Binding and Functional Folding (BFF): A Physiological Framework for Studying Biomolecular Interactions and Allostery.

EF-hand Ca2+-binding proteins (CBPs), such as S100 proteins (S100s) and calmodulin (CaM), are signaling proteins that undergo conformational changes upon increasing intracellular Ca2+. Upon binding Ca2+, S100 proteins and CaM interact with protein targets and induce important biological responses. The Ca2+-binding affinity of CaM and most S100s in the absence of target is weak (CaKD > 1 µM). However, upon effector protein binding, the Ca2+ affinity of these proteins increases via heterotropic allostery (CaKD < 1 µM). Because of the high number and micromolar concentrations of EF-hand CBPs in a cell, at any given time, allostery is required physiologically, allowing for (i) proper Ca2+ homeostasis and (ii) strict maintenance of Ca2+-signaling within a narrow dynamic range of free Ca2+ ion concentrations, [Ca2+]free. In this review, mechanisms of allostery are coalesced into an empirical "binding and functional folding (BFF)" physiological framework. At the molecular level, folding (F), binding and folding (BF), and BFF events include all atoms in the biomolecular complex under study. The BFF framework is introduced with two straightforward BFF types for proteins (type 1, concerted; type 2, stepwise) and considers how homologous and nonhomologous amino acid residues of CBPs and their effector protein(s) evolved to provide allosteric tightening of Ca2+ and simultaneously determine how specific and relatively promiscuous CBP-target complexes form as both are needed for proper cellular function.

Imaging enzyme kinetics at atomic resolution.

Serial crystallography at a synchrotron has been used to obtain time-resolved atomic resolution density maps of enzyme catalysis in copper nitrite reductase. Similar XFEL studies, intended to out-run radiation damage, will also soon appear.

Biostructural Science Inspired by Next-Generation X-Ray Sources.

Next-generation synchrotron radiation sources, such as X-ray free-electron lasers, energy recovery linacs, and ultra-low-emittance storage rings, are catalyzing novel methods of biomolecular microcrystallography and solution scattering. These methods are described and future trends are predicted. Importantly, there is a growing realization that serial microcrystallography and certain cutting-edge solution scattering experiments can be performed at existing storage ring sources by utilizing new technology. In this sense, next-generation sources are serving two distinct functions, namely, provision of new capabilities that require the newer sources and inspiration of new methods that can be performed at existing sources.

Computing spatial information from Fourier coefficient distributions.

The spatial relationships between molecules can be quantified in terms of information. In the case of membranes, the spatial organization of molecules in a bilayer is closely related to biophysically and biologically important properties. Here, we present an approach to computing spatial information based on Fourier coefficient distributions. The Fourier transform (FT) of an image contains a complete description of the image, and the values of the FT coefficients are uniquely associated with that image. For an image where the distribution of pixels is uncorrelated, the FT coefficients are normally distributed and uncorrelated. Further, the probability distribution for the FT coefficients of such an image can readily be obtained by Parseval's theorem. We take advantage of these properties to compute the spatial information in an image by determining the probability of each coefficient (both real and imaginary parts) in the FT, then using the Shannon formalism to calculate information. By using the probability distribution obtained from Parseval's theorem, an effective distance from the uncorrelated or most uncertain case is obtained. The resulting quantity is an information computed in k-space (kSI). This approach provides a robust, facile and highly flexible framework for quantifying spatial information in images and other types of data (of arbitrary dimensions). The kSI metric is tested on a 2D Ising model, frequently used as a model for lipid bilayer; and the temperature-dependent phase transition is accurately determined from the spatial information in configurations of the system.

Why phase errors affect the electron function more than amplitude errors.

If Fexp(ialpha) are the set of structure factors for a structure f, the amplitudes can be converted to those of an uncorrelated structure g (amplitude swapping) by multiplying each F by the positive number G/F. Correspondingly, the image f is convoluted with k, the Fourier transform of G/F; k has a large peak at the origin, so that f * k approximately f. For swapped phases, the image f is convoluted with l, the Fourier transform of exp(iDeltaalpha), where Deltaalpha, the phase difference between F and G, is a random variable; l does not have a large peak at the origin, so that f * l does not resemble f. The paper provides quantitative descriptions of these arguments.

A method for finding candidate conformations for molecular replacement using relative rotation between domains of a known structure.

This paper presents a methodology to obtain candidate conformations of multidomain proteins for use in molecular replacement. For each separate domain, the orientational relationship between the template and the target structure is obtained using standard molecular replacement. The orientational relationships of the domains are then used to calculate the relative rotation between the domains in the target conformation by using pose-estimation techniques from the field of robotics and computer vision. With the angle of relative rotation between the domains as a cost function, iterative normal-mode analysis is used to drive the template structure to a candidate conformation that matches the X-ray crystallographic data obtained for the target conformation. The selection of the correct intra-protein domain orientations from among the many spurious maxima in the rotation function (including orientations obtained from domains in symmetry mates rather than within the same copy of the protein) presents a challenge. This problem is resolved by checking R factors of each domain, measuring the absolute value of relative rotation between domains, and evaluating the cost value after each candidate conformation is driven to convergence with iterative NMA. As a validation, the proposed method is applied to three test proteins: ribose-binding protein, lactoferrin and calcium ATPase. In each test case, the orientation and translation of the final candidate conformation in the unit cell are generated correctly from the suggested procedure. The results show that the proposed method can yield viable candidate conformations for use in molecular replacement and can reveal the structural details and pose of the target conformation in the crystallographic unit cell.

Molecular dynamics study of water penetration in staphylococcal nuclease.

The ionization properties of Lys and Glu residues buried in the hydrophobic core of staphylococcal nuclease (SN) suggest that the interior of this protein behaves as a highly polarizable medium with an apparent dielectric constant near 10. This has been rationalized previously in terms of localized conformational relaxation concomitant with the ionization of the internal residue, and with contributions by internal water molecules. Paradoxically, the crystal structure of the SN V66E variant shows internal water molecules and the structure of the V66K variant does not. To assess the structural and dynamical character of interior water molecules in SN, a series of 10-ns-long molecular dynamics (MD) simulations was performed with wild-type SN, and with the V66E and V66K variants with Glu66 and Lys66 in the neutral form. Internal water molecules were identified based on their coordination state and characterized in terms of their residence times, average location, dipole moment fluctuations, hydrogen bonding interactions, and interaction energies. The locations of the water molecules that have residence times of several nanoseconds and display small mean-square displacements agree well with the locations of crystallographically observed water molecules. Additional, relatively disordered water molecules that are not observed crystallographically were found in internal hydrophobic locations. All of the interior water molecules that were analyzed in detail displayed a distribution of interaction energies with higher mean value and narrower width than a bulk water molecule. This underscores the importance of protein dynamics for hydration of the protein interior. Further analysis of the MD trajectories revealed that the fluctuations in the protein structure (especially the loop elements) can strongly influence protein hydration by changing the patterns or strengths of hydrogen bonding interactions between water molecules and the protein. To investigate the dynamical response of the protein to burial of charged groups in the protein interior, MD simulations were performed with Glu66 and Lys66 in the charged state. Overall, the MD simulations suggest that a conformational change rather than internal water molecules is the dominant determinant of the high apparent polarizability of the protein interior.

Influence of ions, hydration, and the transcriptional inhibitor P4N on the conformations of the Sp1 binding site.

Three crystal structures containing the entire Sp1 consensus sequence d(GGGGCGGGG) with two or three additional base-pairs on either the 5' or 3' ends and overhangs have been determined. Despite the different lengths of DNA in the pseudo-dodecamers and pseudo-tridecamer, all three structures form A-DNA duplexes that share a common set of crystal contacts, including a T*(G.C) base triplet and a 5'-overhang that flips out and away from the helical axes to form a Hoogsteen base-pair with the 3'-overhang of a symmetry mate. The global conformations of the three structures differ, however, in the widths of their respective major grooves, the lengths of the molecules, and the extent of crystal packing. The structures were determined from crystals grown in an unusual precipitant for A-DNA, polyethylene glycol (PEG) 400, in combination with polyamines or ions; cobalt hexamine for the pseudo-tridecamer, and spermidine for the pseudo-dodecamers. As the Sp1 binding site is a target for antiviral and anticancer drugs, pseudo-dodecamer crystals were soaked with one such antiviral and anticancer compound, P4N. Although P4N was not visualized unambiguously in the electron density maps, the effect of the drug is evident from significant differences in the lattice constants, crystal packing, and overall conformation of the structure.

X-ray and thermodynamic studies of staphylococcal nuclease variants I92E and I92K: insights into polarity of the protein interior.

We have used crystallography and thermodynamic analysis to study nuclease variants I92E and I92K, in which an ionizable side-chain is placed in the hydrophobic core of nuclease. We find that the energetic cost of burying ionizable groups is rather modest. The X-ray determinations show water molecules solvating the buried glutamic acid under cryo conditions, but not at room temperature. The lysine side-chain does not appear solvated in either case. Guanidine hydrochloride (GnHCl) denaturation of I92E and I92K, done as a function of pH and monitored by tryptophan fluorescence, showed that I92E and I92K are folded in the pH range pH 3.5-9.0 and pH 5.5-9.5, respectively. The stability of the parental protein is independent of pH over a broad range. In contrast, the stabilities of I92E and I92K exhibit a pH dependence, which is quantitatively explained by thermodynamic analysis: the PK(a) value of the buried K92 is 5.6, while that of the buried E92 is 8.65. The free energy difference between burying the uncharged and charged forms of the groups is modest, about 6 kcal/mol. We also found that epsilon(app) for I92K and I92E is in the range approximately 10-12, instead of 2-4 commonly used to represent the protein interior. Side-chains 92E and 92K were uncharged under the conditions of the X-ray experiment. Both are buried completely inside the well-defined hydrophobic core of the variant proteins without forming salt-bridges or hydrogen bonds to other functional groups of the proteins. Under cryo conditions 92E shows a chain of four water molecules, which hydrate one oxygen atom of the carboxyl group of the glutamic acid. Two other water molecules, which are present in the wild-type at all temperatures, are also connected to the water ring observed inside the hydrophobic core. The ready burial of water with an uncharged E92 raises the possibility that solvent excursions into the interior also take place in the wild-type protein, but in a random, dynamic way not detectable by crystallography. Such transient excursions could increase the average polarity, and thus epsilon(app), of the protein interior.

A compact RNA tertiary structure contains a buried backbone-K+ complex.

The structure of a 58 nucleotide ribosomal RNA fragment buries several phosphate groups of a hairpin loop within a large tertiary core. During refinement of an X-ray crystal structure containing this RNA, a potassium ion was found to be contacted by six oxygen atoms from the buried phosphate groups; the ion is contained completely within the solvent-accessible surface of the RNA. The electrostatic potential at the ion chelation site is unusually large, and more than compensates for the substantial energetic penalties associated with partial dehydration of the ion and displacement of delocalized ions. The very large predicted binding free energy, approximately -30 kcal/mol, implies that the site must be occupied for the RNA to fold. These findings agree with previous studies of the ion-dependent folding of tertiary structure in this RNA, which concluded that a monovalent ion was bound in a partially dehydrated environment where Mg2+ could not easily compete for binding. By compensating the unfavorable free energy of buried phosphate groups with a chelated ion, the RNA is able to create a larger and more complex tertiary fold than would be possible otherwise.

Experimental pK(a) values of buried residues: analysis with continuum methods and role of water penetration.

Lys-66 and Glu-66, buried in the hydrophobic interior of staphylococcal nuclease by mutagenesis, titrate with pK(a) values of 5.7 and 8.8, respectively (Dwyer et al., Biophys. J. 79:1610-1620; García-Moreno E. et al., Biophys. Chem. 64:211-224). Continuum calculations with static structures reproduced the pK(a) values when the protein interior was treated with a dielectric constant (epsilon(in)) of 10. This high apparent polarizability can be rationalized in the case of Glu-66 in terms of internal water molecules, visible in crystallographic structures, hydrogen bonded to Glu-66. The water molecules are absent in structures with Lys-66; the high polarizability cannot be reconciled with the hydrophobic environment surrounding Lys-66. Equilibrium thermodynamic experiments showed that the Lys-66 mutant remained folded and native-like after ionization of the buried lysine. The high polarizability must therefore reflect water penetration, minor local structural rearrangement, or both. When in pK(a) calculations with continuum methods, the internal water molecules were treated explicitly, and allowed to relax in the field of the buried charged group, the pK(a) values of buried residues were reproduced with epsilon(in) in the range 4-5. The calculations show that internal waters can modulate pK(a) values of buried residues effectively, and they support the hypothesis that the buried Lys-66 is in contact with internal waters even though these are not seen crystallographically. When only the one or two innermost water molecules were treated explicitly, epsilon(in) of 5-7 reproduced the pK(a) values. These values of epsilon(in) > 4 imply that some conformational reorganization occurs concomitant with the ionization of the buried groups.