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     

Hydrodynamic characteristics of immobilized cell beads in a liquid-solid fluidized-bed bioreactor

This study examined the hydrodynamic characteristics of a liquid-solid fluidized-bed bioreactor using elastic particles (PVA gel beads) of various diameters as carriers. The drag coefficient-Reynolds number, velocity-voidage, and expansion index-Reynolds number relationships observed during fluidization of PVA gel beads in a fluidized bed in our experiments were compared with the published results. Predictions made from previous correlations were examined with our new experimental findings, revealing the inadequacy of most of these correlations. Thus, new correlations describing the above-mentioned relationships are suggested. The drag coefficient of immobilized cell beads is larger than that of free cell ones at the same Reynolds number because the surface of the immobilized cell beads is rougher. For multiparticle systems, the correction factor, f(epsilon), is a function of the falling gel bead properties (Reynolds number) as well as the fluidized gel bead properties (Archimedes number), and depend strongly on the bed voidage (epsilon). A new simple relation was developed to predict easily the epsilon value from 0.5-0.9 at 4,986 < A(r) < 40,745 or 34 < Re(t) < 186. For all the immobilized cell beads used in this study, the prediction error of the bed voidage was less than 5% at epsilon > 0.5. The prediction equations in this study can be further applied to analyzing the hydrodynamic characteristics of a fluidized-bed reactor using similar entrapped elastic particles as carriers.     

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     

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.     

Chromatin conformation: a systematic analysis of helical parameters from hydrodynamic data

Chromatin has a “bead-and-bridge” appearance when viewed by electron microscopy. We have used quasielastic light scattering and sedimentation velocity techniques to study the hydrodynamic properties of chicken erythrocyte chromatin multimers in an attempt to determine the superstructure in solution. The functional dependence of the friction factor on the number of core particles in the multimer was analyzed by the Garcia de la Torre-Bloomfield formalism for a rigid array of odd-sized beads. The hydrodynamic parameters of the monomeric and dimeric subunit components, i.e., bead size and separation, form the basis of a systematic determination of the superstructure. These calculations support a helical conformation for chromatin multimers containing up to twenty repeat units. It is also shown that an “equivalent” helix can be obtained if the bead separation distance is not constrained to that determined for the dimer.     

Prediction of hydrodynamic and other solution properties of rigid proteins from atomic- and residue-level models

Here we extend the ability to predict hydrodynamic coefficients and other solution properties of rigid macromolecular structures from atomic-level structures, implemented in the computer program HYDROPRO, to models with lower, residue-level resolution. Whereas in the former case there is one bead per nonhydrogen atom, the latter contains one bead per amino acid (or nucleotide) residue, thus allowing calculations when atomic resolution is not available or coarse-grained models are preferred. We parameterized the effective hydrodynamic radius of the elements in the atomic- and residue-level models using a very large set of experimental data for translational and rotational coefficients (intrinsic viscosity and radius of gyration) for >50 proteins. We also extended the calculations to very large proteins and macromolecular complexes, such as the whole 70S ribosome. We show that with proper parameterization, the two levels of resolution yield similar and rather good agreement with experimental data. The new version of HYDROPRO, in addition to considering various computational and modeling schemes, is far more efficient computationally and can be handled with the use of a graphical interface.     

A new dimension in retrograde flow: centripetal movement of engulfed particles

Centripetal motion of surface-adherent particles is a classic experimental system for studying surface dynamics on a eukaryotic cell. To investigate bead migration over the entire cell surface, we have developed an experimental assay using multinuclear giant fibroblasts, which provide expanded length scales and an unambiguous frame of reference. Beads coated by adhesion ligands concanavalin A or fibronectin are placed in specific locations on the cell using optical tweezers, and their subsequent motion is tracked over time. The adhesion, as well as velocity and directionality of their movement, expose distinct regions of the cytoplasm and membrane. Beads placed on the peripheral lamella initiate centripetal motion, whereas beads placed on the central part of the cell attach to a stationary cortex and do not move. Careful examination by complementary three-dimensional methods shows that the motion of a bead placed on the cell periphery takes place after engulfment into the cytoplasm, whereas stationary beads, placed near the cell center, are not engulfed. These results demonstrate that centripetal motion of adhering particles may occur inside as well as outside the cell. Inhibition of actomyosin activity is used to explore requirements for engulfment and aspects of the bead movement. Centripetal movement of adherent particles seems to depend on mechanisms distinct from those driving overall cell contractility.     

Calculation of NMR relaxation, covolume, and scattering-related properties of bead models using the SOLPRO computer program

The hydrodynamic properties of macromolecules and bioparticles, represented by bead models, can be calculated using methods implemented in the computer routine HYDRO. Recently, a new computer routine, SOLPRO, has been presented for the calculation of various SOLution PROperties. These include (1) time-dependent electro-optic and spectroscopic properties related to rotational diffusion, (2) non-dynamic properties like scattering curves, and (3) dimensionless quantities that combine two or more solution properties in a form which depends on the shape of the macromolecule but not on its size. In the present work we describe the inclusion of more of those types of properties in a new version of SOLPRO. Particularly, we describe the calculation of relaxation rates in nuclear magnetic resonance (NMR). For dipolar coupling, given the direction of the dipole the program calculates values of the spectral density, from which the NMR relaxation times can be obtained. We also consider scattering-related properties, namely the distribution of distances for the bead model, which is directly related to the angular dependence of scattered intensity, and the particle's longest distance. We have devised and programmed a procedure to calculate the covolume of the bead model, related to the second virial coefficient and, in general, to the concentration dependence of solution properties. Various shape-dependent dimensionless quantities involving the covolume are calculated. In this paper we also discuss some aspects, namely bead overlapping and hydration, that are not explicitely included in SOLPRO, but should be considered by the user. Received: 25 May 1998 / Revised version: 30 July 1998 / Accepted: 30 July 1998     

Incorporating fluorescent dyes and quantum dots into magnetic microbeads for immunoassays

Microbeads that are both paramagnetic and fluorescently labeled are commercially available in colors spanning the visible spectrum. Although these commercial beads can be bright, polydispersity in both size and fluorescent intensity limit their use in quantitative assays. Very recently, more monodisperse beads have become available, but their large size and surface properties make them less than ideal for some bioassay applications. Here we describe methods to customize commercial nonfluorescent magnetic microparticles with fluorescent dyes and quantum dots (QDs) without affecting their magnetic or surface chemical properties. Fluorescent dyes and 3.3-nm diameter CdSe/ZnS QDs were sequestered within 0.8-micron diameter magnetic beads by swelling the polystyrene matrix of the bead in organic solvent, letting the chromophores partition, and then collapsing the matrix in polar solvents. Chromophore incorporation has been characterized using both UV-visible absorption spectroscopy and fluorescence microscopy, with an average of 3 x 10(8) rhodamine 6G molecules/bead and 6 x 10(4) QDs/bead. The modified beads are uniform in size and intensity, with optical properties comparable to currently available commercial beads. Immunoassay results obtained with our custom fluorescent magnetic microbeads are consistent with those obtained using conventional magnetic microbeads.     

Relevance of rheological properties of gel beads for their mechanical stability in bioreactors

The mechanical stability of biocatalyst particles in bioreactors is of crucial importance for applications of immobilized-cell technology in bioconversions. The common methods for evaluation of the strength of polymer beads (mostly force-to-fracture or tensile tests) are, however, not yet proven to be relevant for the assessment of their mechanical stability in bioreactors. Therefore, we tested fracture properties of gel materials and investigated their relevance for abrasion in bioreactors. Abrasion of gel beads was assumed to be a continuous fracturing of the bead surface. At first, three rheological properties were considered: stress at fracture; strain at fracture; and the total fracture energy. If stress at fracture is the most important property, beads having a similar fracture energy, but a smaller stress at fracture, would abrade faster in a bioreactor than beads with a larger stress at fracture; if fracture energy the determining factor, beads that require less energy to fracture would abrade faster than those having a larger fracture energy for the same fracture stress. To determine this, beads of kappa-carrageenan and agar (at two different polymer concentrations) were tested for abrasion in four identical bubble columns under the same operating conditions. Agar beads were expected to abrade faster than those of carrageenan because agar had either a lower stress at fracture or a lower fracture energy. However, no correlation between fracture properties and abrasion rate was found in any of the combinations tested. Carrageenan beads abraded faster than those of agar in all combinations. Furthermore, both the stress and strain at fracture of agar and carrageenan beads decreased during the run and those of carrageenan decreased faster, suggesting that the gels are liable to fatigue in different ways. This hypothesis was confirmed by oscillating experiments in which gel samples were subjected to repeated compressions below their fracture levels. Their resistance to compression clearly decreased with the number of oscillations. Fatigue is probably related to the development of microcracks and microfracture propagation within the material. We concluded that: (a) the use of tests based on bead rupture do not provide relevant information on the mechanical stability of gel beads to abrasion; and (b) abrasion of polymer beads is likely to be related to fatigue of the gel materials. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 517-529, 1997.     

Differential adhesion of microspheres mediated by DNA hybridization I: experiment

We have developed a novel method to study collective behavior of multiple hybridized DNA chains by measuring the adhesion of DNA-coated micron-scale beads under hydrodynamic flow. Beads coated with single-stranded DNA probes are linked to surfaces coated with single target strands through DNA hybridization, and hydrodynamic shear forces are used to discriminate between strongly and weakly bound beads. The adhesiveness of microspheres depends on the strength of interaction between DNA chains on the bead and substrate surfaces, which is a function of the degree of DNA chain overlap, the fidelity of the match between hybridizing pairs, and other factors that affect the hybridization energy, such as the salt concentration in the hybridization buffer. The force for bead detachment is linearly proportional to the degree of chain overlap. There is a detectable drop in adhesion strength when there is a single base mismatch in one of the hybridizing chains. The effect of single nucleotide mismatch was tested with two different strand chemistries, with mutations placed at several different locations. All mutations were detectable, but there was no comprehensive rule relating the drop in adhesive strength to the location of the defect. Since adhesiveness can be coupled to the strength of overlap, the method holds promise to be a novel methodology for oligonucleotide detection.     

Engineering lipobeads: properties of the hydrogel core and the lipid bilayer shell

We previously reported on a novel system termed Lipobead that consists of hydrogel beads encased within an anchored lipid bilayer. The hydrogel particles are formed by inverse suspension polymerization of dimethylacrylamide with N,N'-ethylenebis(acrylamide). During the polymerization stage, the water in oil emulsion is interfacially stabilized by small molecule surfactants as well as a small percentage of lipid functionalized with a vinyl group. The functionalized lipid becomes tethered to the bead surface and promotes the assembly of a lipid bilayer on the surface of the hydrogel beads. The presence of the functionalized lipid during polymerization dramatically alters the yield, average size, and size distribution of beads produced. This paper examines the effect of various chemical and physical processing parameters on the average size and size distribution of beads produced when lipid is a component of the surfactant mixture. Relationships between the processing parameters, average bead size, and size distribution were established. Macroscopic properties of the lipid bilayers of Lipobeads were also evaluated including phase transition temperature as well as permeability to the small polar molecule, adenosine triphosphate. It was established that the presence of functionalized lipid improves the organization of the bilayer on the Lipobead surface.     

Simulation of the conformation and dynamics of a double-helical model for DNA

We propose a partially flexible, double-helical model for describing the conformational and dynamic properties of DNA. In this model, each nucleotide is represented by one element (bead), and the known geometrical features of the double helix are incorporated in the equilibrium conformation. Each bead is connected to a few neighbor beads in both strands by means of stiff springs that maintain the connectivity but still allow for some extent of flexibility and internal motion. We have used Brownian dynamics simulation to sample the conformational space and monitor the overall and internal dynamics of short DNA pieces, with up to 20 basepairs. From Brownian trajectories, we calculate the dimensions of the helix and estimate its persistence length. We obtain translational diffusion coefficient and various rotational relaxation times, including both overall rotation and internal motion. Although we have not carried out a detailed parameterization of the model, the calculated properties agree rather well with experimental data available for those oligomers.     

Scaling behaviour of different polymer models in dissipative particle dynamics of unentangled melts

We present a dissipative particle dynamics (DPD) study of scaling behaviour for three polymer models. The scaling behaviour is explored for the conformational and dynamic properties of unentangled polymer melts. DPD employs a bead–spring model together with an aggressive coarse-graining to represent polymers at the mesoscale. The first model studied utilises a simple soft repulsion potential for the bead–bead interactions together with a harmonic spring potential to connect beads into a polymer chain. The second model differs from the first model by replacing the harmonic spring with a finitely extensible nonlinear elastic spring. The third model uses realistic coarse-grain potentials for the bead–bead, spring and bending interactions based on the iterative Boltzmann inversion procedure and it corresponds to a mesoscopic model of polyethylene. We systematically vary the chain length and spring constant (in the case of the first and second models), and simulate the conformational properties such as the end-to-end distance or radius of gyration, and dynamic properties such as the centre-of-mass self-diffusion coefficient or viscosity. The scaling of the conformational and dynamic properties with chain length (scaling laws) is compared with the Rouse theory, which is considered as a standard theory for unentangled polymer melts. The comparison shows that simulated scaling laws typically agree with the Rouse scaling laws for the DPD polymer models with more than 10 DPD beads. For the shorter DPD polymers, deviations from the Rouse theory exist and become significant for the dynamic properties, especially for the viscosity of the polymer melts.     

A Convenient Approach to Prepare Topologically Segregated Bilayer Beads for One-Bead Two-Compound Combinatorial Peptide Libraries

One-bead one-compound (OBOC) combinatorial peptide libraries have been used to identify ligands and modulators for a wide variety of biological targets. While being very efficient with linear peptides, OBOC libraries with N-terminally blocked peptides or with unsequenceable building blocks require encoding. To fully exploit OBOC combinatorial methods with cyclic peptides and peptidomimetics, topologically segregated bilayer beads have been developed. This strategy offers the opportunity to synthesize two compounds per bead, i.e. with one compound exposed on the bead surface for screening, and the other one found within the inner layer as a tag for sequencing and compound identification. Bead segregation often involves the use of unstable derivatives or requires a series of protection–deprotection steps. In order to expedite and optimize bead segregation, the performance of various reagents has been studied. The results obtained herein show that bead segregation can be efficiently performed with commercially available reagents. Finally, in order to control outer/inner layer ratios in segregated beads, the effects of different parameters have been evaluated. We report a straightforward and efficient procedure to prepare topologically segregated bilayer beads in a wide range of controllable, predictable, and reproducible outer versus inner ratios.     

Latex beads as probes of a neural crest pathway: effects of laminin, collagen, and surface charge on bead translocation

In the trunk region of avian embryos, neural crest cells migrate along two pathways: dorsally just under the ectoderm, and ventrally between the neural tube and the somites. Previous work from this laboratory has shown that uncoated latex beads are able to translocate along the ventral neural crest pathway after injection into young embryos; however, beads coated with fibronectin are restricted from the ventral route ( Bronner -Fraser, M.E., 1982, Dev. Biol., 91: 50-63). Here, we extend these observations to determine the effects of other macromolecules on bead distribution. The data show that laminin-coated beads, like fibronectin-coated beads, are restricted from the ventral pathway. In contrast, beads coated with type I collagen translocate ventrally after injection. Because macromolecules have characteristic charge properties, changes in surface charge caused by coating the beads may confound interpretation of the results. Electrostatic effects on bead movement were examined by coating the latex beads with polyamino acids in order to predictably alter the initial surface charge. The surface charge before injection was measured for beads coated with amino acid polymers or with various biologically important macromolecules; the subsequent translocation ability of these beads was then monitored in the embryo. Polylysine-coated beads (positively charged) were restricted from the ventral pathway as were fibronectin and laminin-coated beads, even though fibronectin and laminin beads were both negatively charged. In contrast, polytyrosine -coated beads ( neutrally charged) translocated ventrally as did negatively charged collagen-coated or uncoated beads. The results demonstrate that no correlation exists between the charge properties on the latex bead surface and their subsequent ability to translocate along the ventral pathway. Therefore, an adhesion mechanism independent of surface charge effects must explain the restriction or translocation of latex beads on a neural crest pathway.     

The implementation of SOMO (SOlution MOdeller) in the UltraScan analytical ultracentrifugation data analysis suite: enhanced capabilities allow the reliable hydrodynamic modeling of virtually any kind of biomacromolecule

The interpretation of solution hydrodynamic data in terms of macromolecular structural parameters is not a straightforward task. Over the years, several approaches have been developed to cope with this problem, the most widely used being bead modeling in various flavors. We report here the implementation of the SOMO (SOlution MOdeller; Rai et al. in Structure 13:723–734, 2005) bead modeling suite within one of the most widely used analytical ultracentrifugation data analysis software packages, UltraScan (Demeler in Modern analytical ultracentrifugation: techniques and methods, Royal Society of Chemistry, UK, 2005). The US-SOMO version is now under complete graphical interface control, and has been freed from several constraints present in the original implementation. In the direct beads-per-atoms method, virtually any kind of residue as defined in the Protein Data Bank (e.g., proteins, nucleic acids, carbohydrates, prosthetic groups, detergents, etc.) can be now represented with beads whose number, size and position are all defined in user-editable tables. For large structures, a cubic grid method based on the original AtoB program (Byron in Biophys J 72:408–415, 1997) can be applied either directly on the atomic structure, or on a previously generated bead model. The hydrodynamic parameters are then computed in the rigid-body approximation. An extensive set of tests was conducted to further validate the method, and the results are presented here. Owing to its accuracy, speed, and versatility, US-SOMO should allow to fully take advantage of the potential of solution hydrodynamics as a complement to higher resolution techniques in biomacromolecular modeling.     

Reliability of confocal microscopy spectral imaging systems: use of multispectral beads.

BACKGROUND: There is a need for a standardized, impartial calibration, and validation protocol on confocal spectral imaging (CSI) microscope systems. To achieve this goal, it is necessary to have testing tools to provide a reproducible way to evaluate instrument performance. METHODS: We evaluated fluorescent spectral beads (FocalCheck) from Molecular Probes/Invitrogen that consist of four pairs with emissions between 500 and 725 nm and a europium macrocycle quantum dye bead. These bead tools compliment our previously published protocol for testing spectral imaging systems that used an inexpensive multi-ion discharge lamp (MIDL) that contains Hg(+), Ar(+), and inorganic fluorophores that emits distinct, stable spectral features. RESULTS: We acquired the spectra of the FocalCheck beads on a Zeiss 510 Meta, a Leica TCS-SP1, a Leica SP2 AOBS, an Olympus FV 1000, and a Nikon C1Si confocal systems and a PARISS microscopic spectral system and of the europium beads on the Leica TCS-SP1 and PARISS spectral imaging systems. A lack of performance with some equipment between 650 and 750 nm was identified using the far red pair of the FocalCheck beads. The position of the slider in front of PMT 2 that reflects light into PMT 1 and PMT 3 affected the measurement of all bead intensities. Unmixing algorithms were used to separate beads with different fluorochromes and separate two fluorochromes on the same bead. CONCLUSIONS: The FocalCheck multi-spectral beads yielded similar profiles on four CSI systems and a PARISS spectral system. The utilization of the spectral FocalCheck beads is helpful to evaluate proper spectral performance, especially in the far red region. Europium beads provide a very narrow spectrum that can help to identify machines that have spectral problems. The dyes located on individual beads or mixed together in ring-core configuration can be used as test particles to demonstrate spectral unmixing with various algorithms.