Venkatesh Mysore

Prediction of DNA-binding residues from sequence

MOTIVATION Thousands of proteins are known to bind to DNA; for most of them the mechanism of action and the residues that bind to DNA, i.e. the binding sites, are yet unknown. Experimental identification of binding sites requires expensive and laborious methods such as mutagenesis and binding essays. Hence, such studies are not applicable on a large scale. If the 3D structure of a protein is known, it is often possible to predict DNA-binding sites in silico. However, for most proteins, such knowledge is not available. RESULTS It has been shown that DNA-binding residues have distinct biophysical characteristics. Here we demonstrate that these characteristics are so distinct that they enable accurate prediction of the residues that bind DNA directly from amino acid sequence, without requiring any additional experimental or structural information. In a cross-validation based on the largest non-redundant dataset of high-resolution protein-DNA complexes available today, we found that 89% of our predictions are confirmed by experimental data. Thus, it is now possible to identify DNA-binding sites on a proteomic scale even in the absence of any experimental data or 3D-structural information. AVAILABILITY http://cubic.bioc.columbia.edu/services/disis.

Algorithmic algebraic model checking i: challenges from systems biology

In this paper, we suggest a possible confluence of the theory of hybrid automata and the techniques of algorithmic algebra to create a computational basis for systems biology. We describe a method to compute bounded reachability by combining Taylor polynomials and cylindric algebraic decomposition algorithms. We discuss the power and limitations of the framework we propose and we suggest several possible extensions. We briefly show an application to the study of the Delta-Notch protein signaling system in biology.

Algorithmic algebraic model checking II: decidability of semi-algebraic model checking and its applications to systems biology

Motivated by applications to systems biology, and the emergence of semi-algebraic hybrid systems as a natural framework for modeling biochemical networks, we continue exploring the decidability problem for model-checking with TCTL (Timed Computation Tree Logic) over this broad class of semi-algebraic hybrid systems. Previously, we had introduced these models, demonstrated the close connection to the goals of systems biology. However, we had only developed the techniques for bounded reachability, arguing for the adequacy of such an approach in a majority of the biological applications. Here, we present a semi-decidable symbolic algebraic dense-time TCTL model checking algorithm, which satisfies two desirable properties: it can be derived automatically from the symbolic description, and it extends to and generalizes other versions of temporal logics. The main mathematical device at the core of this approach is Tarski-Collins’ real quantifier elimination employed at each fixpoint iteration, whose high complexity is the crux of its unfortunate limitation. Along with these results, we prove the undecidability of this problem in the more powerful “real” Turing machine formalism of Blum, Shub and Smale. We then demonstrate a preliminary version of our model-checker Tolque on the Delta-Notch example.

Structural analysis of the EGFR/HER3 heterodimer reveals the molecular basis for activating HER3 mutations

Cancer-associated mutations in the catalytically inactive receptor HER3 enhance its ability to activate other members of the human epidermal growth factor receptor family. Cancer by Enhanced Allosteric Activation Cancer-associated, oncogenic mutations in kinases often result in increased catalytic activity. Although cancer-associated mutations in the HER3 member of the epidermal growth factor receptor (EGFR) family of receptor tyrosine kinases exist, this receptor has little, if any, catalytic activity. The four members of the EGFR family form homodimers or heterodimers; this dimerization is necessary for the kinase activity of the catalytically active members HER1, HER2, and HER4. In homodimeric structures, one kinase subunit functions as an allosteric activator and the other as the activated receiver. Littlefield et al. crystallized the kinase domain of HER1 in complex with the kinase domain of wild-type HER3 or HER3 with cancer-associated mutations. This analysis, along with in vitro biochemical kinase assays, showed that HER3 functioned as an activator in the heterodimer and that the mutations enhanced the interaction between HER3 and HER1, thereby augmenting the allosteric activator function of HER3. This study provides a rationale for targeting the heterodimer interface with HER3 in cancer associated with aberrant activity of this family of receptors. The human epidermal growth factor receptor (HER) tyrosine kinases homo- and heterodimerize to activate downstream signaling pathways. HER3 is a catalytically impaired member of the HER family that contributes to the development of several human malignancies and is mutated in a subset of cancers. HER3 signaling depends on heterodimerization with a catalytically active partner, in particular epidermal growth factor receptor (EGFR) (the founding family member, also known as HER1) or HER2. The activity of homodimeric complexes of catalytically active HER family members depends on allosteric activation between the two kinase domains. To determine the structural basis for HER3 signaling through heterodimerization with a catalytically active HER family member, we solved the crystal structure of the heterodimeric complex formed by the isolated kinase domains of EGFR and HER3. The structure showed HER3 as an allosteric activator of EGFR and revealed a conserved role of the allosteric mechanism in activation of HER family members through heterodimerization. To understand the effects of cancer-associated HER3 mutations at the molecular level, we solved the structures of two kinase domains of HER3 mutants, each in a heterodimeric complex with the kinase domain of EGFR. These structures, combined with biochemical analysis and molecular dynamics simulations, indicated that the cancer-associated HER3 mutations enhanced the allosteric activator function of HER3 by redesigning local interactions at the dimerization interface.

EGFR oligomerization organizes kinase-active dimers into competent signalling platforms

Epidermal growth factor receptor (EGFR) signalling is activated by ligand-induced receptor dimerization. Notably, ligand binding also induces EGFR oligomerization, but the structures and functions of the oligomers are poorly understood. Here, we use fluorophore localization imaging with photobleaching to probe the structure of EGFR oligomers. We find that at physiological epidermal growth factor (EGF) concentrations, EGFR assembles into oligomers, as indicated by pairwise distances of receptor-bound fluorophore-conjugated EGF ligands. The pairwise ligand distances correspond well with the predictions of our structural model of the oligomers constructed from molecular dynamics simulations. The model suggests that oligomerization is mediated extracellularly by unoccupied ligand-binding sites and that oligomerization organizes kinase-active dimers in ways optimal for auto-phosphorylation in trans between neighbouring dimers. We argue that ligand-induced oligomerization is essential to the regulation of EGFR signalling.

Refining the undecidability frontier of hybrid automata

Reachability becomes undecidable in hybrid automata (HA) that can simulate a Turing (TM) or Minsky (MM) machine. Asarin and Schneider have shown that, between the decidable 2-dim Piecewise Constant Derivative (PCD) class and the undecidable 3-dim PCD class, there lies the “open” class 2-dim Hierarchical PCD (HPCD). This class was shown to be equivalent to the class of 1-dim Piecewise Affine Maps (PAM). In this paper, we first explore 2-dim HPCDs proximity to decidability, by showing that they are equivalent to 2-dim PCDs with translational resets, and to HPCDs without resets. A hierarchy of intermediates also equivalent to the HPCD class is presented, revealing semblance to timed and initialized rectangular automata. We then explore the proximity to the undecidability frontier. We show that 2-dim HPCDs with zeno executions or integer-checks can simulate the 2-counter MM. We conclude by retreating HPCDs as PAMs, to derive a simple over-approximating algorithm for reachability. This also defines a decidable subclass 1-dim Onto PAM (oPAM). The novel non-trivial transformation of 2-dim HPCDs into “almost decidable” systems, is likely to pave the way for approximate reachability algorithms, and the characterization of decidable subclasses. It is hoped that these ideas eventually coalesce into a complete understanding of the reachability problem for the class 2-dim HPCD (1-dim PAM).

Low dimensional hybrid systems - decidable, undecidable, don't know

Even though many attempts have been made to define the boundary between decidable and undecidable hybrid systems, the affair is far from being resolved. More and more low dimensional systems are being shown to be undecidable with respect to reachability, and many open problems in between are being discovered. In this paper, we present various two-dimensional hybrid systems for which the reachability problem is undecidable. We show their undecidability by simulating Minsky machines. Their proximity to the decidability frontier is understood by inspecting the most parsimonious constraints necessary to make reachability over these automata decidable. We also show that for other two-dimensional systems, the reachability question remains unanswered, by proving that it is as hard as the reachability problem for piecewise affine maps on the real line, which is a well known open problem.

Fast and cheap genome wide haplotype construction via optical mapping.

We describe an efficient algorithm to construct genome wide haplotype restriction maps of an individual by aligning single molecule DNA fragments collected with Optical Mapping technology. Using this algorithm and small amount of genomic material, we can construct the parental haplotypes for each diploid chromosome for any individual. Since such haplotype maps reveal the polymorphisms due to single nucleotide differences (SNPs) and small insertions and deletions (RFLPs), they are useful in association studies, studies involving genomic instabilities in cancer, and genetics, and yet incur relatively low cost and provide high throughput. If the underlying problem is formulated as a combinatorial optimization problem, it can be shown to be NP-complete (a special case of K-population problem). But by effectively exploiting the structure of the underlying error processes and using a novel analog of the Baum-Welch algorithm for HMM models, we devise a probabilistic algorithm with a time complexity that is linear in the number of markers for an epsilon-approximate solution. The algorithms were tested by constructing the first genome wide haplotype restriction map of the microbe T. pseudoana, as well as constructing a haplotype restriction map of a 120 Mb region of Human chromosome 4. The frequency of false positives and false negatives was estimated using simulated data. The empirical results were found very promising.

Algorithmic Algebraic Model Checking III: Approximate Methods

We present computationally efficient techniques for approximate model-checking using bisimulation-partitioning, polyhedra, grids and time discretization for semi-algebraic hybrid systems, and demonstrate how they relate to and extend other existing techniques.

Algorithmic algebraic model checking IV: characterization of metabolic networks

A series of papers, all under the title of Algorithmic Algebraic Model Checking (AAMC), has sought to combine techniques from algorithmic algebra, model checking and dynamical systems to examine how a biochemical hybrid dynamical system can be made amenable to temporal analysis, even when the initial conditions and unknown parameters may only be treated as symbolic variables. This paper examines how to specialize this framework to metabolic control analysis (MCA) involving many reactions operating at many dissimilar time-scales. In the earlier AAMC papers, it has been shown that the dynamics of various biochemical semi-algebraic hybrid automata could be unraveled using powerful techniques from computational real algebraic geometry. More specifically, the resulting algebraic model checking techniques were found to be suitable for biochemical networks modeled using general mass action (GMA) based ODEs. This paper scrutinizes how the special properties of metabolic networks-a subclass of the biochemical networks previously handled-can be exploited to gain improvement in computational efficiency. The paper introduces a general framework for performing symbolic temporal reasoning over metabolic network hybrid automata that handles both GMA-based equilibrium estimation and flux balance analysis (FBA).While algebraic polynomial equations over Q[x1, ..., xn] can be symbolically solved using Grobner bases or Wu-Ritt characteristic sets, the FBA-based estimation can be performed symbolically by rephrasing the algebraic optimization problem as a quantifier elimination problem. Effectively, an approximate hybrid automaton that simulates the metabolic network is derived, and is thus amenable to manipulation by the algebraic model checking techniques previously described in the AAMC papers.