The linac coherent light source single particle imaging road map.

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.

Combining single-molecule optical trapping and small-angle x-ray scattering measurements to compute the persistence length of a protein ER/K alpha-helix.

A relatively unknown protein structure motif forms stable isolated single alpha-helices, termed ER/K alpha-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 alpha-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 alpha-helix behaves as a wormlike chain with a persistence length of approximately 15 nm or approximately 28 turns of alpha-helix. The ER/K alpha-helix length in proteins varies from 3 to 60 nm, with a median length of approximately 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.

Dynamic bond constraints in protein Langevin dynamics.

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.

Adaptive time stepping in biomolecular dynamics.

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.

Counterion distribution around DNA probed by solution X-ray scattering.

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.

Solution structural studies and low-resolution model of the Schizosaccharomyces pombe sap1 protein.

Sap1 is a DNA-binding protein involved in controlling the mating type switch in fission yeast Schizosaccharomyces pombe. In the absence of any significant sequence similarity with any structurally known protein, a variety of biophysical techniques has been used to probe the solution low-resolution structure of the sap1 protein. First, sap1 is demonstrated to be an unusually elongated dimer in solution by measuring the translational diffusion coefficient with two independent techniques: dynamic light-scattering and ultracentrifugation. Second, sequence analysis revealed the existence of a long coiled-coil region, which is responsible for dimerization. The length of the predicted coiled-coil matches estimates drawn from the hydrodynamic experimental behaviour of the molecule. In addition, the same measurements done on a shorter construct with a coiled-coil region shortened by roughly one-half confirmed the localization of the long coiled-coil region. A crude T-shape model incorporating all these information was built. Third, small-angle X-ray scattering (SAXS) of the free molecule provided additional evidence for the model. In particular, the P(r) curve strikingly demonstrates the existence of long intramolecular distances. Using a novel 3D reconstruction algorithm, a low resolution 3D model of the protein has been independently constructed that matches the SAXS experimental data. It also fits the translation diffusion coefficients measurements and agrees with the first T-shaped model. This low-resolution model has clearly biologically relevant new functional implications, suggesting that sap1 is a bifunctional protein, with the two active sites being separated by as much as 120 A; a tetrapeptide repeated four times at the C terminus of the molecule is postulated to be of utmost functional importance.

Small angle X-ray scattering reveals a compact intermediate in RNA folding.

We have used small angle X-ray scattering (SAXS) to monitor changes in the overall size and shape of the Tetrahymena ribozyme as it folds. The native ribozyme, formed in the presence of Mg2+, is much more compact and globular than the ensemble of unfolded conformations. Time-resolved measurements show that most of the compaction occurs at least 20-fold faster than the overall folding to the native state, suggesting that a compact intermediate or family of intermediates is formed early and then rearranges in the slow steps that limit the overall folding rate. These results lead to a kinetic folding model in which an initial 'electrostatic collapse' of the RNA is followed by slower rearrangements of elements that are initially mispositioned.

Zn(2+)-mediated structure formation and compaction of the "natively unfolded" human prothymosin alpha.

Human recombinant prothymosin alpha (ProTalpha) is known to have coil-like conformation at neutral pH; i.e., it belongs to the class of "natively unfolded" proteins. By means of circular dichroism, SAXS, and ANS fluorescence, we have investigated the effect of several divalent cations on the structure of this protein. Results of these studies are consistent with the conclusion that ProTalpha conformation is unaffected by large excess of Ca(2+), Mg(2+), Mn(2+), Cu(2+), and Ni(2+). However, Zn(2+) induces compaction and considerable rearrangement of the protein structure. This means that ProTalpha can specifically interact with Zn(2+) (K(D) approximately 10(-3) M), and such interactions induce folding of the natively unfolded protein into a compact partially folded (premolten globule-like) conformation. It is possible that these structural changes may be important for the function of this protein.

Fourth-generation X-ray sources: some possible applications to biology.

The term 'fourth generation X-ray sources' has come to mean X-ray free-electron lasers which use multi-GeV electron beams from linear accelerators to generate X-rays by self-amplified stimulated emission when fired into long undulators. Properties of the radiation expected from such sources are reviewed briefly and two possible applications of the resulting pulsed highly collimated X-radiation to problems in biology are discussed: use of X-ray photon correlation spectroscopy to measure time correlations of atoms in protein crystals, and use of Mössbauer radiation extracted from the photon beams by resonant Bragg diffraction from (57)Fe-containing crystals, for MAD phasing of very large unit-cell biomolecular crystals and possibly for photon echo measurements.

Transient dimer in the refolding kinetics of cytochrome c characterized by small-angle X-ray scattering.

The equilibrium unfolding and the kinetic refolding of cytochrome c (Cyt c) in the presence of imidazole were studied with small-angle X-ray scattering (SAXS). The equilibrium unfolding experiments showed the radius of gyration, R(g), of native Cyt c to swell approximately 1 A with the addition of imidazole. The thermodynamic parameter m also reflects an expansion of the protein as its lower value demonstrates an increase in solvent-accessible surface area over that of native Cyt c in the absence of imidazole. Refolding was studied in the presence of imidazole as it prevents misligated intermediate states from forming during the refolding process, simplifying the kinetics, and making them easier to resolve. Time-resolved decreases in the forward scattering amplitude, I(0), demonstrated the transient formation of an aggregated intermediate. Final protein and denaturant concentrations were varied in the refolding kinetics, and the singular value decomposition (SVD) method was employed to characterize the associated state. This state was determined to be a dimer, with properties consistent with a molten globule.

Natively unfolded human prothymosin alpha adopts partially folded collapsed conformation at acidic pH.

Prothymosin alpha has previously been shown to be unfolded at neutral pH, thus belonging to a growing family of "natively unfolded" proteins. The structural properties and conformational stability of recombinant human prothymosin alpha were characterized at neutral and acidic pH by gel filtration, SAXS, circular dichroism, ANS fluorescence, (1)H NMR, and resistance to urea-induced unfolding. Interestingly, prothymosin alpha underwent a cooperative transition from the unfolded state into a partially folded conformation on lowering the pH. This conformation of prothymosin alpha is a compact denatured state, with structural properties different from those of the molten globule. The formation of alpha-helical structure by the glutamic acid-rich elements of the protein accompanied by the partial hydrophobic collapse is expected at lower pH due to the neutralization of the negatively charged residues. It is possible that such conformational changes may be associated with the protein function.

Chain collapse can occur concomitantly with the rate-limiting step in protein folding.

We have directly characterized the extent of chain collapse early in the folding of protein L using time-resolved small angle X-ray scattering. We find that, immediately after the initiation of refolding, the protein exhibits dimensions indistinguishable from those observed under highly denaturing, equilibrium conditions and that this expanded initial state collapses with the same rate as that of the overall folding reaction. The observation that chain compaction need not significantly precede the rate-limiting step of folding demonstrates that rapid chain collapse is not an obligatory feature of protein folding reactions.

Protein dynamics simulations from nanoseconds to microseconds.

There have been a number of advances in atomic resolution simulations of biomolecules during the past few years. These have arisen partly from improvements to computer power and partly from algorithmic improvements. There have also been advances in measuring time-dependent fluctuations in proteins using NMR spectroscopy, revealing the importance of fluctuations in the microsecond to millisecond time range. Progress has also been made in measuring how far the simulations are able to represent the accessible phase space that is available to the protein in its native state, in solution, at room temperature. Another area of development is the simulation of protein unfolding at atomic resolution.

Characterization of transient intermediates in lysozyme folding with time-resolved small-angle X-ray scattering.

We have used synchrotron radiation, together with stopped-flow and continuous-flow mixing techniques to monitor refolding of lysozyme at pH 5.2. From data measured at times which range from 14 ms to two seconds, we can monitor changes in the size, the shape and the pair distribution function of the polypeptide chain during the folding process. Comparison of the results with the properties of native and GdmCl-unfolded lysozyme shows that a major chain collapse occurs in the dead-time of mixing. During this process about 50 % of the change in radius of gyration between the unfolded protein and the native state occurs and the polypeptide chain adopts a globular shape. Time-resolved fluorescence spectra of this collapsed state suggest that the hydrophobic side-chains are still highly solvent accessible. A subsequently formed intermediate with helical structure in the alpha-domain is nearly identical in size and shape with native lysozyme and has a solvent-inaccessible hydrophobic core. Despite its native-like properties, this intermediate is only slightly more stable (DeltaG0=-4 kJ/mol) than the collapsed state and still much less stable than native lysozyme (DeltaDeltaG0=36 kJ/mol) at 20 degrees C.

Association of partially-folded intermediates of staphylococcal nuclease induces structure and stability.

Staphylococcal nuclease forms three different partially-folded intermediates at low pH in the presence of low to moderate concentration of anions, differing in the amount of secondary structure, globularity, stability, and compactness. Although these intermediates are monomeric at low protein concentration (< or =0.25 mg/mL), increasing concentrations of protein result in the formation of dimers and soluble oligomers, ultimately leading to larger insoluble aggregates. Unexpectedly, increasing protein concentration not only led to association, but also to increased structure of the intermediates. The secondary structure, stability, and globularity of the two less-ordered partially-folded intermediates (A1 and A2) were substantially increased upon association, suggesting that aggregation induces structure. An excellent correlation was found between degree of association and amount of structure measured by different techniques, including circular dichroism, fluorescence, Fourier transform infrared spectroscopy (FTIR), and small-angle X-ray scattering. The associated states were also substantially more stable toward urea denaturation than the monomeric forms. A mechanism is proposed, in which the observed association of monomeric intermediates involves intermolecular interactions which correspond to those found intramolecularly in normal folding to the native state.

Protein denaturation: a small-angle X-ray scattering study of the ensemble of unfolded states of cytochrome c.

Solution X-ray scattering was used to study the equilibrium unfolding of cytochrome c as a function of guanidine hydrochloride concentration at neutral pH. The radius of gyration (Rg) shows a cooperative transition with increasing denaturant with a similar Cm to that observed with circular dichroism. However, the lack of an isoscattering point in the X-ray scattering patterns suggests the equilibrium unfolding is not simply a two-state process. Singular value decomposition (SVD) analysis was applied to the scattering patterns to determine the number of distinct scattering species. SVD analysis reveals the existence of three components, suggesting that at least three equilibrium states of the protein exist. A model was employed to determine the thermodynamic parameters and the scattering profiles of the three equilibrium states. These scattering profiles show that one state is native (N). The other two states (U1, U2) are unfolded, with U2 being fully unfolded and U1 having some residual structure. Using the thermodynamic parameters to calculate fractional populations, U1 is maximally populated at intermediate denaturant concentrations while U2 is maximally populated at high denaturant concentrations. It is likely that there is a multiplicity of denatured states with U1 and U2 representing an average of the denatured states populated at intermediate and high denaturant concentrations, respectively.

Anion-induced folding of Staphylococcal nuclease: characterization of multiple equilibrium partially folded intermediates.

The refolding of acid-unfolded staphylococcal nuclease (SNase) induced by anions was characterized, and revealed the existence of three different partially folded intermediates (A states). The three intermediates lack the rigid tertiary structure characteristic of native states, and differ in their degree of folding as measured by probes of secondary structure, size, stability and globularity. The least structured conformation, A1, is stabilized by chloride (600 mM) or sulfate (100 mM). It is about 50% folded (based on circular dichroism and small angle X-ray scattering (SAXS) data). The next most structured intermediate, A2, is induced by trifluoroacetate (300 mM) and has approximately 70% native-like secondary structure. The most structured intermediate, A3, is stabilized by trichloroacetate (50 mM) and has native-like secondary structure content and is almost as compact as the native state. The stability toward urea denaturation increases with increasing structure of the intermediates. Moreover, ureainduced unfolding studies show that these partially folded species are separated from each other, and from the unfolded state, by significant free energy barriers, suggesting that they are distinct conformational states. Kratky plots, based on the SAXS data, indicate that the two more structured intermediates have significant globularity (i.e. a tightly packed core), whereas the less structured intermediate has very little globularity. These observations support a model of protein folding in which certain conformations are of particularly low free energy and hence populated under conditions which differentially destabilize the native state. These partially folded intermediates probably consist of ensembles of substates with a common core of native-like secondary structure, which is responsible for their stability. Consequently, it is likely that the intermediates observed here represent the equilibrium counterparts of transient kinetic intermediates.

Association-induced folding of globular proteins.

It has generally been assumed that the aggregation of partially folded intermediates during protein refolding results in the termination of further protein folding. We show here, however, that under some conditions the association of partially folded intermediates can induce additional structure leading to soluble aggregates with many native-like properties. The amount of secondary structure in a monomeric, partially folded intermediate of staphylococcal nuclease was found to double on formation of soluble aggregates at high protein or salt concentrations. In addition, more globularity, as determined from Kratky plots of small-angle x-ray scattering data, was also noted in the associated states.