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.

RIGS (repeat-induced gene silencing) in Arabidopsis is transcriptional and alters chromatin configuration.

We have previously reported repeat-induced gene silencing (RIGS) in Arabidopsis, in which transgene expression may be silenced epigenetically when repeated sequences are present. Among an allelic series of lines comprising a primary transformant and various recombinant progeny carrying different numbers of drug resistance gene copies at the same locus, silencing was found to depend strictly on repeated sequences and to correlate with an absence of steady-state mRNA. We now report characterization, in nuclei isolated from the same transgenic lines, of gene expression by nuclear run-on assay and of chromatin structure by nuclease protection assay. We find that silencing is correlated with absence of run-on transcripts, indicating that expression is silenced at the level of transcription. We find further that silencing is also correlated with increased resistance to both DNase I and micrococcal nuclease, indicating that the silenced state reflects a change in chromatin configuration. We propose that silencing results when a locally paired region of homologous repeated nucleotide sequences is flanked by unpaired heterologous DNA, which leads chromatin to adopt a local configuration that is difficult to transcribe, and possibly akin to heterochromatin.

A maximum likelihood algorithm for genome mapping of cytogenetic loci from meiotic configuration data.

Frequencies of meiotic configurations in cytogenetic stocks are dependent on chiasma frequencies in segments defined by centromeres, breakpoints, and telomeres. The expectation maximization algorithm is proposed as a general method to perform maximum likelihood estimations of the chiasma frequencies in the intervals between such locations. The estimates can be translated via mapping functions into genetic maps of cytogenetic landmarks. One set of observational data was analyzed to exemplify application of these methods, results of which were largely concordant with other comparable data. The method was also tested by Monte Carlo simulation of frequencies of meiotic configurations from a monotelodisomic translocation heterozygote, assuming six different sample sizes. The estimate averages were always close to the values given initially to the parameters. The maximum likelihood estimation procedures can be extended readily to other kinds of cytogenetic stocks and allow the pooling of diverse cytogenetic data to collectively estimate lengths of segments, arms, and chromosomes.