Intense femtosecond x-ray pulses from free-electron laser sources allow the imaging of individual particles in a single shot. Early experiments at the Linac Coherent Light Source (LCLS) have led to ...rapid progress in the field and, so far, coherent diffractive images have been recorded from biological specimens, aerosols, and quantum systems with a few-tens-of-nanometers resolution. In March 2014, LCLS held a workshop to discuss the scientific and technical challenges for reaching the ultimate goal of atomic resolution with single-shot coherent diffractive imaging. This paper summarizes the workshop findings and presents the roadmap toward reaching atomic resolution, 3D imaging at free-electron laser sources.
Spectroscopic studies have identified a number of proteins that appear to retain significant residual structure under even strongly denaturing conditions. Intrinsic viscosity, hydrodynamic radii, and ...small-angle x-ray scattering studies, in contrast, indicate that the dimensions of most chemically denatured proteins scale with polypeptide length by means of the power-law relationship expected for random-coil behavior. Here we further explore this discrepancy by expanding the length range of characterized denatured-state radii of gyration (RG) and by reexamining proteins that reportedly do not fit the expected dimensional scaling. We find that only 2 of 28 crosslink-free, prosthetic-group-free, chemically denatured polypeptides deviate significantly from a power-law relationship with polymer length. The RGof the remaining 26 polypeptides, which range from 16 to 549 residues, are well fitted (r2=0.988) by a power-law relationship with a best-fit exponent, 0.598 ± 0.028, coinciding closely with the 0.588 predicted for an excluded volume random coil. Therefore, it appears that the mean dimensions of the large majority of chemically denatured proteins are effectively indistinguishable from the mean dimensions of a random-coil ensemble.
Counterion atmospheres condensed onto charged biopolymers strongly affect their physical properties and biological functions, but have been difficult to quantify experimentally. Here, monovalent and ...divalent counterion atmospheres around DNA double helices in solution are probed using small-angle x-ray scattering techniques. Modulation of the ion scattering factors by anomalous (resonant) x-ray scattering and by interchanging ion identities yields direct measurements of the scattering signal due to the spatial correlation of surrounding ions to the DNA. The quality of the data permit, for the first time, quantitative tests of extended counterion distributions calculated from atomic-scale models of biologically relevant molecules.
A relatively unknown protein structure motif forms stable isolated single
α-helices, termed ER/K
α-helices, in a wide variety of proteins and has been shown to be essential for the function of some ...molecular motors. The flexibility of the ER/K
α-helix determines whether it behaves as a force transducer, rigid spacer, or flexible linker in proteins. In this study, we quantify this flexibility in terms of persistence length, namely the length scale over which it is rigid. We use single-molecule optical trapping and small-angle x-ray scattering, combined with Monte Carlo simulations to demonstrate that the Kelch ER/K
α-helix behaves as a wormlike chain with a persistence length of ∼15 nm or ∼28 turns of
α-helix. The ER/K
α-helix length in proteins varies from 3 to 60 nm, with a median length of ∼5 nm. Knowledge of its persistence length enables us to define its function as a rigid spacer in a translation initiation factor, as a force transducer in the mechanoenzyme myosin VI, and as a flexible spacer in the Kelch-motif-containing protein.
Understanding biological and physical processes involving nucleic acids, such as the binding of proteins to DNA and RNA, DNA condensation, and RNA folding, requires an understanding of the ion ...atmosphere that surrounds nucleic acids. We have used a simple model DNA system to determine how the ion atmosphere modulates interactions between duplexes in the absence of specific metal ion-binding sites and other complicated interactions. In particular, we have tested whether the Coulomb repulsion between nucleic acids can be reversed by counterions to give a net attraction, as has been proposed recently for the rapid collapse observed early in RNA folding. The conformation of two DNA duplexes tethered by a flexible neutral linker was determined in the presence of a series of cations by small angle x-ray scattering. The small angle x-ray scattering profiles of two control molecules with distinct shapes (a continuous duplex and a mimic of the compact DNA) were in good agreement with predictions, establishing the applicability of this approach. Under low-salt conditions (20 mM Na+), the tethered duplexes are extended because of a Coulombic repulsion estimated to be 2-5 kT/bp. Addition of high concentrations of Na+(1.2 M), Mg2+(0.6 M), and spermidine3+(75 mM) resulted in electrostatic relaxation to a random state. These results indicate that a counterion-induced attractive force between nucleic acid duplexes is not significant under physiological conditions. An upper limit on the magnitude of the attractive potential under all tested ionic conditions is estimated.
Large RNAs can collapse into compact conformations well before the stable formation of the tertiary contacts that define their final folds. This study identifies likely physical mechanisms driving ...these early compaction events in RNA folding. We have employed time-resolved small-angle X-ray scattering to monitor the fastest global shape changes of the Tetrahymena ribozyme under different ionic conditions and with RNA mutations that remove long-range tertiary contacts. A partial collapse in each of the folding time-courses occurs within tens of milliseconds with either monovalent or divalent cations. Combined with comparison to predictions from structural models, this observation suggests a relaxation of the RNA to a more compact but denatured conformational ensemble in response to enhanced electrostatic screening at higher ionic concentrations. Further, the results provide evidence against counterion-correlation-mediated attraction between RNA double helices, a recently proposed model for early collapse. A previous study revealed a second 100 ms phase of collapse to a globular state. Surprisingly, we find that progression to this second early folding intermediate requires RNA sequence motifs that eventually mediate native long-range tertiary interactions, even though these regions of the RNA were observed to be solvent-accessible in previous footprinting studies under similar conditions. These results help delineate an analogy between the early conformational changes in RNA folding and the “burst phase” changes and molten globule formation in protein folding.
We present an adaptive time stepping scheme based on the extrapolative method of Barth and Schlick LN, J. Chem. Phys. 109, 1633 (1998) to numerically integrate the Langevin equation with a ...molecular-dynamics potential. This approach allows us to use (on average) a time step for the strong nonbonded force integration corresponding to half the period of the fastest bond oscillation, without compromising the slow degrees of freedom in the problem. We show with simple examples how the dynamic step size stabilizes integration operators, and discuss some of the limitations of such stability. The method introduced uses a slightly more accurate inner integrator than LN to accommodate the larger steps. The adaptive time step approach reproduces temporal features of the bovine pancreatic trypsin inhibitor (BPTI) test system (similar to the one used in the original introduction of LN) compared to short-time integrators, but with energies that are shifted with respect to both LN, and traditional stochastic versions of Verlet. Although the introduction of longer steps has the effect of systematically heating the bonded components of the potential, the temporal fluctuations of the slow degrees of freedom are reproduced accurately. The purpose of this paper is to display a mechanism by which the resonance traditionally associated with using time steps corresponding to half the period of oscillations in molecular dynamics can be avoided. This has theoretical utility in terms of designing numerical integration schemes--the key point is that by factoring a propagator so that time steps are not constant one can recover stability with an overall (average) time step at a resonance frequency. There are, of course, limitations to this approach associated with the complicated, nonlinear nature of the molecular-dynamics (MD) potential (i.e., it is not as straightforward as the linear test problem we use to motivate the method). While the basic notion remains in the full Newtonian problem, it is easier to see the effects when damping is considered to be physical--that is, we do not view our method as a perturbation of Newtonian dynamics, we associate the damping with the environment, for example, a water bath (with gamma approximately 90 ps(-1)) Zagrovic and Pande, J. Comp. Chem. 24, 1432 (2003). All stochastic approaches to MD are stabilized by large physical damping, but here, we are really using it only to show that the resonance frequency can be obtained. Another simplifying assumption used in this paper is "heavy" hydrogen (we take the hydrogen mass to be 10 amu)--the view here is that we are interested primarily in the slowest degrees of freedom, and this approach has effects similar to bond freezing and united atom treatments of hydrogen. So from the point of view of biomolecular applications, the method described here is best suited to studies in which water is not explicit (so that damping in the problem can really be viewed as environmental interaction), and the interest is in slow dynamics where the effects of hydrogen are neglectable. There are a number of parameters in the LN method and the one derived here, and we cannot in a short paper address all adjustments, so our primary goal as a first pass is to show that stability can be recovered for a set of numerically forced (and hence artificial) bond oscillations, and compare stability to fixed-step methods.
Bond constraint algorithms for molecular dynamics typically take, as the target constraint lengths, the values of the equilibrium bond lengths defined in the potential. In Langevin form, the ...equations of motion are temperature dependent, which gives the average value for the individual bond lengths a temperature dependence. In addition to this, locally constant force fields can shift the local equilibrium bond lengths. To restore the average bond lengths in constrained integration to their unconstrained values, we suggest changing the constraint length used by popular constraint methods such as RATTLE H. C. Andersen, J. Comput. Phys. 52, 23 (1983) at each step. This allows us to more accurately capture the equilibrium bond length changes (with respect to the potential) due to the local equilibration and temperature effects. In addition, the approximations to the unconstrained nonbonded energies are closer using the dynamic constraint method than a traditional fixed constraint algorithm. The mechanism for finding the new constrained lengths involves one extra calculation of the bonded components of the force, and therefore adds O(N) time to the constraint algorithm. Since most molecular dynamics calculations are dominated by the O(N2) nonbonded forces, this new method does not take significantly more time than a fixed constraint algorithm.
The use of small-angle X-ray solution scattering (SAXS) as an analytical chemical tool for structural molecular biology is a mature field dating back to the work of Glatter and Kratky in the 1950s. ...Doniach discusses three areas of recent progress in the application of SAXS to the study of changes of conformation of biomolecules.
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