Dr Carina Dunlop

Mathematical models used in pre-clinical drug discovery tend to be empirical growth laws. Such models are well suited to fitting the data available, mostly longitudinal studies of tumour volume, however, they typically have little connection with the underlying physiological processes. This lack of a mechanistic underpinning restricts their flexibility and inhibits their direct translation across studies including from animal to human. Here we present a mathematical model describing tumour growth for the evaluation of single agent cytotoxic compounds that is based on mechanistic principles. The model can predict spatial distributions of cell subpopulations, tumour growth fraction as well as include spatial drug distribution effects within tumours. Importantly, we demonstrate the model can be reduced to a growth law similar in form to the ones currently implemented in pharmaceutical drug development for pre-clinical trials so that it can integrated into the current workflow. We validate this approach for both cell-derived xenograft (CDX) and patient-derived xenograft (PDX) data. This shows that our theoretical model fits as well as the best performing and most widely used models. Our work opens up current pre-clinical modelling studies to also incorporating spatially resolved and multi-modal data without significant added complexity and creates the opportunity to improve translation and tumour response predictions. Competing Interest Statement James Yates was a paid employee of AstraZeneca. Adam Nasim doctoral work benefitted from supplementary funding from AstraZeneca. No other competing interests. Footnotes * Revised version manuscript.

A 2‐day meeting was held by members of the UK Quantitative Systems Pharmacology Network (http://www.qsp‐uk.net/) in November 2018 on the topic of Translational Challenges in Oncology. Participants from a wide range of backgrounds were invited to discuss current and emerging modeling applications in nonclinical and clinical drug development, and to identify areas for improvement. This resulting perspective explores opportunities for impactful quantitative pharmacology approaches. Four key themes arose from the presentations and discussions that were held, leading to the following recommendations: • Evaluate the predictivity and reproducibility of animal cancer models through precompetitive collaboration. • Apply mechanism of action (MoA) based mechanistic models derived from nonclinical data to clinical trial data. • Apply MoA reflective models across trial data sets to more robustly quantify the natural history of disease and response to differing interventions. • Quantify more robustly the dose and concentration dependence of adverse events through mathematical modelling techniques and modified trial design.

It is known that cells grown in 3D are more tolerant to drug treatment than those grown in dispersion but the mechanism for this is still not clear; cells grown in 3D have opportunities to develop inter-cell communication, but are also closely packed which may impede diffusion. In this study we examine methods for dielectrophoresis-based cell aggregation of both suspension and adherent cell lines and compare the effect of various drugs on cells grown in 3D and 2D. Comparing viability of pharmacological interventions on 3D cell clusters against both suspension cells and adherent cells grown in monolayer, as well as against a unicellular organism with no propensity for intracellular communication, we suggest that 3D aggregates of adherent cells, compared to suspension cells, show a substantially different drug response to cells grown in monolayer, which increases as the IC50 is approached. Further, a mathematical model of the system for each agent demonstrates that changes to drug response are due to inherent changes in the system of adherent cells from the 2D to 3D state. Finally, differences within electrophysiological membrane properties of the adherent cell type suggest this parameter plays an important role in the differences found in the 3D drug response.

Follicle development in the ovary must be tightly regulated to ensure cyclical release of oocytes (ovulation). Disruption of this process is a common cause of infertility, for example via polycystic ovary syndrome (PCOS) and premature ovarian insufficiency (POI). Recent ex vivo studies suggest that follicle growth is mechanically regulated, however, crucially, the actual mechanical properties of the follicle microenvironment have remained unknown. Here we use atomic force microscopy (AFM) spherical probe indentation to map and quantify the mechanical microenvironment in the mouse ovary, at high resolution and across the entire width of the intact (bisected) ovarian interior. Averaging over the entire organ, we find the ovary to be a fairly soft tissue comparable to fat or kidney (mean Young’s Modulus 3.3 +/-2.5 kPa). This average, however, conceals substantial spatial variations, with the overall range of tissue stiffnesses from c. 0.5 –10 kPa, challenging the concept that a single Young’s Modulus can effectively summarize this complex organ. Considering the internal architecture of the ovary, we find that stiffness is low at the edge and centre which are dominated by stromal tissue, and highest in an intermediate zone that is dominated by large developmentally-advanced follicles, confirmed by comparison with immunohistology images. These results suggest that largefollicles are mechanically dominant structures in the ovary, contrasting with previous expectations that collagen-rich stroma would dominate. Extending our study to the highest resolutions (c. 5 μm) showed substantial mechanical variations within the larger zones, even over very short (sub-100 μm) lengths, and especially within the stiffer regions of the ovary. Taken together, our results provide a new, physiologically accurate, framework for ovarian biomechanics and follicle tissue engineering.

The ability of cells to sense and respond to the mechanical properties of their environments is fundamental to a range of cellular behaviours, with substrate stiffness increasingly being found to be a key signalling factor. Although active contractility of the cytoskeleton is clearly necessary for stiffness sensing in cells, the physical mechanisms connecting contractility with mechanosensing and molecular conformational change are not well understood. Here we present a contractility-driven mechanism for linking changes in substrate stiffness with internal conformational changes. Cellular contractility is often assumed to imply an associated compressive strain. We show, however, that where the contractility is non-uniform, localized areas of internal stretch can be generated as stiffer substrates are encountered. This suggests a physical mechanism for the stretch-activation of mechanotransductive molecules on stiffer substrates. Importantly, the areas of internal stretch occur deep within the cell and not near the cellular perimeter, which region is more traditionally associated with stiffness sensing through e.g. focal adhesions. This supports recent experimental results on whole-cell mechanically-driven mechanotransduction. Considering cellular shape we show that aspect ratio acts as an additional control parameter, so that the onset of positive strain moves to higher stiffness values in elliptical cells.

Maintenance and activation of the limited supply of primordial follicles in the ovary are important determinants of reproductive lifespan. Currently, the molecular programme that maintains the primordial phenotype and the early events associated with follicle activation are not well defined. Here we have systematically analysed these events using microscopy and detailed image analysis. Using the immature mouse ovary as a model, we demonstrate that the onset of granulosa cell (GC) proliferation results in increased packing density on the oocyte surface and consequent GC cuboidalisation. These events precede oocyte growth and nuclear translocation of FOXO3a, a transcription factor important in follicle activation. Immunolabelling of the TGF signalling mediators and transcription factors, SMAD2/3, revealed a striking expression pattern specific to GCs of small follicles. SMAD2/3 was expressed in the nuclei of primordial GCs but was mostly excluded in early growing follicles. In activated follicles, GC nuclei lacking SMAD2/3 generally expressed Ki67. These findings suggest that the first phenotypic changes during follicle activation are observed in GCs, and that TGF signalling is fundamental for regulating GC arrest and the onset of proliferation.

Syncytial embryos develop through cycles of nuclear division and rearrangement within a common cytoplasm. A paradigm example is Drosophila melanogaster in which nuclei form an ordered array in the embryo surface over cell cycles 10-13. This ordering process is assumed to be essential for subsequent cellularisation. Using quantitative tissue analysis, it has previously been shown that the regrowth of actin and microtubule networks after nuclear division generates reordering forces that counteract its disordering effect (Kanesaki et al., 2011). We present here an individual-based computer simulation modelling the nuclear dynamics. In contrast to similar modelling approaches e.g. epithelial monolayers or tumour spheroids, we focus not on the spatial dependence, but rather on the time-dependence of the interaction laws. We show that appropriate phenomenological inter-nuclear force laws reproduce the experimentally observed dynamics provided that the cytoskeletal network regrows sufficiently quickly after mitosis. Then repulsive forces provided by the actin system are necessary and sufficient to regain the observed level of order in the system, after the strong disruption resulting from cytoskeletal network disassembly and spindle formation. We also observe little mixing of nuclei through cell cycles. Our study highlights the importance of the dynamics of cytoskeletal forces during this critical phase of syncytial development and emphasises the need for real-time experimental data at high temporal resolution. © 2014 Elsevier Ltd.

Abstract Follicle development in the human ovary must be tightly regulated to ensure cyclical release of oocytes (ovulation), and disruption of this process is a common cause of infertility. Recent ex vivo studies suggest that follicle growth may be mechanically regulated, however the actual mechanical properties of the follicle microenvironment have remained unknown. Here we map and quantify the mechanical microenvironment in mouse ovaries using colloidal probe atomic force microscope (AFM) indentation, finding an overall mean Young’s Modulus 3.3 ± 2.5 kPa. Spatially, stiffness is low at the ovarian edge and centre, which are dominated by extra-follicular ECM, and highest in an intermediate zone dominated by large follicles. This suggests that large follicles should be considered as mechanically dominant structures in the ovary, in contrast to previous expectations. Our results provide a new, physiologically accurate framework for investigating how mechanics impacts follicle development and will underpin future tissue engineering of the ovary. Competing Interest Statement The authors have declared no competing interest.

There is increasing experimental interest in mechanotransduction in multi-cellular tissues as opposed to single cells. This is driven by a growing awareness of the importance of physiologically relevant three-dimensional culture and of cell-cell and cell-gel interactions in directing growth and development. The paradigm biophysical technique for investigating tissue level mechanobiology in this context is to grow model tissues in artificial gels with well-defined mechanical properties. These studies often indicate that the sti↵ness of the encapsulating gel can significantly alter cellular behaviours. We demonstrate here potential mechanisms linking tissue growth with sti↵ness-mediated mechanotransduction. We show how tissue growth in gel systems generates points at which there is a significant qualitative change in the cellular stress and strain experienced. We show analytically how these potential switching points depend on the mechanical properties of the constraining gel and predict when they will occur. Significantly, we identify distinct mechanisms that act separately in each of the stress and strain fields at di↵erent times. These observations suggest growth as a potential physical mechanism coupling gel sti↵ness with cellular mechanotransduction in three-dimensional tissues. We additionally show that non-proliferating areas, in the case that the constraining gel is soft compared with the tissue, will expand and contract passively as a result of growth. Central compartment size is thus seen to not be a reliable indicator on its own for growth initiation or active behaviour.

Cell mechanosensing is implicated in the control of a broad range of cell behaviours, with cy-toskeletal contractility a key component. Experimentally, it is observed that the contractility of the cell responds to increasing substrate stiffness, showing increased contractile force and changing the distribution of cytoskeletal elements. Here we show using a theoretical model of active cell contractility that upregulation of contractility need not be energetically expensive, especially when combined with changes in adhesion and contractile distribution. Indeed, we show that a feedback mechanism based on maintenance of strain energy would require an upregulation in contractile pressure on all but the softest substrates. We consider both the commonly reported substrate strain energy and active work done. We demonstrate substrate strain energy would preferentially select for the experimentally observed clustering of cell adhesions on stiffer substrates which effectively soften the substrate and enable an upregulation of total contractile pressure; while localisation of contractility has the greatest impact on the internal work. It is well established that cells sense, adapt and respond to the mechanical properties of their environment. This mechanosensing is key across cell behaviours ultimately affecting e.g. cell growth, development and differentiation [1–3]. Fundamental to mechanosensing are contractile forces generated by myosin motors within an actin rich network in the cell. These forces are transmitted from the cell to the extracellular matrix through adhesions [4]. A focus of mechanotransduction research has traditionally been these sites of cell adhesion, which in stiffer environments, are concentrated into small patches of strong attachment called focal adhesions [1, 3]. Experimental investigations commonly use engineered gels or micropillar arrays with defined mechanical properties to observe cell response [5]. As well as changes in signal transduction, changes in structural elements associated with cellular contractility are observed, including increased actin density and stress fibre formation [6, 7]. Considering contractile forces, myosin and motor activity has been found to be more broadly distributed on soft gels becoming more localised, eventually overlapping with a dense actin cortex on stiffer substrates [8]. Hence it is typically observed that contractile forces increase with increased gel stiffness [9]. The mechanism by which stiffness changes lead to changes in contractile force is unclear although target stress or strain states are often implicated [10, 11]. To quantify the mechanical activity of cells on two-dimensional substrates different approaches have been suggested. Most commonly the applied tractions are measured, through e.g. traction force microscopy, and used to infer activity. Recent work has suggested that the substrate strain energy could be effectively used as a measure for overall mechanical activity [12, 13], leading to the observation that cells may respond directly to changes in substrate strain energy [14]. Substrate strain * c.dunlop@surrey.ac.uk energy has also been observed to be approximately conserved across a range of stiffnesses [15], suggesting mechanical feedback to actively control strain energy. Even without fully constraining the strain energy, it is clear that there are bounds on the energy budget [16], with a link between cell contractility and energy consumption demonstrated [17]. Theoretically models have explored this energy budget using energy constraints as drivers of differentiation [18] or cell shape control [19]. We here use an active matter model to investigate both the substrate strain energy and the work done by the active cell components. We show that over a broad range of stiffnesses upregulation of active contractile pressure does not require an increase in energy expenditure. Indeed, upregulation of contractility is compatible with constant strain energy. We also investigate the localisation of con-tractility into the cell cortex showing that this will have minimal effect on the substrate strain energy at realistic levels of cell adhesion, although the active strain energy is sensitive to these changes. This is consistent with the observation that localisation of contractility can lead to large internal strains [20]. Introducing localised patches of adhesions we see that these generate polarised cells, with clustering of adhesion points particularly energetically favourable in terms of substrate strain energy, thus enabling significantly higher total contractile pressure. Active Matter Model. Active matter models consider the cell as an elastic material with an additional component of stress generated by active contraction. Active contraction may be modelled either through computational simulations of cytoskeletal filaments [21–23] or via a continuum approach [24–26]. We adopt the continuum approach taking the stress within the cell σ = σ P + σ A , where σ P is the passive cell elasticity and σ A is the active stress generated by the contractile pressure. Noting that the timescale for cell adhesion is faster than the relaxation timescale viscoelastic effects may be neglected and we assume a linear elastic response in both the substrate and the cell, see e.g. [26]. Furthermore, as the dimension of the spread cell is greater than its height h we consider