Modeling collective cell behavior in cancer: Perspectives from an interdisciplinary conversation.

Collective cell behavior contributes to all stages of cancer progression. Understanding how collective behavior emerges through cell-cell interactions and decision-making will advance our understanding of cancer biology and provide new therapeutic approaches. Here, we summarize an interdisciplinary discussion on multicellular behavior in cancer, draw lessons from other scientific disciplines, and identify future directions.

Navigation between initial and desired community states using shortcuts.

Ecological management problems often involve navigating from an initial to a desired community state. We ask whether navigation without brute-force additions and deletions of species is possible via: adding/deleting a small number of individuals of a species, changing the environment, and waiting. Navigation can yield direct paths (single sequence of actions) or shortcut paths (multiple sequences of actions with lower cost than a direct path). We ask (1) when is non-brute-force navigation possible?; (2) do shortcuts exist and what are their properties?; and (3) what heuristics predict shortcut existence? Using a state diagram framework applied to several empirical datasets, we show that (1) non-brute-force navigation is only possible between some state pairs, (2) shortcuts exist between many state pairs; and (3) changes in abundance and richness are the strongest predictors of shortcut existence, independent of dataset and algorithm choices. State diagrams thus unveil hidden strategies for manipulating species coexistence and efficiently navigating between states.

Efficient Dynamics Estimation with Adaptive Model Sets.

Robotic systems frequently operate under changing dynamics, such as driving across varying terrain, encountering sensing and actuation faults, or navigating around humans with uncertain and changing intent. In order to operate effectively in these situations, robots must be capable of efficiently estimating these changes in order to adapt at the decision-making, planning, and control levels. Typical estimation approaches maintain a fixed set of candidate models at each time step; however, this can be computationally expensive if the number of models is large. In contrast, we propose a novel algorithm that employs an adaptive model set. We leverage the idea that the current model set must be expanded if its models no longer sufficiently explain the sensor measurements. By maintaining only a small subset of models at each time step, our algorithm improves on efficiency; at the same time, by choosing the appropriate models to keep, we avoid compromising on performance. We show that our algorithm exhibits higher efficiency in comparison to several baselines, when tested on simulated manipulation, driving, and human motion prediction tasks, as well as in hardware experiments on a 7 DOF manipulator.

Education and Outreach in Physical Sciences in Oncology.

Physical sciences are often overlooked in the field of cancer research. The Physical Sciences in Oncology Initiative was launched to integrate physics, mathematics, chemistry, and engineering with cancer research and clinical oncology through education, outreach, and collaboration. Here, we provide a framework for education and outreach in emerging transdisciplinary fields.

Correction: Modeling differentiation-state transitions linked to therapeutic escape in triple-negative breast cancer.

[This corrects the article DOI: 10.1371/journal.pcbi.1006840.].

Modeling differentiation-state transitions linked to therapeutic escape in triple-negative breast cancer.

Drug resistance in breast cancer cell populations has been shown to arise through phenotypic transition of cancer cells to a drug-tolerant state, for example through epithelial-to-mesenchymal transition or transition to a cancer stem cell state. However, many breast tumors are a heterogeneous mixture of cell types with numerous epigenetic states in addition to stem-like and mesenchymal phenotypes, and the dynamic behavior of this heterogeneous mixture in response to drug treatment is not well-understood. Recently, we showed that plasticity between differentiation states, as identified with intracellular markers such as cytokeratins, is linked to resistance to specific targeted therapeutics. Understanding the dynamics of differentiation-state transitions in this context could facilitate the development of more effective treatments for cancers that exhibit phenotypic heterogeneity and plasticity. In this work, we develop computational models of a drug-treated, phenotypically heterogeneous triple-negative breast cancer (TNBC) cell line to elucidate the feasibility of differentiation-state transition as a mechanism for therapeutic escape in this tumor subtype. Specifically, we use modeling to predict the changes in differentiation-state transitions that underlie specific therapy-induced changes in differentiation-state marker expression that we recently observed in the HCC1143 cell line. We report several statistically significant therapy-induced changes in transition rates between basal, luminal, mesenchymal, and non-basal/non-luminal/non-mesenchymal differentiation states in HCC1143 cell populations. Moreover, we validate model predictions on cell division and cell death empirically, and we test our models on an independent data set. Overall, we demonstrate that changes in differentiation-state transition rates induced by targeted therapy can provoke distinct differentiation-state aggregations of drug-resistant cells, which may be fundamental to the design of improved therapeutic regimens for cancers with phenotypic heterogeneity.

Differentiation-state plasticity is a targetable resistance mechanism in basal-like breast cancer.

Intratumoral heterogeneity in cancers arises from genomic instability and epigenomic plasticity and is associated with resistance to cytotoxic and targeted therapies. We show here that cell-state heterogeneity, defined by differentiation-state marker expression, is high in triple-negative and basal-like breast cancer subtypes, and that drug tolerant persister (DTP) cell populations with altered marker expression emerge during treatment with a wide range of pathway-targeted therapeutic compounds. We show that MEK and PI3K/mTOR inhibitor-driven DTP states arise through distinct cell-state transitions rather than by Darwinian selection of preexisting subpopulations, and that these transitions involve dynamic remodeling of open chromatin architecture. Increased activity of many chromatin modifier enzymes, including BRD4, is observed in DTP cells. Co-treatment with the PI3K/mTOR inhibitor BEZ235 and the BET inhibitor JQ1 prevents changes to the open chromatin architecture, inhibits the acquisition of a DTP state, and results in robust cell death in vitro and xenograft regression in vivo.

Correction: Decoupling of the PI3K Pathway via Mutation Necessitates Combinatorial Treatment in HER2+ Breast Cancer.

[This corrects the article DOI: 10.1371/journal.pone.0133219.].

Reconstruction of Gene Regulatory Networks based on Repairing Sparse Low-rank Matrices.

With the growth of high-throughput proteomic data, in particular time series gene expression data from various perturbations, a general question that has arisen is how to organize inherently heterogenous data into meaningful structures. Since biological systems such as breast cancer tumors respond differently to various treatments, little is known about exactly how these gene regulatory networks (GRNs) operate under different stimuli. Challenges due to the lack of knowledge not only occur in modeling the dynamics of a GRN but also cause bias or uncertainties in identifying parameters or inferring the GRN structure. This paper describes a new algorithm which enables us to estimate bias error due to the effect of perturbations and correctly identify the common graph structure among biased inferred graph structures. To do this, we retrieve common dynamics of the GRN subject to various perturbations. We refer to the task as "repairing" inspired by "image repairing" in computer vision. The method can automatically correctly repair the common graph structure across perturbed GRNs, even without precise information about the effect of the perturbations. We evaluate the method on synthetic data sets and demonstrate an application to the DREAM data sets and discuss its implications to experiment design.

Decoupling of the PI3K Pathway via Mutation Necessitates Combinatorial Treatment in HER2+ Breast Cancer.

We report here on experimental and theoretical efforts to determine how best to combine drugs that inhibit HER2 and AKT in HER2(+) breast cancers. We accomplished this by measuring cellular and molecular responses to lapatinib and the AKT inhibitors (AKTi) GSK690693 and GSK2141795 in a panel of 22 HER2(+) breast cancer cell lines carrying wild type or mutant PIK3CA. We observed that combinations of lapatinib plus AKTi were synergistic in HER2(+)/PIK3CA(mut) cell lines but not in HER2(+)/PIK3CA(wt) cell lines. We measured changes in phospho-protein levels in 15 cell lines after treatment with lapatinib, AKTi or lapatinib + AKTi to shed light on the underlying signaling dynamics. This revealed that p-S6RP levels were less well attenuated by lapatinib in HER2(+)/PIK3CA(mut) cells compared to HER2(+)/PIK3CAwt cells and that lapatinib + AKTi reduced p-S6RP levels to those achieved in HER2(+)/PIK3CA(wt) cells with lapatinib alone. We also found that that compensatory up-regulation of p-HER3 and p-HER2 is blunted in PIK3CA(mut) cells following lapatinib + AKTi treatment. Responses of HER2(+) SKBR3 cells transfected with lentiviruses carrying control or PIK3CA(mut )sequences were similar to those observed in HER2(+)/PIK3CA(mut) cell lines but not in HER2(+)/PIK3CA(wt) cell lines. We used a nonlinear ordinary differential equation model to support the idea that PIK3CA mutations act as downstream activators of AKT that blunt lapatinib inhibition of downstream AKT signaling and that the effects of PIK3CA mutations can be countered by combining lapatinib with an AKTi. This combination does not confer substantial benefit beyond lapatinib in HER2+/PIK3CA(wt) cells.

Accelerating Submovement Decomposition With Search-Space Reduction Heuristics.

OBJECTIVE: Movements made by healthy individuals can be characterized as superpositions of smooth bell-shaped velocity curves. Decomposing complex movements into these simpler "submovement" building blocks is useful for studying the neural control of movement as well as measuring motor impairment due to neurological injury. APPROACH: One prevalent strategy to submovement decomposition is to formulate it as an optimization problem. This optimization problem is nonconvex and finding an exact solution is computationally burdensome. We build on previous literature that generated approximate solutions to the submovement optimization problem. RESULTS: First, we demonstrate broad conditions on the submovement building block functions that enable the optimization variables to be partitioned into disjoint subsets, allowing for a faster alternating minimization solution. Specifically, the amplitude parameters of a submovement can typically be fit independently of its shape parameters. Second, we develop a method to concentrate the search in regions of high error to make more efficient use of optimization routine iterations. CONCLUSION: Both innovations result in substantial reductions in computation time across multiple nonhuman primate subjects and diverse task conditions. SIGNIFICANCE: These innovations may accelerate analysis of submovements for basic neuroscience and enable real-time applications of submovement decomposition.

Disentangling multidimensional spatio-temporal data into their common and aberrant responses.

With the advent of high-throughput measurement techniques, scientists and engineers are starting to grapple with massive data sets and encountering challenges with how to organize, process and extract information into meaningful structures. Multidimensional spatio-temporal biological data sets such as time series gene expression with various perturbations over different cell lines, or neural spike trains across many experimental trials, have the potential to acquire insight about the dynamic behavior of the system. For this potential to be realized, we need a suitable representation to understand the data. A general question is how to organize the observed data into meaningful structures and how to find an appropriate similarity measure. A natural way of viewing these complex high dimensional data sets is to examine and analyze the large-scale features and then to focus on the interesting details. Since the wide range of experiments and unknown complexity of the underlying system contribute to the heterogeneity of biological data, we develop a new method by proposing an extension of Robust Principal Component Analysis (RPCA), which models common variations across multiple experiments as the lowrank component and anomalies across these experiments as the sparse component. We show that the proposed method is able to find distinct subtypes and classify data sets in a robust way without any prior knowledge by separating these common responses and abnormal responses. Thus, the proposed method provides us a new representation of these data sets which has the potential to help users acquire new insight from data.

Exact reconstruction of gene regulatory networks using compressive sensing.

BACKGROUND: We consider the problem of reconstructing a gene regulatory network structure from limited time series gene expression data, without any a priori knowledge of connectivity. We assume that the network is sparse, meaning the connectivity among genes is much less than full connectivity. We develop a method for network reconstruction based on compressive sensing, which takes advantage of the network's sparseness. RESULTS: For the case in which all genes are accessible for measurement, and there is no measurement noise, we show that our method can be used to exactly reconstruct the network. For the more general problem, in which hidden genes exist and all measurements are contaminated by noise, we show that our method leads to reliable reconstruction. In both cases, coherence of the model is used to assess the ability to reconstruct the network and to design new experiments. We demonstrate that it is possible to use the coherence distribution to guide biological experiment design effectively. By collecting a more informative dataset, the proposed method helps reduce the cost of experiments. For each problem, a set of numerical examples is presented. CONCLUSIONS: The method provides a guarantee on how well the inferred graph structure represents the underlying system, reveals deficiencies in the data and model, and suggests experimental directions to remedy the deficiencies.

Microtubules provide directional information for core PCP function.

Planar cell polarity (PCP) signaling controls the polarization of cells within the plane of an epithelium. Two molecular modules composed of Fat(Ft)/Dachsous(Ds)/Four-jointed(Fj) and a 'PCP-core' including Frizzled(Fz) and Dishevelled(Dsh) contribute to polarization of individual cells. How polarity is globally coordinated with tissue axes is unresolved. Consistent with previous results, we find that the Ft/Ds/Fj-module has an effect on a MT-cytoskeleton. Here, we provide evidence for the model that the Ft/Ds/Fj-module provides directional information to the core-module through this MT organizing function. We show Ft/Ds/Fj-dependent initial polarization of the apical MT-cytoskeleton prior to global alignment of the core-module, reveal that the anchoring of apical non-centrosomal MTs at apical junctions is polarized, observe that directional trafficking of vesicles containing Dsh depends on Ft, and demonstrate the feasibility of this model by mathematical simulation. Together, these results support the hypothesis that Ft/Ds/Fj provides a signal to orient core PCP function via MT polarization.

Expression-level optimization of a multi-enzyme pathway in the absence of a high-throughput assay.

Engineered metabolic pathways often suffer from flux imbalances that can overburden the cell and accumulate intermediate metabolites, resulting in reduced product titers. One way to alleviate such imbalances is to adjust the expression levels of the constituent enzymes using a combinatorial expression library. Typically, this approach requires high-throughput assays, which are unfortunately unavailable for the vast majority of desirable target compounds. To address this, we applied regression modeling to enable expression optimization using only a small number of measurements. We characterized a set of constitutive promoters in Saccharomyces cerevisiae that spanned a wide range of expression and maintained their relative strengths irrespective of the coding sequence. We used a standardized assembly strategy to construct a combinatorial library and express for the first time in yeast the five-enzyme violacein biosynthetic pathway. We trained a regression model on a random sample comprising 3% of the total library, and then used that model to predict genotypes that would preferentially produce each of the products in this highly branched pathway. This generalizable method should prove useful in engineering new pathways for the sustainable production of small molecules.

A mathematical model to study the dynamics of epithelial cellular networks.

Epithelia are sheets of connected cells that are essential across the animal kingdom. Experimental observations suggest that the dynamical behavior of many single-layered epithelial tissues has strong analogies with that of specific mechanical systems, namely large networks consisting of point masses connected through spring-damper elements and undergoing the influence of active and dissipating forces. Based on this analogy, this work develops a modeling framework to enable the study of the mechanical properties and of the dynamic behavior of large epithelial cellular networks. The model is built first by creating a network topology that is extracted from the actual cellular geometry as obtained from experiments, then by associating a mechanical structure and dynamics to the network via spring-damper elements. This scalable approach enables running simulations of large network dynamics: the derived modeling framework in particular is predisposed to be tailored to study general dynamics (for example, morphogenesis) of various classes of single-layered epithelial cellular networks. In this contribution, we test the model on a case study of the dorsal epithelium of the Drosophila melanogaster embryo during early dorsal closure (and, less conspicuously, germband retraction).

Optimization-based inference for temporally evolving networks with applications in biology.

The problem of identifying dynamics of biological networks is of critical importance in order to understand biological systems. In this article, we propose a data-driven inference scheme to identify temporally evolving network representations of genetic networks. In the formulation of the optimization problem, we use an adjacency map as a priori information and define a cost function that both drives the connectivity of the graph to match biological data as well as generates a sparse and robust network at corresponding time intervals. Through simulation studies of simple examples, it is shown that this optimization scheme can help capture the topological change of a biological signaling pathway, and furthermore, might help to understand the structure and dynamics of biological genetic networks.

Nonparametric variable selection and modeling for spatial and temporal regulatory networks.

Because of the increasing diversity of data sets and measurement techniques in biology, a growing spectrum of modeling methods is being developed. It is generally recognized that it is critical to pick the appropriate method to exploit the amount and type of biological data available for a given system. Here, we describe a method for use in situations where temporal data from a network is collected over multiple time points, and in which little prior information is available about the interactions, mathematical structure, and statistical distribution of the network. Our method results in models that we term Nonparametric exterior derivative estimation Ordinary Differential Equation (NODE) model's. We illustrate the method's utility using spatiotemporal gene expression data from Drosophila melanogaster embryos. We demonstrate that the NODE model's use of the temporal characteristics of the network leads to quantifiable improvements in its predictive ability over nontemporal models that only rely on the spatial characteristics of the data. The NODE model provides exploratory visualizations of network behavior and structure, which can identify features that suggest additional experiments. A new extension is also presented that uses the NODE model to generate a comb diagram, a figure that presents a list of possible network structures ranked by plausibility. By being able to quantify a continuum of interaction likelihoods, this helps to direct future experiments.

Modeling the control of planar cell polarity.

A growing list of medically important developmental defects and disease mechanisms can be traced to disruption of the planar cell polarity (PCP) pathway. The PCP system polarizes cells in epithelial sheets along an axis orthogonal to their apical-basal axis. Studies in the fruitfly, Drosophila, have suggested that components of the PCP signaling system function in distinct modules, and that these modules and the effector systems with which they interact function together to produce emergent patterns. Experimental methods allow the manipulation of individual PCP signaling molecules in specified groups of cells; these interventions not only perturb the polarization of the targeted cells at a subcellular level, but also perturb patterns of polarity at the multicellular level, often affecting nearby cells in characteristic ways. These kinds of experiments should, in principle, allow one to infer the architecture of the PCP signaling system, but the relationships between molecular interactions and tissue-level pattern are sufficiently complex that they defy intuitive understanding. Mathematical modeling has been an important tool to address these problems. This article explores the emergence of a local signaling hypothesis, and describes how a local intercellular signal, coupled with a directional cue, can give rise to global pattern. We will discuss the critical role mathematical modeling has played in guiding and interpreting experimental results, and speculate about future roles for mathematical modeling of PCP. Mathematical models at varying levels of inhibition have and are expected to continue contributing in distinct ways to understanding the regulation of PCP signaling.

Nonparametric identification of regulatory interactions from spatial and temporal gene expression data.

BACKGROUND: The correlation between the expression levels of transcription factors and their target genes can be used to infer interactions within animal regulatory networks, but current methods are limited in their ability to make correct predictions. RESULTS: Here we describe a novel approach which uses nonparametric statistics to generate ordinary differential equation (ODE) models from expression data. Compared to other dynamical methods, our approach requires minimal information about the mathematical structure of the ODE; it does not use qualitative descriptions of interactions within the network; and it employs new statistics to protect against over-fitting. It generates spatio-temporal maps of factor activity, highlighting the times and spatial locations at which different regulators might affect target gene expression levels. We identify an ODE model for eve mRNA pattern formation in the Drosophila melanogaster blastoderm and show that this reproduces the experimental patterns well. Compared to a non-dynamic, spatial-correlation model, our ODE gives 59% better agreement to the experimentally measured pattern. Our model suggests that protein factors frequently have the potential to behave as both an activator and inhibitor for the same cis-regulatory module depending on the factors' concentration, and implies different modes of activation and repression. CONCLUSIONS: Our method provides an objective quantification of the regulatory potential of transcription factors in a network, is suitable for both low- and moderate-dimensional gene expression datasets, and includes improvements over existing dynamic and static models.