Hydrodynamic multibead modeling: problems, pitfalls and solutions. 3. Comparison of new approaches for improved predictions of translational properties.

Modeling simple and complex biopolymers in solution requires the shapes of these molecules to be approximated by bead modeling procedures, primarily for the prediction of hydrodynamic and scattering quantities. Though several bead modeling strategies (strict, shell and filling models) and a variety of computer programs (preferably the HYDRO suite by the García de la Torre group) are available, several subtle questions remain to be answered, in particular concerning the appropriate volume correction for intrinsic viscosity computations. In this context, various versions of the HYDRO programs and different types of volume corrections, as well as the novel, alternative program ZENO of the Mansfield group, were applied to a plethora of thoroughly designed multibead models of spherical, ellipsoidal, cylindrical and prismatic shapes. A critical comparison of the results obtained reveals a variety of new aspects, useful for many future applications. Among these, application of our recently suggested "reduced volume correction" (RVC) together with specially adapted HYDRO versions and use of ZENO turned out to be highly effective, in particular when aiming at filling model strategies and using high bead numbers, a domain not fully supported by the recent HYDRO++ versions. By our approaches, the values of translational properties (diffusion coefficients, D, and intrinsic viscosities, [η]) of all multibead models applied were anticipated correctly.

Hydrodynamic multibead modeling: problems, pitfalls, and solutions. 2. Proteins.

Hydrodynamic models of proteins have been generated by recourse to crystallographic data and applying a filling model strategy in order to predict both hydrodynamic and scattering parameters. The design of accurate protein models retaining the majority of the molecule peculiarities requires usage of many beads and consideration of many serious problems. Applying the expertise obtained with ellipsoid models and pilot tests on proteins, we succeeded in constructing precise models for several anhydrous and hydrated proteins of different shape, size, and complexity. The models constructed consist of many beads (up to about 11,000) for the protein constituents (atoms, amino acid residues, groups) and preferentially bound water molecules. While in the case of small proteins, parameter predictions are straightforward, computations for giant proteins necessitate drastic reductions of the number of initially available beads. Among several auxiliary programs, our advanced hydration programs, HYDCRYST and HYDMODEL, and modified versions of García de la Torre's program HYDRO were successfully employed. This allowed the generation of realistic protein models by imaging details of their fine structure and enabled the prediction of reliable molecular parameters including intrinsic viscosities. The appearance of the models and the agreement of molecular properties and distance distribution functions p(r) of unreduced and reduced models can be used for a meticulous inspection of the data obtained.

Hydrodynamic multibead modeling: problems, pitfalls, and solutions. 1. Ellipsoid models.

The shape of macromolecules can be approximated by filling models, if both hydrodynamic and scattering properties should be predicted. Modeling of complex biological macromolecules, such as oligomeric proteins, or of molecule details calls for usage of many beads to preserve the original features. However, the calculation of precise values for structural and hydrodynamic parameters has to consider many problems and pitfalls. Among these, the huge number of beads required for modeling details and the choice of appropriate volume corrections for the calculation of intrinsic viscosities are pestering problems to date. As a first step to tackle these problems, various tests with multibead models (ellipsoids of different axial ratios) were performed. The agreement of the predicted molecular properties with those derived from whole-body approaches can be used as evaluation criteria. Modification of previously available versions of García de la Torre's program HYDRO allows hydrodynamic modeling of macromolecules composed of a maximum of about 11,000 beads. Moreover, application of our recently suggested "reduced volume correction" enables a fast and efficient anticipation of intrinsic viscosities. Correct parameter predictions were obtained for all models analyzed. The data obtained were compared to the results of calculations based on HYDRO programs available to the public. The calculations revealed some unexpected results and allowed founded conclusions of general importance for precise calculations on multibead models (e.g., the requirement of calculations in the double-precision mode).

Modeling complex biological macromolecules: reduction of multibead models.

The shape of simple and complex biological macromolecules can be approximated by bead modeling procedures. Such approaches are required, for example, for the analysis of the scattering and hydrodynamic behavior of the models under analysis and the prediction of their molecular properties. Using the atomic coordinates of proteins for modeling inevitably leads to models composed of a multitude of beads. In particular, for hydrodynamic modeling, a drastic reduction of the bead number may become unavoidable to enable computation. A systematic investigation of different approaches and computation modes shows that the 'running mean', 'cubic grid,' and 'hexagonal grid' approaches are successful, provided that the extent of reduction does not exceed a factor of 100 and the grid approaches use beads of unequal size and the beads are located at the centers of gravity. Further precautions to be taken include usage of appropriate interaction tensors for overlapping beads of unequal size and appropriate volume corrections when calculating intrinsic viscosities. The applied procedures were tested with the small protein lysozyme in a case study and were then applied to the huge capsid of the phage fr and its trimeric building block. The appearance of the models and the agreement of molecular properties and distance distribution functions of unreduced and reduced models can be used as evaluation criteria.

Small angle X-ray scattering studies and modeling of Eudistylia vancouverii chlorocruorin and Macrobdella decora hemoglobin.

Annelids possess giant extracellular oxygen carriers that exhibit a hexagonal bilayer appearance and have molecular masses of approximately 3.5 MDa. By small angle x-ray scattering (SAXS), Eudistylia vancouverii chlorocruorin and Macrobdella decora hemoglobin were investigated in solution. On the basis of the experimental SAXS data, three-dimensional models were established in a two-step approach (trial and error and averaging). The main differences between the complexes concern the structure of their central part and the subunit architecture. Usage of our SAXS models as templates for automated model generation (program DAMMIN) led to refined models that fit perfectly the experimental data. Special attention was paid to the inhomogeneous density distribution observed within the complexes. DAMMIN models without a priori information could not reproducibly locate low-density areas. The usage of templates, however, improved the results considerably, in particular by applying electron microscopy-based templates. Biologically relevant information on the presence of low-density areas and hints for their presumable location could be drawn from SAXS and sophisticated modeling approaches. Provided that different models are analyzed carefully, this obviously opens a way to gain additional biologically relevant structural information from SAXS data.

Modeling the hydration of proteins: prediction of structural and hydrodynamic parameters from X-ray diffraction and scattering data.

The implications of protein-water interactions are of importance for understanding the solution behavior of proteins and for analyzing the fine structure of proteins in aqueous solution. Starting from the atomic coordinates, by bead modeling the scattering and hydrodynamic properties of proteins can be predicted reliably (Debye modeling, program HYDRO). By advanced modeling techniques the hydration can be taken into account appropriately: by some kind of rescaling procedures, by modeling a water shell, by iterative comparisons to experimental scattering curves (ab initio modeling) or by special hydration algorithms. In the latter case, the surface topography of proteins is visualized in terms of dot surface points, and the normal vectors to these points are used to construct starting points for placing water molecules in definite positions on the protein envelope. Bead modeling may then be used for shaping the individual atomic or amino acid residues and also for individual water molecules. Among the tuning parameters, the choice of the scaling factor for amino acid hydration and of the molecular volume of bound water turned out to be crucial. The number and position of bound water molecules created by our hydration modeling program HYDCRYST were compared with those derived from X-ray crystallography, and the capability to predict hydration, structural and hydrodynamic parameters (hydrated volume, radius of gyration, translational diffusion and sedimentation coefficients) was compared with the findings generated by the water-shell approach CRYSOL. If the atomic coordinates are unknown, ab initio modeling approaches based on experimental scattering curves can provide model structures for hydrodynamic predictions.