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Folding PDZ2 domain using the Molecular Transfer Model

A major challenge in molecular simulations is to describe denaturant-dependent folding of proteins order to make direct comparisons with in vitro experiments. We use the molecular transfer model (MTM), which is currently the only method that accomplishes this goal albeit phenomenologically, to quantitatively describe urea-dependent folding of PDZ domain, which plays a significant role in molecular recognition and signaling. Experiments show that urea-dependent unfolding rates of the PDZ2 domain exhibit a downward curvature at high urea concentrations ([C]s), which has been interpreted by invoking the presence of a sparsely populated high energy intermediate. Simulations using the MTM and a coarse-grained Self-Organized Polymer (SOP) representation of PDZ2 are used to show that the intermediate (IEQ), which has some native-like character, is present in equilibrium both in the presence and absence of urea. The free energy profiles as a function of the structural overlap order parameter show that there are two barriers separating the folded and unfolded states. Structures of the transition state ensembles, (TSE1 separating the unfolded and IEQ and TSE2 separating IEQ and the native state), determined using the Pfold method, show that TSE1 is greatly expanded while TSE2 is compact and native-like. Folding trajectories reveal that PDZ2 folds by parallel routes. In one pathway folding occurs exclusively through I1, which resembles IEQ. In a fraction of trajectories, constituting the second pathway, folding occurs through a combination of I1 and a kinetic intermediate. We establish that the radius of gyration ([Formula]) of the unfolded state is more compact (by [~] 9%) under native conditions. Theory and simulations show that the decrease in [Formula] occurs on the time scale on the order of utmost ~ 20 {beta}. The modest decrease in [Formula] and the rapid collapse suggest that high spatial and temporal resolution, currently beyond the scope of most small angle X-ray scattering experiments, are needed to detect compaction in finite-sized proteins. The present work further establishes that MTM is efficacious in producing nearly quantitative predictions for folding of proteins under conditions used to carry out experiments.

Biophysics

Analysis of Two-State Folding Using Parabolic Approximation II: Temperature-Dependence

Equations that govern the temperature-dependence of the rate constants, Gibbs energies, enthalpies, entropies and heat capacities of activation for folding and unfolding of spontaneously-folding fixed two-state systems have been derived using a procedure that treats the denatured and the native conformers as being confined to harmonic Gibbs energy wells. The notion that a two-state system is physically defined only for a set temperature range is introduced. The implications of this novel treatment for protein folding are discussed.

Biophysics

On the Importance of Hydrodynamic Interactions in the Stepping Kinetics of Kinesin

Conventional kinesin walks by a hand-over-hand mechanism on the microtubule (MT) by taking ~ 8nm discrete steps, and consumes one ATP molecule per step. The time needed to complete a single step is on the order of twenty microseconds. We show, using simulations of a coarse-grained model of the complex containing the two motor heads, the MT, and the coiled coil that in order to obtain quantitative agreement with experiments for the stepping kinetics hydrodynamic interactions (HI) have to be included. In simulations without hydrodynamic interactions spanning nearly twenty s not a single step was completed in hundred trajectories. In sharp contrast, nearly 14% of the steps reached the target binding site within 6s when HI 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. Our results suggest that inclusion of HI is crucial in the accurate description of motility of other motors as well.

Biophysics

How do metal ions direct ribozyme folding?

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 which 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 coordination of Mg2+ ions to specific nucleotides. However, competition for scarce Mg2+ and topological constraints arising from chain connectivity prevent 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.

Biophysics

Analysis of Two-State Folding Using Parabolic Approximation III: Non-Arrhenius Kinetics of FBP28 WW Part-I

A model which treats the denatured and the native conformers as being confined to harmonic Gibbs energy wells has been used to analyse the non-Arrhenius behaviour of spontaneously-folding fixed two-state systems. The results demonstrate that when pressure and solvent are constant: (i) a two-state system is physically defined only for a finite temperature range; (ii) irrespective of the primary sequence, the 3-dimensional structure of the native conformer, the residual structure in the denatured state, and the magnitude of the folding and unfolding rate constants, the equilibrium stability of a two-state system is a maximum when its denatured conformers bury the least amount of solvent accessible surface area (SASA) to reach the activated state; (iii) the Gibbs barriers to folding and unfolding are not always due to the incomplete compensation of the activation enthalpies and entropies; (iv) the difference in heat capacity between the reaction-states is due to both the size of the solvent-shell and the non-covalent interactions; (v) the position of the transition state ensemble along the reaction coordinate (RC) depends on the choice of the RC; and (vi) the atomic structure of the transiently populated reaction-states cannot be inferred from perturbation-induced changes in their energetics.

Biophysics

Signal and Specificity of Protein Ubiquitination for Proteasomal Degradation

The eukaryotic ubiquitin system regulates essential cell events such as DNA repair, protein homeostasis, and signal transduction. Like many biochemical processes, ubiquitination must ensure signaling efficiency and in the meantime maintain substrate specificity. We examine this signal-specificity relationship by theoretical models of polyubiquitinations that tag proteins for the proteasomal degradation. Parsimonious models provide explicit formulas to key measurable quantities and offer guiding insights into the signal-specificity tradeoffs under varying structures and kinetics. Models with measured kinetics from two primary cell-cycle ligases (SCF and APC) explain mechanisms of chain initiation, elongation slowdown, chain-length dependence of E3-substrate affinity, and deubiquitinases. We find that substrate discrimination over ubiquitin transfer rates is consistently more efficient than over substrate-E3 ligase binding energy, regardless of circuit structure, parameter value, and dynamics. E3-associated substrate deubiquitination increases the discrimination over the former and in the meantime decreases the latter, further widening their difference. Both discrimination strategies might be simultaneously explored by an E3 system to effectively proofread substrates as we demonstrated by analyzing experimental data from the CD4-Vpu-SCF system. We also identify that sequential deubiquitination circuit may act as a specificity switch, by which a modest change in deubiquitination and/or processivity can greatly increase substrate discrimination without much compromise in degradation signal. This property may be utilized as a gatekeeper mechanism to direct a temporal polyubiquitination and thus degradation order of substrates with small biochemical differences.

Biophysics

FRETBursts: An Open Source Toolkit for Analysis of Freely-Diffusing Single-Molecule FRET

Single-molecule Forster Resonance Energy Transfer (smFRET) allows probing intermolecular interactions and conformational changes in biomacromolecules, and represents an invaluable tool for studying cellular processes at the molecular scale. smFRET experiments can detect the distance between two fluorescent labels (donor and acceptor) in the 3-10 nm range. In the commonly employed confocal geometry, molecules are free to diffuse in solution. When a molecule traverses the excitation volume, it emits a burst of photons, which can be detected by single-photon avalanche diode (SPAD) detectors. The intensities of donor and acceptor fluorescence can then be related to the distance between the two fluorophores.\n\nWhile recent years have seen a growing number of contributions proposing improvements or new techniques in smFRET data analysis, rarely have those publications been accompanied by so.ware implementation. In particular, despite the widespread application of smFRET, no complete so.ware package for smFRET burst analysis is freely available to date.\n\nIn this paper, we introduce FRETBursts, an open source software for analysis of freely-diffusing smFRET data. FRETBursts allows executing all the fundamental steps of smFRET bursts analysis using state-of-the-art as well as novel techniques, while providing an open, robust and welldocumented implementation. Therefore, FRETBursts represents an ideal platform for comparison and development of new methods in burst analysis.\n\nWe employ modern software engineering principles in order to minimize bugs and facilitate long-term maintainability. Furthermore, we place a strong focus on reproducibility by relying on Jupyter notebooks for FRETBursts execution. Notebooks are executable documents capturing all the steps of the analysis (including data files, input parameters, and results) and can be easily shared to replicate complete smFRET analyzes. Notebooks allow beginners to execute complex workflows and advanced users to customize the analysis for their own needs. By bundling analysis description, code and results in a single document, FRETBursts allows to seamless share analysis workflows and results, encourages reproducibility and facilitates collaboration among researchers in the single-molecule community.

Biophysics

Analysis of Two-State Folding Using Parabolic Approximation IV: Non-Arrhenius Kinetics of FBP28 WW Part-II

A model which treats the denatured and the native conformers as being confined to harmonic Gibbs energy wells has been used to rationalize the physical basis for the non-Arrhenius behaviour of spontaneously-folding fixed two-state systems. It is shown that at constant pressure and solvent conditions: (i) the rate constant for folding will be a maximum when the heat released upon formation of net molecular interactions is exactly compensated by the heat absorbed to desolvate net polar and non-polar solvent accessible surface area (SASA), as the denatured conformers driven by thermal noise bury their SASA and diffuse on the Gibbs energy surface to reach the activated state; (ii) the rate constant for unfolding will be a minimum when the heat absorbed by the native conformers to break various net backbone and sidechain interactions is exactly compensated by the heat of hydration released due to the net increase in SASA, as the native conformers unravel to reach the activated state; (iii) the activation entropy for folding will be zero, and the Gibbs barrier to folding will be a minimum, when the decrease in the backbone and the sidechain mobility is exactly compensated by the increase in entropy due to solvent-release, as the denatured conformers bury their SASA to reach the activated state; (iv) the activation entropy for unfolding will be zero, and the Gibbs barrier to unfolding will be a maximum when the increase in the backbone and sidechain mobility is exactly compensated by the negentropy of solvent-capture on the protein surface, as the native conformers unravel to reach the activated state; (v) while cold denaturation is driven by solvent effects, heat denaturation is primarily due to chain effects; (vi) the speed-limit for the folding is ultimately due to conformational searching; and (vii) Levinthals paradox may have little basis if the entropy of solvent-release that accompanies protein folding is taken into consideration.

Biophysics

Multiscale simulations reveal key features of the proton pumping mechanism in cytochrome c oxidase

Cytochrome c oxidase (CcO) reduces oxygen to water and uses the released free energy to pump protons across the membrane, contributing to the transmembrane proton electrochemical gradient that drives ATP synthesis. We have used multiscale reactive molecular dynamics simulations to explicitly characterize (with free energy profiles and calculated rates) the internal proton transport events that enable pumping and chemistry during the A[->]PR[->]F transition in the aa3-type CcO. Our results show that proton transport from amino acid residue E286 to both the pump loading site (PLS) and to the binuclear center (BNC) are thermodynamically driven by electron transfer from heme a to the BNC, but that the former (i.e., pumping) is kinetically favored while the latter (i.e., transfer of the chemical proton) is rate-limiting. The calculated rates are in quantitative agreement with experimental measurements. The back flow of the pumped proton from the PLS to E286 and from E286 to the inner side of membrane are prevented by the fast reprotonation of E286 through the D-channel and large free energy barriers for the back flow reactions. Proton transport from E286 to the PLS through the hydrophobic cavity (HC) and from D132 to E286 through the D-channel are found to be strongly coupled to dynamical hydration changes in the corresponding pathways. This work presents a comprehensive description of the key steps in the proton pumping mechanism in CcO.\n\nSignificanceThe long studied proton pumping mechanism in cytochrome c oxidase (CcO) continues to be a source of debate. This work provides a comprehensive computational characterization of the internal proton transport dynamics, while explicitly including the role of Grotthuss proton shuttling, that lead to both pumping and catalysis. Focusing on the A to F transition, our results show that the transfer of both the pumped and chemical protons are thermodynamically driven by electron transfer, and explain how proton back leakage is avoided by kinetic gating. This work also explicitly characterizes the coupling of proton transport with hydration changes in the hydrophobic cavity and D-channel, thus advancing our understanding of proton transport in biomolecules in general.

Biophysics

Structure, inhibition and regulation of two-pore channel TPC1 from Arabidopsis thaliana

Two-pore channels (TPCs) comprise a subfamily (TPC1-3) of eukaryotic voltage-and ligand-gated cation channels1,2 that contain two non-equivalent tandem pore-forming subunits that then dimerize to form quasi-tetramers. Found in vacuolar3 or endolysosomal4 membranes, they regulate the conductance of sodium5 and calcium3,6 ions, intravesicular pH5, trafficking7 and excitability8,9. TPCs are activated by a decrease in transmembrane potential1,3,9,10, an increase in cytosolic calcium concentrations1,10, and inhibited by luminal low pH, and calcium11, ...

Biophysics

Fast imaging of DNA motion reveals distinct sub-diffusion regimes at the site of DNA damage

The dynamic organization of genes inside the nucleus is an important determinant for their function. Using ultra-fast microscopy in S. cerevisiae cells and improved analysis of mean square displacements, we quantified DNA motion at time scales ranging from 10 milliseconds to minutes and found that following DNA damage, DNA exhibits distinct sub-diffusive regimes. In response to double-strand breaks, chromatin is more mobile at large time scales but, surprisingly, its mobility is dramatically reduced at short time scales. This effect is even more pronounced at the break. Such pattern of dynamics is consistent with a global increase in chromatin persistence length following DNA damage. Scale-dependent nuclear exploration is regulated by the Rad51 repair protein, both at the break and throughout the genome. We propose a model in which stiffening of the damaged ends by the repair complex, combined with global increased stiffness, act like a \"needle in a decompacted ball of yarn\", enhancing the ability of the break to traverse the chromatin meshwork.

Biophysics

Exact length distribution of filamentous structures assembled from a finite pool of subunits

Self-assembling filamentous structures made of protein subunits are ubiquitous in cell biology. These structures are often highly dynamic, with subunits in a continuous state of flux, binding to and falling off of filaments. In spite of this constant turnover of their molecular parts, many cellular structures seem to maintain a well-defined size over time, which is often required for their proper functioning. One widely discussed mechanism of size regulation involves the cell maintaining a finite pool of protein subunits available for assembly. This finite pool mechanism can control the length of a single filament by having assembly proceed until the pool of free subunits is depleted to the point when assembly and disassembly are balanced. Still, this leaves open the question whether the same mechanism can provide size control for multiple filamentous structures that are assembled from a common pool of protein subunits, as is often the case in cells. We address this question by solving the steady-state master equation governing the stochastic assembly and disassembly of multi-filament structures made from a shared finite pool of subunits. We find that while the total number of subunits within a multi-filament structure is well defined, individual filaments within the structure have a wide, power-law distribution of lengths. We also compute the phase diagram for two multi-filament structures competing for the same pool of subunits and identify conditions for coexistence when both have a well-defined size. These predictions can be tested in cell experiments in which the size of the subunit pool or the number of filament nucleators is tuned.

Biophysics

Structural basis for acyl group discrimination by human Gcn5L2

Gcn5 is a conserved acetyltransferase that regulates transcription by acetylating the N-terminal tails of histones. Motivated by recent studies identifying a chemically diverse array of lysine acyl modifications in vivo, we examined the acyl chain specificity of the acetyltransferase, human Gcn5 (Gcn5L2). Whereas Gcn5L2 robustly catalyzes lysine acetylation, the acyltransferase activity of Gcn5L2 gets progressively weaker with increasing acyl chain length. To understand how Gcn5 discriminates between different acyl-CoA molecules, we determined structures of the catalytic domain of human Gcn5L2 bound to propionyl-CoA and butyryl-CoA. Although the active site of Gcn5L2 can accommodate propionyl-CoA and butyryl-CoA without major structural rearrangements, butyryl-CoA adopts a conformation incompatible with catalysis that obstructs the path of the incoming lysine residue and acts as a competitive inhibitor for Gcn5L2 versus acetyl-CoA. These structures demonstrate how Gcn5L2 discriminates between acyl chain donors and explain why Gcn5L2 has weak activity for acyl moieties that are larger than an acetyl group.

Biophysics

Experimental tests of the quantum property of protein folding

Experimental tests on the quantum property of protein folding are discussed. It includes: the test of the instantaneousness of torsion transition through observation of protein structural change in a short time scale of microsecond; the test of non-Arrhenius temperature dependence of protein folding rate and other biomolecular conformational changes; and the search for the narrow spectral lines of the protein photo-folding.

Biophysics

Connecting the sequence-space of bacterial signaling proteins to phenotypes using coevolutionary landscapes

Two-component signaling (TCS) is the primary means by which bacteria sense and respond to the environment. TCS involves two partner proteins working in tandem, which interact to perform cellular functions while limiting interactions with non-partners (i.e., \"cross-talk\"). We construct a Potts model for TCS that can quantitatively predict how mutating amino acid identities affect the interaction between TCS partners and non-partners. The parameters of this model are inferred directly from protein sequence data. This approach drastically reduces the computational complexity of exploring the sequence-space of TCS proteins. As a stringent test, we compare its predictions to a recent comprehensive mutational study, which characterized the functionality of 204 mutational variants of the PhoQ kinase in Escherichia coli. We find that our best predictions accurately reproduce the amino acid combinations found in experiment, which enable functional signaling with its partner PhoP. These predictions demonstrate the evolutionary pressure to preserve the interaction between TCS partners as well as prevent unwanted \"crosstalk\". Further, we calculate the mutational change in the binding affinity between PhoQ and PhoP, providing an estimate to the amount of destabilization needed to disrupt TCS.

Biophysics

Self-assembly Controls Self-cleavage of HHR from ASBVd(-): a Combined SANS and Modeling Study.

In the Avocado Sunblotch Viroid (ASBVd: 249-nt) from the Avsunviroidae family, a symmetric rolling-circle replication operates through an autocatalytic mechanism mediated by hammerhead ribozymes (HHR) embedded in both polarity strands. The concatenated multimeric ASBVd (+) and ASBVd (-) RNAs thus generated are processed by cleavage to unit-length where ASBVd (-) self-cleaves with more efficiency. Absolute scale small angle neutron scattering (SANS) revealed a temperature-dependent dimer association in both ASBVd (-) and its derived 79-nt HHR (-). A joint thermodynamic analysis of SANS and catalytic data indicates the rate-determining step corresponds to the dimer/monomer transition. 2D and 3D models of monomeric and dimeric HHR (-) suggest that the inter-molecular contacts stabilizing the dimer (between HI and HII domains) compete with the intra-molecular ones stabilizing the active conformation of the full-length HHR required for an efficient self-cleavage. Similar competing intra- and inter-molecular contacts are proposed in ASBVd (-) though with a remoter region from an extension of the HI domain.

Biophysics

Modeling multi-particle complexes in stochastic chemical systems

Large complexes of classical particles play central roles in biology, in polymer physics, and in other disciplines. However, physics currently lacks mathematical methods for describing such complexes in terms of component particles, interaction energies, and assembly rules. Here we describe a Fock space structure that addresses this need, as well as diagrammatic methods that facilitate the use of this formalism. These methods can dramatically simplify the equations governing both equilibrium and non-equilibrium stochastic chemical systems. A mathematical relationship between the set of all complexes and a list of rules for complex assembly is also identified.

Biophysics