SOLPRO: theory and computer program for the prediction of SOLution PROperties of rigid macromolecules and bioparticles

Single-valued hydrodynamic coefficients of a rigid particle can be calculated from existing theories and computer programs for either bead models or ellipsoids. Starting from these coefficients, we review the procedures for the calculation of complex solution properties depending on rotational diffusion, such as the decays of electric birefringence and fluorescence anisotropy. We also describe the calculation of the scattering form factor of bead models. The hydrodynamic coefficients and solution properties can be combined to give universal, shape-dependent functions, which were initially intended for ellipsoidal particles, and are extended here for the most general case. We have implemented all these developments in a new computer program, SOLPRO, for calculation of SOLution PROperties, which can be linked to existing software for bead models or ellipsoids. Accepted: 1 November 1996     

MULTIHYDRO and MONTEHYDRO: conformational search and Monte Carlo calculation of solution properties of rigid or flexible bead models

A computer program, MULTIHYDRO, has been constructed for the calculation of hydrodynamic coefficients and other solution properties of multiple possible conformations of a bead model. With minimal additional programming to describe the model under study, this program interfaces efficiently with HYDRO for the calculation of solution properties, including hydrodynamic coefficients, radius of gyration, covolume, etc. A useful application is the conformation search of rigid macromolecules, because many possible conformations can be evaluated in a single run of the program. In this paper we also pay attention to the properties of flexible macromolecules, in the so-called Monte Carlo rigid-body approximation, which is virtually exact for the simpler solution properties. The theoretical aspects of the procedure are described, and we show how MULTIHYDRO can be employed for this calculation. However, for flexible molecules, a more general simulation scheme is importance-sampling Monte Carlo generation. We describe how this procedure is implemented in another computer program, MONTEHYDRO. Examples of the usage of these tools are provided.     

Equivalent radii and ratios of radii from solution properties as indicators of macromolecular conformation, shape, and flexibility

The equivalent radius for any solution property is the radius of a spherical particle having the same value of solution property as that of the macromolecule under consideration. Equivalent radii for different properties present a dependence on size and shape that are more similar than the values of the properties themselves. Furthermore, the ratios of equivalent radii of two properties depend on the conformation (shape or flexibility), but not on the absolute sizes. We define equivalent radii and their ratios, and describe their evaluation for some common models of rigid and flexible macromolecules. Using radii and ratios, we have devised procedures to fit macromolecular models to experimental properties, allowing the determination of the model parameters. Using these quantities, we can construct target functions for an equilibrated, unbiased optimization. The procedures, which have been implemented in public-domain computer programs, are illustrated for rigid, globular proteins, and the rodlike tobacco mosaic virus, and for semiflexible, wormlike heparin molecules.     

Dodecylphosphocholine micelles as a membrane-like environment: new results from NMR relaxation and paramagnetic relaxation enhancement analysis

To further examine to what extent a dodecylphosphocholine (DPC) micelle mimics a phosphatidylcholine bilayer environment, we performed ¹³C, ²H, and ³¹P NMR relaxation measurements. Our data show that the dynamic behavior of DPC phosphocholine groups at low temperature (12 °C) corresponds to that of a phosphatidylcholine interface at high temperature (51 °C). In the presence of helical peptides, a PMP1 fragment, or an annexin fragment, the DPC local dynamics are not affected whereas the DPC aggregation number is increased to match an appropriate area/volume ratio for accommodating the bound peptides. We also show that quantitative measurements of paramagnetic relaxation enhancements induced by small amounts of spin-labeled phospholipids on peptide proton signals provide a meaningful insight on the location of both PMP1 and annexin fragments in DPC micelles. The paramagnetic contributions to the relaxation were extracted from intra-residue cross-peaks of NOESY spectra for both peptides. The location of each peptide in the micelles was found consistent with the corresponding relaxation data. As illustrated by the study of the PMP1 fragment, paramagnetic relaxation data also allow us to supply the missing medium-range NOEs and therefore to complete a standard conformational analysis of peptides in micelles. Received: 16 April 1998 / Revised version: 19 June 1998 / Accepted: 30 July 1998     

Hydration from hydrodynamics. General considerations and applications of bead modelling to globular proteins.

The effect of hydration on hydrodynamic properties of globular proteins can be expressed in terms of two quantities: the delta (g/g) parameter and the thickness of the hydration layer. The two paradigms on hydration that originate these alternative measures are described and compared. For the numerical calculation of hydrodynamic properties, from which estimates of hydration can be made, we employ the bead modelling with atomic resolution implemented in programs HYDROPRO and HYDRONMR. As typical, average values, we find 0.3 g/g and a thickness of only approximately 1.2 A. However, noticeable differences in this parameter are found from one protein to another. We have made a numerical analysis, which leaves apart marginal influences of modelling imperfections by simulating properties of a spherical protein. This analysis confirms that the errors that one can attribute to the experimental quantities suffice to explain the observed fluctuations in the hydration parameters. However, for the main purpose of predicting protein solution properties, the above mentioned typical values may be safely used. Particularly for atomic bead modelling, a hydrodynamic radius of approximately 3.2 A yields predictions in very good agreement with experiments.     

Bead modeling using HYDRO and SOLPRO of the conformation of multisubunit proteins: sunflower and rape-seed 11S globulins

Oil seed globulins from sunflower and rape seed are multi-subunit, oligomeric proteins whose native 11S form is a hexamer. In this work we try to determine the spatial structure in which the six subunits of 11S globulin are arranged. Experimental values of solution properties, including radius of gyration, sedimentation and diffusion coefficients and intrinsic viscosity, are compared with theoretical predictions for hexamers of various geometries. Bead model calculations of solution properties are carried out using the HYDRO and SOLPRO computer programs. A most compact shape, the regular octahedron, is the hexameric structure that fits best the experimental values.     

Diffusion of lipids in supported bilayers as an NMR probe for topological studies in nanoporous solids

The diffusion of lipids in bilayers on curved supports of porous silica beads is studied by deuterium solid state NMR relaxation. We demonstrate that the combination of bilayers coated on curved silica substrates with NMR experiments and simulations which are sensitive to the diffusive motion of the fluid bilayer lipids can provide information about the substrate topology. This provides a new approach for the exploration of the complex internal surface topology of silica gels widely used in biomolecule chromatography. Received: 10 December 1997 / Revised version: 26 January 1998 / Accepted: 4 February 1998     

Murine interleukin-3: structure, dynamics, and conformational heterogeneity in solution

Interleukin-3 (IL-3), a cytokine produced primarily by activated T-cells during immune responses, is a crucial regulator of allergic inflammation. The three-dimensional structure of murine IL-3 (mIL-3) has remained elusive owing to its poor solubility and strong tendency toward aggregation under solution conditions typically used for structural studies. Here we describe the solution properties and structure of mIL-3 determined by NMR using an engineered construct of mIL-3 (mIL-3(33-156)). mIL-3 adopts a four-helical bundle fold, typical of proteins belonging to the short-chain cytokine family, and features a core of highly conserved hydrophobic residues. While significant line broadening and peak disappearance were observed in NMR spectra at higher temperatures, there was no evidence for temperature-dependent changes of the oligomeric state of mIL-3(33-156). Further analysis of the temperature dependence of amide (1)H chemical shifts and backbone (15)N relaxation parameters, including (15)N relaxation dispersion, revealed the presence of significant conformational exchange and local conformational heterogeneity. Residues recently shown by mutagenesis to play key roles in β(IL-3) receptor recognition and activation, which are located within the α(A) and α(C) helices and aligned on one face of the mIL-3(33-156) structure, are relatively rigid. In contrast, pronounced conformational heterogeneity was observed for a cluster of residues located on the opposite side of mIL-3, which corresponds spatially to sites in the related cytokines human IL-3, IL-5, and GM-CSF that are known to mediate interactions with their respective α-receptor subunits. Such conformational heterogeneity may facilitate the interaction of mIL-3 with each of two naturally occurring mIL-3Rα isoforms, leading to structurally distinct high-affinity complexes.     

A mechanism for the establishment of polar cell morphology based on the cytoskeleton-derived forces exerted on the cell boundary

A mechanism for the establishment of polar cell morphology is presented, based on the internal forces that the cytoskeletal structures exert on the cell boundary. Cell shapes are determined by postulating that they correspond to the minimum of the total energy of the system, which is the sum of the bending energy of the cell boundary and the potential energies of the involved forces. Axisymmetrical cell shapes are considered, and it is assumed that the cytoskeletal structures exert an extensional axial force and are involved in controlling the area of the cell boundary. The dependence of cell shapes on the axial force is presented for different values of this area. The results show that, at increasing axial force, the cell undergoes a discontinuous transition from an oval shape, exhibiting an equatorial mirror symmetry into a polar shape. The proposed mechanism is related to previously documented specific effects of microtubule- and actin-modifying drugs on polar shapes of developing isolated retinal photoreceptor cells. Received: 28 January 1998 / Revised version: 25 July 1998 / Accepted: 29 July 1998     

Structure, dynamics, and thermodynamics of the structural domain of troponin C in complex with the regulatory peptide 1-40 of troponin I

The structure of the calcium-saturated C-domain of skeletal troponin C (CTnC) in complex with a regulatory peptide comprising residues 1-40 (Rp40) of troponin I (TnI) was determined using nuclear magnetic resonance (NMR) spectroscopy. The solution structure determined by NMR is similar to the structure of the C-domain from intact TnC in complex with TnI(1)(-)(47) determined by X-ray crystallography [Vassylyev, D. G., Takeda, S., Wakatsuki, S., Maeda, K., and Maeda, Y. (1998) Proc. Natl. Acad. Sci. U.S.A. 95, 4847-4852]. Changes in the dynamic properties of CTnC.2Ca2+ induced by Rp40 binding were investigated using backbone amide (15)N NMR relaxation measurements. Analysis of NMR relaxation data allows for extraction of motional order parameters on a per residue basis, from which the contribution of changes in picosecond to nanosecond time scale motions to the conformational entropy associated with complex formation can be estimated. The results indicate that binding of Rp40 decreases backbone flexibility in CTnC, particularly at the end of the C-terminal helix. The backbone conformational entropy change (-TDeltaS) associated with binding of Rp40 to CTnC.2Ca2+ determined from (15)N relaxation data is 9.6 +/- 0.7 kcal mol(-1) at 30 degrees C. However, estimation of thermodynamic quantities using a structural approach [Lavigne, P., Bagu, J. R., Boyko, R., Willard, L., Holmes, C. F., and Sykes, B. D. (2000) Protein Sci. 9, 252-264] reveals that the change in solvation entropy upon complex formation is dominant and overcomes the thermodynamic "cost" associated with "stiffening" of the protein backbone upon Rp40 binding. Additionally, backbone amide (15)N relaxation data measured at different concentrations of CTnC.2Ca2+.Rp40 reveal that the complex dimerizes in solution. Fitting of the apparent global rotational correlation time as a function of concentration to a monomer-dimer equilibrium yields a dimerization constant of approximately 8.3 mM.     

Refinement of protein structure against non-redundant carbonyl <Superscript>13</Superscript>C NMR relaxation

Carbonyl ¹³C′ relaxation is dominated by the contribution from the ¹³C′ chemical shift anisotropy (CSA). The relaxation rates provide useful and non-redundant structural information in addition to dynamic parameters. It is straightforward to acquire, and offers complimentary structural information to the ¹⁵N relaxation data. Furthermore, the non-axial nature of the ¹³C′ CSA tensor results in a T₁/T₂ value that depends on an additional angular variable even when the diffusion tensor of the protein molecule is axially symmetric. This dependence on an extra degree of freedom provides new geometrical information that is not available from the NH dipolar relaxation. A protocol that incorporates such structural restraints into NMR structure calculation was developed within the program Xplor-NIH. Its application was illustrated with the yeast Fis1 NMR structure. Refinement against the ¹³C′ T₁/T₂ improved the overall quality of the structure, as evaluated by cross-validation against the residual dipolar coupling as well as the ¹⁵N relaxation data. In addition, possible variations of the CSA tensor were addressed. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Light scattering characterization of extruded lipid vesicles

By modeling extruded unilamellar lipid vesicles as thin-walled ellipsoidal shells, mathematical analysis provides simple equations which relate the mean elongation and other morphological characteristics of a vesicle population to quantities readily obtained from combined static and dynamic light scattering measurements. For SOPC vesicles extruded through a 100 nm pore-size filter into a 72.9 mm NaCl solution, the inferred elongation ratio (vesicle long axis to short axis) is approximately 3.7±0.6. When these vesicles were dialyzed into hypertonic or hypotonic solutions, this elongation ratio varied from 1 (for spherical liposomes) in strongly hypotonic solutions to greater than 6 in increasingly hypertonic solutions, beyond which abrupt morphological transformations appear. These results are quantitatively consistent with a mechanism of vesicle formation by extrusion and with the expectation that vesicle volumes change to equalize internal and external osmolarity via water flow, subject to the constraint of constant bilayer area. Our analysis also provides simplified equations to assess the effects of vesicle elongation and polydispersity on liposome parameters that are commonly required to characterize vesicle preparations for diverse applications. The implications of this study for routine light scattering characterization of extruded vesicles are discussed. Received: 31 July 1998 / Revised version: 26 October 1998 / Accepted: 5 November 1998     

A model actin comet tail disassembling by severing

We use a numerical simulation to model an actin comet tail as it grows from the surface of a small object (a bead) and disassembles by severing. We explore the dependence of macroscopic properties such as the local tail radius and tail length on several controllable properties, namely the bead diameter, the bead velocity, the severing rate per unit length, and the actin gel mesh size. The model predicts an F-actin density with an initial exponential decay followed by an abrupt decay at the edge of the tail, and predicts that the comet tail diameter is constant along the length of the tail. The simulation results are used to fit a formula relating the comet tail length to the control parameters, and it is proposed that this formula offers a means to extract quantitative information on the actin gel mesh size and severing kinetics from simple macroscopic measurements.     

Hydrodynamic properties of rigid macromolecules composed of ellipsoidal and cylindrical subunits.

A procedure is devised for the calculation of hydrodynamic properties of rigid macromolecules composed subunits that are modeled as ellipsoids of revolution and cylinders. Owing to the axial symmetry of these shapes, smooth shell models can be constructured for the subunit structure. The bead shell model so constructed is employed for the calculation of the properties. A computer program, HYDROSUB, has been written implementing both the model building and the hydrodynamic calculation. A detailed example of the use of this methodology is presented for the case of the solution properties of the human antibody molecule immunoglobulin G3 (IgG3). Finally, hints are given on other uses and applications of the procedure.     

Hydrodynamic properties of rigid particles: comparison of different modeling and computational procedures.

The hydrodynamic properties of rigid particles are calculated from models composed of spherical elements (beads) using theories developed by Kirkwood, Bloomfield, and their coworkers. Bead models have usually been built in such a way that the beads fill the volume occupied by the particles. Sometimes the beads are few and of varying sizes (bead models in the strict sense), and other times there are many small beads (filling models). Because hydrodynamic friction takes place at the molecular surface, another possibility is to use shell models, as originally proposed by Bloomfield. In this work, we have developed procedures to build models of the various kinds, and we describe the theory and methods for calculating their hydrodynamic properties, including approximate methods that may be needed to treat models with a very large number of elements. By combining the various possibilities of model building and hydrodynamic calculation, several strategies can be designed. We have made a quantitative comparison of the performance of the various strategies by applying them to some test cases, for which the properties are known a priori. We provide guidelines and computational tools for bead modeling.     

Hyaluronan chain conformation and dynamics

An overview of the present state of research in the field of hyaluronan chain conformational aspects is presented. The relationship between structure and dynamics are illustrated for a series of hyaluronan oligomers. Conformational characteristics of hyaluronan chains are discussed, together with the dynamic chain patterns, evaluated by using a theoretical approach to diffusive polymer dynamics. The dependence of correlation times and NMR relaxation parameters from the chain dimension are investigated. Topological features and dimensional properties are related to the structural determinants by using classical computational methods of molecular mechanics and Monte Carlo simulation.     

Choice of Force Field for Proteins Containing Structured and Intrinsically Disordered Regions

Biomolecular force fields optimized for globular proteins fail to properly reproduce properties of intrinsically disordered proteins. In particular, parameters of the water model need to be modified to improve applicability of the force fields to both ordered and disordered proteins. Here, we compared performance of force fields recommended for intrinsically disordered proteins in molecular dynamics simulations of three proteins differing in the content of ordered and disordered regions (two proteins consisting of a well-structured domain and of a disordered region with and without a transient helical motif and one disordered protein containing a region of increased helical propensity). The obtained molecular dynamics trajectories were used to predict measurable parameters, including radii of gyration of the proteins and chemical shifts, residual dipolar couplings, paramagnetic relaxation enhancement, and NMR relaxation data of their individual residues. The predicted quantities were compared with experimental data obtained within this study or published previously. The results showed that the NMR relaxation parameters, rarely used for benchmarking, are particularly sensitive to the choice of force-field parameters, especially those defining the water model. Interestingly, the TIP3P water model, leading to an artificial structural collapse, also resulted in unrealistic relaxation properties. The TIP4P-D water model, combined with three biomolecular force-field parameters for the protein part, significantly improved reliability of the simulations. Additional analysis revealed only one particular force field capable of retaining the transient helical motif observed in NMR experiments. The benchmarking protocol used in our study, being more sensitive to imperfections than the commonly used tests, is well suited to evaluate the performance of newly developed force fields.     

Use of the indirect immunofluorescence method for the comparative analysis of histones

With the help of indirect immunofluorescence on the model systems--a ploid line of wheat, haploid and diploid cells of Chlamydomonas reinhardii, glass beads with adsorbed histones--a study was made of the dependence of ultimate dilutions (UD) of antihistone sera on the quantity, density and immunochemical properties of histones--antigens. The UD value in the artificial model system (glass beads) increased with the rise in the quantity and density of histones on bead to some definite limits, and then the UD remains constant to be determined only by the titre of antiserum. In natural model system (wheat, Chlamydomonas reinhardii), with the rise in quantities of DNA and histones in the nucleus their densities remain constant, with no changes of UD values being observed. The results obtained are discussed in terms of establishing the dependence of UD on immunochemical properties of histones-antigens. Thus, the method of indirect immunofluorescence may be used for comparative analysis of immunochemical properties of histones in various objects.     

A general pre-steady-state solution to complex kinetic mechanisms

We have developed a general method for solving transient kinetic equations using Laplace transforms. Laplace transforms can be used to transform systems of differential equations that describe pre-steady-state kinetics to systems of linear algebraic equations. The general form of the pre-steady-state solution is (formula; see text) where I(t) is the time dependence of the physically observed property of the system, n is the number of intermediates, lambda i are the observed rate constants (reciprocals of the relaxation times), t is time, and Ii are the amplitude coefficients associated with each observed rate constant. We have written a program in compiled BASIC to run on a personal computer to evaluate Ii and lambda i. The program will evaluate the rate constants and coefficients of a mechanism with eight intermediates and seven relaxation times in 4 s on an 8-MHz PC-XT equipped with a math coprocessor. The most complex mechanism that we have solved, a mechanism containing 20 intermediates and 19 relaxation times, required approximately 5 min. We believe that this method will be useful to evaluate the differences in transient properties of complex biochemical mechanisms.     

Preparation of encapsulated proteins dissolved in low viscosity fluids

The majority of proteins are too large to be comprehensively examined by solution NMR methods, primarily because they tumble too slowly in solution. One potential approach to making the NMR relaxation properties of large proteins amenable to modern solution NMR techniques is to encapsulate them in a reverse micelle which is dissolved in a low viscosity fluid. Unfortunately, promising low viscosity fluids such as the short chain alkanes, supercritical carbon dioxide, and various halocarbon refrigerants all require the application of significant pressure to be kept liquefied at room temperature. Here we describe the design and use of a simple cost effective NMR tube suitable for the preparation of solutions of proteins encapsulated in reverse micelles dissolved in such fluids.