Streptavidin tetramerization and 2D crystallization: a mean-field approach.

A mean-field theoretical approach is applied to streptavidin tetramerization and two-dimensional (2D) crystallization. This theory includes, in particular, solvent-residue interactions following the inhomogeneous Flory-Huggins model for polymers. It also takes into account residue-residue interactions by using tabulated pair interaction parameters. This theory allows one to explicitly calculate the entropy of the inhomogeneous system. We show that hydrophobic interactions are responsible for the stability of tetramerization. Within the present theory, the equilibrium distance between the two dimers is the same as that determined experimentally. The free energy of tetramerization (i.e., dissociation of the two dimers) is 50 k(B)T. Unlike tetramerization, hydrophobic interactions alone are not sufficient to stabilize the 2D crystal C(222), but solvent-mediated residue-residue interactions give the most important contribution.

Meanfield approach to the thermodynamics of protein-solvent systems with application to p53.

We present a meanfield theoretical approach for studying protein-solvent interactions. Starting with the partition function of the system, we develop a field theory by introducing densities for the different components of the system. At this point, protein-solvent interactions are introduced following the inhomogeneous Flory-Huggins model for polymers. Finally, we calculate the free energy in a meanfield approximation. We apply this method to study the stability of the tetramerization domain of the tumor suppressor protein p53 when subjected to site-directed mutagenesis. The four chains of this protein are held together by hydrophobic interactions, and some mutations can weaken this bond while preserving the secondary structure of the single protein chains. We find good qualitative agreement between our numerical results and experimental data, thus encouraging the use of this method as a guide in designing experiments.

A meanfield approach to the thermodynamics of a protein-solvent system with application to the oligomerization of the tumor suppressor p53.

The thermodynamic stability and oligomerization status of the tumor suppressor p53 tetramerization domain have been studied experimentally and theoretically. A series of hydrophilic mutations at Met-340 and Leu-344 of human p53 were designed to disrupt the hydrophobic dimer-dimer interface of the tetrameric oligomerization domain of p53 (residues 325-355). Meanfield calculations of the free energy of the solvated mutants as a function of interdimer distance were compared with experimental data on the thermal stability and oligomeric state (tetramer, dimer, or equilibrium mixture of both) of each mutant. The calculations predicted a decreasing stability and oligomeric state for the following amino acids at residue 340: Met (tetramer) > Ser Asp, His, Gln, > Glu, Lys (dimer), whereas the experimental results showed the following order: Met (tetramer) > Ser > Gln > His, Lys > Asp, Glu (dimers). For residue 344, the calculated trend was Leu (tetramer) > Ala > Arg, Gln, Lys (dimer), and the experimental trend was Leu (tetramer) > Ala, Arg, Gln, Lys (dimer). The discrepancy for the lysine side chain at residue 340 is attributed to the dual nature of lysine, both hydrophobic and charged. The incorrect prediction of stability of the mutant with Asp at residue 340 is attributed to the fact that within the meanfield approach, we use the wild-type backbone configuration for all mutants, but low melting temperatures suggest a softening of the alpha-helices at the dimer-dimer interface. Overall, this initial application of meanfield theory toward a protein-solvent system is encouraging for the application of the theoretical model to more complex systems.

Electrophoresis between sieving and reptation: an investigation of the role of shape fluctuations in electrophoresis.

We present numerical simulation results of electrophoretic mobilities of flexible polyelectrolytes over a wide molecular size range moving through gels with various pore sizes. The data are compared to existing models for different molecular size regimes and to experimental results. We observe rather pronounced shape fluctuations of the polyelectrolytes which, especially for larger gel pores or small molecules, have a strong impact on the dynamics of the molecules. Electrophoretic separation, as is used e.g. for DNA sequencing, is best achieved for polyelectrolytes with a radius of gyration of the order of the average pore radius of the gel, i.e. in a molecular size regime where the polyelectrolyte interacts with only a few gel fibers at a given time. A decrease of the gel pore size leads to a systematic decrease of the electrophoretic mobility, but does not lead to a qualitative change in the molecular size dependence, as long as the pore size is larger than the persistence length of the polyelectrolyte.

Preparation, manipulation, and pulse strategy for one-dimensional pulsed-field gel electrophoresis (ODPFGE).

The underlying principles for zero-integrated-field electrophoresis (ZIFE) pulses and more general forward-biased pulse schemes are reviewed for one-dimensional pulsed-field gel electrophoresis (ODPFGE) separations of large DNA molecules. Detailed descriptions of materials, preparation protocols, hardware requirements, and procedures are given. A variety of gel pictures for known yeast DNA markers are shown.

Sequencing using pulsed field and image reconstruction.

The use of pulsed fields in a standard manual sequencing set-up results in the separation of > 2 kb on a single gel, as compared to 300-400 bases with a dc field. However, visual reading of the sequence from a film exposed to a pulsed-field gel is not possible for more than 800-900 bases under the best conditions. The use of image reconstruction and enhancement techniques allows the reading of the M13mp18 sequence to > 1 kb, and individual bands can be identified at > 2 kb.

A new concept for separating nucleic acids by electrophoresis in solution using hybrid synthetic end labelled-nucleic acid molecules.

Analogy between the symmetry breaking of the electrical driving force and the opposing friction force in gels using pulsed electric fields is made with the corresponding effect for polyelectrolyte coils in solution related to the molecular weight-independent charge density. The synthesis of hybrid molecules to break the symmetry of constant charge density is proposed, in which standard polypeptide end labels are attached to nucleic acid fragments. The combinatorial chemical library scheme of Brenner and Lerner (Proc. Natl. Acad. Sci. USA 1992, 89, 5381-5383), making use of hybrid molecules for another purpose, is mentioned, with the suggestion that for electrophoresis in solution a neutral end-labelled polypeptide chain would give the largest molecular weight and time-dependent change in the charge density for pulsed fields.

Effect of one-dimensional pulsed-field gel electrophoresis on linear and circular DNA.

A summary of the three main one-dimensional pulsed-field strategies (zero-integrated field, forward-biased field, and high frequency modulation) used for separating DNA molecules without band inversion within a preselected size range is given. Each of these strategies has size-specific features which make separations up to 6 Mbp possible. We applied the same methodology to circular DNAs varying in size from 2 kbp to about 4 Mbp. The migration of intermediate-sized circular plasmids (50 kbp-400 kbp) under these pulse conditions remains unexplained. On the other hand, preliminary results show that the migration of very large molecules, which are expected to be circular, comigrate with linear chromosomes of the same size under certain pulse conditions. We hypothesize that sample preparation, or the effect of the pulsed field, can create breakage and linearize very large circular DNAs, or that very large circular DNAs (> 2 Mbp) act like linear DNAs of the same size when submitted to one-dimensional pulsed-field gel electrophoresis conditions. The most likely possibility is that some of the circular DNAs have been linearized with one break during sample preparation, giving rise to a band at about 4 Mbp. The circular DNAs with more than one break may form an indistinguishable smear.

Manual sequencing using pulsed field.

The use of pulsed fields in manual sequencing opens up the compression zone found with a DC field and extends the range of resolution from a few hundred bases to several thousand bases. The band inversion problem is overcome with the proper pulsing conditions, and the bands are sharper than for the DC field case. Accurate visual reading is possible up to about 800-900 bases. The method is compatible with automation techniques, since the band spectrum is stretched continuously during migration, and the smaller fragments are run off the gel.

Pulsed field sequencing gel electrophoresis.

The effect of pulsed fields on sequencing gel electrophoresis is investigated, using DNA fragment markers ranging in size from 20 to 6557 bases. For high continuous electric fields (5000 V/55 cm) band inversion is observed in which fragments larger than 4000 bases migrate faster than those of 800-1000 bases. The use of one-dimensional pulsed field gel electrophoresis (ODPFGE) eliminates band inversion and extends the monotonic size-mobility relationship of the DNA markers up to about 4000 bases. The relevance of these results, obtained using a manual sequencing process with autoradiographic detection, to automated sequences is discussed.

A new concept for sequencing DNA by capillary electrophoresis.

It is proposed that the scaling symmetry of constant charge density with increasing molecular weight, which prevents the separation by electrophoresis of DNA molecules in solution (with respect to molecular weight) be broken by the attachment of a perturbing entity (protein, virus or charged sphere) to one end of the molecule. An application of this idea to a concept for sequencing DNA by capillary electrophoresis is discussed, and the possibility of using the reattachment of the RecA protein to separate large segments of DNA in solution by electrophoresis following sequence-specific cleavage is mentioned.

Preparation, Manipulation, and Pulse Strategy for One-Dimensional Pulsed-Field Gel Electrophoresis (ODPFGE).

The preparation and manipulation of very large DNA molecules for pulsed-field gel electrophoresis (PFGE) requires more care than normally used for smaller molecules. The general protocol used is the preparation of DNA directly in solid agarose blocks (plugs) or beads. Intact cells are encapsidated in agarose (plugs or beads) and are treated with different combinations of enzymes and detergent to remove cell walls, membranes, RNA, proteins, and other materials in order to obtain naked DNA. This is possible because detergent and enzymes can diffuse by Brownian motion through the agarose pores of the plug, whereas the large pieces of DNA cannot and remain sequestered inside the plug. Here, we give detailed protocols of preparation for yeast and mammalian DNA. In addition, we describe the power supplies, switchers, gels, and gel trays required for one-dimensional pulsed-field gel electrophoresis (ODPFGE), as well as the pulse strategies used for the separations.

Preparation and Separation of Intact Chromosomes of Vertebrates by One-Dimensional Pulsed-Field Gel Electrophoresis (ODPFGE).

This novel way of preparing chromosomes for pulsed-field gel electrophoresis (PFGE) takes advantage of the fact that the whole chromosome population is synchronized in metaphase. This is a very important step toward their intact separation by PFGE; for instance, a standard preparation as used for digestion with rarecutter enzymes shows a different pattern of resolution, characterized by diffuse bands and nonspecific migration (see Chapter 7 ). Here, vertebrate chromosomal DNA was prepared by a modified chromosome isolation procedure for flow cytometry (1). This procedure involves lysis of cells (blocked in metaphase by colcemide) with digitonine in the presence of spermidine and spermine as described below. The structural integrity of metaphase-blocked chromosomes is given by the presence of spermine and spermidine, which act as chromosomal morphology stabilizers. The digestion with proteinase K is carried out as described before in order to eliminate chromosomal proteins. The pulse parameters for separating intact chicken microchromosomes by one-dimensional pulsed-field gel electrophoresis (ODPFGE) are also given.

Elastic Bag Model of One-Dimensional Pulsed-Field Gel Electrophoresis (ODPFGE).

Gel electrophoresis is one of the most common techniques used in molecular biology for the separation of DNA molecules. Conventional gel electrophoresis (using a static electric field) does not permit separation of DNA fragments larger than 30-50 kbp (1) as shown in Fig. 1A of Chapter 7 . This is a surprising result as one would think that larger molecules would suffer a larger retardation, and separation over any size range would be possible. The inability to separate is related to the molecular conformation of a polyelectrolyte, such as DNA, migrating in a disordered medium, such as a gel, under the influence of a static electric field. During continuous field electrophoresis, the larger DNA fragments tend to orient and stretch in the field direction because they migrate in a one-dimensional fashion between the gel fibers (2-4). When this orientation is negligible, e.g., for smaller molecules or for very low field intensities, they maintain a three-dimensional random-walk conformation intertwined with the gel fibers during migration, and experience a retardation that is proportional to the mol size. However, when the orientation becomes large, the molecules become stretched and migrate essentially linearly along the field direction (5). The electrophoretic mobility then becomes independent of the mol size and no separation of molecules of different sizes is possible (Fig. 1A of Chapter 7 ). Physically, this is a consequence of the fact that for long molecules stretched and oriented in the field direction, both the electrical force on the molecule and the average friction opposing the forward motion are proportional to the length. It follows that the velocity, which is the ratio of these two quantities, depends only on the force per unit length and is independent of the actual mol length. This explains why a plateau of length-independent mobility is reached in a continuous electric field (Fig. 2 of Chapter 7 ).

Fluctuating bond model of DNA gel electrophoresis.

We present a Monte Carlo algorithm that allows a small length scale numerical study of DNA gel electrophoresis in high electric fields, similar to the fluctuating bond model for dynamical properties of polymeric systems. This approach combines advantages of lattice Monte Carlo methods with those from continuous Brownian dynamics algorithms, and also takes into account the persistence length of DNA, as well as the random nature of the gel. The initial orientation and acceleration of a random-walk DNA conformation shows a number of features that can be related to experimental results. The detailed description of DNA motion provided by this approach may lead to a first realistic computer study of the process of DNA sequencing.