Data-Driven Supervised Learning for Life Science Data

Life science data are often encoded in a non-standard way by means of alpha-numeric sequences, graph representations, numerical vectors of variable length, or other formats. Domain-specific or data-driven similarity measures like alignment functions have been employed with great success. The vast majority of more complex data analysis algorithms require fixed-length vectorial input data, asking for substantial preprocessing of life science data. Data-driven measures are widely ignored in favor of simple encodings. These preprocessing steps are not always easy to perform nor particularly effective, with a potential loss of information and interpretability. We present some strategies and concepts of how to employ data-driven similarity measures in the life science context and other complex biological systems. In particular, we show how to use data-driven similarity measures effectively in standard learning algorithms

Bifurcations of maps: numerical algorithms and applications

Dynamical systems theory provides mathematical models for systems which evolve in time according to a rule, originally expressed in analytical form as a system of equations. Discrete-time dynamical systems defined by an iterated map depending on control parameters, \begin{equation} \label{Map:g} g(x,\alpha) := f^{(J)}(x,\alpha)= \underbrace{f(f(f(\cdots f}_{J \mbox{~times}}(x,\alpha),\alpha),\alpha),\alpha), \end{equation} appear naturally in, e.g., ecology and economics, where $x\in \R^n$ and $\alpha \in \R^k$ are vectors of state variables and parameters, respectively. %The system dynamics describe a sequence of points \left\{x_k{\right\} \subset \R^n (orbit), provided an initial $x_0 \in \R^n$ is given. The main goal in the study of a dynamical system is to find a complete characterization of the geometry of the orbit structure and the change in orbit structure under parameter variation. An aspect of this study is to identify the invariant objects and the local behaviour around them. This local information then needs to be assembled in a consistent way by means of geometric and topological arguments, to obtain a global picture of the system. At local bifurcations, the number of steady states can change, or the stability properties of a steady state may change. The computational analysis of local bifurcations usually begins with an attempt to compute the coefficients that appear in the normal form after coordinate transformation. These coefficients, called critical normal form coefficients, determine the direction of branching of new objects and their stability near the bifurcation point. After locating a codim 1 bifurcation point, the logical next step is to consider the variation of a second parameter to enhance our knowledge about the system and its dynamical behaviour. % % In codim 2 bifurcation points branches of various codim 1 bifurcation curves are rooted. % These curve can be computed by a combination of parameter-dependent center manifold reduction and asymptotic expressions for the new emanating curves. We implemented new and improved algorithms for the bifurcation analysis of fixed points and periodic orbits of maps in the {\sc Matlab} software package {\sc Cl\_MatcontM}. This includes the numerical continuation of fixed points of iterates of the map with one control parameter, detecting and locating their bifurcation points, and their continuation in two control parameters, as well as detection and location of all codim 2 bifurcation points on the corresponding curves. For all bifurcations of codim 1 and 2, the critical normal form coefficients are computed with finite directional differences, automatic differentiation and symbolic derivatives of the original map. Asymptotics are derived for bifurcation curves of double and quadruple period cycles rooted at codim 2 points of cycles with arbitrary period to continue the double and quadruple period bifurcations. In the case $n=2$ we compute one-dimensional invariant manifolds and their transversal intersections to obtain initial connections of homoclinic and heteroclinic orbits orbits to fixed points of (\ref{Map:g}). We continue connecting orbits, using an algorithm based on the continuation of invariant subspaces, and compute their fold bifurcation curves, corresponding to the tangencies of the invariant manifolds. {\sc Cl\_MatcontM} is freely available at {\bf www.matcont.ugent.be} and {\bf www. sourceforge.net}

Modulation of calmodulin lobes by different targets: an allosteric model with hemiconcerted conformational transitions

Calmodulin, the ubiquitous calcium-activated second messenger in eukaryotes, is an extremely versatile molecule involved in many biological processes: muscular contraction, synaptic plasticity, circadian rhythm, and cell cycle, among others. The protein is structurally organised into two globular lobes, joined by a flexible linker. Calcium modulates calmodulin activity by favoring a conformational transition of each lobe from a closed conformation to an open conformation. Most targets have a strong preference for one conformation over the other, and depending on the free calcium concentration in a cell, particular sets of targets will preferentially interact with calmodulin. In turn, targets can increase or decrease the calcium affinity of the calmodulin molecules to which they bind. Interestingly, experiments with the tryptic fragments showed that most targets have a much lower affinity for the N-lobe than for the C-lobe. Hence, the latter predominates in the formation of most calmodulin-target complexes. We showed that a relatively simple allosteric mechanism, based the classic MWC model, can capture the observed modulation of both the isolated C-lobe, and intact calmodulin, by individual targets. Moreover, our model can be naturally extended to study how the calcium affinity of a single pool of calmodulin is modulated by a mixture of competing targets in vivo

Smooth Key-framing using the Image Plane

This paper demonstrates the use of image-space constraints for key frame interpolation. Interpolating in image-space results in sequences with predictable and controlable image trajectories and projected size for selected objects, particularly in cases where the desired center of rotation is not fixed or when the key frames contain perspective distortion changes. Additionally, we provide the user with direct image-space control over {\em how} the key frames are interpolated by allowing them to directly edit the object\u27s projected size and trajectory. Image-space key frame interpolation requires solving the inverse camera problem over a sequence of point constraints. This is a variation of the standard camera pose problem, with the additional constraint that the sequence be visually smooth. We use image-space camera interpolation to globally control the projection, and traditional camera interpolation locally to avoid smoothness problems. We compare and contrast three different constraint-solving systems in terms of accuracy, speed, and stability. The first approach was originally developed to solve this problem [Gleicher and Witken 1992]; we extend it to include internal camera parameter changes. The second approach uses a standard single-frame solver. The third approach is based on a novel camera formulation and we show that it is particularly suited to solving this problem

Inferring gene ontologies from pairwise similarity data.

MotivationWhile the manually curated Gene Ontology (GO) is widely used, inferring a GO directly from -omics data is a compelling new problem. Recognizing that ontologies are a directed acyclic graph (DAG) of terms and hierarchical relations, algorithms are needed that: analyze a full matrix of gene-gene pairwise similarities from -omics data; infer true hierarchical structure in these data rather than enforcing hierarchy as a computational artifact; and respect biological pleiotropy, by which a term in the hierarchy can relate to multiple higher level terms. Methods addressing these requirements are just beginning to emerge-none has been evaluated for GO inference.MethodsWe consider two algorithms [Clique Extracted Ontology (CliXO), LocalFitness] that uniquely satisfy these requirements, compared with methods including standard clustering. CliXO is a new approach that finds maximal cliques in a network induced by progressive thresholding of a similarity matrix. We evaluate each method's ability to reconstruct the GO biological process ontology from a similarity matrix based on (a) semantic similarities for GO itself or (b) three -omics datasets for yeast.ResultsFor task (a) using semantic similarity, CliXO accurately reconstructs GO (>99% precision, recall) and outperforms other approaches (<20% precision, <20% recall). For task (b) using -omics data, CliXO outperforms other methods using two -omics datasets and achieves ∼30% precision and recall using YeastNet v3, similar to an earlier approach (Network Extracted Ontology) and better than LocalFitness or standard clustering (20-25% precision, recall).ConclusionThis study provides algorithmic foundation for building gene ontologies by capturing hierarchical and pleiotropic structure embedded in biomolecular data