On the hydrodynamic analysis of macromolecular conformation

Hydrodynamics provides a powerful complementary role to the traditional "high resolution" techniques for the investigation of macromolecular conformation, especially in dilute solution, conditions which are generally inaccessible to other structural techniques. This paper describes the state of art of hydrodynamic representations for macromolecular conformation, in terms of (1) simple but straightforward ellipsoid of revolution modelling; (2) general triaxial ellipsoid modelling; (3) hydrodynamic bead modelling; (4) the ability, especially for polydisperse macromolecular systems, to distinguish between various conformation types; (5) analysis of macromolecular flexibility.     

Calculation of hydrodynamic properties of macromolecular bead models with overlapping spheres

For the calculation of hydrodynamic properties of rigid macromolecules using bead modelling, models with overlapping beads of different sizes are used in some applications. The hydrodynamic interaction tensor between unequal overlapping beads is unknown, and an oversimplified treatment with the Oseen tensor may introduce important errors. Here we discuss some aspects of the overlapping problem, and explore an ad hoc form of the interaction tensor, proposed by Zipper and Durchschlag. We carry out a systematic numerical study of the hydrodynamic properties of a two-spheres model, showing how the Zipper-Durchschlag correction removes efficiently the numerical instabilities, and predicts the correct limits. Received: 15 February 1999 / Revised version: 29 April 1999 / Accepted: 11 May 1999     

Recent advances in macromolecular hydrodynamic modeling

The modern implementation of the boundary element method [23] has ushered unprecedented accuracy and precision for the solution of the Stokes equations of hydrodynamics with stick boundary conditions. This article begins by reviewing computations with the program BEST of smooth surface objects such as ellipsoids, the dumbbell, and cylinders that demonstrate that the numerical solution of the integral equation formulation of hydrodynamics yields very high precision and accuracy. When BEST is used for macromolecular computations, the limiting factor becomes the definition of the molecular hydrodynamic surface and the implied effective solvation of the molecular surface. Studies on 49 different proteins, ranging in molecular weight from 9 to over 400kDa, have shown that a model using a 1.1? thick hydration layer describes all protein transport properties very well for the overwhelming majority of them. In addition, this data implies that the crystal structure is an excellent representation of the average solution structure for most of them. In order to investigate the origin of a handful of significant discrepancies in some multimeric proteins (about -20% observed in the intrinsic viscosity), the technique of Molecular Dynamics simulation (MD) has been incorporated into the research program. A preliminary study of dimeric α-chymotrypsin using approximate implicit water MD is presented. In addition I describe the successful validation of modern protein force fields, ff03 and ff99SB, for the accurate computation of solution structure in explicit water simulation by comparison of trajectory ensemble average computed transport properties with experimental measurements. This work includes small proteins such as lysozyme, ribonuclease and ubiquitin using trajectories around 10ns duration. We have also studied a 150kDa flexible monoclonal IgG antibody, Trastuzumab, with multiple independent trajectories encompassing over 320ns of simulation. The close agreement within experimental error of the computed and measured properties allows us to conclude that MD does produce structures typical of those in solution, and that flexible molecules can be properly described using the method of ensemble averaging over a trajectory. We review similar work on the study of a transfer RNA molecule and DNA oligomers that demonstrate that within 3% a simple uniform hydration model 1.1? thick provides agreement with experiment for these nucleic acids. In the case of linear oligomers, the precision can be improved close to 1% by a non-uniform hydration model that hydrates mainly in the DNA grooves, in agreement with high resolution X-ray diffraction. We conclude with a vista on planned improvements for the BEST program to decrease its memory requirements and increase its speed without sacrificing accuracy.     

Numerical and exact solutions for continuum of alleles models

 Two results are presented for problems involving alleles with a continuous range of effects. The first result is a simple yet highly accurate numerical method that determines the equilibrium distribution of allelic effects, moments of this distribution, and the mutational load. The numerical method is explicitly applied to the mutation-selection balance problem of stabilising selection. The second result is an exact solution for the distribution of allelic effects under weak stabilising selection for a particular distribution of mutant effects. The exact solution is shown to yield a distribution of allelic effects that, depending on the mutation rate, interpolates between the ``House of Cards' approximation and the Gaussian approximation. The exact solution is also used to test the accuracy of the numerical method. Received: 7 November 2001 / Revised version: 5 September 2002 / Published online: 18 December 2002 Key words or phrases: Continuum of alleles – Numerical solution – Exact solution – Mutation selection balance – Stabilising selection     

Conformation of heparin studied with macromolecular hydrodynamic methods and X-ray scattering

The hydrodynamic characteristics of heparin fractions in a 0.2 M NaCl solution have been determined. Experimental values varied over the following ranges: the sedimentation coefficient (at 20.0 °C), 1.3<s₀×10¹³<3.2 s; the Gralen coefficient (sedimentation concentration-dependence parameter), 10<k_s<70 cm³ g^–1; the translational diffusion coefficient, 3.9<D₀×10⁷<15.4 cm² s^–1; the intrinsic viscosity, 7.9<[]<40 cm³ g^–1. Combination of s₀ with D₀ using the Svedberg equation yielded molecular weights in the range 3.9<M×10^–3<37 g mol^–1. The value of the mass per unit length of the heparin molecule, M_L, was determined using the theory of hydrodynamic properties of a weakly bending rod, giving M_L=570±50 g nm^–1 mol^–1. The equilibrium rigidity, Kuhn segment length (A=9±2 nm) and hydrodynamic diameter (d=0.9±0.1 nm) of heparin were evaluated on the basis of the worm-like coil theory without the excluded volume effect, using the combination of hydrodynamic data obtained from fractions of different sizes. Small-angle X-ray scattering for three heparin fractions allowed an estimate for the cross-sectional radius of gyration as 0.43 nm; from the evolution with the macromolecule contour length of the radius of gyration, a value for the Kuhn segment length of 9±1 nm was obtained. A good correlation is thus observed for the conformational parameters of heparin from hydrodynamic and X-ray scattering data. These values describe heparin as a semi-rigid polymer, with an equilibrium rigidity that is essentially determined by a structural component, the electrostatic contribution being negligible in 0.2 M NaCl.Presented at the conference for Advances in Analytical Ultracentrifugation and Hydrodynamics, 8–11 June 2002, Grenoble, France     

Analysis of conformational variation in macromolecular structural models

Experimental conditions or the presence of interacting components can lead to variations in the structural models of macromolecules. However, the role of these factors in conformational selection is often omitted by in silico methods to extract dynamic information from protein structural models. Structures of small peptides, considered building blocks for larger macromolecular structural models, can substantially differ in the context of a larger protein. This limitation is more evident in the case of modeling large multi-subunit macromolecular complexes using structures of the individual protein components. Here we report an analysis of variations in structural models of proteins with high sequence similarity. These models were analyzed for sequence features of the protein, the role of scaffolding segments including interacting proteins or affinity tags and the chemical components in the experimental conditions. Conformational features in these structural models could be rationalized by conformational selection events, perhaps induced by experimental conditions. This analysis was performed on a non-redundant dataset of protein structures from different SCOP classes. The sequence-conformation correlations that we note here suggest additional features that could be incorporated by in silico methods to extract dynamic information from protein structural models.     

构建一种精确表达小分子蛋白的技术平台

目的:克服原核表达的小分子蛋白难以去除附加氨基酸的问题,为基因工程精确表达小分子蛋白提供一种简便有效的解决方案.方法:以73个氨基酸的小分子蛋白(黑色素瘤生长激活因子CXCL1的功能区)为例,用PCR方法扩增了基因,TA克隆到载体PET SUMO.测序验证后的重组质粒转化至表达茵BL21(DE3)中诱导表达,融合蛋白用基质辅助解吸电离飞行时间质谱仪进行串联质谱鉴定(MALDI-TOF-MS/MS).通过特异性的SUMO蛋白酶酶解载体SUMO蛋白,利用SUMO蛋白和其蛋白酶带6x His标签的性质,经镍螯合柱亲和层析将二者去除,以Western blotting证明目的小分子蛋白的分离.结果:①经测序,重组质粒无突变,TA克隆方向正确,重组载体构建成功.②MALDI-TOF-MS/MS证明融合蛋白由SUMO蛋白和CXCLl蛋白组成,除去SUMO蛋白后的表达终产物经Westem blotting鉴定,与其相应的抗体有特异性结合,证明分离得到的小分子蛋白即为目的蛋白.结论:运用这一技术可将载体蛋白完全去除从而达到精确表达小分子蛋白的目的,在分子生物学的实验研究中有很好的应用前景.     

Building hydrodynamic bead-shell models for rigid bioparticles of arbitrary shape.

The calculation of hydrodynamic and other solution properties of rigid macromolecules, using bead-shell model methodologies, requires the specification of the macromolecular shape in a format that can be interfaced with existing programs for hydrodynamic computations. Here, a procedure is presented for such a structural specification that is applicable to arbitrarily shaped particles. A computer program (MAKEPIXB), in which the user inserts the code needed to determine the structure, produces an structural file that is interpreted by another program (HYDROPIX) which is in charge of the computation of properties. As simple and yet illustrative examples we consider two cases: (1) dimeric structures composed of ellipsoidal subunits; and (2) toroidal structures, presenting simple equations that predict the properties of toroids with varying radial ratios.     

Perspectives on protein evolution from simple exact models

Understanding the evolution of biopolymers is important to rationalise the directed and undirected design of functional molecules. Large scale experiments or detailed computational studies are often impractical. Therefore, simple model systems, such as RNA secondary structure and lattice proteins have been adapted to study general statistical and topological features of genotype (sequence) to phenotype (structure) maps. We review findings from such models that address aspects of thermodynamic and mutational robustness, neutral evolution and recombination of proteins. We compare various modelling approaches, and discuss their generality, parameter dependency and experimental verifications of their predictions. The most striking observation is the universal emergence of neutral nets--sets of phenotypically identical genotypes that are interconnected by series of point mutations. However, fast adaptation by point mutations appears to be problematic for proteins. This may explain why proteins appear to be more specific while RNA is rather versatile. This could even be the reason why RNA had to evolve before proteins. Similar principles of biological organisation are reflected in sequence and structure databases of real proteins. Insights gained from modelling are useful for designing more efficient database organisation and search strategies.     

Some selection models in catalytically coupled selfreproducing macromolecular systems

Some models for selection in enzyme coupled, selfreproducing, macromolecular systems are considered. The enzyme coupling provides a mechanism for the buildup of systems with large information content. The concept of “selective value” and criteria for selection is discussed.     

Time-dependent propagators for stochastic models of gene expression: an analytical method

The inherent stochasticity of gene expression in the context of regulatory networks profoundly influences the dynamics of the involved species. Mathematically speaking, the propagators which describe the evolution of such networks in time are typically defined as solutions of the corresponding chemical master equation (CME). However, it is not possible in general to obtain exact solutions to the CME in closed form, which is due largely to its high dimensionality. In the present article, we propose an analytical method for the efficient approximation of these propagators. We illustrate our method on the basis of two categories of stochastic models for gene expression that have been discussed in the literature. The requisite procedure consists of three steps: a probability-generating function is introduced which transforms the CME into (a system of) partial differential equations (PDEs); application of the method of characteristics then yields (a system of) ordinary differential equations (ODEs) which can be solved using dynamical systems techniques, giving closed-form expressions for the generating function; finally, propagator probabilities can be reconstructed numerically from these expressions via the Cauchy integral formula. The resulting ‘library’ of propagators lends itself naturally to implementation in a Bayesian parameter inference scheme, and can be generalised systematically to related categories of stochastic models beyond the ones considered here.

     

HYDROMIC: prediction of hydrodynamic properties of rigid macromolecular structures obtained from electron microscopy images

We have developed a procedure for the prediction of hydrodynamic coefficients and other solution properties of macromolecules and macromolecular complexes whose volumes have been generated from electron microscopy images. Starting from the structural files generated in the three-dimensional reconstructions of such molecules, it is possible to construct a hydrodynamic model for which the solution properties can be calculated. We have written a computer program, HYDROMIC, that implements all the stages of the calculation. The use of this procedure is illustrated with a calculation of the solution properties of the volume of the cytosolic chaperonin CCT, obtained from cryoelectron microscopy images.     

Rigid-cluster models of conformational transitions in macromolecular machines and assemblies

We present a rigid-body-based technique (called rigid-cluster elastic network interpolation) to generate feasible transition pathways between two distinct conformations of a macromolecular assembly. Many biological molecules and assemblies consist of domains which act more or less as rigid bodies during large conformational changes. These collective motions are thought to be strongly related with the functions of a system. This fact encourages us to simply model a macromolecule or assembly as a set of rigid bodies which are interconnected with distance constraints. In previous articles, we developed coarse-grained elastic network interpolation (ENI) in which, for example, only Calpha atoms are selected as representatives in each residue of a protein. We interpolate distance differences of two conformations in ENI by using a simple quadratic cost function, and the feasible conformations are generated without steric conflicts. Rigid-cluster interpolation is an extension of the ENI method with rigid-clusters replacing point masses. Now the intermediate conformations in an anharmonic pathway can be determined by the translational and rotational displacements of large clusters in such a way that distance constraints are observed. We present the derivation of the rigid-cluster model and apply it to a variety of macromolecular assemblies. Rigid-cluster ENI is then modified for a hybrid model represented by a mixture of rigid clusters and point masses. Simulation results show that both rigid-cluster and hybrid ENI methods generate sterically feasible pathways of large systems in a very short time. For example, the HK97 virus capsid is an icosahedral symmetric assembly composed of 60 identical asymmetric units. Its original Hessian matrix size for a Calpha coarse-grained model is >(300,000)(2). However, it reduces to (84)(2) when we apply the rigid-cluster model with icosahedral symmetry constraints. The computational cost of the interpolation no longer scales heavily with the size of structures; instead, it depends strongly on the minimal number of rigid clusters into which the system can be decomposed.     

ISPyB: an information management system for synchrotron macromolecular crystallography

MOTIVATION: Individual research groups now analyze thousands of samples per year at synchrotron macromolecular crystallography (MX) resources. The efficient management of experimental data is thus essential if the best possible experiments are to be performed and the best possible data used in downstream processes in structure determination pipelines. Information System for Protein crystallography Beamlines (ISPyB), a Laboratory Information Management System (LIMS) with an underlying data model allowing for the integration of analyses down-stream of the data collection experiment was developed to facilitate such data management. RESULTS: ISPyB is now a multisite, generic LIMS for synchrotron-based MX experiments. Its initial functionality has been enhanced to include improved sample tracking and reporting of experimental protocols, the direct ranking of the diffraction characteristics of individual samples and the archiving of raw data and results from ancillary experiments and post-experiment data processing protocols. This latter feature paves the way for ISPyB to play a central role in future macromolecular structure solution pipelines and validates the application of the approach used in ISPyB to other experimental techniques, such as biological solution Small Angle X-ray Scattering and spectroscopy, which have similar sample tracking and data handling requirements.