Optimal combination of theory and experiment for the characterization of the protein folding landscape of S6: how far can a minimalist model go?

The detailed characterization of the overall free energy landscape associated with the folding process of a protein is the ultimate goal in protein folding studies. Modern experimental techniques provide accurate thermodynamic and kinetic measurements on restricted regions of a protein landscape. Although simplified protein models can access larger regions of the landscape, they are oftentimes built on assumptions and approximations that affect the accuracy of the results. We present a new methodology that allows to combine the complementary strengths of theory and experiment for a more complete characterization of a protein folding landscape. We prove that this new procedure allows a simplified protein model to reproduce remarkably well (correlation coefficient > 0.9) all experimental data available on free energies differences upon single mutations for S6 ribosomal protein and two circular permutants. Our results confirm and quantify the hypothesis, recently formulated on the basis of experimental data, that the folding landscape of protein S6 is strongly affected by an atypical distribution of contact energies.     

Estimating protein turnover with a [15N,13C]leucine tracer: a study using simulated data.

We explore the use of [15N,13C]leucine tracer to estimate whole-body fractional rates of a fast-turning-over protein pool employing synthetic data. The kinetics of [15N,13C]leucine tracer are simplified compared with those of traditional leucine tracers and benefit from irreversible transamination to [13C]alpha-ketoisocaproaic acid (KIC) resulting in a simplified model structure. A three-compartment model of [15N,13C]leucine kinetics was proposed and evaluated using data generated by a Reference Model (based on a model by Cobelli et al.). The results suggest that fractional turnover rates of a fast-turning-over protein pool can be estimated with a low but acceptable precision during a six-hour constant intravenous infusion of [15N,13C]leucine with frequent sampling of plasma tracer-to-tracee ratio (TTR) of [15N,13C]leucine. We conclude that [15N,13C]leucine may be useful for the measurement of protein kinetics and its full potential should be explored in clinical studies with compartmental data analysis.     

Retrospective optimization of time-dependent fermentation control strategies using time-independent historical data

We have previously shown the usefulness of historical data for fermentation process optimization. The methodology developed includes identification of important process inputs, training of an artificial neural network (ANN) process model, and ultimately use of the ANN model with a genetic algorithm to find the optimal values of each critical process input. However, this approach ignores the time-dependent nature of the system, and therefore, does not fully utilize the available information within a database. In this work, we propose a method for incorporating time-dependent optimization into our previously developed three-step optimization routine. This is achieved by an additional step that uses a fermentation model (consisting of coupled ordinary differential equations (ODE)) to interpret important time-course features of the collected data through adjustments in model parameters. Important process variables not explicitly included in the model were then identified for each model parameter using automatic relevance determination (ARD) with Gaussian process (GP) models. The developed GP models were then combined with the fermentation model to form a hybrid neural network model that predicted the time-course activity of the cell and protein concentrations of novel fermentation conditions. A hybrid-genetic algorithm was then used in conjunction with the hybrid model to suggest optimal time-dependent control strategies. The presented method was implemented upon an E. coli fermentation database generated in our laboratory. Optimization of two different criteria (final protein yield and a simplified economic criteria) was attempted. While the overall protein yield was not increased using this methodology, we were successful in increasing a simplified economic criterion by 15% compared to what had been previously observed. These process conditions included using 35% less arabinose (the inducer) and 33% less typtone in the media and reducing the time required to reach the maximum protein concentration by 10% while producing approximately the same level of protein as the previous optimum.     

Computer simulations aimed at structure prediction of supersecondary motifs in proteins

It is well established that protein structures are more conserved than protein sequences. One-third of all known protein structures can be classified into ten protein folds, which themselves are composed mainly of alpha-helical hairpin, beta hairpin, and betaalphabeta supersecondary structural elements. In this study, we explore the ability of a recent Monte Carlo-based procedure to generate the 3D structures of eight polypeptides that correspond to units of supersecondary structure and three-stranded antiparallel beta sheet. Starting from extended or misfolded compact conformations, all Monte Carlo simulations show significant success in predicting the native topology using a simplified chain representation and an energy model optimized on other structures. Preliminary results on model peptides from nucleotide binding proteins suggest that this simple protein folding model can help clarify the relation between sequence and topology.     

Computer analysis of protein-protein interaction

An automatic procedure which generates possible modes of protein-protein association is developed and applied to the bovine pancreatic trypsin inhibitor-trypsin complex as a test case. Using a simplified model in which each residue is replaced by one interaction center, all possible modes of interaction between the inhibitor and the active center of the enzyme are generated systematically. The non-bonded interactions between the molecules and the protein surface area buried in the generated interfaces are evaluated and used as criteria for selecting stable complexes. We show that satisfactory estimates of accessible and buried surface areas can be made using the simplified model.The procedure leads to about nine structures having non-bonded interactions and buried surface areas similar to those of the native complex. This suggests that the major contributions to the free energy of dissociation are taken into account by our selection procedure, though complementarity and specificity are not properly represented in the simplified model. However, it makes it possible to scan a much larger number of configurations than would otherwise be feasible, chiefly through elimination of side-chain detail.     

Design of a folding inhibitor of the HIV-1 protease

A novel way to inhibit HIV-1 protease by destabilizing its native state is discussed. A simplified protein model is used together with Monte Carlo simulations, to assess the destabilizing effect of peptides displaying the same sequence as specific fragments of the protein which are essential for its stability. Model calculations also show that it is unlikely that the protein can escape the inhibitory peptide by point mutations.     

In vivo monitoring of intracellular expression of human interleukin-2 using green fluorescent protein fusion partner in Pichia pastoris

The use of Pichia pastoris for protein production was simplified by creation of fusion proteins containing green fluorescent protein (GFP) and the product of interest. Human interleukin-2 (hIL-2) was used as a model product: GFP enabled clear identification of fusion protein expression and, more importantly, the quantification of hIL-2. Although GFP fusions for bioprocess monitoring have been demonstrated in other hosts, this is its first use in P. pastoris.     

基于氨基酸特征序列对人类Rh血型系统的蛋白质结构分析

利用代数学中同态思想和物理中的“粗粒化”思想,以及HP模型,根据a,t,c,g的化学结构分类,提出了DNA序列的特征序列概念（σ-,τ-,σ∩τ-）并推广到蛋白质序列中,从而给出一种数值刻划,将蛋白质序列简化成一个（0,1）序列,基于上述给出特征序列的方法,根据氨基酸分子量与简并度的关系,提出了另外一种DNA序列的特征序列概念（-）并推广到蛋白质序列中,进而给出了另外一种数值刻划,将蛋白质序列简化成一个（0,1,2）序列,通过比较RHD基因和RHCE基因的特征序列的数值刻划图,得出RHD基因和RHCE基因均偏爱使用低分子量且高简并度的氨基酸。     

A computer model to dynamically simulate protein folding: studies with crambin

The current work describes a simplified representation of protein structure with uses in the simulation of protein folding. The model assumes that a protein can be represented by a freely rotating rigid chain with a single atom approximating the effect of each side chain. Potentials describing the attraction or repulsion between different types of amino acids are determined directly from the distribution of amino acids in the database of known protein structures. The optimization technique of simulated annealing has been used to dynamically sample the conformations available to this simple model, allowing the protein to evolve from an extended, random coil into a compact globular structure. Many characteristics expected of true proteins, such as the sequence-dependent formation of secondary structure, the partitioning of hydrophobic residues, and specific disulfide pairing, are reproduced by the simulation, suggesting the model may accurately simulate the folding process.     

Folding Trp-cage to NMR resolution native structure using a coarse-grained protein model

We develop a coarse-grained protein model with a simplified amino acid interaction potential. Using this model, we perform discrete molecular dynamics folding simulations of a small 20-residue protein--Trp-cage--from a fully extended conformation. We demonstrate the ability of the Trp-cage model to consistently reach conformations within 2-angstroms backbone root-mean-square distance from the corresponding NMR structures. The minimum root-mean-square distance of Trp-cage conformations in simulations can be <1 angstroms. Our findings suggest that, at least in the case of Trp-cage, a detailed all-atom protein model with a molecular mechanics force field is not necessary to reach the native state of a protein. Our results also suggest that the success of folding Trp-cage in our simulations and in the reported all-atom molecular mechanics simulation studies may be mainly due to the special stabilizing features specific to this miniprotein.     

Single-molecule unfolding force distributions reveal a funnel-shaped energy landscape

The protein folding process is described as diffusion on a high-dimensional energy landscape. Experimental data showing details of the underlying energy surface are essential to understanding folding. So far in single-molecule mechanical unfolding experiments a simplified model assuming a force-independent transition state has been used to extract such information. Here we show that this so-called Bell model, although fitting well to force velocity data, fails to reproduce full unfolding force distributions. We show that by applying Kramers' diffusion model, we were able to reconstruct a detailed funnel-like curvature of the underlying energy landscape and establish full agreement with the data. We demonstrate that obtaining spatially resolved details of the unfolding energy landscape from mechanical single-molecule protein unfolding experiments requires models that go beyond the Bell model.     

Phase separation and bistability in a three-dimensional model for protein domain formation at biomembranes

Proteins in living cells interact with membranes. They may bind to or unbind from the membrane to the cytosol depending on the lipid composition of the membrane and their interaction with cytosolic enzymes. Moreover, proteins can accumulate at the membrane and assemble in spatial domains. Here, a simple model of protein cycling at biomembranes is studied, when the total number of proteins is conserved. Specifically, we consider the spatio-temporal dynamics of MARCKS proteins and their interactions with enzymes facilitating translocation from and rebinding to the membrane. The model exhibits two qualitatively different mechanisms of protein domain formation: phase separation related to a long-wave instability of a membrane state with homogeneous protein coverage and stable coexistence of two states with different homogeneous protein coverage in bistable media. We evaluate the impact of the cytosolic volume on the occurrence of protein pattern formation by simulations in a three-dimensional model. We show that the explicit treatment of the volume in the model leads to an effective rescaling of the reaction rates. For a simplified model of protein cycling, we can derive analytical expressions for the rescaling coefficients and verify them by direct simulations with the complete three-dimensional model.     

Changes of protein stiffness during folding detect protein folding intermediates

Single-molecule force-quench atomic force microscopy (FQ-AFM) is used to detect folding intermediates of a simple protein by detecting changes of molecular stiffness of the protein during its folding process. Those stiffness changes are obtained from shape and peaks of an autocorrelation of fluctuations in end-to-end length of the folding molecule. The results are supported by predictions of the equipartition theorem and agree with existing Langevin dynamics simulations of a simplified model of a protein folding. In the light of the Langevin simulations the experimental data probe an ensemble of random-coiled collapsed states of the protein, which are present both in the force-quench and thermal-quench folding pathways.     

A computational approach to simplifying the protein folding alphabet.

What is the minimal number of residue types required to form a structured protein? This question is important for understanding protein modeling and design. Recently, an experimental finding by Baker and coworkers suggested a five-residue solution to this problem. We were motivated by their results and by the arguments of Wolynes to study reductions of protein representation based on the concept of mismatch between a reduced interaction matrix and the Miyazawa and Jernigan (MJ) matrix. We find several possible simplified schemes from the relationship of minimized mismatch versus the number of residue types (N = approximately 2-20). As a specific case, an optimal reduction with five types of residues has the same form as the simplified palette of Baker and coworkers. Statistical and kinetic features of a number of sequences are tested. Comparison of results from sequences with 20 residue types and their reduced representations indicates that the reduction by mismatch minimization is successful. For example, sequences with five types of residues have good folding ability and kinetic accessibility in model studies.     

A simple reaction kinetic model of rapid (G protein dependent) and slow (beta-Arrestin dependent) transmission

In this paper the qualitative dynamic behavior of reaction kinetic models of G protein signaling is examined. A simplified basic G protein signaling structure is defined, which is extended to be able to take the effect of slow transmission, RGS mediated feedback regulation and ERK-phosphatase mediated feedback regulation into account. The resulting model gives rise to an acceptable qualitative approximation of the G protein dependent and independent ERK activation dynamics that is in good agreement with the experimentally observed behavior.     

Intermediate filament networks: in vitro and in vivo assembly models

We propose two systems of ordinary differential equations modeling the assembly of intermediate filament networks. The first one describes the in vitro intermediate filament assembly dynamics. The second one deals with the in vivo evolution of cytokeratin, which is the intermediate filament protein expressed by epithelial cells. The in vitro model is then briefly analyzed in a simplified case.     

Computational Modeling of Proteins based on Cellular Automata: A Method of HP Folding Approximation

The design of a protein folding approximation algorithm is not straightforward even when a simplified model is used. The folding problem is a combinatorial problem, where approximation and heuristic algorithms are usually used to find near optimal folds of proteins primary structures. Approximation algorithms provide guarantees on the distance to the optimal solution. The folding approximation approach proposed here depends on two-dimensional cellular automata to fold proteins presented in a well-studied simplified model called the hydrophobic–hydrophilic model. Cellular automata are discrete computational models that rely on local rules to produce some overall global behavior. One-third and one-fourth approximation algorithms choose a subset of the hydrophobic amino acids to form H–H contacts. Those algorithms start with finding a point to fold the protein sequence into two sides where one side ignores H’s at even positions and the other side ignores H’s at odd positions. In addition, blocks or groups of amino acids fold the same way according to a predefined normal form. We intend to improve approximation algorithms by considering all hydrophobic amino acids and folding based on the local neighborhood instead of using normal forms. The CA does not assume a fixed folding point. The proposed approach guarantees one half approximation minus the H–H endpoints. This lower bound guaranteed applies to short sequences only. This is proved as the core and the folds of the protein will have two identical sides for all short sequences.