ABSTRACT
A general method for facilitating the interpretation of computer simulations of protein folding with minimally frustrated energy landscapes is detailed and applied to a designed ankyrin repeat protein (4ANK). In the method, groups of residues are assigned to foldons and these foldons are used to map the conformational space of the protein onto a set of discrete macrobasins. The free energies of the individual macrobasins are then calculated, informing practical kinetic analysis. Two simple assumptions about the universality of the rate for downhill transitions between macrobasins and the natural local connectivity between macrobasins lead to a scheme for predicting overall folding and unfolding rates, generating chevron plots under varying thermodynamic conditions, and inferring dominant kinetic folding pathways. To illustrate the approach, free energies of macrobasins were calculated from biased simulations of a non-additive structure-based model using two structurally motivated foldon definitions at the full and half ankyrin repeat resolutions. The calculated chevrons have features consistent with those measured in stopped flow chemical denaturation experiments. The dominant inferred folding pathway has an "inside-out", nucleation-propagation like character.
Subject(s)
Ankyrin Repeat , Computer Simulation , Models, Molecular , Protein Conformation , Proteins/chemistry , Kinetics , Protein FoldingABSTRACT
Many transcription factors bind to DNA with a remarkable lack of specificity, so that regulatory binding sites compete with an enormous number of nonregulatory "decoy" sites. For an autoregulated gene, we show decoy sites decrease noise in the number of unbound proteins to a Poisson limit that results from binding and unbinding. This noise buffering is optimized for a given protein concentration when decoys have a 1/2 probability of being occupied. Decoys linearly increase the time to approach steady state and exponentially increase the time to switch epigenetically between bistable states.
Subject(s)
Biophysics/methods , DNA/chemistry , Gene Expression Regulation , Algorithms , Amino Acid Motifs , Binding Sites , DNA/metabolism , Epigenesis, Genetic , Evolution, Molecular , Gene Expression , Genome , Models, Biological , Models, Statistical , Models, Theoretical , Poisson Distribution , Probability , Promoter Regions, Genetic , Protein Binding , Transcription Factors/metabolismABSTRACT
Recent studies suggest that there are many nonfunctional transcription factor binding sites along a genome. Although these "decoy" sites compete with the promoter region for binding of transcription factors, they may also protect these proteins from degradation. We show that in the limit of perfect protection, where bound transcription factors are never degraded, the competitive effect of nonfunctional binding sites is completely canceled out by the stability gained from reduced degradation. We examine the response of an autoregulated gene to the total number of transcription factors to quantify the consequences of competition for transcription factors. We show that intuition about this system can be gained by mathematically constructing a single gene with effective parameters that reproduce the behavior of a gene with added decoy sites. In analogy to dressed particles in many-body systems we term this description a "quasi gene." We find that protective decoys buffer against noise by reducing correlations between transcription factors, specifically in the case of production of transcription factors in bursts. We show that the addition of protective decoy sites causes the level of gene expression to approach that predicted from deterministic mass action models. Finally, we show that protective decoy sites decrease the size of the region of parameter space that exhibits bistability.
