Predicting in vivo glioma growth with the reaction diffusion equation constrained by quantitative magnetic resonance imaging data.

Reaction-diffusion models have been widely used to model glioma growth. However, it has not been shown how accurately this model can predict future tumor status using model parameters (i.e., tumor cell diffusion and proliferation) estimated from quantitative in vivo imaging data. To this end, we used in silico studies to develop the methods needed to accurately estimate tumor specific reaction-diffusion model parameters, and then tested the accuracy with which these parameters can predict future growth. The analogous study was then performed in a murine model of glioma growth. The parameter estimation approach was tested using an in silico tumor 'grown' for ten days as dictated by the reaction-diffusion equation. Parameters were estimated from early time points and used to predict subsequent growth. Prediction accuracy was assessed at global (total volume and Dice value) and local (concordance correlation coefficient, CCC) levels. Guided by the in silico study, rats (n = 9) with C6 gliomas, imaged with diffusion weighted magnetic resonance imaging, were used to evaluate the model's accuracy for predicting in vivo tumor growth. The in silico study resulted in low global (tumor volume error <8.8%, Dice >0.92) and local (CCC values >0.80) level errors for predictions up to six days into the future. The in vivo study showed higher global (tumor volume error >11.7%, Dice <0.81) and higher local (CCC <0.33) level errors over the same time period. The in silico study shows that model parameters can be accurately estimated and used to accurately predict future tumor growth at both the global and local scale. However, the poor predictive accuracy in the experimental study suggests the reaction-diffusion equation is an incomplete description of in vivo C6 glioma biology and may require further modeling of intra-tumor interactions including segmentation of (for example) proliferative and necrotic regions.

Modeling and measuring signal relay in noisy directed migration of cell groups.

We develop a coarse-grained stochastic model for the influence of signal relay on the collective behavior of migrating Dictyostelium discoideum cells. In the experiment, cells display a range of collective migration patterns, including uncorrelated motion, formation of partially localized streams, and clumping, depending on the type of cell and the strength of the external, linear concentration gradient of the signaling molecule cyclic adenosine monophosphate (cAMP). From our model, we find that the pattern of migration can be quantitatively described by the competition of two processes, the secretion rate of cAMP by the cells and the degradation rate of cAMP in the gradient chamber. Model simulations are compared to experiments for a wide range of strengths of an external linear-gradient signal. With degradation, the model secreting cells form streams and efficiently transverse the gradient, but without degradation, we find that model secreting cells form clumps without streaming. This indicates that the observed effective collective migration in streams requires not only signal relay but also degradation of the signal. In addition, our model allows us to detect and quantify precursors of correlated motion, even when cells do not exhibit obvious streaming.

Direct biochemical measurements of signal relay during Dictyostelium development.

Upon starvation, individual Dictyostelium discoideum cells enter a developmental program that leads to collective migration and the formation of a multicellular organism. The process is mediated by extracellular cAMP binding to the G protein-coupled cAMP receptor 1, which initiates a signaling cascade leading to the activation of adenylyl cyclase A (ACA), the synthesis and secretion of additional cAMP, and an autocrine and paracrine activation loop. The release of cAMP allows neighboring cells to polarize and migrate directionally and form characteristic chains of cells called streams. We now report that cAMP relay can be measured biochemically by assessing ACA, ERK2, and TORC2 activities at successive time points in development after stimulating cells with subsaturating concentrations of cAMP. We also find that the activation profiles of ACA, ERK2, and TORC2 change in the course of development, with later developed cells showing a loss of sensitivity to the relayed signal. We examined mutants in PKA activity that have been associated with precocious development and find that this loss in responsiveness occurs earlier in these mutants. Remarkably, we show that this loss in sensitivity correlates with a switch in migration patterns as cells transition from streams to aggregates. We propose that as cells proceed through development, the cAMP-induced desensitization and down-regulation of cAMP receptor 1 impacts the sensitivities of chemotactic signaling cascades leading to changes in migration patterns.

Real-time measurements of cAMP production in live Dictyostelium cells.

Cyclic AMP has a crucial role during the entire developmental program of the social amoebae Dictyostelium, acting both as an intracellular second messenger and, when secreted, as a directional cue that is relayed to neighboring cells during chemotaxis. Although significant knowledge about cAMP production in chemotaxing cells has been derived from studies performed on cell populations, cAMP dynamics at the single cell level have not been investigated. To examine this, we used a FRET-based cAMP sensor that possesses high cAMP sensitivity and great temporal resolution. We show the transient profile of cAMP accumulation in live Dictyostelium cells and establish that chemoattractants control intracellular cAMP dynamics by regulating synthesis via the adenylyl cyclase ACA. aca(-) cells show no significant change in FRET response following chemoattractant addition. Furthermore, cells lacking ACB, the other adenylyl cyclase expressed in chemotaxing cells, behave similarly to wild-type cells. We also establish that the RegA is the major phosphodiesterase that degrades intracellular cAMP in chemotaxis-competent cells. Interestingly, we failed to measure intracellular cAMP compartmentalization in actively chemotaxing cells. We conclude that cytosolic cAMP, which is destined to activate PKA, is regulated by ACA and RegA and does not compartmentalize during chemotaxis.

A mechanically coupled reaction-diffusion model that incorporates intra-tumoural heterogeneity to predict in vivo glioma growth.

While gliomas have been extensively modelled with a reaction-diffusion (RD) type equation it is most likely an oversimplification. In this study, three mathematical models of glioma growth are developed and systematically investigated to establish a framework for accurate prediction of changes in tumour volume as well as intra-tumoural heterogeneity. Tumour cell movement was described by coupling movement to tissue stress, leading to a mechanically coupled (MC) RD model. Intra-tumour heterogeneity was described by including a voxel-specific carrying capacity (CC) to the RD model. The MC and CC models were also combined in a third model. To evaluate these models, rats (n = 14) with C6 gliomas were imaged with diffusion-weighted magnetic resonance imaging over 10 days to estimate tumour cellularity. Model parameters were estimated from the first three imaging time points and then used to predict tumour growth at the remaining time points which were then directly compared to experimental data. The results in this work demonstrate that mechanical-biological effects are a necessary component of brain tissue tumour modelling efforts. The results are suggestive that a variable tissue carrying capacity is a needed model component to capture tumour heterogeneity. Lastly, the results advocate the need for additional effort towards capturing tumour-to-tissue infiltration.

Shear stress induces noncanonical autophagy in intestinal epithelial monolayers.

Flow of fluids through the gut, such as milk from a neonatal diet, generates a shear stress on the unilaminar epithelium lining the lumen. We report that exposure to physiological levels of fluid shear stress leads to the formation of large vacuoles, containing extracellular contents within polarizing intestinal epithelial cell monolayers. These observations lead to two questions: how can cells lacking primary cilia transduce shear stress, and what molecular pathways support the formation of vacuoles that can exceed 80% of the cell volume? We find that shear forces are sensed by actin-rich microvilli that eventually generate the apical brush border, providing evidence that these structures possess mechanosensing ability. Importantly, we identified the molecular pathway that regulates large vacuole formation downstream from mechanostimulation to involve central components of the autophagy pathway, including ATG5 and LC3, but not Beclin. Together our results establish a novel link between the actin-rich microvilli, the macroscopic transport of fluids across cells, and the noncanonical autophagy pathway in organized epithelial monolayers.

Toward a science of tumor forecasting for clinical oncology.

We propose that the quantitative cancer biology community makes a concerted effort to apply lessons from weather forecasting to develop an analogous methodology for predicting and evaluating tumor growth and treatment response. Currently, the time course of tumor response is not predicted; instead, response is only assessed post hoc by physical examination or imaging methods. This fundamental practice within clinical oncology limits optimization of a treatment regimen for an individual patient, as well as to determine in real time whether the choice was in fact appropriate. This is especially frustrating at a time when a panoply of molecularly targeted therapies is available, and precision genetic or proteomic analyses of tumors are an established reality. By learning from the methods of weather and climate modeling, we submit that the forecasting power of biophysical and biomathematical modeling can be harnessed to hasten the arrival of a field of predictive oncology. With a successful methodology toward tumor forecasting, it should be possible to integrate large tumor-specific datasets of varied types and effectively defeat one cancer patient at a time.

Dictyostelium cells migrate similarly on surfaces of varying chemical composition.

During cell migration, cell-substrate binding is required for pseudopod anchoring to move the cell forward, yet the interactions with the substrate must be sufficiently weak to allow parts of the cell to de-adhere in a controlled manner during typical protrusion/retraction cycles. Mammalian cells actively control cell-substrate binding and respond to extracellular conditions with localized integrin-containing focal adhesions mediating mechanotransduction. We asked whether mechanotransduction also occurs during non-integrin mediated migration by examining the motion of the social amoeba Dictyostelium discoideum, which is thought to bind non-specifically to surfaces. We discovered that Dictyostelium cells are able to regulate forces generated by the actomyosin cortex to maintain optimal cell-surface contact area and adhesion on surfaces of various chemical composition and that individual cells migrate with similar speed and contact area on the different surfaces. In contrast, during collective migration, as observed in wound healing and metastasis, the balance between surface forces and protrusive forces is altered. We found that Dictyostelium collective migration dynamics are strongly affected when cells are plated on different surfaces. These results suggest that the presence of cell-cell contacts, which appear as Dictyostelium cells enter development, alter the mechanism cells use to migrate on surfaces of varying composition.

Clinically relevant modeling of tumor growth and treatment response.

Current mathematical models of tumor growth are limited in their clinical application because they require input data that are nearly impossible to obtain with sufficient spatial resolution in patients even at a single time point--for example, extent of vascularization, immune infiltrate, ratio of tumor-to-normal cells, or extracellular matrix status. Here we propose the use of emerging, quantitative tumor imaging methods to initialize a new generation of predictive models. In the near future, these models could be able to forecast clinical outputs, such as overall response to treatment and time to progression, which will provide opportunities for guided intervention and improved patient care.

Myosin II activity regulates vinculin recruitment to focal adhesions through FAK-mediated paxillin phosphorylation.

Focal adhesions (FAs) are mechanosensitive adhesion and signaling complexes that grow and change composition in response to myosin II-mediated cytoskeletal tension in a process known as FA maturation. To understand tension-mediated FA maturation, we sought to identify proteins that are recruited to FAs in a myosin II-dependent manner and to examine the mechanism for their myosin II-sensitive FA association. We find that FA recruitment of both the cytoskeletal adapter protein vinculin and the tyrosine kinase FA kinase (FAK) are myosin II and extracellular matrix (ECM) stiffness dependent. Myosin II activity promotes FAK/Src-mediated phosphorylation of paxillin on tyrosines 31 and 118 and vinculin association with paxillin. We show that phosphomimic mutations of paxillin can specifically induce the recruitment of vinculin to adhesions independent of myosin II activity. These results reveal an important role for paxillin in adhesion mechanosensing via myosin II-mediated FAK phosphorylation of paxillin that promotes vinculin FA recruitment to reinforce the cytoskeletal ECM linkage and drive FA maturation.

The group migration of Dictyostelium cells is regulated by extracellular chemoattractant degradation.

Starvation of Dictyostelium induces a developmental program in which cells form an aggregate that eventually differentiates into a multicellular structure. The aggregate formation is mediated by directional migration of individual cells that quickly transition to group migration in which cells align in a head-to-tail manner to form streams. Cyclic AMP acts as a chemoattractant and its production, secretion, and degradation are highly regulated. A key protein is the extracellular phosphodiesterase PdsA. In this study we examine the role and localization of PdsA during chemotaxis and streaming. We find that pdsA(-) cells respond chemotactically to a narrower range of chemoattractant concentrations compared with wild-type (WT) cells. Moreover, unlike WT cells, pdsA(-) cells do not form streams at low cell densities and form unusual thick and transient streams at high cell densities. We find that the intracellular pool of PdsA is localized to the endoplasmic reticulum, which may provide a compartment for storage and secretion of PdsA. Because we find that cAMP synthesis is normal in cells lacking PdsA, we conclude that signal degradation regulates the external cAMP gradient field generation and that the group migration behavior of these cells is compromised even though their signaling machinery is intact.

Steering in quadruplet: the complex signaling pathways directing chemotaxis.

Studies in the social amoeba Dictyostelium discoideum reveal that signaling cascades coordinating chemotactic directional sensing and migration are complex, with redundant pathways emerging as cells differentiate. Lack of accumulation of the leading-edge marker phosphatidylinositol-3,4,5-trisphosphate can be compensated by a pathway containing phospholipase A2 (PLA2) in early developed cells and guanylyl cyclase (GC) in later developed, polarized cells. Because numerous signaling networks operational during Dictyostelium chemotaxis are conserved in mammalian cells, PLA2 and GC pathways may also be effective in higher eukaryotes, providing avenues for future research.

Collective cell migration requires vesicular trafficking for chemoattractant delivery at the trailing edge.

Chemoattractant signaling induces the polarization and directed movement of cells secondary to the activation of multiple effector pathways. In addition, chemotactic signals can be amplified and relayed to proximal cells via the synthesis and secretion of additional chemoattractant. The mechanisms underlying such remarkable features remain ill defined. We show that the asymmetrical distribution of adenylyl cyclase (ACA) at the back of Dictyostelium discoideum cells, an essential determinant of their ability to migrate in a head-to-tail fashion, requires vesicular trafficking. This trafficking results in a local accumulation of ACA-containing intracellular vesicles and involves intact actin, microtubule networks, and de novo protein synthesis. We also show that migrating cells leave behind ACA-containing vesicles, likely secreted as multivesicular bodies and presumably involved in the formation of head-to-tail arrays of migrating cells. We propose that similar compartmentalization and shedding mechanisms exist in mammalian cells during embryogenesis, wound healing, neuron growth, and metastasis.

Shocks in supersonic sand.

We measure time-averaged velocity, density, and temperature fields for steady granular flow past a wedge. We find the flow to be supersonic with a speed of granular pressure disturbances (sound speed) equal to about 10% of the flow speed, and we observe shocks nearly identical to those in a supersonic gas. Molecular dynamics simulations of Newton's laws yield fields in quantitative agreement with experiment. A numerical solution of Navier-Stokes-like equations agrees with a molecular dynamics simulation for experimental conditions excluding wall friction.

Persistent holes in a fluid.

We observe stable holes in a vertically oscillated 0.5 cm deep aqueous suspension of cornstarch. Holes appear only if a finite perturbation is applied to the layer for accelerations a above 10g. Holes are circular and approximately 0.5 cm wide, and can persist for more than 10(6) cycles. Above a approximately equal to 17g the rim of the hole becomes unstable, producing fingerlike protrusions or hole division. At higher acceleration, the hole delocalizes, growing to cover the entire surface with erratic undulations. We find similar behavior in an aqueous suspension of glass microspheres.