Marek Kochańczyk

Prediction of functional sites based on the fuzzy oil drop model

A description of many biological processes requires knowledge of the 3-D structure of proteins and, in particular, the defined active site responsible for biological function. Many proteins, the genes of which have been identified as the result of human genome sequencing, and which were synthesized experimentally, await identification of their biological activity. Currently used methods do not always yield satisfactory results, and new algorithms need to be developed to recognize the localization of active sites in proteins. This paper describes a computational model that can be used to identify potential areas that are able to interact with other molecules (ligands, substrates, inhibitors, etc.). The model for active site recognition is based on the analysis of hydrophobicity distribution in protein molecules. It is shown, based on the analyses of proteins with known biological activity and of proteins of unknown function, that the region of significantly irregular hydrophobicity distribution in proteins appears to be function related.

Spontaneous NF-κB Activation by Autocrine TNFα Signaling: A Computational Analysis

NF-κB is a key transcription factor that regulates innate immune response. Its activity is tightly controlled by numerous feedback loops, including two negative loops mediated by NF-κB inducible inhibitors, IκBα and A20, which assure oscillatory responses, and by positive feedback loops arising due to the paracrine and autocrine regulation via TNFα, IL-1 and other cytokines. We study the NF-κB system of interlinked negative and positive feedback loops, combining bifurcation analysis of the deterministic approximation with stochastic numerical modeling. Positive feedback assures the existence of limit cycle oscillations in unstimulated wild-type cells and introduces bistability in A20-deficient cells. We demonstrated that cells of significant autocrine potential, i.e., cells characterized by high secretion of TNFα and its receptor TNFR1, may exhibit sustained cytoplasmic–nuclear NF-κB oscillations which start spontaneously due to stochastic fluctuations. In A20-deficient cells even a small TNFα expression rate qualitatively influences system kinetics, leading to long-lasting NF-κB activation in response to a short-pulsed TNFα stimulation. As a consequence, cells with impaired A20 expression or increased TNFα secretion rate are expected to have elevated NF-κB activity even in the absence of stimulation. This may lead to chronic inflammation and promote cancer due to the persistent activation of antiapoptotic genes induced by NF-κB. There is growing evidence that A20 mutations correlate with several types of lymphomas and elevated TNFα secretion is characteristic of many cancers. Interestingly, A20 loss or dysfunction also leaves the organism vulnerable to septic shock and massive apoptosis triggered by the uncontrolled TNFα secretion, which at high levels overcomes the antiapoptotic action of NF-κB. It is thus tempting to speculate that some cancers of deregulated NF-κB signaling may be prone to the pathogen-induced apoptosis.

Feedbacks, Bifurcations, and Cell Fate Decision-Making in the p53 System

The p53 transcription factor is a regulator of key cellular processes including DNA repair, cell cycle arrest, and apoptosis. In this theoretical study, we investigate how the complex circuitry of the p53 network allows for stochastic yet unambiguous cell fate decision-making. The proposed Markov chain model consists of the regulatory core and two subordinated bistable modules responsible for cell cycle arrest and apoptosis. The regulatory core is controlled by two negative feedback loops (regulated by Mdm2 and Wip1) responsible for oscillations, and two antagonistic positive feedback loops (regulated by phosphatases Wip1 and PTEN) responsible for bistability. By means of bifurcation analysis of the deterministic approximation we capture the recurrent solutions (i.e., steady states and limit cycles) that delineate temporal responses of the stochastic system. Direct switching from the limit-cycle oscillations to the “apoptotic” steady state is enabled by the existence of a subcritical Neimark—Sacker bifurcation in which the limit cycle loses its stability by merging with an unstable invariant torus. Our analysis provides an explanation why cancer cell lines known to have vastly diverse expression levels of Wip1 and PTEN exhibit a broad spectrum of responses to DNA damage: from a fast transition to a high level of p53 killer (a p53 phosphoform which promotes commitment to apoptosis) in cells characterized by high PTEN and low Wip1 levels to long-lasting p53 level oscillations in cells having PTEN promoter methylated (as in, e.g., MCF-7 cell line).

Dynamics of a stochastic spatially extended system predicted by comparing deterministic and stochastic attractors of the corresponding birth-death process

Living cells may be considered as biochemical reactors of multiple steady states. Transitions between these states are enabled by noise, or, in spatially extended systems, may occur due to the traveling wave propagation. We analyze a one-dimensional bistable stochastic birth-death process by means of potential and temperature fields. The potential is defined by the deterministic limit of the process, while the temperature field is governed by noise. The stable steady state in which the potential has its global minimum defines the global deterministic attractor. For the stochastic system, in the low noise limit, the stationary probability distribution becomes unimodal, concentrated in one of two stable steady states, defined in this study as the global stochastic attractor. Interestingly, these two attractors may be located in different steady states. This observation suggests that the asymptotic behavior of spatially extended stochastic systems depends on the substrate diffusivity and size of the reactor. We confirmed this hypothesis within kinetic Monte Carlo simulations of a bistable reaction- diffusion model on the hexagonal lattice. In particular, we found that although the kinase-phosphatase system remains inactive in a small domain, the activatory traveling wave may propagate when a larger domain is considered.

Stochastic transitions in a bistable reaction system on the membrane

Transitions between steady states of a multi-stable stochastic system in the perfectly mixed chemical reactor are possible only because of stochastic switching. In realistic cellular conditions, where diffusion is limited, transitions between steady states can also follow from the propagation of travelling waves. Here, we study the interplay between the two modes of transition for a prototype bistable system of kinase–phosphatase interactions on the plasma membrane. Within microscopic kinetic Monte Carlo simulations on the hexagonal lattice, we observed that for finite diffusion the behaviour of the spatially extended system differs qualitatively from the behaviour of the same system in the well-mixed regime. Even when a small isolated subcompartment remains mostly inactive, the chemical travelling wave may propagate, leading to the activation of a larger compartment. The activating wave can be induced after a small subdomain is activated as a result of a stochastic fluctuation. Such a spontaneous onset of activity is radically more probable in subdomains characterized by slower diffusion. Our results show that a local immobilization of substrates can lead to the global activation of membrane proteins by the mechanism that involves stochastic fluctuations followed by the propagation of a semi-deterministic travelling wave.

Levels of pro-apoptotic regulator Bad and anti-apoptotic regulator Bcl-xL determine the type of the apoptotic logic gate.

BackgroundApoptosis is a tightly regulated process: cellular survive-or-die decisions cannot be accidental and must be unambiguous. Since the suicide program may be initiated in response to numerous stress stimuli, signals transmitted through a number of checkpoints have to be eventually integrated.ResultsIn order to analyze possible mechanisms of the integration of multiple pro-apoptotic signals, we constructed a simple model of the Bcl-2 family regulatory module. The module collects upstream signals and processes them into life-or-death decisions by employing interactions between proteins from three subgroups of the Bcl-2 family: pro-apoptotic multidomain effectors, pro-survival multidomain restrainers, and pro-apoptotic single domain BH3-only proteins. Although the model is based on ordinary differential equations (ODEs), it demonstrates that the Bcl-2 family module behaves akin to a Boolean logic gate of the type dependent on levels of BH3-only proteins (represented by Bad) and restrainers (represented by Bcl-xL). A low level of pro-apoptotic Bad or a high level of pro-survival Bcl-xL implies gate AND, which allows for the initiation of apoptosis only when two stress stimuli are simultaneously present: the rise of the p53 killer level and dephosphorylation of kinase Akt. In turn, a high level of Bad or a low level of Bcl-xL implies gate OR, for which any of these stimuli suffices for apoptosis.ConclusionsOur study sheds light on possible signal integration mechanisms in cells, and spans a bridge between modeling approaches based on ODEs and on Boolean logic. In the proposed scheme, logic gates switching results from the change of relative abundances of interacting proteins in response to signals and involves system bistability. Consequently, the regulatory system may process two analogous inputs into a digital survive-or-die decision.

In silico Structural Study of Random Amino Acid Sequence Proteins Not Present in Nature

The three‐dimensional structures of a set of ‘never born proteins’ (NBP, random amino acid sequence proteins with no significant homology with known proteins) were predicted using two methods: Rosetta and the one based on the ‘fuzzy‐oil‐drop’ (FOD) model. More than 3000 different random amino acid sequences have been generated, filtered against the non redundant protein sequence data base, to remove sequences with significant homology with known proteins, and subjected to three‐dimensional structure prediction. Comparison between Rosetta and FOD predictions allowed to select the ten top (highest structural similarity) and the ten bottom (the lowest structural similarity) structures from the ranking list organized according to the RMS‐D value. The selected structures were taken for detailed analysis to define the scale of structural accordance and discrepancy between the two methods. The structural similarity measurements revealed discrepancies between structures generated on the basis of the two methods. Their potential biological function appeared to be quite different as well. The ten bottom structures appeared to be ‘unfoldable’ for the FOD model. Some aspects of the general characteristics of the NBPs are also discussed. The calculations were performed on the EUChinaGRID grid platform to test the performance of this infrastructure for massive protein structure predictions.

Relaxation oscillations and hierarchy of feedbacks in MAPK signaling

We formulated a computational model for a MAPK signaling cascade downstream of the EGF receptor to investigate how interlinked positive and negative feedback loops process EGF signals into ERK pulses of constant amplitude but dose-dependent duration and frequency. A positive feedback loop involving RAS and SOS, which leads to bistability and allows for switch-like responses to inputs, is nested within a negative feedback loop that encompasses RAS and RAF, MEK, and ERK that inhibits SOS via phosphorylation. This negative feedback, operating on a longer time scale, changes switch-like behavior into oscillations having a period of 1 hour or longer. Two auxiliary negative feedback loops, from ERK to MEK and RAF, placed downstream of the positive feedback, shape the temporal ERK activity profile but are dispensable for oscillations. Thus, the positive feedback introduces a hierarchy among negative feedback loops, such that the effect of a negative feedback depends on its position with respect to the positive feedback loop. Furthermore, a combination of the fast positive feedback involving slow-diffusing membrane components with slower negative feedbacks involving faster diffusing cytoplasmic components leads to local excitation/global inhibition dynamics, which allows the MAPK cascade to transmit paracrine EGF signals into spatially non-uniform ERK activity pulses.

Prediction of functionally important residues in globular proteins from unusual central distances of amino acids

BackgroundWell-performing automated protein function recognition approaches usually comprise several complementary techniques. Beside constructing better consensus, their predictive power can be improved by either adding or refining independent modules that explore orthogonal features of proteins. In this work, we demonstrated how the exploration of global atomic distributions can be used to indicate functionally important residues.ResultsUsing a set of carefully selected globular proteins, we parametrized continuous probability density functions describing preferred central distances of individual protein atoms. Relative preferred burials were estimated using mixture models of radial density functions dependent on the amino acid composition of a protein under consideration. The unexpectedness of extraordinary locations of atoms was evaluated in the information-theoretic manner and used directly for the identification of key amino acids. In the validation study, we tested capabilities of a tool built upon our approach, called SurpResi, by searching for binding sites interacting with ligands. The tool indicated multiple candidate sites achieving success rates comparable to several geometric methods. We also showed that the unexpectedness is a property of regions involved in protein-protein interactions, and thus can be used for the ranking of protein docking predictions. The computational approach implemented in this work is freely available via a Web interface at http://www.bioinformatics.org/surpresi.ConclusionsProbabilistic analysis of atomic central distances in globular proteins is capable of capturing distinct orientational preferences of amino acids as resulting from different sizes, charges and hydrophobic characters of their side chains. When idealized spatial preferences can be inferred from the sole amino acid composition of a protein, residues located in hydrophobically unfavorable environments can be easily detected. Such residues turn out to be often directly involved in binding ligands or interfacing with other proteins.

RAF1/BRAF dimerization integrates the signal from RAS to ERK and ROKα

The signal to move or proliferate diverges at RAF1. Coordinating proliferation and migration with RAF1 The kinase RAF1 is the mitogen-activated protein kinase kinase kinase (MAPKKK) that sits at the top of the proliferative pathway activated by growth factors. Growth factors stimulate a transient increase in the kinase activity of RAF1 through a complex set of phosphorylation and dephosphorylation events. Through a kinase-independent mechanism, RAF1 is also an inhibitor of the kinase ROKα, thereby coupling growth factor signaling to the cytoskeleton. Varga et al. identified how these two activities are controlled by the formation of specific phosphorylated forms of RAF1, as this kinase interacts with the signaling complex that activates the MAPK cascade. By combining the analysis of protein interactions detected by immunoprecipitation with computational modeling, the authors determined that the interaction with BRAF as part of the MAPK signaling complex stimulated the formation of the RAF1 phosphorylated form that signaled as a MAPKKK and also the formation of a distinct form that inhibited ROKα. Given the importance of RAF signaling in development, physiology, and various pathologies, such as cancer, this finding provides valuable insight into the molecular events controlling the output of this protein. Downstream of growth factor receptors and of the guanine triphosphatase (GTPase) RAS, heterodimers of the serine/threonine kinases BRAF and RAF1 are critical upstream kinases and activators of the mitogen-activated protein kinase (MAPK) module containing the mitogen-activated and extracellular signal–regulated kinase kinase (MEK) and their targets, the extracellular signal–regulated kinase (ERK) family. Either direct or scaffold protein–mediated interactions among the components of the ERK module (the MAPKKKs BRAF and RAF1, MEK, and ERK) facilitate signal transmission. RAF1 also has essential functions in the control of tumorigenesis and migration that are mediated through its interaction with the kinase ROKα, an effector of the GTPase RHO and regulator of cytoskeletal rearrangements. We combined mutational and kinetic analysis with mathematical modeling to show that the interaction of RAF1 with ROKα is coordinated with the role of RAF1 in the ERK pathway. We found that the phosphorylated form of RAF1 that interacted with and inhibited ROKα was generated during the interaction of RAF1 with the ERK module. This mechanism adds plasticity to the ERK pathway, enabling signal diversification at the level of both ERK and RAF. Furthermore, by connecting ERK activation with the regulation of ROKα and cytoskeletal rearrangements by RAF1, this mechanism has the potential to precisely coordinate the proper timing of proliferation with changes in cell shape, adhesion, or motility.