James Lu

Controlled vocabularies and semantics in systems biology

The use of computational modeling to describe and analyze biological systems is at the heart of systems biology. Model structures, simulation descriptions and numerical results can be encoded in structured formats, but there is an increasing need to provide an additional semantic layer. Semantic information adds meaning to components of structured descriptions to help identify and interpret them unambiguously. Ontologies are one of the tools frequently used for this purpose. We describe here three ontologies created specifically to address the needs of the systems biology community. The Systems Biology Ontology (SBO) provides semantic information about the model components. The Kinetic Simulation Algorithm Ontology (KiSAO) supplies information about existing algorithms available for the simulation of systems biology models, their characterization and interrelationships. The Terminology for the Description of Dynamics (TEDDY) categorizes dynamical features of the simulation results and general systems behavior. The provision of semantic information extends a models longevity and facilitates its reuse. It provides useful insight into the biology of modeled processes, and may be used to make informed decisions on subsequent simulation experiments.

Inverse problems in systems biology

Systems biology is a new discipline built upon the premise that an understanding of how cells and organisms carry out their functions cannot be gained by looking at cellular components in isolation. Instead, consideration of the interplay between the parts of systems is indispensable for analyzing, modeling, and predicting systems behavior. Studying biological processes under this premise, systems biology combines experimental techniques and computational methods in order to construct predictive models. Both in building and utilizing models of biological systems, inverse problems arise at several occasions, for example, (i) when experimental time series and steady state data are used to construct biochemical reaction networks, (ii) when model parameters are identified that capture underlying mechanisms or (iii) when desired qualitative behavior such as bistability or limit cycle oscillations is engineered by proper choices of parameter combinations. In this paper we review principles of the modeling process in systems biology and illustrate the ill-posedness and regularization of parameter identification problems in that context. Furthermore, we discuss the methodology of qualitative inverse problems and demonstrate how sparsity enforcing regularization allows the determination of key reaction mechanisms underlying the qualitative behavior.

The SBML ODE Solver Library: a native API for symbolic and fast numerical analysis of reaction networks

The SBML ODE Solver Library (SOSlib) is a programming library for symbolic and numerical analysis of chemical reaction network models encoded in the Systems Biology Markup Language (SBML). It is written in ISO C and distributed under the open source LGPL license. The package employs libSBML structures for formula representation and associated functions to construct a system of ordinary differential equations, their Jacobian matrix and other derivatives. SUNDIALS CVODES is incorporated for numerical integration and sensitivity analysis. Preliminary benchmarking results give a rough overview on the behavior of different tools and are discussed in the Supplementary Material. The native application program interface provides fine-grained interfaces to all internal data structures, symbolic operations and numerical routines, enabling the construction of very efficient analytic applications and hybrid or multi-scale solvers with interfaces to SBML and non SBML data sources. Optional modules based on XMGrace and Graphviz allow quick inspection of structure and dynamics.

In vivo Polycomb kinetics and mitotic chromatin binding distinguish stem cells from differentiated cells.

Epigenetic memory mediated by Polycomb group (PcG) proteins must be maintained during cell division, but must also be flexible to allow cell fate transitions. Here we quantify dynamic chromatin-binding properties of PH::GFP and PC::GFP in living Drosophila in two cell types that undergo defined differentiation and mitosis events. Quantitative fluorescence recovery after photobleaching (FRAP) analysis demonstrates that PcG binding has a higher plasticity in stem cells than in more determined cells and identifies a fraction of PcG proteins that binds mitotic chromatin with up to 300-fold longer residence times than in interphase. Mathematical modeling examines which parameters best distinguish stem cells from differentiated cells. We identify phosphorylation of histone H3 at Ser 28 as a potential mechanism governing the extent and rate of mitotic PC dissociation in different lineages. We propose that regulation of the kinetic properties of PcG-chromatin binding is an essential factor in the choice between stability and flexibility in the establishment of cell identities.

An in-silico model of lipoprotein metabolism and kinetics for the evaluation of targets and biomarkers in the reverse cholesterol transport pathway.

High-density lipoprotein (HDL) is believed to play an important role in lowering cardiovascular disease (CVD) risk by mediating the process of reverse cholesterol transport (RCT). Via RCT, excess cholesterol from peripheral tissues is carried back to the liver and hence should lead to the reduction of atherosclerotic plaques. The recent failures of HDL-cholesterol (HDL-C) raising therapies have initiated a re-examination of the link between CVD risk and the rate of RCT, and have brought into question whether all target modulations that raise HDL-C would be atheroprotective. To help address these issues, a novel in-silico model has been built to incorporate modern concepts of HDL biology, including: the geometric structure of HDL linking the core radius with the number of ApoA-I molecules on it, and the regeneration of lipid-poor ApoA-I from spherical HDL due to remodeling processes. The ODE model has been calibrated using data from the literature and validated by simulating additional experiments not used in the calibration. Using a virtual population, we show that the model provides possible explanations for a number of well-known relationships in cholesterol metabolism, including the epidemiological relationship between HDL-C and CVD risk and the correlations between some HDL-related lipoprotein markers. In particular, the model has been used to explore two HDL-C raising target modulations, Cholesteryl Ester Transfer Protein (CETP) inhibition and ATP-binding cassette transporter member 1 (ABCA1) up-regulation. It predicts that while CETP inhibition would not result in an increased RCT rate, ABCA1 up-regulation should increase both HDL-C and RCT rate. Furthermore, the model predicts the two target modulations result in distinct changes in the lipoprotein measures. Finally, the model also allows for an evaluation of two candidate biomarkers for in-vivo whole-body ABCA1 activity: the absolute concentration and the % lipid-poor ApoA-I. These findings illustrate the potential utility of the model in drug development.

Evaluation of HDL-modulating interventions for cardiovascular risk reduction using a systems pharmacology approach.

The recent failures of cholesteryl ester transport protein inhibitor drugs to decrease CVD risk, despite raising HDL cholesterol (HDL-C) levels, suggest that pharmacologic increases in HDL-C may not always reflect elevations in reverse cholesterol transport (RCT), the process by which HDL is believed to exert its beneficial effects. HDL-modulating therapies can affect HDL properties beyond total HDL-C, including particle numbers, size, and composition, and may contribute differently to RCT and CVD risk. The lack of validated easily measurable pharmacodynamic markers to link drug effects to RCT, and ultimately to CVD risk, complicates target and compound selection and evaluation. In this work, we use a systems pharmacology model to contextualize the roles of different HDL targets in cholesterol metabolism and provide quantitative links between HDL-related measurements and the associated changes in RCT rate to support target and compound evaluation in drug development. By quantifying the amount of cholesterol removed from the periphery over the short-term, our simulations show the potential for infused HDL to treat acute CVD. For the primary prevention of CVD, our analysis suggests that the induction of ApoA-I synthesis may be a more viable approach, due to the long-term increase in RCT rate.

Physiological Environment Induces Quick Response – Slow Exhaustion Reactions

In vivo environments are highly crowded and inhomogeneous, which may affect reaction processes in cells. In this study we examined the effects of intracellular crowding and an inhomogeneity on the behavior of in vivo reactions by calculating the spectral dimension (ds), which can be translated into the reaction rate function. We compared estimates of anomaly parameters obtained from fluorescence correlation spectroscopy (FCS) data with fractal dimensions derived from transmission electron microscopy (TEM) image analysis. FCS analysis indicated that the anomalous property was linked to physiological structure. Subsequent TEM analysis provided an in vivo illustration; soluble molecules likely percolate between intracellular clusters, which are constructed in a self-organizing manner. We estimated a cytoplasmic spectral dimension ds to be 1.39u2009±u20090.084. This result suggests that in vivo reactions initially run faster than the same reactions in a homogeneous space; this conclusion is consistent with the anomalous character indicated by FCS analysis. We further showed that these results were compatible with our Monte-Carlo simulation in which the anomalous behavior of mobile molecules correlates with the intracellular environment, leading to description as a percolation cluster, as demonstrated using TEM analysis. We confirmed by the simulation that the above-mentioned in vivo like properties are different from those of homogeneously concentrated environments. Additionally, simulation results indicated that crowding level of an environment might affect diffusion rate of reactant. Such knowledge of the spatial information enables us to construct realistic models for in vivo diffusion and reaction systems.

Inverse problems from biomedicine: inference of putative disease mechanisms and robust therapeutic strategies.

Many complex diseases that are difficult to treat cannot be mapped onto a single cause, but arise from the interplay of multiple contributing factors. In the study of such diseases, it is becoming apparent that therapeutic strategies targeting a single protein or metabolite are often not efficacious. Rather, a systems perspective describing the interaction of physiological components is needed. In this paper, we demonstrate via examples of disease models the kind of inverse problems that arise from the need to infer disease mechanisms and/or therapeutic strategies. We identify the challenges that arise, in particular the need to devise strategies that are robust against variable physiological states and parametric uncertainties.

Rational Design of Robust Biomolecular Circuits : from Specification to Parameters

Despite the early success stories synthetic biology, the development of larger, more complex synthetic systems necessitates the use of appropriate design methodologies. In particular, the integration of smaller circuits in order to perform complex tasks remains one of the most important challenges faced in synthetic biology. We propose here a methodology to determine the region in the parameter space where a given dynamical model works as desired. It is based on the inverse problem of finding parameter sets that exhibit the specified behavior for a defined topology. The main issue we face is that such inverse mapping is highly expansive and suffers from instability: small changes in the specified dynamic property could lead to large deviations in the parameters for the identified models. To solve this issue, we discuss regularized maps complemented by local analysis. With a stabilized inversion map, small neighborhoods in the property space are mapped to small neighborhoods in the parameter space, thereby finding parameter vectors that are robust to the problem specification. To specify dynamic circuit properties we discuss Linear Temporal Logic (LTL). We apply these concepts to two models of the cyanobacterial circadian oscillation.

Mathematical models of lipoprotein metabolism and kinetics: current status and future perspective

Abstract Lipoprotein metabolism and kinetics comprises the time-dependent processes of synthesis, transformation and clearance of lipids, apolipoproteins and their assembled particles. By integrating and explaining the wealth of in vitro and clinical data available on lipoprotein metabolism and kinetics, mathematical models can provide novel insights into the underlying pathophysiology of lipid disorders, as well as quantify the effects of drugs intended for their treatment. In this article, we first discuss some basic principles of mathematical modeling in biology and drug development, and then review a number of recent publications in which different types of mathematical models have been used to investigate lipoprotein metabolism and kinetics. We conclude by posing a set of ten fundamental questions in this field that we believe mathematical modeling can potentially address, in the effort to develop novel and effective therapies for patients with high cardiovascular risk.