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1.  Compartment Model Predicts VEGF Secretion and Investigates the Effects of VEGF Trap in Tumor-Bearing Mice 
Frontiers in Oncology  2013;3:196.
Angiogenesis, the formation of new blood vessels from existing vasculature, is important in tumor growth and metastasis. A key regulator of angiogenesis is vascular endothelial growth factor (VEGF), which has been targeted in numerous anti-angiogenic therapies aimed at inhibiting tumor angiogenesis. Systems biology approaches, including computational modeling, are useful for understanding this complex biological process and can aid in the development of novel and effective therapeutics that target the VEGF family of proteins and receptors. We have developed a computational model of VEGF transport and kinetics in the tumor-bearing mouse, which includes three-compartments: normal tissue, blood, and tumor. The model simulates human tumor xenografts and includes human (VEGF121 and VEGF165) and mouse (VEGF120 and VEGF164) isoforms. The model incorporates molecular interactions between these VEGF isoforms and receptors (VEGFR1 and VEGFR2), as well as co-receptors (NRP1 and NRP2). We also include important soluble factors: soluble VEGFR1 (sFlt-1) and α-2-macroglobulin. The model accounts for transport via macromolecular transendothelial permeability, lymphatic flow, and plasma clearance. We have fit the model to available in vivo experimental data on the plasma concentration of free VEGF Trap and VEGF Trap bound to mouse and human VEGF in order to estimate the rates at which parenchymal cells (myocytes and tumor cells) and endothelial cells secrete VEGF. Interestingly, the predicted tumor VEGF secretion rates are significantly lower (0.007–0.023 molecules/cell/s, depending on the tumor microenvironment) than most reported in vitro measurements (0.03–2.65 molecules/cell/s). The optimized model is used to investigate the interstitial and plasma VEGF concentrations and the effect of the VEGF-neutralizing agent, VEGF Trap (aflibercept). This work complements experimental studies performed in mice and provides a framework with which to examine the effects of anti-VEGF agents, aiding in the optimization of such anti-angiogenic therapeutics as well as analysis of clinical data. The model predictions also have implications for biomarker discovery with anti-angiogenic therapies.
doi:10.3389/fonc.2013.00196
PMCID: PMC3727077  PMID: 23908970
systems biology; mathematical model; computational model; angiogenesis; tumor xenograft model; anti-angiogenic therapy; cancer
2.  Predicting the Effects of Anti-angiogenic Agents Targeting Specific VEGF Isoforms 
The AAPS Journal  2012;14(3):500-509.
Vascular endothelial growth factor (VEGF) is a key mediator of angiogenesis, whose effect on cancer growth and development is well characterized. Alternative splicing of VEGF leads to several different isoforms, which are differentially expressed in various tumor types and have distinct functions in tumor blood vessel formation. Many cancer therapies aim to inhibit angiogenesis by targeting VEGF and preventing intracellular signaling leading to tumor vascularization; however, the effects of targeting specific VEGF isoforms have received little attention in the clinical setting. In this work, we investigate the effects of selectively targeting a single VEGF isoform, as compared with inhibiting all isoforms. We utilize a molecular-detailed whole-body compartment model of VEGF transport and kinetics in the presence of breast tumor. The model includes two major VEGF isoforms, VEGF121 and VEGF165, receptors VEGFR1 and VEGFR2, and co-receptors Neuropilin-1 and Neuropilin-2. We utilize the model to predict the concentrations of free VEGF, the number of VEGF/VEGFR2 complexes (considered to be pro-angiogenic), and the receptor occupancy profiles following inhibition of VEGF using isoform-specific anti-VEGF agents. We predict that targeting VEGF121 leads to a 54% and 84% reduction in free VEGF in tumors that secrete both VEGF isoforms or tumors that overexpress VEGF121, respectively. Additionally, 21% of the VEGFR2 molecules in the blood are ligated following inhibition of VEGF121, compared with 88% when both isoforms are targeted. Targeting VEGF121 reduces tumor free VEGF and is an effective treatment strategy. Our results provide a basis for clinical investigation of isoform-specific anti-VEGF agents.
Electronic supplementary material
The online version of this article (doi:10.1208/s12248-012-9363-4) contains supplementary material, which is available to authorized users.
doi:10.1208/s12248-012-9363-4
PMCID: PMC3385824  PMID: 22547351
angiogenesis; cancer drug target; computational model; pharmacokinetic model; systems biology
3.  Timescale analysis of rule-based biochemical reaction networks 
Biotechnology Progress  2011;28(1):33-44.
The flow of information within a cell is governed by a series of protein-protein interactions that can be described as a reaction network. Mathematical models of biochemical reaction networks can be constructed by repetitively applying specific rules that define how reactants interact and what new species are formed upon reaction. To aid in understanding the underlying biochemistry, timescale analysis is one method developed to prune the size of the reaction network. In this work, we extend the methods associated with timescale analysis to reaction rules instead of the species contained within the network. To illustrate this approach, we applied timescale analysis to a simple receptor-ligand binding model and a rule-based model of Interleukin-12 (IL-12) signaling in näive CD4+ T cells. The IL-12 signaling pathway includes multiple protein-protein interactions that collectively transmit information; however, the level of mechanistic detail sufficient to capture the observed dynamics has not been justified based upon the available data. The analysis correctly predicted that reactions associated with JAK2 and TYK2 binding to their corresponding receptor exist at a pseudo-equilibrium. In contrast, reactions associated with ligand binding and receptor turnover regulate cellular response to IL-12. An empirical Bayesian approach was used to estimate the uncertainty in the timescales. This approach complements existing rank- and flux-based methods that can be used to interrogate complex reaction networks. Ultimately, timescale analysis of rule-based models is a computational tool that can be used to reveal the biochemical steps that regulate signaling dynamics.
doi:10.1002/btpr.704
PMCID: PMC3381993  PMID: 21954150
Bayesian statistics; JAK-STAT signaling; model-based inference; cellular signal transduction
4.  Pharmacokinetics and pharmacodynamics of VEGF-neutralizing antibodies 
BMC Systems Biology  2011;5:193.
Background
Vascular endothelial growth factor (VEGF) is a potent regulator of angiogenesis, and its role in cancer biology has been widely studied. Many cancer therapies target angiogenesis, with a focus being on VEGF-mediated signaling such as antibodies to VEGF. However, it is difficult to predict the effects of VEGF-neutralizing agents. We have developed a whole-body model of VEGF kinetics and transport under pathological conditions (in the presence of breast tumor). The model includes two major VEGF isoforms VEGF121 and VEGF165, receptors VEGFR1, VEGFR2 and co-receptors Neuropilin-1 and Neuropilin-2. We have added receptors on parenchymal cells (muscle fibers and tumor cells), and incorporated experimental data for the cell surface density of receptors on the endothelial cells, myocytes, and tumor cells. The model is applied to investigate the action of VEGF-neutralizing agents (called "anti-VEGF") in the treatment of cancer.
Results
Through a sensitivity study, we examine how model parameters influence the level of free VEGF in the tumor, a measure of the response to VEGF-neutralizing drugs. We investigate the effects of systemic properties such as microvascular permeability and lymphatic flow, and of drug characteristics such as the clearance rate and binding affinity. We predict that increasing microvascular permeability in the tumor above 10-5 cm/s elicits the undesired effect of increasing tumor interstitial VEGF concentration beyond even the baseline level. We also examine the impact of the tumor microenvironment, including receptor expression and internalization, as well as VEGF secretion. We find that following anti-VEGF treatment, the concentration of free VEGF in the tumor can vary between 7 and 233 pM, with a dependence on both the density of VEGF receptors and co-receptors and the rate of neuropilin internalization on tumor cells. Finally, we predict that free VEGF in the tumor is reduced following anti-VEGF treatment when VEGF121 comprises at least 25% of the VEGF secreted by tumor cells.
Conclusions
This study explores the optimal drug characteristics required for an anti-VEGF agent to have a therapeutic effect and the tumor-specific properties that influence the response to therapy. Our model provides a framework for investigating the use of VEGF-neutralizing drugs for personalized medicine treatment strategies.
doi:10.1186/1752-0509-5-193
PMCID: PMC3229549  PMID: 22104283
5.  A Two-Compartment Model of VEGF Distribution in the Mouse 
PLoS ONE  2011;6(11):e27514.
Vascular endothelial growth factor (VEGF) is a key regulator of angiogenesis – the growth of new microvessels from existing microvasculature. Angiogenesis is a complex process involving numerous molecular species, and to better understand it, a systems biology approach is necessary. In vivo preclinical experiments in the area of angiogenesis are typically performed in mouse models; this includes drug development targeting VEGF. Thus, to quantitatively interpret such experimental results, a computational model of VEGF distribution in the mouse can be beneficial. In this paper, we present an in silico model of VEGF distribution in mice, determine model parameters from existing experimental data, conduct sensitivity analysis, and test the validity of the model.
The multiscale model is comprised of two compartments: blood and tissue. The model accounts for interactions between two major VEGF isoforms (VEGF120 and VEGF164) and their endothelial cell receptors VEGFR-1, VEGFR-2, and co-receptor neuropilin-1. Neuropilin-1 is also expressed on the surface of parenchymal cells. The model includes transcapillary macromolecular permeability, lymphatic transport, and macromolecular plasma clearance. Simulations predict that the concentration of unbound VEGF in the tissue is approximately 50-fold greater than in the blood. These concentrations are highly dependent on the VEGF secretion rate. Parameter estimation was performed to fit the simulation results to available experimental data, and permitted the estimation of VEGF secretion rate in healthy tissue, which is difficult to measure experimentally. The model can provide quantitative interpretation of preclinical animal data and may be used in conjunction with experimental studies in the development of pro- and anti-angiogenic agents. The model approximates the normal tissue as skeletal muscle and includes endothelial cells to represent the vasculature. As the VEGF system becomes better characterized in other tissues and cell types, the model can be expanded to include additional compartments and vascular elements.
doi:10.1371/journal.pone.0027514
PMCID: PMC3210788  PMID: 22087332
6.  Inferring relevant control mechanisms for Interleukin-12 signaling in naïve CD4+ T cells 
Immunology and cell biology  2010;89(1):100-110.
Interleukin-12 (IL-12) is a key cytokine involved in shaping cell-mediated immunity to intracellular pathogens. IL-12 initiates a cellular response via the IL-12 signaling pathway, a member of the JAK/STAT family of signaling networks. The JAK/STAT pathway includes several regulatory elements; however, the dynamics of these mechanisms are not fully understood. Therefore, the objective of this study was to infer the relative importance of regulatory mechanisms that modulate the activation of STAT4 in naïve CD4+ T cells. Dynamic changes in protein expression and activity were measured using flow cytometry and these data were used to calibrate a mathematical model of IL-12 signaling. An empirical Bayesian approach was used to infer the relative strength of different regulatory mechanism in the system. The model predicted that IL-12 receptor expression is regulated via a dynamic, autonomous program that was independent of STAT4 activation. A time scale analysis identified the signaling events that limited the cellular response, including ligand binding and receptor degradation. In summary, a mathematical model of the canonical IL-12 signaling pathway used in conjunction with a Bayesian framework provided high confidence predictions of the system-specific control mechanisms from the available experimental observations.
doi:10.1038/icb.2010.69
PMCID: PMC3004982  PMID: 20479776
Interleukin-12; Bayesian inference; CD4+ T cells; signal transduction; ordinary differential equations
7.  In silico feasibility of novel biodegradation pathways for 1,2,4-trichlorobenzene 
Background
Bioremediation offers a promising pollution treatment method in the reduction and elimination of man-made compounds in the environment. Computational tools to predict novel biodegradation pathways for pollutants allow one to explore the capabilities of microorganisms in cleaning up the environment. However, given the wealth of novel pathways obtained using these prediction methods, it is necessary to evaluate their relative feasibility, particularly within the context of the cellular environment.
Results
We have utilized a computational framework called BNICE to generate novel biodegradation routes for 1,2,4-trichlorobenzene (1,2,4-TCB) and incorporated the pathways into a metabolic model for Pseudomonas putida. We studied the cellular feasibility of the pathways by applying metabolic flux analysis (MFA) and thermodynamic constraints. We found that the novel pathways generated by BNICE enabled the cell to produce more biomass than the known pathway. Evaluation of the flux distribution profiles revealed that several properties influenced biomass production: 1) reducing power required, 2) reactions required to generate biomass precursors, 3) oxygen utilization, and 4) thermodynamic topology of the pathway. Based on pathway analysis, MFA, and thermodynamic properties, we identified several promising pathways that can be engineered into a host organism to accomplish bioremediation.
Conclusions
This work was aimed at understanding how novel biodegradation pathways influence the existing metabolism of a host organism. We have identified attractive targets for metabolic engineers interested in constructing a microorganism that can be used for bioremediation. Through this work, computational tools are shown to be useful in the design and evaluation of novel xenobiotic biodegradation pathways, identifying cellularly feasible degradation routes.
doi:10.1186/1752-0509-4-7
PMCID: PMC2830930  PMID: 20122273

Results 1-7 (7)