Display omitted
•SAXS/WAXS experiments provide increasingly accurate structural information on biomolecules in solution.•Major challenges with the interpretation of SAXS/WAXS data are ...described.•Molecular dynamics (MD) simulations may guide the interpretation of the data.•Recent MD-related method developments for SAXS/WAXS interpretation are discussed.
Small-angle and wide-angle X-ray scattering in solution (SAXS, WAXS, SWAXS) is an increasingly accurate method for obtaining information on biomolecular structures, ensembles, and time-resolved dynamics at near-native conditions. However, the interpretation of the solution scattering data by computational methods is complicated by the low information content of the data, by scattering contributions from the hydration layer, and by unknown systematic errors. In the light of available computational methods, we first review the main computational challenges with the interpretation of SWAXS data. Molecular dynamics (MD) simulations may help to overcome these challenges and guide the interpretation of SWAXS in multiple ways. The physical information in atomistic force fields complements the low-information SWAXS data; explicit-solvent MD may be used to predict solvent scattering, and the MD-related sampling methods may guide the structure refinement against SWAXS data.
Small-angle X-ray scattering is an increasingly popular technique used to detect protein structures and ensembles in solution. However, the refinement of structures and ensembles against SAXS data is ...often ambiguous due to the low information content of SAXS data, unknown systematic errors, and unknown scattering contributions from the solvent. We offer a solution to such problems by combining Bayesian inference with all-atom molecular dynamics simulations and explicit-solvent SAXS calculations. The Bayesian formulation correctly weights the SAXS data versus prior physical knowledge, it quantifies the precision or ambiguity of fitted structures and ensembles, and it accounts for unknown systematic errors due to poor buffer matching. The method further provides a probabilistic criterion for identifying the number of states required to explain the SAXS data. The method is validated by refining ensembles of a periplasmic binding protein against calculated SAXS curves. Subsequently, we derive the solution ensembles of the eukaryotic chaperone heat shock protein 90 (Hsp90) against experimental SAXS data. We find that the SAXS data of the apo state of Hsp90 is compatible with a single wide-open conformation, whereas the SAXS data of Hsp90 bound to ATP or to an ATP-analogue strongly suggest heterogenous ensembles of a closed and a wide-open state.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
Wide-angle x-ray scattering (WAXS) experiments of biomolecules in solution have become increasingly popular because of technical advances in light sources and detectors. However, the structural ...interpretation of WAXS profiles is problematic, partly because accurate calculations of WAXS profiles from structural models have remained challenging. In this work, we present the calculation of WAXS profiles from explicit-solvent molecular dynamics (MD) simulations of five different proteins. Using only a single fitting parameter that accounts for experimental uncertainties because of the buffer subtraction and dark currents, we find excellent agreement to experimental profiles both at small and wide angles. Because explicit solvation eliminates free parameters associated with the solvation layer or the excluded solvent, which would require fitting to experimental data, we minimize the risk of overfitting. We further find that the influence from water models and protein force fields on calculated profiles are insignificant up to q≈15nm−1. Using a series of simulations that allow increasing flexibility of the proteins, we show that incorporating thermal fluctuations into the calculations significantly improves agreement with experimental data, demonstrating the importance of protein dynamics in the interpretation of WAXS profiles. In addition, free MD simulations up to one microsecond suggest that the calculated profiles are highly sensitive with respect to minor conformational rearrangements of proteins, such as an increased flexibility of a loop or an increase of the radius of gyration by < 1%. The present study suggests that quantitative comparison between MD simulations and experimental WAXS profiles emerges as an accurate tool to validate solution ensembles of biomolecules.
Small- and wide-angle X-ray scattering (SWAXS) has evolved into a powerful tool to study biological macromolecules in solution. The interpretation of SWAXS curves requires their accurate predictions ...from structural models. Such predictions are complicated by scattering contributions from the hydration layer and by effects from thermal fluctuations. Here, we describe the new web server WAXSiS (WAXS in solvent) that computes SWAXS curves based on explicit-solvent all-atom molecular dynamics (MD) simulations (http://waxsis.uni-goettingen.de/). The MD simulations provide a realistic model for both the hydration layer and the excluded solvent, thereby avoiding any solvent-related fitting parameters, while naturally accounting for thermal fluctuations.
Small- and wide-angle x-ray scattering (SWAXS) and molecular dynamics (MD) simulations are complementary approaches that probe conformational transitions of biomolecules in solution, even in a ...time-resolved manner. However, the structural interpretation of the scattering signals is challenging, while MD simulations frequently suffer from incomplete sampling or from a force-field bias. To combine the advantages of both techniques, we present a method that incorporates solution scattering data as a differentiable energetic restraint into explicit-solvent MD simulations, termed SWAXS-driven MD, with the aim to direct the simulation into conformations satisfying the experimental data. Because the calculations fully rely on explicit solvent, no fitting parameters associated with the solvation layer or excluded solvent are required, and the calculations remain valid at wide angles. The complementarity of SWAXS and MD is illustrated using three biological examples, namely a periplasmic binding protein, aspartate carbamoyltransferase, and a nuclear exportin. The examples suggest that SWAXS-driven MD is capable of refining structures against SWAXS data without foreknowledge of possible reaction paths. In turn, the SWAXS data accelerates conformational transitions in MD simulations and reduces the force-field bias.
Many biological membranes are asymmetric and exhibit complex lipid composition, comprising hundreds of distinct chemical species. Identifying the biological function and advantage of this complexity ...is a central goal of membrane biology. Here, we study how membrane complexity controls the energetics of the first steps of membrane fusions, that is, the formation of a stalk. We first present a computationally efficient method for simulating thermodynamically reversible pathways of stalk formation at coarse-grained resolution. The method reveals that the inner leaflet of a typical plasma membrane is far more fusogenic than the outer leaflet, which is likely an adaptation to evolutionary pressure. To rationalize these findings by the distinct lipid compositions, we computed ~200 free energies of stalk formation in membranes with different lipid head groups, tail lengths, tail unsaturations, and sterol content. In summary, the simulations reveal a drastic influence of the lipid composition on stalk formation and a comprehensive fusogenicity map of many biologically relevant lipid classes.
Topological transitions of membranes, such as pore formation or membrane fusion, play key roles in biology, biotechnology, and in medical applications. Calculating the related free-energy landscapes ...has been complicated by the fact that such processes involve a sequence of transitions along highly distinct directions in conformational space, making it difficult to define good reaction coordinates (RCs) for the overall process. In this study, a new RC capable of driving both pore nucleation and pore expansion in lipid membranes is presented. The potential of mean force (PMF) along the RC computed with molecular dynamics simulations provides a comprehensive view on the free-energy landscape of pore formation, including a barrier for pore nucleation; the size, free energy, and metastability of the open pore; and the energetic cost for further pore expansion against the line tension of the pore rim. The RC is illustrated by quantifying the effects of (i) simulation system size and (ii) the addition of dimethyl sulfoxide on the free-energy landscape of pore formation. PMF calculations along the RC provide mechanistic and energetic understanding of pore formation, hence they will be useful to rationalize the effects of membrane-active peptides, electric fields, and membrane composition on transmembrane pores.
The permeability of lipid membranes for metabolic molecules or drugs is routinely estimated from the solute’s oil/water partition coefficient. However, the molecular determinants that modulate the ...permeability in different lipid compositions have remained unclear. Here, we combine scanning electrochemical microscopy and molecular-dynamics simulations to study the effect of cholesterol on membrane permeability, because cholesterol is abundant in all animal membranes. The permeability of membranes from natural lipid mixtures to both hydrophilic and hydrophobic solutes monotonously decreases with cholesterol concentration Chol. The same is true for hydrophilic solutes and planar bilayers composed of dioleoyl-phosphatidylcholine or dioleoyl-phosphatidyl-ethanolamine. However, these synthetic lipids give rise to a bell-shaped dependence of membrane permeability on Chol for very hydrophobic solutes. The simulations indicate that cholesterol does not affect the diffusion constant inside the membrane. Instead, local partition coefficients at the lipid headgroups and at the lipid tails are modulated oppositely by cholesterol, explaining the experimental findings. Structurally, these modulations are induced by looser packing at the lipid headgroups and tighter packing at the tails upon the addition of cholesterol.
The Weighted Histogram Analysis Method (WHAM) is a standard technique used to compute potentials of mean force (PMFs) from a set of umbrella sampling simulations. Here, we present a new WHAM ...implementation, termed g_wham, which is distributed freely with the GROMACS molecular simulation suite. g_wham estimates statistical errors using the technique of bootstrap analysis. Three bootstrap methods are supported: (i) bootstrapping new trajectories based on the umbrella histograms, (ii) bootstrapping of complete histograms, and (iii) Bayesian bootstrapping of complete histograms, that is, bootstrapping via the assignment of random weights to the histograms. Because methods ii and iii consider only complete histograms as independent data points, these methods do not require the accurate calculation of autocorrelation times. We demonstrate that, given sufficient sampling, bootstrapping new trajectories allows for an accurate error estimate. In the presence of long autocorrelations, however, (Bayesian) bootstrapping of complete histograms yields a more reliable error estimate, whereas bootstrapping of new trajectories may underestimate the error. In addition, we emphasize that the incorporation of autocorrelations into WHAM reduces the bias from limited sampling, in particular, when computing periodic PMFs in inhomogeneous systems such as solvated lipid membranes or protein channels.
The formation of pores over lipid membranes by the application of electric fields, termed membrane electroporation, is widely used in biotechnology and medicine to deliver drugs, vaccines, or genes ...into living cells. Continuum models for describing the free energy landscape of membrane electroporation were proposed decades ago, but they have never been tested against spatially detailed atomistic models. Using molecular dynamics (MD) simulations with a recently proposed reaction coordinate, we computed potentials of mean force of pore nucleation and pore expansion in lipid membranes at various transmembrane potentials. Whereas the free energies of pore expansion are compatible with previous continuum models, the experimentally important free energy barrier of pore nucleation is at variance with established models. The discrepancy originates from different geometries of the transition state; previous continuum models assumed the presence of a membrane-spanning defect throughout the process, whereas, according to the MD simulations, the transition state of pore nucleation is typically passed before a transmembrane defect has formed. A modified continuum model is presented that qualitatively agrees with the MD simulations. Using kinetics of pore opening together with transition state theory, our free energies of pore nucleation are in excellent agreement with previous experimental data.
PDF
