While the structure of the transmembrane domain has been well characterized, little is known about the structure of the flanking domains and their role in C99 processing by {gamma}-secretase. To gain insight into the structure of full-length C99, REMD simulations were performed for monomeric C99 in model membranes of varying thickness. We find equilibrium ensembles of C99 from simulation agree with experimentally-inferred residue insertion depths and protein backbone chemical shifts. In thin membranes, the transmembrane domain structure is correlated with extra-membrane structural states. Mean and variance of the transmembrane and G37G38 hinge angles are found to increase with thinning membrane. The N-terminus of C99 forms {beta}-strands that may seed aggregation of A{beta} on the membrane surface, promoting amyloid formation. The N-terminus, which forms -helices that interact with the nicastrin domain of {gamma}-secretase. The C-terminus of C99 becomes more -helical as the membrane thickens, forming structures that may be suitable for binding by cytoplasmic proteins, while C-terminal residues essential to cytotoxic function become -helical as the membrane thins. The heterogeneous but discrete extra-membrane domain states analyzed here open the path to new investigations of the role of C99 structure and membrane in amyloidogenesis.

biophysics↗

bioRxiv2018

Sequence-dependent Three Interaction Site (TIS) Model for Single and Double-stranded DNA

We develop a robust coarse-grained model for single and double stranded DNA by representing each nucleotide by three interaction sites (TIS) located at the centers of mass of sugar, phosphate, and base. The resulting TIS model includes base-stacking, hydrogen bond, and electrostatic interactions as well as bond-stretching and bond angle potentials that account for the polymeric nature of DNA. The choices of force constants for stretching and the bending potentials were guided by a Boltzmann inversion procedure using a large representative set of DNA structures extracted from the Protein Data Bank. Some of the parameters in the stacking interactions were calculated using a learning procedure, which ensured that the experimentally measured melting temperatures of dimers are faithfully reproduced. Without any further adjustments, the calculations based on the TIS model reproduces the experimentally measured salt and sequence dependence of the size of single stranded DNA (ssDNA), as well as the persistence lengths of poly(dA) and poly(dT) chains. Interestingly, upon application of mechanical force the extension of poly(dA) exhibits a plateau, which we trace to the formation of stacked helical domains. In contrast, the force-extension curve (FEC) of poly(dT) is entropic in origin, and could be described by a standard polymer model. We also show that the persistence length of double stranded DNA, formed from two complementary ssDNAs with one hundred and thirty base pairs, is consistent with the prediction based on the worm-like chain. The persistence length, which decreases with increasing salt concentration, is in accord with the Odijk-Skolnick-Fixman theory intended for stiff polyelectrolyte chains near the rod limit. The range of applications, which did not require adjusting any parameter after the initial construction based solely on PDB structures and melting profiles of dimers, attests to the transferability and robustness of the TIS model for ssDNA and dsDNA.

biophysics↗

bioRxiv2017

Architecture of human interphase chromosome determines the spatiotemporal dynamics of chromatin loci

By incorporating the information of human chromosome inferred from Hi-C experiments into a heteropolymer model of chromatin chain, we generate a conformational ensemble to investigate its spatiotemporal dynamics. The heterogeneous loci interactions result in hierarchical organization of chromatin chain, which obeys compact space-filling (SF) statistics at intermediate length scale. Remarkably, the higher order architecture of the chromatin, characterized by the single universal Flory exponent ({nu} = 1/3) for condensed homopolymers, provides quantitative account of the dynamical properties of the chromosome. The local chromosome structures, exemplified by topologically associated domains (~ 0.1 - 1 Mb), display dynamics with fast relaxation time ([lsim] 50 sec), whereas the long-range spatial reorganization of the entire chromatin [Formula] occurs on a much longer time scale ({gtrsim} hour), suggestive of glass-like behavior. This key finding provides the dynamic basis of cell-to-cell variability. Active forces, modeled using stronger isotropic white noises, accelerate the relaxation dynamics of chromatin domain described by the low frequency modes. Surprisingly, they do not significantly change the local scale dynamics from those under passive condition. By linking the spatiotemporal dynamics of chromosome with its organization, our study highlights the importance of physical constraints in chromosome architecture on the sluggish dynamics.\n\nSignificance StatementChromosomes are giant chain molecules made of hundreds of megabase-long DNA intercalated with proteins. Structure and dynamics of interphase chromatin in space and time hold the key to understanding the cell type-dependent gene regulation. In this study, we establish that the crumpled and space-filling organization of chromatin fiber in the chromosome territory, characterized by a single universal exponent used to describe polymer sizes, is sufficient to explain the complex spatiotemporal hierarchy in chromatin dynamics as well as the subdiffusive motion of the chromatin loci. While seemingly a daunting problem at a first glance, our study shows that relatively simple principles, rooted in polymer physics, can be used to grasp the essence of dynamical properties of the interphase chromatin.

biophysics↗

bioRxiv2017

Denaturants alter the flux through multiple pathways in the folding of PDZ domain

Although we understand many aspects of how small proteins (number of residues less than about hundred) fold, it is a major challenge to understand how large proteins self-assemble. To partially overcome this challenge, we performed simulations using the Self-Organized Polymer model with Side Chains (SOP-SC) in guanidinium chloride (GdmCl), using the Molecular Transfer Model (MTM), to describe the folding of the 110-residue PDZ3 domain. The simulations reproduce the folding thermodynamics accurately including the melting temperature (Tm), the stability of the folded state with respect to the unfolded state. We show that the calculated dependence of ln kobs (kobs is the relaxation rate) has the characteristic Chevron shape. The slopes of the Chevron plots are in good agreement with experiments. We show that PDZ3 folds by four major pathways populating two metastable intermediates, in accord with the kinetic partitioning mechanism. The structure of one of the intermediates, populated after polypeptide chain collapse, is structurally similar to an equilibrium intermediate. Surprisingly, the connectivities between the intermediates and hence, the fluxes through the pathways depend on the concentration of GdmCl. The results are used to predict possible outcomes for unfolding of PDZ domain subject to mechanical forces. Our study demonstrates that, irrespective of the size or topology, simulations based on MTM and SOP-SC offer a framework for describing the folding of proteins, mimicking precisely the conditions used in experiments.

biophysics↗

bioRxiv2017

Forced-rupture of Cell-Adhesion Complexes Reveals abrupt switch between two Brittle States

Cell adhesion complexes (CACs), which are activated by ligand binding, play key roles in many cellular functions ranging from cell cycle regulation to mediation of cell extracellular matrix adhesion. Inspired by single molecule pulling experiments using atomic force spectroscopy on leukocyte function-associated antigen-1 (LFA-1), expressed in T-cells, bound to intercellular adhesion molecules (ICAM), we performed constant loading rate (rf) and constant force (F) simulations using the Self-Organized Polymer (SOP) model to describe the mechanism of ligand rupture from CACs. The simulations reproduce the major experimental finding on the kinetics of the rupture process, namely, the dependence of the most probable rupture forces (f*s) on ln rf (rf is the loading rate) exhibits two distinct linear regimes. The first, at low rf, has a shallow slope whereas the the slope at high rf is much larger, especially for LFA-1/ICAM-1 complex with the transition between the two occurring over a narrow rf range. Locations of the two transition states (TSs), extracted from the simulations show an abrupt change from a high value at low rf or F to a low value at high rf or F. This unusual behavior in which the CACs switch from one brittle (TS position is a constant over a range of forces) state to another brittle state is not found in forced-rupture in other protein complexes. We explain this novel behavior by constructing the free energy profiles, F ({Lambda})s, as a function of a collective reaction coordinate ({Lambda}), involving many key charged residues and a critical metal ion (M g2+). The TS positions in F({Lambda}), which quantitatively agree with the parameters extracted using the Bell-Evans model, change abruptly at a critical force, demonstrating that it, rather than the molecular extension is a good reaction coordinate. Our combined analyses using simulations performed in both the pulling modes (constant rf and force) reveal a new mechanism for the two loading regimes observed in the rupture kinetics in CACs.

biophysics↗

bioRxiv2017

Signaling Networks and Dynamics of Allosteric Transitions in Bacterial Chaperonin GroEL: Implications for Iterative Annealing of Misfolded Proteins

Signal transmission at the molecular level in many biological complexes occurs through allosteric transitions. They describe the response a complex to binding of ligands at sites that are spatially well separated from the binding region. We describe the Structural Perturbation Method (SPM), based on phonon propagation in solids, that can be used to determine the signal transmitting allostery wiring diagram (AWD) in large but finite-sized biological complexes. Applications to the bacterial chaperonin GroEL-GroES complex shows that the AWD determined from structures also drive the allosteric transitions dynamically. Both from a structural and dynamical perspective these transitions are largely determined by formation and rupture of salt-bridges. The molecular description of allostery in GroEL provides insights into its function, which is quantitatively described by the Iterative Annealing Mechanism. Remarkably, in this complex molecular machine, a deep connection is established between the structures, reaction cycle during which GroEL undergoes a sequence of allosteric transitions, and function in a self-consistent manner.

biophysics↗

bioRxiv2017

Monovalent ions modulate the flux through multiple folding pathways of an RNA pseudoknot

The functions of RNA pseudoknots (PKs), which are minimal tertiary structural motifs and an integral part of several ribozymes and ribonucleoprotein complexes, are determined by their structure, stability and dynamics. Therefore, it is important to elucidate the general principles governing their thermodynamics/folding mechanisms. Here, we combine experiments and simulations to examine the folding/unfolding pathways of the VPK pseudoknot, a variant of the Mouse Mammary Tumor Virus (MMTV) PK involved in ribosomal frameshifting. Fluorescent nucleotide analogs (2-aminopurine and pyrrolocytidine) placed at different stem/loop positions in the PK, and laser temperature-jump approaches serve as local probes allowing us to monitor the order of assembly of VPK with two helices with different intrinsic stabilities. The experiments and molecular simulations show that at 50 mM KCl the dominant folding pathway populates only the more stable partially folded hairpin. As the salt concentration is increased a parallel folding pathway emerges, involving the less stable hairpin structure as an alternate intermediate. Notably, the flux between the pathways is modulated by the ionic strength. The findings support the principle that the order of PK structure formation is determined by the relative stabilities of the hairpins, which can be altered by sequence variations or salt concentrations. Our study not only unambiguously demonstrates that PK folds by parallel pathways, but also establishes that quantitative description of RNA self-assembly requires a synergistic combination of experiments and simulations.\n\nSIGNIFICANCEThe assembly mechanism of RNA, vital to describing their functions, depends on both the sequence and the metal ion concentration. How the latter influences the folding trajectories remains an important unsolved problem. Here, we examine the folding pathways of an RNA pseudoknot (PK) with key functional roles in transcription and translation, using a combination of experiments and simulations. We demonstrate that the PK, consisting of two helices with differing stabilities, folds by parallel pathways. Surprisingly, the flux between them is modulated by monovalent salt concentration. Our work shows that the order of assembly of PKs is determined by the relative stability of the helices, implying that the folding landscape can be controlled by sequence and ion concentration.

biophysics↗

bioRxiv2017

Interphase Human Chromosome Exhibits Out of Equilibrium Glassy Dynamics

The structural organization of the condensed chromosomes is being revealed using chromosome conformation capture experiments and super-resolution imaging techniques. Fingerprints of their three-dimensional organization on length scale from about hundred kilo base pairs to millions of base pairs have emerged using advances in Hi-C and super-resolution microscopy. To determine the poorly understood dynamics of human interphase chromosomes, we created the Chromosome Copolymer Model (CCM) by representing the chromosomes as a self-avoiding polymer with two loci types corresponding to euchromatin and heterochromatin. Using advanced clustering algorithms we establish quantitatively that the simulated contact maps for chromosomes 5 and 10 and those inferred from Hi-C experiments are in agreement. Ward Linkage Matrix (WLM), constructed from spatial distance information, shows that the Topologically Associated Domains (TADs) and compartments predicted from simulations are in agreement with inferred WLM computed using data from super-resolution microscopy experiments. Glassy dynamics is manifested in the stretched exponential relaxation of the structure factor and caging in the mean square displacement of individual loci, {triangleup}i(t) [~] t with 0 < < 1. Remarkably, the distribution of , is extremely broad suggestive of highly heterogeneous dynamics, which is also reflected in the large cell-to-cell variations in the contact maps. Chromosome organization is hierarchical involving the formation of chromosome droplets (CDs) on short genomic scale followed by coalescence of the CDs, reminiscent of Ostwald ripening. We propose that glassy landscapes for the condensed active chromosomes might provide a balance between genomic conformational stability and biological functions.

biophysics↗

bioRxiv2017

Parsing the roles of neck-linker docking and tethered head diffusion in the stepping dynamics of kinesin

Kinesin walks processively on microtubules (MTs) in an asymmetric hand-over-hand manner consuming one ATP molecule per 16 nm step. The contributions due to docking of the approximately thirteen residue neck linker to the leading head (deemed to be the power stroke), and diffusion of the trailing head contribute in propelling the motor by 16 nm have not been quantified. We use molecular simulations by creating a new coarse-grained model of the microtubule-kinesin complex, which reproduces the measured stall force as well as the force required to dislodge the motor head from the MT, to show that nearly three quarters of the step occurs by bidirectional stochastic motion of the TH. However, docking of the neck linker to the leading head constrains the extent of diffusion and minimizes the probability that kinesin takes side steps implying that both the events are necessary in the motility of kinesin, and for the maintenance of processivity. Surprisingly, we find that during a single step the trailing head stochastically hops multiple times between the geometrically accessible neighboring sites on the MT prior to forming a stable interaction with the target binding site with correct orientation between the motor head and the /{beta} tubulin dimer.\n\nSignificance StatementLike all motors, the stepping of the two headed conventional Kinesin on the microtubule is facilitated by conformational changes in the motor domain upon ATP binding and hydrolysis. Numerous experiments have revealed that docking of the thirteen residue neck linker (NL) to the motor domain of the leading plays a critical role in propelling the trailing head towards the plus end of the microtubule by nearly 16 nm in a single step. Surprisingly our molecular simulations reveal that nearly three quarters of the step occurs by stochastic diffusion of the trailing head. Docking of the NL restricts the extent of diffusion, thus forcing the motor to walk with overwhelming probability on a single protofilament of the MT.

biophysics↗

bioRxiv2017

Cell growth rate dictates the onset of glass to fluid-like transition and long time super-diffusion in an evolving cell colony

Collective migration dominates many phenomena, from cell movement in living systems to abiotic self-propelling particles. Focusing on the early stages of tumor evolution, we enunciate the principles involved in cell dynamics and highlight their implications in understanding similar behavior in seemingly unrelated soft glassy materials and possibly chemokine-induced migration of CD8+ T cells. We performed simulations of tumor invasion using a minimal three dimensional model, accounting for cell elasticity and adhesive cell-cell interactions as well as cell birth and death to establish that cell growth rate-dependent tumor expansion results in the emergence of distinct topological niches. Cells at the periphery move with higher velocity perpendicular to the tumor boundary, while motion of interior cells is slower and isotropic. The mean square displacement, {Delta}(t), of cells exhibits glassy behavior at times comparable to the cell cycle time, while exhibiting super-diffusive behavior, {Delta}(t) {approx} t ( > 1), at longer times. We derive the value of {approx} 1.33 using a field theoretic approach based on stochastic quantization. In the process we establish the universality of super-diffusion in a class of seemingly unrelated non-equilibrium systems. Super diffusion at long times arises only if there is an imbalance between cell birth and death rates. Our findings for the collective migration, which also suggests that tumor evolution occurs in a polarized manner, are in quantitative agreement with in vitro experiments. Although set in the context of tumor invasion the findings should also hold in describing collective motion in growing cells and in active systems where creation and annihilation of particles play a role.

biophysics↗

bioRxiv2017

Molecular chaperones maximize the native state yield per unit time by driving substrates out of equilibrium

Molecular chaperones have evolved to facilitate folding of proteins and RNA in vivo where spontaneous self-assembly is sometimes prohibited. Folding of Tetrahymena ribozyme, assisted by the RNA chaperone CYT-19, surprisingly shows that at physiological Mg2+ ion concentrations, increasing the chaperone concentration reduces the yield of native ribozymes. In contrast, the more extensively investigated protein chaperone GroEL works in exactly the opposite manner--the yield of native substrate increases with the increase in chaperone concentration. Thus, the puzzling observation on the assisted-ribozyme folding seems to contradict the expectation that a molecular chaperone acts as an efficient annealing machine. We suggest a resolution to this apparently paradoxical behavior by developing a minimal stochastic model that captures the essence of the Iterative Annealing Mechanism (IAM), providing a unified description of chaperone mediated-folding of proteins and RNA. Our theory provides a general relation involving the kinetic rates of the system, which quantitatively predicts how the yield of native state depends on chaperone concentration. By carefully analyzing a host of experimental data on Tetrahymena (and its mutants) as well as the protein Rubisco and Malate Dehydrogenase, we show that although the absolute yield of native states decreases in the ribozyme, the rate of native state production increases in both the cases. By utilizing energy from ATP hydrolysis, both CYT-19 and GroEL drive their substrate concentrations far out of equilibrium, in an endeavor to maximize the native yield in a short time. Our findings are consistent with the general expectation that proteins or RNA need to be folded by the cellular machinery on biologically relevant timescales, even if the final yield is lower than what equilibrium thermodynamics would dictate. Besides establishing the IAM as the basis for functions of RNA and protein chaperones, our work shows that cellular copy numbers have been adjusted to optimize the rate of native state production of the folded states of RNA and proteins under physiological conditions.\n\nSignificance statementMolecular chaperones have evolved to assist the folding of proteins and RNA, thus avoiding the deleterious consequences of misfolding. Thus, it is expected that increasing chaperone concentration should lead to an enhancement in native yield. While this has been observed in GroEL-mediated protein folding, experiments on Tetrahymena ribozyme folding assisted by CYT-19, surprisingly show the opposite trend. Here, we reconcile these divergent experimental observations by developing a unified stochastic model of chaperone assisted protein and RNA folding. We show that chaperones drive their substrates out of equilibrium, and in the process maximize the rate of native substrate production rather than the absolute yield or the folding rate. In vivo the number of chaperones is regulated to optimize their functions.

biophysics↗

bioRxiv2017

Optimal Information Transfer In Enzymatic Networks: A Field Theoretic Formulation

Signaling in enzymatic networks is typically triggered by environmental fluctuations, resulting in a series of stochastic chemical reactions, leading to corruption of the signal by noise. For example, information flow is initiated by binding of extracellular ligands to receptors, which is transmitted through a cascade involving kinase-phosphatase stochastic chemical reactions. For a class of such networks, we develop a general field-theoretic approach in order to calculate the error in signal transmission as a function of an appropriate control variable. Application of the theory to a simple push-pull network, a module in the kinase-phosphatase cascade, recovers the exact results for error in signal transmission previously obtained using umbral calculus (Phys. Rev. X., 4, 041017 (2014)). We illustrate the generality of the theory by studying the minimal errors in noise reduction in a reaction cascade with two connected push-pull modules. Such a cascade behaves as an effective three-species network with a pseudo intermediate. In this case, optimal information transfer, resulting in the smallest square of the error between the input and output, occurs with a time delay, which is given by the inverse of the decay rate of the pseudo intermediate. Surprisingly, in these examples the minimum error computed using simulations that take non-linearities and discrete nature of molecules into account coincides with the predictions of a linear theory. In contrast, there are substantial deviations between simulations and predictions of the linear theory in error in signal propagation in an enzymatic push-pull network for a certain range of parameters. Inclusion of second order perturbative corrections shows that differences between simulations and theoretical predictions are minimized. Our study establishes that a field theoretic formulation of stochastic biological signaling offers a systematic way to understand error propagation in networks of arbitrary complexity.

biophysics↗