Oscillatory regulation of Hes1: Discrete stochastic delay modelling and simulation

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

Prediction of cis/trans isomerization in proteins using PSI-BLAST profiles and secondary structure information

Background The majority of peptide bonds in proteins are found to occur in the trans conformation. However, for proline residues, a considerable fraction of Prolyl peptide bonds adopt the cis form. Proline cis/trans isomerization is known to play a critical role in protein folding, splicing, cell signaling and transmembrane active transport. Accurate prediction of proline cis/trans isomerization in proteins would have many important applications towards the understanding of protein structure and function. Results In this paper, we propose a new approach to predict the proline cis/trans isomerization in proteins using support vector machine (SVM). The preliminary results indicated that using Radial Basis Function (RBF) kernels could lead to better prediction performance than that of polynomial and linear kernel functions. We used single sequence information of different local window sizes, amino acid compositions of different local sequences, multiple sequence alignment obtained from PSI-BLAST and the secondary structure information predicted by PSIPRED. We explored these different sequence encoding schemes in order to investigate their effects on the prediction performance. The training and testing of this approach was performed on a newly enlarged dataset of 2424 non-homologous proteins determined by X-Ray diffraction method using 5-fold cross-validation. Selecting the window size 11 provided the best performance for determining the proline cis/trans isomerization based on the single amino acid sequence. It was found that using multiple sequence alignments in the form of PSI-BLAST profiles could significantly improve the prediction performance, the prediction accuracy increased from 62.8% with single sequence to 69.8% and Matthews Correlation Coefficient (MCC) improved from 0.26 with single local sequence to 0.40. Furthermore, if coupled with the predicted secondary structure information by PSIPRED, our method yielded a prediction accuracy of 71.5% and MCC of 0.43, 9% and 0.17 higher than the accuracy achieved based on the singe sequence information, respectively. Conclusion A new method has been developed to predict the proline cis/trans isomerization in proteins based on support vector machine, which used the single amino acid sequence with different local window sizes, the amino acid compositions of local sequence flanking centered proline residues, the position-specific scoring matrices (PSSMs) extracted by PSI-BLAST and the predicted secondary structures generated by PSIPRED. The successful application of SVM approach in this study reinforced that SVM is a powerful tool in predicting proline cis/trans isomerization in proteins and biological sequence analysis.

Identifying optimal lipid raft characteristics required to promote nanoscale protein-protein interactions on the plasma membrane

The dynamic lateral segregation of signaling proteins into microdomains is proposed to facilitate signal transduction, but the constraints on microdomain size, mobility, and diffusion that might realize this function are undefined. Here we interrogate a stochastic spatial model of the plasma membrane to determine how microdomains affect protein dynamics. Taking lipid rafts as representative microdomains, we show that reduced protein mobility in rafts segregates dynamically partitioning proteins, but the equilibrium concentration is largely independent of raft size and mobility. Rafts weakly impede small-scale protein diffusion but more strongly impede long-range protein mobility. The long-range mobility of raft-partitioning and raft-excluded proteins, however, is reduced to a similar extent. Dynamic partitioning into rafts increases specific interprotein collision rates, but to maximize this critical, biologically relevant function, rafts must be small (diameter, 6 to 14 nm) and mobile. Intermolecular collisions can also be favored by the selective capture and exclusion of proteins by rafts, although this mechanism is generally less efficient than simple dynamic partitioning. Generalizing these results, we conclude that microdomains can readily operate as protein concentrators or isolators but there appear to be significant constraints on size and mobility if microdomains are also required to function as reaction chambers that facilitate nanoscale protein-protein interactions. These results may have significant implications for the many signaling cascades that are scaffolded or assembled in plasma membrane microdomains.