Session X6: Physics of Development and Disease I

Multiscale biomechanics of brain tumours favours cancer invasion by cell softening and tissue stiffening.

Cancer progression needs two contradictory mechanical prerequisites. For metastasis individual cancer cells or small clusters have to flow through the microenvironment by overcoming the yield stress exerted by the surrounding. On the other hand a tumour has to behave as a solid to permit cell proliferation and spreading of the tumour mass against its surrounding. We determine that the high mechanical adaptability of cancer cells and the scale controlled viscoelastic properties of tissues reconcile both conflicting properties, fluid and solid, simultaneously in brain tumours. We resolve why different techniques that assess cell and tissue mechanics have produced apparently conflicting results by our finding that tumours generate different viscoelastic behaviours on different length scales, which are in concert optimal for tumour spreading and metastasis. Single cancer cells become very soft in their elastic behavior which promotes cell unjamming. On the level of direct cell-to-cell interactions cells feel their micro-environment as rigid elastic substrate that stimulates cancer on the molecular level. All over a tumour has predominately a stiff elastic character in terms of viscoelastic behaviour caused by a solid backbone. Simultaneously, the tumour mass is characterized by a large local variability in the storage and loss modulus that is caused by areas of a more fluid nature.   

Modeling the Arrest of Tissue Growth in Epithelia

The mechanisms of control and eventual arrest of growth of tissues is an area that has received considerable attention, both experimentally and in the development of quantitative models. In particular, the~\textit{Drosophila}~wing disc epithelium appears to robustly arrive at a unique final size. One mechanism that has the potential to play a role in the eventual cessation of growth is mechanical feedback from stresses induced by nonuniform growth. There is experimental support for an effect on the tissue growth rate by such mechanical stresses, and a number of numerical or cell-based models have been proposed that show that the arrest of growth can be achieved by mechanical feedback. We introduce an analytic framework that allows us to understand different coarse-grained feedback mechanisms on the same terms. We use the framework to distinguish between families of models that do not have a unique final size and those that do and give rough estimates for how much variability in the eventual organ size can be expected in models that do not have a unique final size.   

Defects and Disorder in the Drosophila Eye

Cell division and differentiation tightly control the regular pattern in the normal eye of the Drosophila fruit fly while certain genetic mutations introduce disorder in the form of topological defects. Analyzing data from pupal retinas, we develop a model based on Voronoi construction that explains the defect statistics as a consequence of area variation of individual facets (ommatidia). The analysis reveals a previously unknown systematic long-range area variation that spans the entire eye, with distinct effects on topological disorder compared to local fluctuations. The internal structure of the ommatidia and the stiffness of their interior cells also plays a crucial role in the defect generation. Accurate predictions of the correlation between the area variation and the defect density in both normal and mutant animals are obtained without free parameters. This approach can potentially be applied to cellular systems in many other contexts to identify size-topology correlations near the onset of symmetry breaking.   

Local and systemic tumor immune dynamics

Tumor-associated antigens, stress proteins, and danger-associated molecular patterns are endogenous immune adjuvants that can both initiate and continually stimulate an immune response against a tumor. In retaliation, tumors can hijack intrinsic immune regulatory programs that are intended to prevent autoimmune disease, thereby facilitating continued growth despite the activated antitumor immune response. In metastatic disease, this ongoing tumor-immune battle occurs at each site. Adding an additional layer of complexity, T cells activated at one tumor site can cycle through the blood circulation system and extravasate in a different anatomic location to surveil a distant metastasis. We propose a mathematical modeling framework that incorporates the trafficking of activated T cells between metastatic sites. We extend an ordinary differential equation model of tumor-immune system interactions to multiple metastatic sites. Immune cells are activated in response to tumor burden and tumor cell death, and are recruited from tumor sites elsewhere in the body. A model of T cell trafficking throughout the circulatory system can inform the tumor-immune interaction model about the systemic distribution and arrival of T cells at specific tumor sites. Model simulations suggest that metastases not only contribute to immune surveillance, but also that this contribution varies between metastatic sites. Such information may ultimately help harness the synergy of focal therapy with the immune system to control metastatic disease.   

Probing the non-equilibrium force fluctuation spectrum of actomyosin cortices in vivo

Mechanics of the cortex govern the shape of animal cells, and its dynamics underlie cell migration, cytokinesis and embryogenesis. The molecular players involved are largely known, yet it is unclear how their collective dynamics give rise to large scale behavior. This is mostly due to the lack of experimental tools to probe the spatially varying active mechanical properties of the cortex. Here, we introduce a novel technique based on fluorescent single walled carbon nanotubes to generate non-equilibrium force fluctuation spectrum of actomysion cortices in starfish oocytes. The quantitative measurements combined with a theoretical model reveal the role of stress organization in active mechanics and dynamics of the cortex.   

Physical Guidance of Cell Migration

Cells migrate as individuals or groups, to perform critical functions in life from organ development to wound healing and the immune response. While directed migration of cells is often mediated by chemical or physical gradients, our recent work has demonstrated that the physical properties of the microenvironment can also control and guide migration. I will describe how an underlying wave-like process of the actin scaffolding drives persistent migration, and how such actin waves are nucleated and guided by the texture of the microenvironment. Based on this observation we design textures capable of guiding cells in a single preferred direction using local asymmetries in nano/microtopography on subcellular scales, or altering migration in other ways. This phenomenon is observed both for the pseudopod-dominated migration of Dictyostelium cells and for the lamellipod-driven migration of human neutrophils. The conservation of this mechanism across cell types suggests that actin-wave-based guidance is important in biology and physiology.   

A Phenomenlogical Model of Durotaxis

Cells exhibit qualitatively different behaviors on substrates with different rigidities. The fact that cells are more polarized on the stiffer substrate motivates us to construct a two-dimensional cell with the distribution of focal adhesions dependent on substrate rigidities. Our model reproduces the experimental observation that the persistence time is higher on the stiffer substrate. We show that stiffness dependent polarization will lead to the so-called durotaxis, the preference in moving towards stiffer substrates. This propensity is then characterized by the durotactic index first defined in experiments. We also derive and validate the 2D corresponding Fokker-Planck equation associated with our model. Our model highlights the role of focal adhesion arrangement in durotaxis. It may be applied to manipulate the movement of cells for clinical purposes.   

Systematic changes in invasive cancer cell shape

We study the shape characteristics of osteosarcoma cancer cell lines using both Zernike moments and geometric parameters to represent cell shape. We compare the shape characteristics of four invasive cell lines with a corresponding less-invasive parental line on three substrates. Cell shapes of each pair of cell lines display overlapping characteristics. To quantitatively study shape changes in high-dimensional parameter space we define a vector representing average shape changes in principal component space. Using this vector we find that three of the four pairs of cell lines show similar changes in shape, while the fourth pair shows a very different pattern of changes. We find that shape differences are robust enough to enable a neural network to classify cells accurately as belonging to the highly invasive or the less invasive phenotype. The patterns of shape changes were also reproducible for repetitions of the experiment. Shape changes on different substrates as well as after treatment with pharmacological agents also show reproducible patterns. Our paper strongly suggests that shape may provide a means to read out the phenotypic state of at least some cell types, and shape analysis can be usefully performed using a Zernike moment representation.   

Dynamic changes in cortical tensions in multiple cell types during germband retraction

The process of germband retraction in Drosophila embryogenesis involves the coordinated mechanics of both germband and amnioserosa cells. These two tissues simultaneously and coordinately uncurl from their interlocking U-like shapes. As tissue-level retraction proceeds, individual cells change shape in stereotypical ways. Using time-lapse confocal images, analysis of dynamic cellular triple-junction angles, and whole-embryo finite-element models, we have quantified dynamic changes in cortical tensions - including their anisotropy - in both germband and amnioserosa cells. We find a strong transition midway through the two-hour course of retraction at which point tensions and anisotropies undergo a near step change. These changes take place among amnioserosa cells, in multiple segments of the germband, and at the interface between these two tissues.   

Computational Modeling of Two-dimensional Tissues

Structural and mechanical properties regulate cell migration, interaction forces, and packing geometry during tissue development. We have developed a new model for tissue development in two spatial dimensions (2D) that includes different rates for cell growth, cell-cell interactions, and extracellular matrix. Cells are represented as polygons and the total energy of the system includes contributions from cell elasticity, contraction and excluded volume. We study the formation of tissues by slowly increasing cell sizes followed by energy minimization. We then measure the structural and mechanical properties of the tissue as a function of the cell density. The results from our simulations will be compared to experiments that are able visualize the spatiotemporal evolution of monolayers of keratinocytes.   

Stem cell motility enables a density-dependent rate of fate commitment during scaled resizing of adult organs

Many adult organs grow or shrink to accommodate fluctuating levels of physiological demand. Specifically, the intestine of the fruit fly (the midgut) expands four-fold in the number of mature cells and, proportionally, the number of stem cells when the fly eats. However, the cellular behaviors that give rise to this stem scaling are not well-understood. Here we present a biophysical model of the adult fly midgut. A set of differential equations can recapitulate the physiological kinetics of cells during midgut growth and shrinkage as long as the rate of stem cell fate commitment depends on the stem cell number density in the tissue. To elucidate the source of this dependence, we model the tissue in a 2D simulation with soft spheres, where stem cells choose fate commitment through Delta-Notch pathway interactions with other stem cells, a known process in fly midguts. We find that as long as stem cells exhibit a large enough amplitude of random motion through the tissue (`stem cell motility'), and explore a large enough `territory' in their lifetime, stem cell scaling can occur. These model observations are confirmed through in vivo live-imaging, where we indeed see that stem cells are motile in the fly midgut.   

Assessment of Hepatic Fibrosis with the Stiffness of Liver and the Dynamic of Blood in Liver

Cirrhosis affects liver functions, and is a significant public health problem. Early stages of liver fibrosis are difficult to diagnose. The mechanism of fibrosis changing the mechanical properties of the liver tissue and altering the dynamic of blood flow is still unclear. In collaboration with clinicians specialized in hepatic fibrosis, we have developed a mechanical model to integrate our empirical understanding of fibrosis development and connect the fibrosis stage to mechanical properties of tissue and the consequential blood flow pattern changes. We modeled toxin distribution in the liver that leads to tissue damage and collagen deposition. We showed that the excessive collagen forms polygonal patterns, resembling those found in pathology images. Treating the collagen bundles as elastic spring networks, we also showed a nonlinear relationship between liver stiffness and fibrosis stage, which is consistent with experimental observations. We further modeled the stiffness affecting the mechanical properties of the portal veins, resulting in altered blood flow pattern. These results are supported by ultrasound Doppler measurements from hepatic fibrosis patients. These results promise a new noninvasive diagnostic tool for early fibrosis.   

Critical radius in the organisation of synuclein-alpha interacting protein in living cells

We report a super-resolution imaging study of protein aggregation in the living cell. Focusing on the aggregation of the Parkinsons's disease linked Synuclein-alpha interacting protein, we found and characterized sub-diffraction aggregates in healthy cells and studied the progression of these aggregates in stressed cells. Our results allowed us to establish the aggregation process as amenable to a simple physical description - the well-established thermodynamics of condensation phenomena. This description turned out to be both robust and useful. Not only did the distribution of aggregate sizes fit exceedingly well to the thermodynamic predictions in all tested conditions, but its evolving shape under pharmacological and genetic perturbations correlated intuitively with predictions from cell biology. ~The picture emerging from measurements in different genetic and pharmacological states is a view of protein aggregate size distribution as resulting from a non-equilibrium steady state maintained - even in healthy cells - with continuous and concurrent aggregate production and clearance.~