Combinatorial mathematical modelling approaches to interrogate rear retraction dynamics in 3D cell migration

Cell migration in 3D microenvironments is a complex process which depends on the coordinated activity of leading edge protrusive force and rear retraction in a push-pull mechanism. While the potentiation of protrusions has been widely studied, the precise signalling and mechanical events that lead to retraction of the cell rear are much less well understood, particularly in physiological 3D extra-cellular matrix (ECM). We previously discovered that rear retraction in fast moving cells is a highly dynamic process involving the precise spatiotemporal interplay of mechanosensing by caveolae and signalling through RhoA. To further interrogate the dynamics of rear retraction, we have adopted three distinct mathematical modelling approaches here based on (i) Boolean logic, (ii) deterministic kinetic ordinary differential equations (ODEs) and (iii) stochastic simulations. The aims of this multi-faceted approach are twofold: firstly to derive new biological insight into cell rear dynamics via generation of testable hypotheses and predictions; and secondly to compare and contrast the distinct modelling approaches when used to describe the same, relatively under-studied system. Overall, our modelling approaches complement each other, suggesting that such a multi-faceted approach is more informative than methods based on a single modelling technique to interrogate biological systems. Whilst Boolean logic was not able to fully recapitulate the complexity of rear retraction signalling, an ODE model could make plausible population level predictions. Stochastic simulations added a further level of complexity by accurately mimicking previous experimental findings and acting as a single cell simulator. Our approach highlighted the unanticipated role for CDK1 in rear retraction, a prediction we confirmed experimentally. Moreover, our models led to a novel prediction regarding the potential existence of a 'set point' in local stiffness gradients that promotes polarisation and rapid rear retraction.

Realizing Cancer Precision Medicine by Integrating Systems Biology and Nanomaterial Engineering

Many clinical trials for cancer precision medicine have yielded unsatisfactory results due to challenges such as drug resistance and low efficacy. Drug resistance is often caused by the complex compensatory regulation within the biomolecular network in a cancer cell. Recently, systems biological studies have modeled and simulated such complex networks to unravel the hidden mechanisms of drug resistance and identify promising new drug targets or combinatorial or sequential treatments for overcoming resistance to anticancer drugs. However, many of the identified targets or treatments present major difficulties for drug development and clinical application. Nanocarriers represent a path forward for developing therapies with these "undruggable" targets or those that require precise combinatorial or sequential application, for which conventional drug delivery mechanisms are unsuitable. Conversely, a challenge in nanomedicine has been low efficacy due to heterogeneity of cancers in patients. This problem can also be resolved through systems biological approaches by identifying personalized targets for individual patients or promoting the drug responses. Therefore, integration of systems biology and nanomaterial engineering will enable the clinical application of cancer precision medicine to overcome both drug resistance of conventional treatments and low efficacy of nanomedicine due to patient heterogeneity.

Periodic propagating waves coordinate RhoGTPase network dynamics at the leading and trailing edges during cell migration

Migrating cells need to coordinate distinct leading and trailing edge dynamics but the underlying mechanisms are unclear. Here, we combine experiments and mathematical modeling to elaborate the minimal autonomous biochemical machinery necessary and sufficient for this dynamic coordination and cell movement. RhoA activates Rac1 via DIA and inhibits Rac1 via ROCK, while Rac1 inhibits RhoA through PAK. Our data suggest that in motile, polarized cells, RhoA–ROCK interactions prevail at the rear, whereas RhoA-DIA interactions dominate at the front where Rac1/Rho oscillations drive protrusions and retractions. At the rear, high RhoA and low Rac1 activities are maintained until a wave of oscillatory GTPase activities from the cell front reaches the rear, inducing transient GTPase oscillations and RhoA activity spikes. After the rear retracts, the initial GTPase pattern resumes. Our findings show how periodic, propagating GTPase waves coordinate distinct GTPase patterns at the leading and trailing edge dynamics in moving cells.

Simple Rho GTPase Dynamics Generate a Complex Regulatory Landscape Associated with Cell Shape

Migratory cells exhibit a variety of morphologically distinct responses to their environments that manifest in their cell shape. Some protrude uniformly to increase substrate contacts, others are broadly contractile, some polarize to facilitate migration, and yet others exhibit mixtures of these responses. Prior studies have identified a discrete collection of shapes that the majority of cells display and demonstrated that activity levels of the cytoskeletal regulators Rac1 and RhoA GTPase regulate those shapes. Here, we use computational modeling to assess whether known GTPase dynamics can give rise to a sufficient diversity of spatial signaling states to explain the observed shapes. Results show that the combination of autoactivation and mutually antagonistic cross talk between GTPases, along with the conservative membrane binding, generates a wide array of distinct homogeneous and polarized regulatory phenotypes that arise for fixed model parameters. From a theoretical perspective, these results demonstrate that simple GTPase dynamics can generate complex multistability in which six distinct stable steady states (three homogeneous and three polarized) coexist for a fixed set of parameters, each of which naturally maps to an observed morphology. From a biological perspective, although we do not explicitly model the cytoskeleton or resulting cell morphologies, these results, along with prior literature linking GTPase activity to cell morphology, support the hypothesis that GTPase signaling dynamics can generate the broad morphological characteristics observed in many migratory cell populations. Further, the observed diversity may be the result of cells populating a complex morphological landscape generated by GTPase regulation rather than being the result of intrinsic cell-cell variation. These results demonstrate that Rho GTPases may have a central role in regulating the broad characteristics of cell shape (e.g., expansive, contractile, polarized, etc.) and that shape heterogeneity may be (at least partly) a reflection of the rich signaling dynamics regulating the cytoskeleton rather than intrinsic cell heterogeneity.

Acetylation of ACAP4 regulates CCL18-elicited breast cancer cell migration and invasion

Tumor metastasis represents the main causes of cancer-related death. Our recent study showed that chemokine CCL18 secreted from tumor-associated macrophages regulates breast tumor metastasis, but the underlying mechanisms remain less clear. Here, we show that ARF6 GTPase-activating protein ACAP4 regulates CCL18-elicited breast cancer cell migration via the acetyltransferase PCAF-mediated acetylation. CCL18 stimulation elicited breast cancer cell migration and invasion via PCAF-dependent acetylation. ACAP4 physically interacts with PCAF and is a cognate substrate of PCAF during CCL18 stimulation. The acetylation site of ACAP4 by PCAF was mapped to Lys311 by mass spectrometric analyses. Importantly, dynamic acetylation of ACAP4 is essential for CCL18-induced breast cancer cell migration and invasion, as overexpression of the persistent acetylation-mimicking or non-acetylatable ACAP4 mutant blocked CCL18-elicited cell migration and invasion. Mechanistically, the acetylation of ACAP4 at Lys311 reduced the lipid-binding activity of ACAP4 to ensure a robust and dynamic cycling of ARF6-ACAP4 complex with plasma membrane in response to CCL18 stimulation. Thus, these results present a previously undefined mechanism by which CCL18-elicited acetylation of the PH domain controls dynamic interaction between ACAP4 and plasma membrane during breast cancer cell migration and invasion.

Computational Modeling of the Dynamics of Spatiotemporal Rho GTPase Signaling: A Systematic Review

The Rho family of GTPases are known to play pivotal roles in the regulation of fundamental cellular processes, ranging from cell migration and polarity to wound healing and regulation of actin cytoskeleton. Over the past decades, accumulating experimental work has increasingly mapped out the mechanistic details and interactions between members of the family and their regulators, establishing detailed interaction circuits within the Rho GTPase signaling network. These circuits have served as a vital foundation based on which a multitude of mathematical models have been developed to explain experimental data, gain deeper insights into the biological phenomenon they describe, as well as make new testable predictions and hypotheses. Due to the diverse nature and purpose of these models, they often vary greatly in size, scope, complexity, and formulation. Here, we provide a systematic, categorical, and comprehensive account of the recent modeling studies of Rho family GTPases, with an aim to offer a broad perspective of the field. The modeling limitations and possible future research directions are also discussed.

Modeling Rho GTPase Dynamics Using Boolean Logic

Rho GTPases such as the canonical Rac1 and RhoA are embedded within complex networks requiring the precise spatiotemporal balance of GEFs, GAPs, upstream regulators, growth factors, and downstream effectors. A modeling approach based on Boolean logical networks is becoming an increasingly relied-upon tool to harness this complexity and elucidate further details regarding Rho GTPase signaling. In this methods chapter we describe how to initially create appropriately sized networks based on literature evidence; formalize these networks with reactions based on Boolean logical operators; implement the network into appropriate simulation software (CellNetAnalyzer); and finally perform simulations and make novel, testable predictions via in silico knockouts. Given this predictive power, the Boolean approach may ultimately help to highlight potential future avenues of experimental research.

EZH2-, CHD4-, and IDH-linked epigenetic perturbation and its association with survival in glioma patients

Glioma is a complex disease with limited treatment options. Recent advances have identified isocitrate dehydrogenase (IDH) mutations in up to 80% lower grade gliomas (LGG) and in 76% secondary glioblastomas (GBM). IDH mutations are also seen in 10%-20% of acute myeloid leukemia (AML). In AML, it was determined that mutations of IDH and other genes involving epigenetic regulations are early events, emerging in the pre-leukemic stem cells (pre-LSCs) stage, whereas mutations in genes propagating oncogenic signal are late events in leukemia. IDH mutations are also early events in glioma, occurring before TP53 mutation, 1p/19q deletion, etc. Despite these advances in glioma research, studies into other molecular alterations have lagged considerably. In this study, we analyzed currently available databases. We identified EZH2, KMT2C, and CHD4 as important genes in glioma in addition to the known gene IDH1/2. We also showed that genomic alterations of PIK3CA, CDKN2A, CDK4, FIP1L1, or FUBP1 collaborate with IDH mutations to negatively affect patients' survival in LGG. In LGG patients with TP53 mutations or IDH1/2 mutations, additional genomic alterations of EZH2, KMC2C, and CHD4 individually or in combination were associated with a markedly decreased disease-free survival than patients without such alterations. Alterations of EZH2, KMT2C, and CHD4 at genetic level or protein level could perturb epigenetic program, leading to malignant transformation in glioma. By reviewing current literature on both AML and glioma and performing bioinformatics analysis on available datasets, we developed a hypothetical model on the tumorigenesis from premalignant stem cells to glioma.

Paving the Rho in cancer metastasis: Rho GTPases and beyond

Malignant carcinomas are often characterized by metastasis, the movement of carcinoma cells from a primary site to colonize distant organs. For metastasis to occur, carcinoma cells first must adopt a pro-migratory phenotype and move through the surrounding stroma towards a blood or lymphatic vessel. Currently, there are very limited possibilities to target these processes therapeutically. The family of Rho GTPases is an ubiquitously expressed division of GTP-binding proteins involved in the regulation of cytoskeletal dynamics and intracellular signaling. The best characterized members of the Rho family GTPases are RhoA, Rac1 and Cdc42. Abnormalities in Rho GTPase function have major consequences for cancer progression. Rho GTPase activation is driven by cell surface receptors that activate GTP exchange factors (GEFs) and GTPase-activating proteins (GAPs). In this review, we summarize our current knowledge on Rho GTPase function in the regulation of metastasis. We will focus on key discoveries in the regulation of epithelial-mesenchymal-transition (EMT), cell-cell junctions, formation of membrane protrusions, plasticity of cell migration and adaptation to a hypoxic environment. In addition, we will emphasize on crosstalk between Rho GTPase family members and other important oncogenic pathways, such as cyclic AMP-mediated signaling, canonical Wnt/β-catenin, Yes-associated protein (YAP) and hypoxia inducible factor 1α (Hif1α) and provide an overview of the advancements and challenges in developing pharmacological tools to target Rho GTPase and the aforementioned crosstalk in the context of cancer therapeutics.

Modelling GTPase dynamics to understand RhoA-driven cancer cell invasion

Metastasis, initially driven by cells migrating and invading through the local environment, leads to most cancer-associated deaths. Cells can use a variety of modes to move in vitro, all of which depend on Rho GTPases at some level. While traditionally it was thought that Rac1 activity drives protrusive lamellipodia at the leading edge of a polarised cell while RhoA drives rear retraction, more recent work in 3D microenvironments has revealed a much more complicated picture of GTPase dynamics. In particular, RhoA activity can dominate the leading edge polymerisation of actin to form filopodial actin-spike protrusions that drive more invasive cell migration. We recently described a potential mechanism to abrogate this pro-invasive localised leading edge Rac1 to RhoA switch via manipulation of a negative feedback loop that was revealed by adopting a logical modelling approach. Both challenging dogma and taking a formal, mathematical approach to understanding signalling involved in motility may be vital to harnessing harmful cell migration and preventing metastasis in future research.

Crosstalk of cell polarity signaling pathways

Cell polarity, the asymmetric organization of cellular components along one or multiple axes, is present in most cells. From budding yeast cell polarization induced by pheromone signaling, oocyte polarization at fertilization to polarized epithelia and neuronal cells in multicellular organisms, similar mechanisms are used to determine cell polarity. Crucial role in this process is played by signaling lipid molecules, small Rho family GTPases and Par proteins. All these signaling circuits finally govern the cytoskeleton, which is responsible for oriented cell migration, cell shape changes, and polarized membrane and organelle trafficking. Thus, typically in the process of cell polarization, most cellular constituents become polarized, including plasma membrane lipid composition, ion concentrations, membrane receptors, and proteins in general, mRNA, vesicle trafficking, or intracellular organelles. This review gives a brief overview how these systems talk to each other both during initial symmetry breaking and within the signaling feedback loop mechanisms used to preserve the polarized state.

Mechanisms of Cell Polarization

Cell polarization is a key step in the migration, development, and organization of eukaryotic cells, both at the single cell and multicellular level. Research on the mechanisms that give rise to polarization of a given cell, and organization of polarity within a tissue has led to new understanding across cellular and developmental biology. In this review, we describe some of the history of theoretical and experimental aspects of the field, as well as some interesting questions and challenges for the future.

Attractor landscape analysis of colorectal tumorigenesis and its reversion

Background

Colorectal cancer arises from the accumulation of genetic mutations that induce dysfunction of intracellular signaling. However, the underlying mechanism of colorectal tumorigenesis driven by genetic mutations remains yet to be elucidated.

Results

To investigate colorectal tumorigenesis at a system-level, we have reconstructed a large-scale Boolean network model of the human signaling network by integrating previous experimental results on canonical signaling pathways related to proliferation, metastasis, and apoptosis. Throughout an extensive simulation analysis of the attractor landscape of the signaling network model, we found that the attractor landscape changes its shape by expanding the basin of attractors for abnormal proliferation and metastasis along with the accumulation of driver mutations. A further hypothetical study shows that restoration of a normal phenotype might be possible by reversely controlling the attractor landscape. Interestingly, the targets of approved anti-cancer drugs were highly enriched in the identified molecular targets for the reverse control.

Conclusions

Our results show that the dynamical analysis of a signaling network based on attractor landscape is useful in acquiring a system-level understanding of tumorigenesis and developing a new therapeutic strategy.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0341-9) contains supplementary material, which is available to authorized users.

Rationalizing Rac1 and RhoA GTPase signaling: A mathematical approach

Precise spatiotemporal dynamics of Rho GTPases are essential for efficient cell migration. Manipulating Rac1 and RhoA signaling is thus a potential intervention strategy to abrogate harmful cell invasion and subsequent metastasis; however GTPase signaling can be extremely complicated due to crosstalk and the multitude of upstream regulators and downstream effectors. Studying Rho GTPase networks in a formal mathematical setting can therefore be of great use. We recently built a predictive model based on Boolean logic which identified a negative feedback loop critical for RhoA and Rac1 activity. Here, we discuss the value and potential pitfalls of different mathematical approaches which have been used to study Rho GTPase dynamics, and highlight the importance of choosing the correct approach given the data available and outputs desired. Overall, a mathematical approach, particularly when combined iteratively with in vitro experiments, can be of great use in deriving new biological insight to further harness the activity of Rho GTPases.

A MAPK-Driven Feedback Loop Suppresses Rac Activity to Promote RhoA-Driven Cancer Cell Invasion

Cell migration in 3D microenvironments is fundamental to development, homeostasis and the pathobiology of diseases such as cancer. Rab-coupling protein (RCP) dependent co-trafficking of α5β1 and EGFR1 promotes cancer cell invasion into fibronectin (FN) containing extracellular matrix (ECM), by potentiating EGFR1 signalling at the front of invasive cells. This promotes a switch in RhoGTPase signalling to inhibit Rac1 and activate a RhoA-ROCK-Formin homology domain-containing 3 (FHOD3) pathway and generate filopodial actin-spike protrusions which drive invasion. To further understand the signalling network that drives RCP-driven invasive migration, we generated a Boolean logical model based on existing network pathways/models, where each node can be interrogated by computational simulation. The model predicted an unanticipated feedback loop, whereby Raf/MEK/ERK signalling maintains suppression of Rac1 by inhibiting the Rac-activating Sos1-Eps8-Abi1 complex, allowing RhoA activity to predominate in invasive protrusions. MEK inhibition was sufficient to promote lamellipodia formation and oppose filopodial actin-spike formation, and led to activation of Rac and inactivation of RhoA at the leading edge of cells moving in 3D matrix. Furthermore, MEK inhibition abrogated RCP/α5β1/EGFR1-driven invasive migration. However, upon knockdown of Eps8 (to suppress the Sos1-Abi1-Eps8 complex), MEK inhibition had no effect on RhoGTPase activity and did not oppose invasive migration, suggesting that MEK-ERK signalling suppresses the Rac-activating Sos1-Abi1-Eps8 complex to maintain RhoA activity and promote filopodial actin-spike formation and invasive migration. Our study highlights the predictive potential of mathematical modelling approaches, and demonstrates that a simple intervention (MEK-inhibition) could be of therapeutic benefit in preventing invasive migration and metastasis.

The majority of cancer-related fatalities are caused by the movement of cancer cells away from the primary site to form metastases, making understanding the signalling mechanisms which underpin cell migration and invasion through their local environment of paramount importance. Much has been discovered about key events leading to invasive cell migration. Here, we have taken this prior knowledge to build a powerful predictive model based on simple ON/OFF relations and logic to determine potential intervention targets to reduce harmful invasive migration. Interrogating our model, we have identified a negative feedback loop important to the signalling that determines invasive migration, the breaking of which reverts cells to a slower, less invasive phenotype. We have supported this feedback loop prediction using an array of in vitro experiments performed in cells within 2-D and physiologically relevant 3-D environments. Our findings demonstrate the predictive power of such modelling techniques, and could form the basis for clinical intervention to prevent metastasis in certain cancers.

An analysis toolbox to explore mesenchymal migration heterogeneity reveals adaptive switching between distinct modes

Mesenchymal (lamellipodial) migration is heterogeneous, although whether this reflects progressive variability or discrete, 'switchable' migration modalities, remains unclear. We present an analytical toolbox, based on quantitative single-cell imaging data, to interrogate this heterogeneity. Integrating supervised behavioral classification with multivariate analyses of cell motion, membrane dynamics, cell-matrix adhesion status and F-actin organization, this toolbox here enables the detection and characterization of two quantitatively distinct mesenchymal migration modes, termed 'Continuous' and 'Discontinuous'. Quantitative mode comparisons reveal differences in cell motion, spatiotemporal coordination of membrane protrusion/retraction, and how cells within each mode reorganize with changed cell speed. These modes thus represent distinctive migratory strategies. Additional analyses illuminate the macromolecular- and cellular-scale effects of molecular targeting (fibronectin, talin, ROCK), including 'adaptive switching' between Continuous (favored at high adhesion/full contraction) and Discontinuous (low adhesion/inhibited contraction) modes. Overall, this analytical toolbox now facilitates the exploration of both spontaneous and adaptive heterogeneity in mesenchymal migration.