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.

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.

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.

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.

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).

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.

Cell packing influences planar cell polarity signaling.

Some epithelial cells display asymmetry along an axis orthogonal to the apical-basal axis, referred to as planar cell polarity (PCP). A Frizzled-mediated feedback loop coordinates PCP between neighboring cells, and the cadherin Fat transduces a global directional cue that orients PCP with respect to the tissue axes. The feedback loop can propagate polarity across clones of cells that lack the global directional signal, although this polarity propagation is error prone. Here, we show that, in the Drosophila wing, a combination of cell geometry and nonautonomous signaling at clone boundaries determines the correct or incorrect polarity propagation in clones that lack Fat mediated global directional information. Pattern elements, such as veins, and sporadic occurrences of irregular geometry are obstacles to polarity propagation. Hence, in the wild type, broad distribution of the global directional cue combines with a local feedback mechanism to overcome irregularities in cell packing geometry during PCP signaling.

Biology by numbers: mathematical modelling in developmental biology.

In recent years, mathematical modelling of developmental processes has earned new respect. Not only have mathematical models been used to validate hypotheses made from experimental data, but designing and testing these models has led to testable experimental predictions. There are now impressive cases in which mathematical models have provided fresh insight into biological systems, by suggesting, for example, how connections between local interactions among system components relate to their wider biological effects. By examining three developmental processes and corresponding mathematical models, this Review addresses the potential of mathematical modelling to help understand development.

Mathematical modeling of planar cell polarity to understand domineering nonautonomy.

Planar cell polarity (PCP) signaling generates subcellular asymmetry along an axis orthogonal to the epithelial apical-basal axis. Through a poorly understood mechanism, cell clones that have mutations in some PCP signaling components, including some, but not all, alleles of the receptor frizzled, cause polarity disruptions of neighboring wild-type cells, a phenomenon referred to as domineering nonautonomy. Here, a contact-dependent signaling hypothesis, derived from experimental results, is shown by reaction-diffusion, partial differential equation modeling and simulation to fully reproduce PCP phenotypes, including domineering nonautonomy, in the Drosophila wing. The sufficiency of this model and the experimental validation of model predictions reveal how specific protein-protein interactions produce autonomy or domineering nonautonomy.