Theory of multivalent binding in one and two-dimensional lattices

Ligand binding to a linear lattice composed of N sites, under general conditions of cooperativity and number of sites covered upon binding, m, is approached in terms of the theory of contracted partition functions. The partition function of the system obeys a recursion relation leading to a generating function that provides an exact analytical solution for any case of interest. Site-specific properties of the lattice are derived from simple transformations of the analytical expressions. The McGhee-von Hippel model is obtained as a special case in the limit N --> infinity. The derivation is straightforward and involves no combinatorial arguments. Partition functions and site-specific properties are also derived for the case of non-cooperative binding to a two-dimensional torus of length N, containing s sites in its section for a total of sN sites. The torus provides a relevant model for ligand binding to double-stranded DNA (s = 2) or protein helices (s = 3,4). It is proved that non-cooperative binding to the two-dimensional torus can mimic cooperative binding to a one-dimensional linear lattice when m = s. The dimensional embedding of the lattice and the geometry of interaction of its sites play a crucial role in defining the binding properties of the system accessible to experimental measurements. Hence, caution must be exercised in the interpretation of Scatchard plots in terms of the one-dimensional McGhee-von Hippel model, especially when m < or = 4 and the geometry of the system is clearly two-dimensional.     

Site-Specific Structural Variations Accompanying Tubular Assembly of the HIV-1 Capsid Protein

The 231-residue capsid (CA) protein of human immunodeficiency virus type 1 (HIV-1) spontaneously self-assembles into tubes with a hexagonal lattice that is believed to mimic the surface lattice of conical capsid cores within intact virions. We report the results of solid-state nuclear magnetic resonance (NMR) measurements on HIV-1 CA tubes that provide new information regarding changes in molecular structure that accompany CA self-assembly, local dynamics within CA tubes, and possible mechanisms for the generation of lattice curvature. This information is contained in site-specific assignments of signals in two- and three-dimensional solid-state NMR spectra, conformation-dependent ¹⁵N and ¹³C NMR chemical shifts, detection of highly dynamic residues under solution NMR conditions, measurements of local variations in transverse spin relaxation rates of amide ¹H nuclei, and quantitative measurements of site-specific ¹⁵N–¹⁵N dipole–dipole couplings. Our data show that most of the CA sequence is conformationally ordered and relatively rigid in tubular assemblies and that structures of the N-terminal domain (NTD) and the C-terminal domain (CTD) observed in solution are largely retained. However, specific segments, including the N-terminal β-hairpin, the cyclophilin A binding loop, the inter-domain linker, segments involved in intermolecular NTD–CTD interactions, and the C-terminal tail, have substantial static or dynamical disorder in tubular assemblies. Other segments, including the 3₁₀-helical segment in CTD, undergo clear conformational changes. Structural variations associated with curvature of the CA lattice appear to be localized in the inter-domain linker and intermolecular NTD–CTD interface, while structural variations within NTD hexamers, around local 3-fold symmetry axes, and in CTD–CTD dimerization interfaces are less significant.     

Monte Carlo studies on equilibrium globular protein folding. III. The four helix bundle

The nature of the equilibrium conformational transition from the denatured state to a four-member alpha-helical bundle was studied employing a dynamic Monte Carlo algorithm in which the model protein chain was confined to a tetrahedral lattice. The model chain was allowed to hunt over all phase space, the target native state was not assumed a priori, and no site-specific interactions were introduced. The exterior vs the interior part of the protein is distinguished by the pattern of hydrophilic and hydrophobic interactions encoded into the primary sequence. The importance of a statistical preference for forming bends, as a function of bend location in the primary sequence, and helical wheel type cooperative interactions were examined, and the necessary conditions for collapse of the chain to the unique native structure were investigated. It was found that an amphipathic pattern of hydrophobic/hydrophilic interactions along with a statistical preference of the central residues for bend formation are sufficient to obtain the four-helix bundle. The transition to the native state has an all-or-none character.     

Thermodynamic basis of site-specific cooperativity

Cooperative phenomena in biological macromolecules arise from the interaction of many distinct subsystems, such as structural domains or binding sites. Cooperative properties of the system as a whole, like protein folding or allosteric transitions, are subject to the restrictions imposed by thermodynamic stability. These restrictions, however, do not apply in the case of individual subsystems open to interactions with the rest of the macromolecule. The site-specific properties of such subsystems can be understood in general thermodynamic terms from those of a multicomponent system under particular conditions. The analogy provides a thermodynamic basis for site-specific Cooperativity. © 1994 John Wiley & Sons, Inc.     

Structure of ferricytochrome c' from Rhodospirillum molischianum at 1.67 A resolution

The structure of ferricytochrome c' from Rhodospirillum molischianum has been crystallographically refined to 1.67 A resolution using a combination of reciprocal space and restrained least-squares refinement methods. The final crystallographic R-factor for 30,533 reflections measured with I greater than sigma (I) between infinity and 1.67 A is 0.188. The final model incorporates 1944 unique protein atoms (of a total of 1972) together with 194 bound solvent molecules. The structure has been analysed with respect to its detailed conformational properties, secondary structural features, temperature factor behavior, bound solvent sites, and heme geometry. The asymmetric unit of the cytochrome c' crystal contains a dimer composed of chemically identical 128-residue polypeptide chains. Although the refined structure shows the monomers to be very similar, examination of the differences that do occur allows an evaluation of how different lattice contacts affect protein conformation and solvent binding. In particular, comparison of solvent binding sites in the two subunits allows identification of a common set that are not altered by lattice interactions. The preservation of these solvent interactions in different lattice environments suggests that they play a structural role in protein stabilization in solution. The refined structure additionally reveals some new features that relate to the ligand binding properties and unusual mixed-spin state character of cytochrome c'. Finally, comparison of the heme binding geometry in cytochrome c' and other structurally unrelated c-type cytochromes shows that two alternative, but sterically favorable, conformational variants occur among the seven examples examined.     

Mapping the interactions of the single-stranded DNA binding protein of bacteriophage T4 (gp32) with DNA lattices at single nucleotide resolution: polynucleotide binding and cooperativity

We here use our site-specific base analog mapping approach to study the interactions and binding equilibria of cooperatively-bound clusters of the single-stranded DNA binding protein (gp32) of the T4 DNA replication complex with longer ssDNA (and dsDNA) lattices. We show that in cooperatively bound clusters the binding free energy appears to be equi-partitioned between the gp32 monomers of the cluster, so that all bind to the ssDNA lattice with comparable affinity, but also that the outer domains of the gp32 monomers at the ends of the cluster can fluctuate on and off the lattice and that the clusters of gp32 monomers can slide along the ssDNA. We also show that at very low binding densities gp32 monomers bind to the ssDNA lattice at random, but that cooperatively bound gp32 clusters bind preferentially at the 5′-end of the ssDNA lattice. We use these results and the gp32 monomer-binding results of the companion paper to propose a detailed model for how gp32 might bind to and interact with ssDNA lattices in its various binding modes, and also consider how these clusters might interact with other components of the T4 DNA replication complex.     

Critical jump sizes in DNA-protein interactions

Interaction of a protein molecule with a specific-site on the DNA lattice can be modeled as an unbiased random jump process. Here we show that there exists a critical jump size (kc) beyond which site-specific association of a protein molecule with a DNA lattice cannot be facilitated. The maximum achievable association rate is predicted to be approximately 10(10) mol-1 s-1. This critical jump size scales with the total length of DNA lattice (N) as kc proportional, variantN2/3. Beyond kc the mean first passage time MFPT (denoted as T) required for the protein molecule to target the specific-site follows a linear scaling law as T proportional, variantN rather than the usual T proportional, variantN2 scaling law. On the basis of these results we argue that the evolution of the super coiled structures of the genomic DNA must be a consequence of the existence of this critical jump sizes. We finally show that the random jump method of searching for the specific-site by the protein molecule on the DNA lattice itself introduce an abstract linear type potential favoring the site-specific association rate.     

Inter-chromophore interactions in pigment-modified and dimer-less bacterial photosynthetic reaction centers

The magnitudes of inter-chromophore interactions in bacterial photosynthetic reaction centers are investigated by measuring absorption and Stark spectra of reaction centers in which monomeric chromophores are modified and in a novel triplet mutant which lacks the special pair. The circular dichroism spectrum of the triple mutant reaction center was also measured. Only small changes in the spectroscopic properties are observed, as has also been found for several types of reaction centers in which the absorption or chemical properties of a chromophore are altered by site-specific mutations. We conclude that the electronic absorption, circular dichroism and Stark features of the special pair and the monomeric chromophores in the reaction center are relatively insensitive to inter-chromophore interactions.     

Site-specific protein backbone and side-chain NMR chemical shift and relaxation analysis of human vinexin SH3 domain using a genetically encoded 15N/19F-labeled unnatural amino acid

SH3 is a ubiquitous domain mediating protein-protein interactions. Recent solution NMR structural studies have shown that a proline-rich peptide is capable of binding to the human vinexin SH3 domain. Here, an orthogonal amber tRNA/tRNA synthetase pair for ¹⁵N/¹⁹F-trifluoromethyl-phenylalanine (¹⁵N/¹⁹F-tfmF) has been applied to achieve site-specific labeling of SH3 at three different sites. One-dimensional solution NMR spectra of backbone amide (¹⁵N)¹H and side-chain ¹⁹F were obtained for SH3 with three different site-specific labels. Site-specific backbone amide (¹⁵N)¹H and side-chain ¹⁹F chemical shift and relaxation analysis of SH3 in the absence or presence of a peptide ligand demonstrated different internal motions upon ligand binding at the three different sites. This site-specific NMR analysis might be very useful for studying large-sized proteins or protein complexes.     

Effect of site-specific modification on restriction endonucleases and DNA modification methyltransferases.

Restriction endonucleases have site-specific interactions with DNA that can often be inhibited by site-specific DNA methylation and other site-specific DNA modifications. However, such inhibition cannot generally be predicted. The empirically acquired data on these effects are tabulated for over 320 restriction endonucleases. In addition, a table of known site-specific DNA modification methyltransferases and their specificities is presented along with EMBL database accession numbers for cloned genes.     

A novel hybrid simulation for study of multiscale phenomena

A novel multiscale model and simulation has been developed by combining the algorithms from a course grained 2D lattice model with Brownian dynamics (BD). The lattice model incorporates Lennard-Jones and coulombic interactions between particles, as well as nearest-neighbor interactions. The BD simulation allows the particles to move in solution before they adsorb to the surface. This hybrid simulation is used to study the behavior of nanoparticles in the presence of a surface and evaporation of solvent. The simulation is able to produce amorphous topologies of nanoparticles on the surface.     

Protein-protein interactions as a tool for site-specific labeling of proteins

Probing structures and dynamics within biomolecules using ensemble and single-molecule fluorescence resonance energy transfer requires the conjugation of fluorophores to proteins in a site-specific and thermodynamically nonperturbative fashion. Using single-molecule fluorescence-aided molecular sorting and the chymotrypsin inhibitor 2-subtilisin BPN' complex as an example, we demonstrate that protein-protein interactions can be exploited to afford site-specific labeling of a recombinant double-cysteine variant of CI2 without the need for extensive and time-consuming chromatography. The use of protein-protein interactions for site-specific labeling of proteins is compatible with and complementary to existing chemistries for selective labeling of N-terminal cysteines, and could be extended to label multiple positions within a given polypeptide chain.     

Elastic vibrations in seamless microtubules

Parameters characterizing elastic properties of microtubules, measured in several recent experiments, reflect an anisotropic character. We describe the microscopic dynamical properties of microtubules using a discrete model based on an appropriate lattice of dimers. Adopting a harmonic approximation for the dimer–dimer interactions and estimating the lattice elastic constants, we make predictions regarding vibration dispersion relations and vibration propagation velocities. Vibration frequencies and velocities are expressed as functions of the elastic constants and of the geometrical characteristics of the microtubules. We show that vibrations which propagate along the protofilament do so significantly faster than those along the helix.     

Intrinsic lattice formation by the ryanodine receptor calcium-release channel

Recent theoretical analysis of a model lattice of interacting transmembrane receptor proteins has indicated that such clustering in the membrane could provide a novel mechanism for regulating receptor signalling in cells. It has been calculated that cooperative interactions between receptors organized into a cluster, or array, in the membrane would dramatically increase their sensitivity to activation by ligand. Sensitivity to ligand would increase with the extent of spread of activity within the receptor lattice. Hence, formation of extensive receptor lattices in the membrane would allow a large population of receptors to be simultaneously switched on, or off, by a very small change in ligand concentration. We show here that lattice formation is an intrinsic property of an integral membrane protein, the ryanodine-sensitive calcium-release channel (RyR) of endoplasmic reticulum. The purified protein spontaneously assembled into two-dimensional lattices in solution, enabling the construction of a 25 A projection map that identifies the mode of interaction between RyR oligomers. Our observations on the RyR provide a new perspective on various properties of cell signalling via this and other receptors.     

Protein folding coupled to DNA binding in the catalytic domain of bacteriophage lambda integrase detected by mass spectrometry

Bacteriophage lambda integrase (lambda-Int) is the prototypical member of a large family of enzymes that catalyze site-specific DNA recombination via single-strand cleavage and the formation of a Holliday junction intermediate. Crystallographic and biochemical evidence indicate that substantial conformational change (i.e., folding) in the catalytic domain of the protein is required for substrate recognition and catalysis. We have examined the solution conformation of the catalytic domain (C170) in the absence and presence of a cognate "half-site" DNA oligonucleotide by electrospray ionization mass spectrometry, and circular dichroism and fluorescence spectroscopy. The distribution of ions in the positive ion electrospray mass spectrum of the free protein reveals the presence of three distinct species in solution, one corresponding to the folded protein, one to the unfolded protein, and one to a dimer. In the presence of DNA, ions are observed only for the protein-DNA complex and the folded form of the free protein. We therefore conclude that DNA binding stabilizes the global fold of the protein in a manner that is consistent with folding-coupled target recognition as a mechanism to control site-specific recombination. Furthermore, we find that inspection of the charge state distribution of ions in electrospray mass spectra provides a quick and effective means to identify conformational heterogeneity of proteins in solution and to investigate dynamic protein-nucleic acid interactions.     

Coarse-grained Monte Carlo simulations of mucus: structure, dynamics, and thermodynamics

A simple coarse-grained model of mucus structure and dynamics is proposed and evaluated. The model is based on simple cubic, face-centered lattice representation. Mucins are simulated as lattice chains in which each bead of the model chains represents a mucin domain, equivalent to its Kuhn segment. The remaining lattice sites are considered to be occupied by the solvent. Model mucins consist of three types of domains: polar (glycosylated central segments), hydrophobic, and cysteine-rich, located at the terminal part of the mucin chains. The sequence of these domains mimics the sequence of real mucins. Static and dynamic properties of the system were studied by means of Monte Carlo dynamics. It was shown that the model system undergoes sol-gel transition and that the interactions between hydrophobic domains are responsible for the transition and characteristic properties of the dynamic network in the gel phase. Cysteine-rich domains are essential for frictional properties of the system. Structural and dynamic properties of the model mucus observed in simulations are in qualitative agreement with known experimental facts and provide mechanistic explanation of complex properties of real mucus.     

Asymmetry as the Key to Clathrin Cage Assembly

The self-assembly of clathrin proteins into polyhedral cages is simulated for the first time (to our knowledge) by introducing a coarse-grain triskelion particle modeled after clathrin's characteristic shape. The simulations indicate that neither this shape, nor the antiparallel binding of four legs along the lattice edges, is sufficient to induce cage formation from a random solution. Asymmetric intersegmental interactions, which probably result from a patchy distribution of interactions along the legs' surfaces, prove to be crucial for the efficient self-assembly of cages.     

Estimation of inter-residue distances in spin labeled proteins at physiological temperatures: experimental strategies and practical limitations.

Magnetic dipolar interactions between pairs of solvent-exposed nitroxide side chains separated by approximately one to four turns along an alpha-helix in T4 lysozyme are investigated. The interactions are analyzed both in frozen solution (rigid lattice conditions) and at room temperature as a function of solvent viscosity. At room temperature, a novel side chain with hindered internal motion is used, along with a more commonly employed nitroxide side chain. The results suggest that methods developed for rigid lattice conditions can be used to analyze dipolar interactions between nitroxides even in the presence of motion of the individual spins, provided the rotational correlation time of the interspin vector is sufficiently long. The distribution of distances observed for the various spin pairs is consistent with rotameric equilibria in the nitroxide side chain, as observed in crystal structures. The existence of such distance distributions places important constraints on the interpretation of internitroxide distances in terms of protein structure and structural changes.