Learning the Kernel Matrix with Semi-Definite Programming

Kernel-based learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information is contained in the so-called kernel matrix, a symmetric and positive definite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space -- classical model selection problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semi-definite programming (SDP) techniques. When applied to a kernel matrix associated with both training and test data this gives a powerful transductive algorithm -- using the labelled part of the data one can learn an embedding also for the unlabelled part. The similarity between test points is inferred from training points and their labels. Importantly, these learning problems are convex, so we obtain a method for learning both the model class and the function without local minima. Furthermore, this approach leads directly to a convex method to learn the 2-norm soft margin parameter in support vector machines, solving another important open problem. Finally, the novel approach presented in the paper is supported by positive empirical results.

Stochastic models for regulatory networks of the genetic toggle switch

Bistability arises within a wide range of biological systems from the λ phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. In this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

Extracellular matrix of the human cyclic corpus luteum

Extracellular matrix regulates many cellular processes likely to be important for development and regression of corpora lutea. Therefore, we identified the types and components of the extracellular matrix of the human corpus luteum at different stages of the menstrual cycle. Two different types of extracellular matrix were identified by electron microscopy; subendothelial basal laminas and an interstitial matrix located as aggregates at irregular intervals between the non-vascular cells. No basal laminas were associated with luteal cells. At all stages, collagen type IV α1 and laminins α5, β2 and γ1 were localized by immunohistochemistry to subendothelial basal laminas, and collagen type IV α1 and laminins α2, α5, β1 and β2 localized in the interstitial matrix. Laminin α4 and β1 chains occurred in the subendothelial basal lamina from mid-luteal stage to regression; at earlier stages, a punctate pattern of staining was observed. Therefore, human luteal subendothelial basal laminas potentially contain laminin 11 during early luteal development and, additionally, laminins 8, 9 and 10 at the mid-luteal phase. Laminin α1 and α3 chains were not detected in corpora lutea. Versican localized to the connective tissue extremities of the corpus luteum. Thus, during the formation of the human corpus luteum, remodelling of extracellular matrix does not result in basal laminas as present in the adrenal cortex or ovarian follicle. Instead, novel aggregates of interstitial matrix of collagen and laminin are deposited within the luteal parenchyma, and it remains to be seen whether this matrix is important for maintaining the luteal cell phenotype.

Homodimerization controls the fibroblast growth factor 9 subfamily's receptor binding and heparan sulfate-dependent diffusion in the extracellular matrix

Uncontrolled fibroblast growth factor (FGF) signaling can lead to human diseases, necessitating multiple layers of self-regulatory control mechanisms to keep its activity in check. Herein, we demonstrate that FGF9 and FGF20 ligands undergo a reversible homodimerization, occluding their key receptor binding sites. To test the role of dimerization in ligand autoinhibition, we introduced structure-based mutations into the dimer interfaces of FGF9 and FGF20. The mutations weakened the ability of the ligands to dimerize, effectively increasing the concentrations of monomeric ligands capable of binding and activating their cognate FGF receptor in vitro and in living cells. Interestingly, the monomeric ligands exhibit reduced heparin binding, resulting in their increased radii of heparan sulfate-dependent diffusion and biologic action, as evidenced by the wider dilation area of ex vivo lung cultures in response to implanted mutant FGF9-loaded beads. Hence, our data demonstrate that homodimerization autoregulates FGF9 and FGF20's receptor binding and concentration gradients in the extracellular matrix. Our study is the first to implicate ligand dimerization as an autoregulatory mechanism for growth factor bioactivity and sets the stage for engineering modified FGF9 subfamily ligands, with desired activity for use in both basic and translational research.

Stochastic simulation of chemical reactions in spatially complex media

Discrete stochastic simulations, via techniques such as the Stochastic Simulation Algorithm (SSA) are a powerful tool for understanding the dynamics of chemical kinetics when there are low numbers of certain molecular species. However, an important constraint is the assumption of well-mixedness and homogeneity. In this paper, we show how to use Monte Carlo simulations to estimate an anomalous diffusion parameter that encapsulates the crowdedness of the spatial environment. We then use this parameter to replace the rate constants of bimolecular reactions by a time-dependent power law to produce an SSA valid in cases where anomalous diffusion occurs or the system is not well-mixed (ASSA). Simulations then show that ASSA can successfully predict the temporal dynamics of chemical kinetics in a spatially constrained environment.

Oscillatory regulation of Hes1: Discrete stochastic delay modelling and simulation

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.