Molecular dynamics and free-energy calculations applied to affinity maturation in antibody 48G7

We investigated the relative free energies of hapten binding to the germ line and mature forms of the 48G7 antibody Fab fragments by applying a continuum model to structures sampled from molecular dynamics simulations in explicit solvent. Reasonable absolute and very good relative free energies were obtained. As a result of nine somatic mutations that do not contact the hapten, the affinity-matured antibody binds the hapten >104 tighter than the germ line antibody. Energetic analysis reveals that van der Waals interactions and nonpolar contributions to solvation are similar and drive the formations of both the germ line and mature antibody–hapten complexes. Affinity maturation of the 48G7 antibody therefore appears to occur through reorganization of the combining site geometry in a manner that optimizes the balance of gaining favorable electrostatic interactions with the hapten and losing those with solvent during the binding process. As reflected by lower rms fluctuations in the antibody–hapten complex, the mature complex undergoes more restricted fluctuations than the germ line complex. The dramatically increased affinity of the 48G7 antibody over its germ line precursor is thus made possible by electrostatic optimization.

Brownian dynamics simulations of protein folding: Access to milliseconds time scale and beyond

Protein folding occurs on a time scale ranging from milliseconds to minutes for a majority of proteins. Computer simulation of protein folding, from a random configuration to the native structure, is nontrivial owing to the large disparity between the simulation and folding time scales. As an effort to overcome this limitation, simple models with idealized protein subdomains, e.g., the diffusion–collision model of Karplus and Weaver, have gained some popularity. We present here new results for the folding of a four-helix bundle within the framework of the diffusion–collision model. Even with such simplifying assumptions, a direct application of standard Brownian dynamics methods would consume 10,000 processor-years on current supercomputers. We circumvent this difficulty by invoking a special Brownian dynamics simulation. The method features the calculation of the mean passage time of an event from the flux overpopulation method and the sampling of events that lead to productive collisions even if their probability is extremely small (because of large free-energy barriers that separate them from the higher probability events). Using these developments, we demonstrate that a coarse-grained model of the four-helix bundle can be simulated in several days on current supercomputers. Furthermore, such simulations yield folding times that are in the range of time scales observed in experiments.

Dynamics of contacts between lamellae of fibroblasts: Essential role of the actin cytoskeleton

We investigated actin cytoskeletal and adhesion molecule dynamics during collisions of leading lamellae of nontransformed and oncogene-transformed fibroblasts. By using real-time video microscopy, it was found that during lamellar collision there was considerable overlapping of leading lamellae followed by subsequent retraction. Overlapping of nontransformed fibroblasts was accompanied by formation of β-catenin-positive contact structures organized into strands oriented parallel to the long axis of the cell that were associated with bundles of actin filaments. Maintenance of such cell–cell contact structures critically depended on the contractility of actin cytoskeleton, as inhibition of contractility with serum-free medium or 2,3-butanedione 2-monoxime (BDM) resulted in loss of strand formation. Strand formation was recovered when cells in serum-free medium were incubated with the microtubule inhibitor nocodazole, which is known to increase contractility. Oncogene-transformed fibroblasts reacted to collisions with responses similar to nontransformed fibroblasts but did not develop well-organized cell–cell contacts. A model is presented to describe how differences in the organization of the actin cytoskeleton could account for the structurally distinct responses to cell–cell contact by polarized fibroblastic cells versus nonpolarized epithelial cells.

A theory for controlling cell cycle dynamics using a reversibly binding inhibitor

We demonstrate, by using mathematical modeling of cell division cycle (CDC) dynamics, a potential mechanism for precisely controlling the frequency of cell division and regulating the size of a dividing cell. Control of the cell cycle is achieved by artificially expressing a protein that reversibly binds and inactivates any one of the CDC proteins. In the simplest case, such as the checkpoint-free situation encountered in early amphibian embryos, the frequency of CDC oscillations can be increased or decreased by regulating the rate of synthesis, the binding rate, or the equilibrium constant of the binding protein. In a more complex model of cell division, where size-control checkpoints are included, we show that the same reversible binding reaction can alter the mean cell mass in a continuously dividing cell. Because this control scheme is general and requires only the expression of a single protein, it provides a practical means for tuning the characteristics of the cell cycle in vivo.

Dynamics and folding of single two-stranded coiled-coil peptides studied by fluorescent energy transfer confocal microscopy

We report single-molecule measurements on the folding and unfolding conformational equilibrium distributions and dynamics of a disulfide crosslinked version of the two-stranded coiled coil from GCN4. The peptide has a fluorescent donor and acceptor at the N termini of its two chains and a Cys disulfide near its C terminus. Thus, folding brings the two N termini of the two chains close together, resulting in an enhancement of fluorescent resonant energy transfer. End-to-end distance distributions have thus been characterized under conditions where the peptide is nearly fully folded (0 M urea), unfolded (7.4 M urea), and in dynamic exchange between folded and unfolded states (3.0 M urea). The distributions have been compared for the peptide freely diffusing in solution and deposited onto aminopropyl silanized glass. As the urea concentration is increased, the mean end-to-end distance shifts to longer distances both in free solution and on the modified surface. The widths of these distributions indicate that the molecules are undergoing millisecond conformational fluctuations. Under all three conditions, these fluctuations gave nonexponential correlations on 1- to 100-ms time scale. A component of the correlation decay that was sensitive to the concentration of urea corresponded to that measured by bulk relaxation kinetics. The trajectories provided effective intramolecular diffusion coefficients as a function of the end-to-end distances for the folded and unfolded states. Single-molecule folding studies provide information concerning the distributions of conformational states in the folded, unfolded, and dynamically interconverting states.

Solution structure and dynamics of GCN4 cognate DNA: NMR investigations

A 12 bp long GCN4-binding, self-complementary duplex DNA d(CATGACGTCATG)2 has been investigated by NMR spectroscopy to study the structure and dynamics of the molecule in aqueous solution. The NMR structure of the DNA obtained using simulated annealing and iterative relaxation matrix calculations compares quite closely with the X-ray structure of ATF/CREB DNA in complex with GCN4 protein (DNA-binding domain). The DNA is also seen to be curved in the free state and this has a significant bearing on recognition by the protein. The dynamic characteristics of the molecule have been studied by 13C relaxation measurements at natural abundance. A correlation has been observed between sequence-dependent dynamics and recognition by GCN4 protein.

Dynamics of Cytokinins in Apical Shoot Meristems of a Day-Neutral Tobacco during Floral Transition and Flower Formation1

This study considered cytokinin distribution in tobacco (Nicotiana tabacum L.) shoot apices in distinct phases of development using immunocytochemistry and quantitative tandem mass spectrometry. In contrast to vegetative apices and flower buds, we detected no free cytokinin bases (zeatin, dihydrozeatin, or isopentenyladenine) in prefloral transition apices. We also observed a 3-fold decrease in the content of cytokinin ribosides (zeatin riboside, dihydrozeatin riboside, and isopentenyladenosine) during this transition phase. The group concluded that organ formation (e.g. leaves and flowers) is characterized by enhanced cytokinin content, in contrast to the very low endogenous cytokinin levels found in prefloral transition apices, which showed no organogenesis. The immunocytochemical analyses revealed a differing intracellular localization of the cytokinin bases. Dihydrozeatin and isopentenyladenine were mainly cytoplasmic and perinuclear, whereas zeatin showed a clear-cut nuclear labeling. To our knowledge, this is the first time that this phenomenon has been reported. Cytokinins do not seem to act as positive effectors in the prefloral transition phase in tobacco shoot apices. Furthermore, the differences in distribution at the cellular level may be indicative of a specific physiological role of zeatin in nuclear processes.

Configurational diffusion down a folding funnel describes the dynamics of DNA hairpins

Elucidating the mechanism of folding of polynucleotides depends on accurate estimates of free energy surfaces and a quantitative description of the kinetics of structure formation. Here, the kinetics of hairpin formation in single-stranded DNA are measured after a laser temperature jump. The kinetics are modeled as configurational diffusion on a free energy surface obtained from a statistical mechanical description of equilibrium melting profiles. The effective diffusion coefficient is found to be strongly temperature-dependent in the nucleation step as a result of formation of misfolded loops that do not lead to subsequent zipping. This simple system exhibits many of the features predicted from theoretical studies of protein folding, including a funnel-like energy surface with many folding pathways, trapping in misfolded conformations, and non-Arrhenius folding rates.

Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay.

Anti-viral drug treatment of human immunodeficiency virus type I (HIV-1) and hepatitis B virus (HBV) infections causes rapid reduction in plasma virus load. Viral decline occurs in several phases and provides information on important kinetic constants of virus replication in vivo and pharmacodynamical properties. We develop a mathematical model that takes into account the intracellular phase of the viral life-cycle, defined as the time between infection of a cell and production of new virus particles. We derive analytic solutions for the dynamics following treatment with reverse transcriptase inhibitors, protease inhibitors, or a combination of both. For HIV-1, our results show that the phase of rapid decay in plasma virus (days 2-7) allows precise estimates for the turnover rate of productively infected cells. The initial quasi-stationary phase (days 0-1) and the transition phase (days 1-2) are explained by the combined effects of pharmacological and intracellular delays, the clearance of free virus particles, and the decay of infected cells. Reliable estimates of the first three quantities are not possible from data on virus load only; such estimates require additional measurements. In contrast with HIV-1, for HBV our model predicts that frequent early sampling of plasma virus will lead to reliable estimates of the free virus half-life and the pharmacological properties of the administered drug. On the other hand, for HBV the half-life of infected cells cannot be estimated from plasma virus decay.

Viral dynamics in hepatitis B virus infection.

Treatment of chronic hepatitis B virus (HBV) infections with the reverse transcriptase inhibitor lamivudine leads to a rapid decline in plasma viremia and provides estimates for crucial kinetic constants of HBV replication. We find that in persistently infected patients, HBV particles are cleared from the plasma with a half-life of approximately 1.0 day, which implies a 50% daily turnover of the free virus population. Total viral release into the periphery is approximately 10(11) virus particles per day. Although we have no direct measurement of the infected cell mass, we can estimate the turnover rate of these cells in two ways: (i) by comparing the rate of viral production before and after therapy or (ii) from the decline of hepatitis B antigen during treatment. These two independent methods give equivalent results: we find a wide distribution of half-lives for virus-producing cells, ranging from 10 to 100 days in different patients, which may reflect differences in rates of lysis of infected cells by immune responses. Our analysis provides a quantitative understanding of HBV replication dynamics in vivo and has implications for the optimal timing of drug treatment and immunotherapy in chronic HBV infection. This study also represents a comparison for recent findings on the dynamics of human immunodeficiency virus (HIV) infection. The total daily production of plasma virus is, on average, higher in chronic HBV carriers than in HIV-infected patients, but the half-life of virus-producing cells is much shorter in HIV. Most strikingly, there is no indication of drug resistance in HBV-infected patients treated for up to 24 weeks.

Thermodynamic parameters for the helix-coil transition of oligopeptides: molecular dynamics simulation with the peptide growth method.

The helix-coil transition equilibrium of polypeptides in aqueous solution was studied by molecular dynamics simulation. The peptide growth simulation method was introduced to generate dynamic models of polypeptide chains in a statistical (random) coil or an alpha-helical conformation. The key element of this method is to build up a polypeptide chain during the course of a molecular transformation simulation, successively adding whole amino acid residues to the chain in a predefined conformation state (e.g., alpha-helical or statistical coil). Thus, oligopeptides of the same length and composition, but having different conformations, can be incrementally grown from a common precursor, and their relative conformational free energies can be calculated as the difference between the free energies for growing the individual peptides. This affords a straightforward calculation of the Zimm-Bragg sigma and s parameters for helix initiation and helix growth. The calculated sigma and s parameters for the polyalanine alpha-helix are in reasonable agreement with the experimental measurements. The peptide growth simulation method is an effective way to study quantitatively the thermodynamics of local protein folding.