Protein folding through kinetic discrimination

Proteins fold on a micros-ms time scale. However, the number of possible conformations of the polypeptide backbone is so large that random sampling would not allow the protein to fold within the lifetime of the universe, the Levinthal paradox. We show here that a protein chain can fold efficiently with high fidelity if on average native contacts survive longer than non-native ones, that is, if the dissociation rate constant for breakage of a contact is lower for native than for non-native interactions. An important consequence of this finding is that no pathway needs to be specified for a protein to fold. Instead, kinetic discrimination among formed contacts is a sufficient criterion for folding to proceed to the native state. Successful protein folding requires that productive contacts survive long enough to obtain a certain level of probability that other native contacts form before the first interacting unit dissociates. If native contacts survive longer than non-native ones, this prevents misfolding and provides the folding process with directionality toward the native state. If on average all contacts survive equally long, the protein chain is deemed to fold through random search through all possible conformations (i.e., the Levinthal paradox). A modest degree of cooperativity among the native contacts, that is, decreased dissociation rate next to neighboring contacts, shifts the required ratio of dissociation rates into a realistic regime and makes folding a stochastic process with a nucleation step. No kinetic discrimination needs to be invoked in regards to the association process, which is modeled as dependent on the diffusion rate of chain segments.     

Phase behavior and structure of an ABC triblock copolymer dissolved in selective solvent

A mean-field lattice theory is applied to predict the self-assembly into ordered structures of an ABC triblock copolymer in selective solvent. More specifically, the composition-temperature phase diagram has been constructed for the system (C)₁₄(PO)₁₂(EO)₁₇/water, where C stands for methylene, PO for propylene oxide and EO for ethylene oxide. The model predicts thermotropic phase transitions between the ordered hexagonal, lamellar, reverse hexagonal, and reverse cubic phases, as well as the disordered phase. The thermotropic behavior is a result of the temperature dependence of water interaction with EO- and PO-segments. The lyotropic effect (caused by changing the solvent concentration) on the formation of different structures has been found weak. The structure in the ordered phases is described by analyzing the species volume fraction profiles and the end segment and junction distributions. A “triple-layer” structure has been found for each of the ordered phases, with each layer rich in C-, PO-, and EO-segments, respectively. The blocks forming the layers are not stretched. The dependence of the domain spacing on polymer volume fraction and temperature is also considered. Received 17 April 2002 Published online: 21 January 2003     

Binding of charged ligands to macromolecules. Anomalous salt dependence

Although interactions in biological systems occur in the presence of a large number of charged species, the binding of charged ligands to different biomolecules is often analyzed in a simplified model focusing only upon the receptor, ligand, and added salt. Here we demonstrate that the presence of charged macromolecules can affect binding to the receptor in an unexpected way. Experimental studies of the binding of barium ions to the chelator 5,5'-dibromo-1,2-bis(O-amino-phenoxy)-ethane-N,N,N',N'-tetraacetic acid in the presence of charged silica sols show that the binding affinity increases with added salt. The experimental findings are verified in Monte Carlo simulations using a dielectric continuum model with a uniform dielectric permittivity throughout the solution. The anomalous salt behavior is caused by a reduction of the chemical potential of the free ligand, which even in the absence of binding interacts strongly with the oppositely charged receptor. These results are also relevant for the interpretation of competition studies often used in the case of strong ligand binding.     

Protein reconstitution and 3D domain swapping

The native structures of proteins are governed by a large number of non-covalent interactions yielding a high specificity for the native packing of structural elements. This allows for the reconstitution of proteins from disconnected polypeptide fragments. The specificity for the native arrangement also enables interchange of structural elements with another identical protein chain resulting in dimers with swapped segments. Proteins are not static structures, but open up repetitively on a timescale of minutes to years depending on the identity of the protein and solution conditions. The open protein may self-close and return to the native state, or it may close with another polypeptide chain leading to 3D domain swapping. The term describes two or more protein molecules swapping identical domains or smaller secondary structure elements. The non-covalent intra-molecular interactions between domains in the monomer are thus broken and restored in the oligomer by identical inter-molecular contacts. This review will discuss 3D domain swapping in relation to protein reconstitution and fibril formation. Examples of reconstituted and domain-swapped proteins will be given. The physiological benefits of 3D domain swapping will be discussed, as well as its role in the evolution of proteins and pathology.     

Polymer distribution in connected spherical domains

The distribution of neutral and charged polymers with different flexibilities between two spheres of varying volume connected by a short and narrow cylinder has been investigated by Monte Carlo simulations. The uncharged chain displayed mostly a single-sphere occupancy due to the high conformational entropy penalty of crossing the cylindrical domain, whereas for the charged polymer a double-sphere occupancy was obtained, except for very different spherical volumes. The origin of this different occupancy behavior stems from the counterion entropy. At increasing stiffness, a stronger preference for double-sphere occupancy was predicted.     

Monte Carlo simulations of oppositely charged macroions in solution

The structure and phase behavior of oppositely charged macroions in solution have been studied with Monte Carlo simulations using the primitive model where the macroions and small ions are described as charged hard spheres. Size and charge symmetric, size asymmetric, and charge asymmetric macroions at different electrostatic coupling strengths are considered, and the properties of the solutions have been examined using cluster size distribution functions, structure factors, and radial distribution functions. At increasing electrostatic coupling, the macroions form clusters and eventually the system displays a phase instability, in analogy to that of simple electrolyte solutions. The relation to the similar cluster formation and phase instability occurring in solutions containing oppositely charged polymers is also discussed.     

Structure of microemulsion-ABA triblock copolymer networks

Structural equilibrium properties of transient networks formed by microemulsion droplets and ABA triblock copolymers in solution have been studied by Monte Carlo simulation. The droplets were represented by soft spheres, and the polymers were represented by junctions connected by harmonic bonds with an angular potential regulating the intrinsic chain stiffness. The interaction parameters were selected such that the end A-blocks were localized inside the droplets and the middle B-block in the continuous phase. The influence of (i) the polymer concentration, (ii) the polymer stiffness, and (iii) the contour length of the middle B-block on the formation and the structure of the microemulsion-polymer network were investigated using polymer end-to-end separation probability distribution functions, droplet radial distribution functions, droplet-droplet nearest-neighbor probability distribution functions, and network connectivity indicators. An increase of the polymer-droplet number ratio had a strong impact on the network formation. Under typical conditions and at an intermediate polymer-droplet number ratio, (i) the fraction of polymers forming bridges between droplets increased from essentially zero to unity and (ii) the fraction of polymers that were forming loops decreased as the ratio of the polymer end-to-end separation and the surface-to-surface separation between neighboring droplets for a hypothetical homogeneous droplet distribution was increased from 0.5 to 2. For long and flexible polymers, a mesoscopic segregation triggered by a depletion attraction between droplets appeared, and, furthermore, for sufficiently stiff chains, only bridge conformations occurred. The percolation probability could be represented as a function of the average droplet cluster size only, across all systems.     

Molecular design of specific metal-binding peptide sequences from protein fragments: theory and experiment

A novel strategy is presented for designing peptides with specific metal-ion chelation sites, based on linking computationally predicted ion-specific combinations of amino acid side chains coordinated at the vertices of the desired coordination polyhedron into a single polypeptide chain. With this aim, a series of computer programs have been written that 1) creates a structural combinatorial library containing Z(i)-(X)(n)-Z(j) sequences (n=0-14; Z: amino acid that binds the metal through the side chain; X: any amino acid) from the existing protein structures in the non-redundant Protein Data Bank; 2) merges these fragments into a single Z(1)-(X)(n(1) )-Z(2)-(X)(n(2) )-Z(3)-(X)(n(3) )--Z(j) polypeptide chain; and 3) automatically performs two simple molecular mechanics calculations that make it possible to estimate the internal strain in the newly designed peptide. The application of this procedure for the most M(2+)-specific combinations of amino acid side chains (M: metal; see L. Rulísek, Z. Havlas J. Phys. Chem. B 2003, 107, 2376-2385) yielded several peptide sequences (with lengths of 6-20 amino acids) with the potential for specific binding with six metal ions (Co(2+), Ni(2+), Cu(2+), Zn(2+), Cd(2+) and Hg(2+)). The gas-phase association constants of the studied metal ions with these de novo designed peptides were experimentally determined by MALDI mass spectrometry by using 3,4,5-trihydroxyacetophenone as a matrix, whereas the thermodynamic parameters of the metal-ion coordination in the condensed phase were measured by isothermal titration calorimetry (ITC), chelatometry and NMR spectroscopy methods. The data indicate that some of the computationally predicted peptides are potential M(2+)-specific metal-ion chelators.