Building Disease-Specific Drug-Protein Connectivity Maps from Molecular Interaction Networks and PubMed Abstracts

The recently proposed concept of molecular connectivity maps enables researchers to integrate experimental measurements of genes, proteins, metabolites, and drug compounds under similar biological conditions. The study of these maps provides opportunities for future toxicogenomics and drug discovery applications. We developed a computational framework to build disease-specific drug-protein connectivity maps. We integrated gene/protein and drug connectivity information based on protein interaction networks and literature mining, without requiring gene expression profile information derived from drug perturbation experiments on disease samples. We described the development and application of this computational framework using Alzheimer''s Disease (AD) as a primary example in three steps. First, molecular interaction networks were incorporated to reduce bias and improve relevance of AD seed proteins. Second, PubMed abstracts were used to retrieve enriched drug terms that are indirectly associated with AD through molecular mechanistic studies. Third and lastly, a comprehensive AD connectivity map was created by relating enriched drugs and related proteins in literature. We showed that this molecular connectivity map development approach outperformed both curated drug target databases and conventional information retrieval systems. Our initial explorations of the AD connectivity map yielded a new hypothesis that diltiazem and quinidine may be investigated as candidate drugs for AD treatment. Molecular connectivity maps derived computationally can help study molecular signature differences between different classes of drugs in specific disease contexts. To achieve overall good data coverage and quality, a series of statistical methods have been developed to overcome high levels of data noise in biological networks and literature mining results. Further development of computational molecular connectivity maps to cover major disease areas will likely set up a new model for drug development, in which therapeutic/toxicological profiles of candidate drugs can be checked computationally before costly clinical trials begin.     

Prediction in the face of uncertainty: a Monte Carlo-based approach for systems biology of cancer treatment

Cancer is known to be a complex disease and its therapy is difficult. Much information is available on molecules and pathways involved in cancer onset and progression and this data provides a valuable resource for the development of predictive computer models that can help to identify new potential drug targets or to improve therapies. Modeling cancer treatment has to take into account many cellular pathways usually leading to the construction of large mathematical models. The development of such models is complicated by the fact that relevant parameters are either completely unknown, or can at best be measured under highly artificial conditions. Here we propose an approach for constructing predictive models of such complex biological networks in the absence of accurate knowledge on parameter values, and apply this strategy to predict the effects of perturbations induced by anti-cancer drug target inhibitions on an epidermal growth factor (EGF) signaling network. The strategy is based on a Monte Carlo approach, in which the kinetic parameters are repeatedly sampled from specific probability distributions and used for multiple parallel simulations. Simulation results from different forms of the model (e.g., a model that expresses a certain mutation or mutation pattern or the treatment by a certain drug or drug combination) can be compared with the unperturbed control model and used for the prediction of the perturbation effects. This framework opens the way to experiment with complex biological networks in the computer, likely to save costs in drug development and to improve patient therapy.     

Designing a nanotube using naturally occurring protein building blocks

Here our goal is to carry out nanotube design using naturally occurring protein building blocks. Inspection of the protein structural database reveals the richness of the conformations of proteins, their parts, and their chemistry. Given target functional protein nanotube geometry, our strategy involves scanning a library of candidate building blocks, combinatorially assembling them into the shape and testing its stability. Since self-assembly takes place on time scales not affordable for computations, here we propose a strategy for the very first step in protein nanotube design: we map the candidate building blocks onto a planar sheet and wrap the sheet around a cylinder with the target dimensions. We provide examples of three nanotubes, two peptide and one protein, in atomistic model detail for which there are experimental data. The nanotube models can be used to verify a nanostructure observed by low-resolution experiments, and to study the mechanism of tube formation.     

Two models for transforming auditory signals from head-centered to eye-centered coordinates

Two models for transforming auditory signals from head-centered to eye-centered coordinates are presented. The vector subtraction model subtracts a rate-coded eye position signal from a topographically weighted auditory target position signal to produce a rate-code of target location with respect to the eye. The rate-code is converted into a place-code through a graded synaptic weighting scheme and inhibition. The dendrite model performs a mapping of head-centered auditory space onto the dendrites of eye-centered units. Individual dendrites serve as logical comparators of target location and eye position. Both models produce a topographic map of auditory space in eye-centered coordinates like that found in the primate superior colliculus. Either type can be converted into a model for transforming visual signals from retinal to head-centered coordinates.     

Models from experiments: combinatorial drug perturbations of cancer cells

We present a novel method for deriving network models from molecular profiles of perturbed cellular systems. The network models aim to predict quantitative outcomes of combinatorial perturbations, such as drug pair treatments or multiple genetic alterations. Mathematically, we represent the system by a set of nodes, representing molecular concentrations or cellular processes, a perturbation vector and an interaction matrix. After perturbation, the system evolves in time according to differential equations with built‐in nonlinearity, similar to Hopfield networks, capable of representing epistasis and saturation effects. For a particular set of experiments, we derive the interaction matrix by minimizing a composite error function, aiming at accuracy of prediction and simplicity of network structure. To evaluate the predictive potential of the method, we performed 21 drug pair treatment experiments in a human breast cancer cell line (MCF7) with observation of phospho‐proteins and cell cycle markers. The best derived network model rediscovered known interactions and contained interesting predictions. Possible applications include the discovery of regulatory interactions, the design of targeted combination therapies and the engineering of molecular biological networks.     

Human NK cells differ more in their KIR2DL1-dependent thresholds for HLA-Cw6-mediated inhibition than in their maximal killing capacity

In this study we have addressed the question of how activation and inhibition of human NK cells is regulated by the expression level of MHC class I protein on target cells. Using target cell transfectants sorted to stably express different levels of the MHC class I protein HLA-Cw6, we show that induction of degranulation and that of IFN-γ secretion are not correlated. In contrast, the inhibition of these two processes by MHC class-I occurs at the same level of class I MHC protein. Primary human NK cell clones were found to differ in the amount of target MHC class I protein required for their inhibition, rather than in their maximum killing capacity. Importantly, we show that KIR2DL1 expression determines the thresholds (in terms of MHC I protein levels) required for NK cell inhibition, while the expression of other receptors such as LIR1 is less important. Furthermore, using mathematical models to explore the dynamics of target cell killing, we found that the observed delay in target cell killing is exhibited by a model in which NK cells require some activation or priming, such that each cell can lyse a target cell only after being activated by a first encounter with the same or a different target cell, but not by models which lack this feature.     

Efficient Modeling and Active Learning Discovery of Biological Responses

High throughput and high content screening involve determination of the effect of many compounds on a given target. As currently practiced, screening for each new target typically makes little use of information from screens of prior targets. Further, choices of compounds to advance to drug development are made without significant screening against off-target effects. The overall drug development process could be made more effective, as well as less expensive and time consuming, if potential effects of all compounds on all possible targets could be considered, yet the cost of such full experimentation would be prohibitive. In this paper, we describe a potential solution: probabilistic models that can be used to predict results for unmeasured combinations, and active learning algorithms for efficiently selecting which experiments to perform in order to build those models and determining when to stop. Using simulated and experimental data, we show that our approaches can produce powerful predictive models without exhaustive experimentation and can learn them much faster than by selecting experiments at random.     

Complex systems biology approach to understanding coordination of JAK-STAT signaling

In this work, we search for coordination as an organizing principle in a complex signaling system using a multilevel hierarchical paradigm. The objective is to explain the underlying mechanism of Interferon (IFN_γ) induced JAK-STAT (specifically JAK1/JAK2-STAT1) pathway behavior. Starting with a mathematical model of the pathway from the literature, we modularize the system using biological knowledge via principles of biochemical cohesion, biological significance, and functionality. The modularized system is then used as a basis for in silico inhibition, knockdown/deletion and perturbation experiments to discover a coordination mechanism. Our analysis shows that a module representing the SOCS1 complex can be identified as the coordinator. Analysis of the coordinator can then be used for the selection of biological experiments for the discovery of ‘soft’ molecular drug targets, that could lead to the development of improved therapeutics. The coordinator identified is also being investigated to determine its relationship to pathological conditions.     

A model describing chemical interference caused by decomposing residues at different densities of growing plants

In literature, the biological response of plants to phytochemicals has been modelled and then used to simulate phytotoxicity caused by plant residues during decomposition. According to the resulting residue allelopathy model, stimulation dominates in the beginning of the residue decomposition process for a short while. Thereafter, severe inhibition is predicted to occur rapidly, until stimulation gradually re-emerges at the later stages of residue decomposition. Also in literature, direct chemical interference has been shown to be density-dependent; with increasing target plant density, the effects of phytochemicals are diluted. As a result, inhibition is the most probable outcome in density-dependent phytochemical interactions at low target plant densities, but phytotoxic effects often become stimulatory as target plant density increases. In this paper, these models that have been reported in literature are combined. While the original residue allelopathy model predicts inhibitory effects in most cases, the new density-dependent extension of the residue allelopathy model predicts that the density of target plants determines whether or not inhibition occurs. According to the new model, the intensity of inhibition decreases and the final stimulatory period begins earlier if target plant density increases. Therefore, combining the effects of density-dependency to the residue allelopathy model enhances our understanding of chemical interference. In addition, the new model may partially explain why several field studies have not observed chemically driven inhibitory effects similar to those observed in laboratory experiments.     

Inhibition of platelet-surface-bound proteins during coagulation under flow II: Antithrombin and heparin

Blood coagulation is a self-repair process regulated by activated platelet surfaces, clotting factors, and inhibitors. Antithrombin (AT) is one such inhibitor that impedes coagulation by targeting and inactivating several key coagulation enzymes. The effect of AT is greatly enhanced in the presence of heparin, a common anticoagulant drug. When heparin binds to AT, it either bridges with the target enzyme or induces allosteric changes in AT leading to more favorable binding with the target enzyme. AT inhibition of fluid-phase enzymes caused little suppression of thrombin generation in our previous mathematical models of blood coagulation under flow. This is because in that model, flow itself was a greater inhibitor of the fluid-phase enzymes than AT. From clinical observations, it is clear that AT and heparin should have strong inhibitory effects on thrombin generation, and thus we hypothesized that AT could be inhibiting enzymes bound to activated platelet surfaces that are not subject to being washed away by flow. We extended our mathematical model to include the relevant reactions of AT inhibition at the activated platelet surfaces as well as those for unfractionated heparin and a low molecular weight heparin. Our results show that AT alone is only an effective inhibitor at low tissue factor densities, but in the presence of heparin, it can greatly alter, and in some cases shut down, thrombin generation. Additionally, we studied each target enzyme separately and found that inactivation of no single enzyme could substantially suppress thrombin generation.     

Complex systems biology approach to understanding coordination of JAK-STAT signaling

In this work, we search for coordination as an organizing principle in a complex signaling system using a multilevel hierarchical paradigm. The objective is to explain the underlying mechanism of Interferon (IFN_γ) induced JAK-STAT (specifically JAK1/JAK2-STAT1) pathway behavior. Starting with a mathematical model of the pathway from the literature, we modularize the system using biological knowledge via principles of biochemical cohesion, biological significance, and functionality. The modularized system is then used as a basis for in silico inhibition, knockdown/deletion and perturbation experiments to discover a coordination mechanism. Our analysis shows that a module representing the SOCS1 complex can be identified as the coordinator. Analysis of the coordinator can then be used for the selection of biological experiments for the discovery of ‘soft’ molecular drug targets, that could lead to the development of improved therapeutics. The coordinator identified is also being investigated to determine its relationship to pathological conditions.     

Dual interaction producing both territorial and schooling behavior in fish

Fish schools are frequently observed without a leader and an explicit condition forming school. Several models of schooling have been proposed focusing on the influence of neighbors, and introducing probability distributions, while these models are based on the separation of schooling and territorial behavior. We frequently consider the duality of aggregation of animals, in which behavioral patterns involve both attraction and repulsion, antagonistic with each other. The idea of probability does not explain this duality that can provide both schooling and territorial behavior. From these biological facts, we have constructed a behavior model in which the influence of neighbors is formulated by the interface between the states of neighbors and a map of changes in these states. This interface uses a self-similar nowhere differentiable transition map which is temporally constructed, encompassing a crucial duality of repulsive and attractive forces hidden in the interaction among fishes. We tested it with computer simulations against the biological reality of schooling and territorial behavior. Due to the influence neighbors can have on duality, the same model can show both schooling behavior with a high degree of polarization and territorial behavior.     

Perturbation Biology: Inferring Signaling Networks in Cellular Systems

We present a powerful experimental-computational technology for inferring network models that predict the response of cells to perturbations, and that may be useful in the design of combinatorial therapy against cancer. The experiments are systematic series of perturbations of cancer cell lines by targeted drugs, singly or in combination. The response to perturbation is quantified in terms of relative changes in the measured levels of proteins, phospho-proteins and cellular phenotypes such as viability. Computational network models are derived de novo, i.e., without prior knowledge of signaling pathways, and are based on simple non-linear differential equations. The prohibitively large solution space of all possible network models is explored efficiently using a probabilistic algorithm, Belief Propagation (BP), which is three orders of magnitude faster than standard Monte Carlo methods. Explicit executable models are derived for a set of perturbation experiments in SKMEL-133 melanoma cell lines, which are resistant to the therapeutically important inhibitor of RAF kinase. The resulting network models reproduce and extend known pathway biology. They empower potential discoveries of new molecular interactions and predict efficacious novel drug perturbations, such as the inhibition of PLK1, which is verified experimentally. This technology is suitable for application to larger systems in diverse areas of molecular biology.     

Role of substrate inhibition kinetics in enzymatic chemical oscillations.

Two chemical kinetic models are investigated using standard nonlinear dynamics techniques to determine the conditions under which substrate inhibition kinetics can lead to oscillations. The first model is a classical substrate inhibition scheme based on Michaelis-Menten kinetics and involves a single substrate. Only when this reaction takes place in a flow reactor (i.e., both substrate and product are taken to follow reversible flow terms) are oscillations observed; however, the range of parameter values over which such oscillations occur is so narrow it is experimentally unobservable. A second model based on a general mechanism applied to the kinetics of many pH-dependent enzymes is also studied. This second model includes both substrate inhibition kinetics as well as autocatalysis through the activation of the enzyme by hydrogen ion. We find that it is the autocatalysis that is always responsible for oscillatory behavior in this scheme. The substrate inhibition terms affect the steady-state behavior but do not lead to oscillations unless product inhibition or multiple substrates are present; this is a general conclusion we can draw from our studies of both the classical substrate inhibition scheme and the pH-dependent enzyme mechanism. Finally, an analysis of the nullclines for these two models allows us to prove that the nullcline slopes must have a negative value for oscillatory behavior to exist; this proof can explain our results. From our analysis, we conclude with a brief discussion of other enzymes that might be expected to produce oscillatory behavior based on a pH-dependent substrate inhibition mechanism.     

Modeling plasma virus concentration during primary HIV infection

During primary HIV infection the viral load in plasma increases, reaches a peak, and then declines. Phillips has suggested that the decline is due to a limitation in the number of cells susceptible to HIV infection, while other authors have suggested that the decline in viremia is due to an immune response. Here we address this issue by developing models of primary HIV-1 infection, and by comparing predictions from these models with data from ten anti-retroviral, drug-naive, infected patients. Applying nonlinear least-squares estimation, we find that relatively small variations in parameters are capable of mimicking the highly diverse patterns found in patient viral load data. This approach yields an estimate of 2.5 days for the average lifespan of productively infected cells during primary infection, a value that is consistent with results obtained by drug perturbation experiments. We find that the data from all ten patients are consistent with a target-cell-limited model from the time of initial infection until shortly after the peak in viremia. However, the kinetics of the subsequent fall and recovery in virus concentration in some patients are not consistent with the predictions of the target-cell-limited model. We illustrate that two possible immune response mechanisms, cytotoxic T lymphocyte destruction of infected target cells and cytokine suppression of viral replication, could account for declines in viral load data not predicted by the original target-cell-limited model. We conclude that some additional process, perhaps mediated by CD8+ T cells, is important in at least some patients.     

Rank–rank hypergeometric overlap: identification of statistically significant overlap between gene-expression signatures

Comparing independent high-throughput gene-expression experiments can generate hypotheses about which gene-expression programs are shared between particular biological processes. Current techniques to compare expression profiles typically involve choosing a fixed differential expression threshold to summarize results, potentially reducing sensitivity to small but concordant changes. We present a threshold-free algorithm called Rank–rank Hypergeometric Overlap (RRHO). This algorithm steps through two gene lists ranked by the degree of differential expression observed in two profiling experiments, successively measuring the statistical significance of the number of overlapping genes. The output is a graphical map that shows the strength, pattern and bounds of correlation between two expression profiles. To demonstrate RRHO sensitivity and dynamic range, we identified shared expression networks in cancer microarray profiles driving tumor progression, stem cell properties and response to targeted kinase inhibition. We demonstrate how RRHO can be used to determine which model system or drug treatment best reflects a particular biological or disease response. The threshold-free and graphical aspects of RRHO complement other rank-based approaches such as Gene Set Enrichment Analysis (GSEA), for which RRHO is a 2D analog. Rank–rank overlap analysis is a sensitive, robust and web-accessible method for detecting and visualizing overlap trends between two complete, continuous gene-expression profiles. A web-based implementation of RRHO can be accessed at http://systems.crump.ucla.edu/rankrank/.     

Mathematical modeling links Wnt signaling to emergent patterns of metabolism in colon cancer

Cell‐intrinsic metabolic reprogramming is a hallmark of cancer that provides anabolic support to cell proliferation. How reprogramming influences tumor heterogeneity or drug sensitivities is not well understood. Here, we report a self‐organizing spatial pattern of glycolysis in xenograft colon tumors where pyruvate dehydrogenase kinase (PDK1), a negative regulator of oxidative phosphorylation, is highly active in clusters of cells arranged in a spotted array. To understand this pattern, we developed a reaction–diffusion model that incorporates Wnt signaling, a pathway known to upregulate PDK1 and Warburg metabolism. Partial interference with Wnt alters the size and intensity of the spotted pattern in tumors and in the model. The model predicts that Wnt inhibition should trigger an increase in proteins that enhance the range of Wnt ligand diffusion. Not only was this prediction validated in xenograft tumors but similar patterns also emerge in radiochemotherapy‐treated colorectal cancer. The model also predicts that inhibitors that target glycolysis or Wnt signaling in combination should synergize and be more effective than each treatment individually. We validated this prediction in 3D colon tumor spheroids.     

Discovery of Drug Synergies in Gastric Cancer Cells Predicted by Logical Modeling

Discovery of efficient anti-cancer drug combinations is a major challenge, since experimental testing of all possible combinations is clearly impossible. Recent efforts to computationally predict drug combination responses retain this experimental search space, as model definitions typically rely on extensive drug perturbation data. We developed a dynamical model representing a cell fate decision network in the AGS gastric cancer cell line, relying on background knowledge extracted from literature and databases. We defined a set of logical equations recapitulating AGS data observed in cells in their baseline proliferative state. Using the modeling software GINsim, model reduction and simulation compression techniques were applied to cope with the vast state space of large logical models and enable simulations of pairwise applications of specific signaling inhibitory chemical substances. Our simulations predicted synergistic growth inhibitory action of five combinations from a total of 21 possible pairs. Four of the predicted synergies were confirmed in AGS cell growth real-time assays, including known effects of combined MEK-AKT or MEK-PI3K inhibitions, along with novel synergistic effects of combined TAK1-AKT or TAK1-PI3K inhibitions. Our strategy reduces the dependence on a priori drug perturbation experimentation for well-characterized signaling networks, by demonstrating that a model predictive of combinatorial drug effects can be inferred from background knowledge on unperturbed and proliferating cancer cells. Our modeling approach can thus contribute to preclinical discovery of efficient anticancer drug combinations, and thereby to development of strategies to tailor treatment to individual cancer patients.