Piotr Pokarowski

AAindex: amino acid index database, progress report 2008

AAindex is a database of numerical indices representing various physicochemical and biochemical properties of amino acids and pairs of amino acids. We have added a collection of protein contact potentials to the AAindex as a new section. Accordingly AAindex consists of three sections now: AAindex1 for the amino acid index of 20 numerical values, AAindex2 for the amino acid substitution matrix and AAindex3 for the statistical protein contact potentials. All data are derived from published literature. The database can be accessed through the DBGET/LinkDB system at GenomeNet (http://www.genome.jp/dbget-bin/www_bfind?aaindex) or downloaded by anonymous FTP (ftp://ftp.genome.jp/pub/db/community/aaindex/).

Inferring ideal amino acid interaction forms from statistical protein contact potentials

We have analyzed 29 different published matrices of protein pairwise contact potentials (CPs) between amino acids derived from different sets of proteins, either crystallographic structures taken from the Protein Data Bank (PDB) or computer‐generated decoys. Each of the CPs is similar to 1 of the 2 matrices derived in the work of Miyazawa and Jernigan (Proteins 1999;34:49–68). The CP matrices of the first class can be approximated with a correlation of order 0.9 by the formula eij = hi + hj, 1 ≤ i, j ≤ 20, where the residue‐type dependent factor h is highly correlated with the frequency of occurrence of a given amino acid type inside proteins. Electrostatic interactions for the potentials of this class are almost negligible. In the potentials belonging to this class, the major contribution to the potentials is the one‐body transfer energy of the amino acid from water to the protein environment. Potentials belonging to the second class can be approximated with a correlation of 0.9 by the formula eij = c0 − hihj + qiqj, where c0 is a constant, h is highly correlated with the Kyte–Doolittle hydrophobicity scale, and a new, less dominant, residue‐type dependent factor q is correlated (∼0.9) with amino acid isoelectric points pI. Including electrostatic interactions significantly improves the approximation for this class of potentials. While, the high correlation between potentials of the first class and the hydrophobic transfer energies is well known, the fact that this approximation can work well also for the second class of potentials is a new finding. We interpret potentials of this class as representing energies of contact of amino acid pairs within an average protein environment. Proteins 2005.

Novel Proteins Regulated by mTOR in Subependymal Giant Cell Astrocytomas of Patients with Tuberous Sclerosis Complex and New Therapeutic Implications

Subependymal giant cell astrocytomas (SEGAs) are rare brain tumors associated with tuberous sclerosis complex (TSC), a disease caused by mutations in TSC1 or TSC2, resulting in enhancement of mammalian target of rapamycin (mTOR) activity, dysregulation of cell growth, and tumorigenesis. Signaling via mTOR plays a role in multifaceted genomic responses, but its effectors in the brain are largely unknown. Therefore, gene expression profiling on four SEGAs was performed with Affymetrix Human Genome arrays. Of the genes differentially expressed in TSC, 11 were validated by real-time PCR on independent tumor samples and 3 SEGA-derived cultures. Expression of several proteins was confirmed by immunohistochemistry. The differentially-regulated proteins were mainly involved in tumorigenesis and nervous system development. ANXA1, GPNMB, LTF, RND3, S100A11, SFRP4, and NPTX1 genes were likely to be mTOR effector genes in SEGA, as their expression was modulated by an mTOR inhibitor, rapamycin, in SEGA-derived cells. Inhibition of mTOR signaling affected size of cultured SEGA cells but had no influence on their proliferation, morphology, or migration, whereas inhibition of both mTOR and extracellular signal-regulated kinase signaling pathways led to significant alterations of these processes. For the first time, we identified genes related to the occurrence of SEGA and regulated by mTOR and demonstrated an effective modulation of SEGA growth by pharmacological inhibition of both mTOR and extracellular signal-regulated kinase signaling pathways, which could represent a novel therapeutic approach.

A minimal physically realistic protein-like lattice model: designing an energy landscape that ensures all-or-none folding to a unique native state

A simple protein model restricted to the face-centered cubic lattice has been studied. The model interaction scheme includes attractive interactions between hydrophobic (H) residues, repulsive interactions between hydrophobic and polar (P) residues, and orientation-dependent P-P interactions. Additionally, there is a potential that favors extended beta-type conformations. A sequence has been designed that adopts a native structure, consisting of an antiparallel, six-member Greek-key beta-barrel with protein-like structural degeneracy. It has been shown that the proposed model is a minimal one, i.e., all the above listed types of interactions are necessary for cooperative (all-or-none) type folding to the native state. Simulations were performed via the Replica Exchange Monte Carlo method and the numerical data analyzed via a multihistogram method.

Ideal amino acid exchange forms for approximating substitution matrices

We have analyzed 29 published substitution matrices (SMs) and five statistical protein contact potentials (CPs) for comparison. We find that popular, ‘classical’ SMs obtained mainly from sequence alignments of globular proteins are mostly correlated by at least a value of 0.9. The BLOSUM62 is the central element of this group. A second group includes SMs derived from alignments of remote homologs or transmembrane proteins. These matrices correlate better with classical SMs (0.8) than among themselves (0.7). A third group consists of intermediate links between SMs and CPs ‐ matrices and potentials that exhibit mutual correlations of at least 0.8. Next, we show that SMs can be approximated with a correlation of 0.9 by expressions c0 + xixj + yiyj + zizj, 1≤ i, j ≤ 20, where c0 is a constant and the vectors (xi), (yi), (zi) correlate highly with hydrophobicity, molecular volume and coil preferences of amino acids, respectively. The present paper is the continuation of our work (Pokarowski et al., Proteins 2005;59:49–57), where similar approximation were used to derive ideal amino acid interaction forms from CPs. Both approximations allow us to understand general trends in amino acid similarity and can help improve multiple sequence alignments using the fast Fourier transform (MAFFT), fast threading or another methods based on alignments of physicochemical profiles of protein sequences. The use of this approximation in sequence alignments instead of a classical SM yields results that differ by less than 5%. Intermediate links between SMs and CPs, new formulas for approximating these matrices, and the highly significant dependence of classical SMs on coil preferences are new findings. Proteins 2007.

Microscopic model of protein crystal growth

A microscopic, reversible model to study protein crystal nucleation and growth is presented. The probability of monomer attachment to the growing crystal was assumed to be proportional to the protein volume fraction and the orientational factor representing the anisotropy of protein molecules. The rate of detachment depended on the free energy of association of the given monomer in the lattice, as calculated from the buried surface area. The proposed algorithm allowed the simulation of the process of crystal growth from free monomers to complexes having 10(5) molecules, i.e. microcrystals with already formed faces. These simulations correctly reproduced the crystal morphology of the chosen model system--the tetragonal lysozyme crystal. We predicted the critical size, after which the growth rate rapidly increased to approximately 50 protein monomers. The major factors determining the protein crystallisation kinetics were the geometry of the protein molecules and the resulting number of kinetics traps on the growth pathway.

Lattice simulations of protein crystal formation.

A new algorithm is presented for the lattice simulation of protein crystal growth. The algorithm allows the calculation of the size distribution of microcrystals in the volume and timescale of experiments and within the framework of the previously-published microscopic model [A.M. Kierzek, W.M. Wolf, P. Zielenkiewicz, Biophys. J. 73 (1997) 571-580]. Simulations for the tetragonal lysozyme crystal show that there are two critical sizes in the development of ordered phase. The first one corresponds to the size of the smallest stable complex which, in the case of the tetragonal lysozyme crystal, is the particular tetramer. In a volume of 5 mul the tetramer appears in the millisecond timescale. The second critical radius of approximately 100 monomers is only reached by a few of all the smallest stable complexes formed in the solution. The model predicts that out of 10(7) tetramers which appear in solution, only eight reach the size of 100 monomers within 8 h. After exceeding the second critical radius the microcrystals grow to the size of 10(4) monomers in the minute timescale and are thus assumed to quickly lead to macroscopic crystals. The predicted number of crystals formed during 8 h of nucleation is in qualitative agreement with arrested nucleation experiments.

A minimal proteinlike lattice model: An alpha-helix motif

A simple protein model of a four-helix bundle motif on a face-centered cubic lattice has been studied. Total energy of a conformation includes attractive interactions between hydrophobic residues, repulsive interactions between hydrophobic and polar residues, and a potential that favors helical turns. Using replica exchange Monte Carlo simulations we have estimated a set of parameters for which the native structure is a global minimum of conformational energy. Then we have shown that all the above types of interactions are necessary to guarantee the cooperativity of folding transition and to satisfy the thermodynamic hypothesis.

The Tarski–Kantorovitch prinicple and the theory of iterated function systems

We show how some results of the theory of iterated function systems can be derived from the Tarski–Kantorovitch fixed–point principle for maps on partialy ordered sets. In particular, this principle yields, without using the Hausdorff metric, the Hutchinson–Barnsley theorem with the only restriction that a metric space considered has the Heine–Borel property. As a by–product, we also obtain some new characterisations of continuity of maps on countably compact and sequential spaces.

Uncoupling measures and eigenvalues of stochastic matrices

Abstract This paper gives bounds for the uncoupling measures of a stochastic matrix P in terms of its eigenvalues. The proofs are combinatorial. We use the Matrix–Tree Theorem which represents principal minors of I – P as sums of weights of directed forests.