Computer simulations of enzyme catalysis: Finding out what has been optimized by evolution

The origin of the catalytic power of enzymes is discussed, paying attention to evolutionary constraints. It is pointed out that enzyme catalysis reflects energy contributions that cannot be determined uniquely by current experimental approaches without augmenting the analysis by computer simulation studies. The use of energy considerations and computer simulations allows one to exclude many of the popular proposals for the way enzymes work. It appears that the standard approaches used by organic chemists to catalyze reactions in solutions are not used by enzymes. This point is illustrated by considering the desolvation hypothesis and showing that it cannot account for a large increase in kcat relative to the corresponding kcage for the reference reaction in a solvent cage. The problems associated with other frequently invoked mechanisms also are outlined. Furthermore, it is pointed out that mutation studies are inconsistent with ground state destabilization mechanisms. After considering factors that were not optimized by evolution, we review computer simulation studies that reproduced the overall catalytic effect of different enzymes. These studies pointed toward electrostatic effects as the most important catalytic contributions. The nature of this electrostatic stabilization mechanism is far from being obvious because the electrostatic interaction between the reacting system and the surrounding area is similar in enzymes and in solution. However, the difference is that enzymes have a preorganized dipolar environment that does not have to pay the reorganization energy for stabilizing the relevant transition states. Apparently, the catalytic power of enzymes is stored in their folding energy in the form of the preorganized polar environment.

Extent of genomic rearrangement after genome duplication in yeast

Whole-genome duplication approximately 108 years ago was proposed as an explanation for the many duplicated chromosomal regions in Saccharomyces cerevisiae. Here we have used computer simulations and analytic methods to estimate some parameters describing the evolution of the yeast genome after this duplication event. Computer simulation of a model in which 8% of the original genes were retained in duplicate after genome duplication, and 70–100 reciprocal translocations occurred between chromosomes, produced arrangements of duplicated chromosomal regions very similar to the map of real duplications in yeast. An analytical method produced an independent estimate of 84 map disruptions. These results imply that many smaller duplicated chromosomal regions exist in the yeast genome in addition to the 55 originally reported. We also examined the possibility of determining the original order of chromosomal blocks in the ancestral unduplicated genome, but this cannot be done without information from one or more additional species. If the genome sequence of one other species (such as Kluyveromyces lactis) were known it should be possible to identify 150–200 paired regions covering the whole yeast genome and to reconstruct approximately two-thirds of the original order of blocks of genes in yeast. Rates of interchromosome translocation in yeast and mammals appear similar despite their very different rates of homologous recombination per kilobase.

Instability of signaling resolution models of parent–offspring conflict

Recent signaling resolution models of parent–offspring conflict have provided an important framework for theoretical and empirical studies of communication and parental care. According to these models, signaling of need is stabilized by its cost. However, our computer simulations of the evolutionary dynamics of chick begging and parental investment show that in Godfray’s model the signaling equilibrium is evolutionarily unstable: populations that start at the signaling equilibrium quickly depart from it. Furthermore, the signaling and nonsignaling equilibria are linked by a continuum of equilibria where chicks above a certain condition do not signal and we show that, contrary to intuition, fitness increases monotonically as the proportion of young that signal decreases. This result forces us to reconsider much of the current literature on signaling of need and highlights the need to investigate the evolutionary stability of signaling equilibria based on the handicap principle.

Spatial scales of desert locust gregarization

Central to swarm formation in migratory locusts is a crowding-induced change from a “solitarious” to a “gregarious” phenotype. This change can occur within the lifetime of a single locust and accrues across generations. It represents an extreme example of phenotypic plasticity. We present computer simulations and a laboratory experiment that show how differences in resource distributions, conspicuous only at small spatial scales, can have significant effects on phase change at the population level; local spatial concentration of resource induces gregarization. Simulations also show that populations inhabiting a locally concentrated resource tend to change phase rapidly and synchronously in response to altered population densities. Our results show why information about the structure of resource at small spatial scales should become key components in monitoring and control strategies.

Comparative T cell receptor repertoire selection by antigen after adoptive transfer: A glimpse at an antigen-specific preimmune repertoire

The low frequency of precursor cells specific for any particular antigen (Ag) makes it difficult to characterize preimmune T cell receptor (TCR) repertoires and to understand repertoire selection during an immune response. We have undertaken a combined adoptive transfer single-cell PCR approach to probe the Ag-specific preimmune repertoires of individual mice. Our strategy was to inject paired irradiated recipient mice with normal spleen cells prepared from individual donors and to compare the TCR repertoires subsequently selected during a CD8 response to a defined model Ag. We found that although some TCRs were shared, the TCR repertoires selected by mice receiving splenocytes from the same donor were not identical in terms of the TCRs selected and their relative frequencies. Our results together with computer simulations imply that individual mice express distinct Ag-specific preimmune TCR repertoires composed of expanded clones and that selection by Ag is a random process.

Shape anisotropy of a single random-walk polymer

Random walks have been used to describe a wide variety of systems ranging from cell colonies to polymers. Sixty-five years ago, Kuhn [Kuhn, W. (1934) Kolloid-Z. 68, 2–11] made the prediction, backed later by computer simulations, that the overall shape of a random-walk polymer is aspherical, yet no experimental work has directly tested Kuhn's general idea and subsequent computer simulations. By using fluorescence microscopy, we monitored the conformation of individual, long, random-walk polymers (fluorescently labeled DNA molecules) at equilibrium. We found that a polymer most frequently adopts highly extended, nonfractal structures with a strongly anisotropic shape. The ensemble-average ratio of the lengths of the long and short axes of the best-fit ellipse of the polymer was much larger than unity.

Mechanism of topology simplification by type II DNA topoisomerases

Type II DNA topoisomerases actively reduce the fractions of knotted and catenated circular DNA below thermodynamic equilibrium values. To explain this surprising finding, we designed a model in which topoisomerases introduce a sharp bend in DNA. Because the enzymes have a specific orientation relative to the bend, they act like Maxwell's demon, providing unidirectional strand passage. Quantitative analysis of the model by computer simulations proved that it can explain much of the experimental data. The required sharp DNA bend was demonstrated by a greatly increased cyclization of short DNA fragments from topoisomerase binding and by direct visualization with electron microscopy.

A New Model for Nuclear Envelope BreakdownV⃞

Nuclear envelope breakdown was investigated during meiotic maturation of starfish oocytes. Fluorescent 70-kDa dextran entry, as monitored by confocal microscopy, consists of two phases, a slow uniform increase and then a massive wave. From quantitative analysis of the first phase of dextran entry, and from imaging of green fluorescent protein chimeras, we conclude that nuclear pore disassembly begins several minutes before nuclear envelope breakdown. The best fit for the second phase of entry is with a spreading disruption of the membrane permeability barrier determined by three-dimensional computer simulations of diffusion. We propose a new model for the mechanism of nuclear envelope breakdown in which disassembly of the nuclear pores leads to a fenestration of the nuclear envelope double membrane.

Evolution of RNA editing in trypanosome mitochondria

Two different RNA editing systems have been described in the kinetoplast-mitochondrion of trypanosomatid protists. The first involves the precise insertion and deletion of U residues mostly within the coding regions of maxicircle-encoded mRNAs to produce open reading frames. This editing is mediated by short overlapping complementary guide RNAs encoded in both the maxicircle and the minicircle molecules and involves a series of enzymatic cleavage-ligation steps. The second editing system is a C34 to U34 modification in the anticodon of the imported tRNATrp, thereby permitting the decoding of the UGA stop codon as tryptophan. U-insertion editing probably originated in an ancestor of the kinetoplastid lineage and appears to have evolved in some cases by the replacement of the original pan-edited cryptogene with a partially edited cDNA. The driving force for the evolutionary fixation of these retroposition events was postulated to be the stochastic loss of entire minicircle sequence classes and their encoded guide RNAs upon segregation of the single kinetoplast DNA network into daughter cells at cell division. A large plasticity in the relative abundance of minicircle sequence classes has been observed during cell culture in the laboratory. Computer simulations provide theoretical evidence for this plasticity if a random distribution and segregation model of minicircles is assumed. The possible evolutionary relationship of the C to U and U-insertion editing systems is discussed.

Human cooperation in the simultaneous and the alternating Prisoner's Dilemma: Pavlov versus Generous Tit-for-Tat.

The iterated Prisoner's Dilemma has become the paradigm for the evolution of cooperation among egoists. Since Axelrod's classic computer tournaments and Nowak and Sigmund's extensive simulations of evolution, we know that natural selection can favor cooperative strategies in the Prisoner's Dilemma. According to recent developments of theory the last champion strategy of "win--stay, lose--shift" ("Pavlov") is the winner only if the players act simultaneously. In the more natural situation of players alternating the roles of donor and recipient a strategy of "Generous Tit-for-Tat" wins computer simulations of short-term memory strategies. We show here by experiments with humans that cooperation dominated in both the simultaneous and the alternating Prisoner's Dilemma. Subjects were consistent in their strategies: 30% adopted a Generous Tit-for-Tat-like strategy, whereas 70% used a Pavlovian strategy in both the alternating and the simultaneous game. As predicted for unconditional strategies, Pavlovian players appeared to be more successful in the simultaneous game whereas Generous Tit-for-Tat-like players achieved higher payoffs in the alternating game. However, the Pavlovian players were smarter than predicted: they suffered less from defectors and exploited cooperators more readily. Humans appear to cooperate either with a Generous Tit-for-Tat-like strategy or with a strategy that appreciates Pavlov's advantages but minimizes its handicaps.

Sequence scanning: A method for rapid sequence acquisition from large-fragment DNA clones.

A strategy of "sequence scanning" is proposed for rapid acquisition of sequence from clones such as bacteriophage P1 clones, cosmids, or yeast artificial chromosomes. The approach makes use of a special vector, called LambdaScan, that reliably yields subclones with inserts in the size range 8-12 kb. A number of subclones, typically 96 or 192, are chosen at random, and the ends of the inserts are sequenced using vector-specific primers. Then long-range spectrum PCR is used to order and orient the clones. This combination of shotgun and directed sequencing results in a high-resolution physical map suitable for the identification of coding regions or for comparison of sequence organization among genomes. Computer simulations indicate that, for a target clone of 100 kb, the scanning of 192 subclones with sequencing reads as short as 350 bp results in an approximate ratio of 1:2:1 of regions of double-stranded sequence, single-stranded sequence, and gaps. Longer sequencing reads tip the ratio strongly toward increased double-stranded sequence.

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.

Analysis of the role of the Spitzenkörper in fungal morphogenesis by computer simulation of apical branching in Aspergillus niger

High-resolution video microscopy, image analysis, and computer simulation were used to study the role of the Spitzenkörper (Spk) in apical branching of ramosa-1, a temperature-sensitive mutant of Aspergillus niger. A shift to the restrictive temperature led to a cytoplasmic contraction that destabilized the Spk, causing its disappearance. After a short transition period, new Spk appeared where the two incipient apical branches emerged. Changes in cell shape, growth rate, and Spk position were recorded and transferred to the fungus simulator program to test the hypothesis that the Spk functions as a vesicle supply center (VSC). The simulation faithfully duplicated the elongation of the main hypha and the two apical branches. Elongating hyphae exhibited the growth pattern described by the hyphoid equation. During the transition phase, when no Spk was visible, the growth pattern was nonhyphoid, with consecutive periods of isometric and asymmetric expansion; the apex became enlarged and blunt before the apical branches emerged. Video microscopy images suggested that the branch Spk were formed anew by gradual condensation of vesicle clouds. Simulation exercises where the VSC was split into two new VSCs failed to produce realistic shapes, thus supporting the notion that the branch Spk did not originate by division of the original Spk. The best computer simulation of apical branching morphogenesis included simulations of the ontogeny of branch Spk via condensation of vesicle clouds. This study supports the hypothesis that the Spk plays a major role in hyphal morphogenesis by operating as a VSC—i.e., by regulating the traffic of wall-building vesicles in the manner predicted by the hyphoid model.

Computer determination of peptide conformations in water: different roads to structure.

Fragments of proteins (short peptides) that "fold" suggest a mechanism of how complete conformational search in protein folding is avoided. We used a computational method to determine structures of two foldable peptides in explicit water: RVEW and CSVTC. The optimization starts from random structures and no experimental constraints are used. In agreement with NMR data, the simulations find a hydrophobic pair (Val/Trp) in REVW. The structure of CSVTC is induced by a surface water that bridges two amide hydrogens, a drive to structure hypothesized by Ben-Naim [Ben-Naim, A. (1990) J. Chem. Phys. 93, 8196-8210] that is largely ignored in studies of folding. Tendency to structure in short peptide chains suggests a mechanism for the formation of short-range nucleation sites in protein folding.