Research Interests

Overview

My current research involves developing methodologies to analyse cell-cell communication patterns directly from non-spatial single-cell RNA-sequencing (scRNA-seq) and spatial transcriptomics (ST) data, two data modalities that have their complementary strengths and limitations. I am interested in understanding how one may infer what we call “cellular flows” of information triggered by cell-cell communication, where one ligand-receptor interaction may trigger tissue-scale patterns that can be described by coordinated sets of gene expression and, in turn, subsequent outflow of other ligand-receptor interactions. These sorts of cellular flows can be thought of as extensions of the classical French Flag and Turing Pattern models from mathematical biology, which both describe how spatially varying chemical signals can trigger an array of complex patterning (for example, through transcription factor expression).

One of the aspects of these cellular flows that I am most interested in is whether we can infer the underlying directionalities of dependence from scRNA-seq data or ST data directly using frameworks from graphical causal modeling and concepts such as conditional independence, conditional invariance, and faithfulness assumptions. These high-dimensional transcriptomic data are nice candidates to apply such models because 1) scRNA-seq and ST data have relatively large sample sizes available, 2) we can examine an unprecedented number of genes simultaneously (10K–20K), and 3) many studies, particularly scRNA-seq studies, are equipped with a “control vs. perturbed” comparison that we can use to more accurately infer the directions and reduce the set of possible graphs (Markov equivalence class) via conditional invariance testing.

Other research

Up to my DPhil, my research involved using mathematical models to gain insight into various processes related to tissue morphogenesis, homeostasis, and pathology, focussing on problems where spatially dependent effects are an important factor.

The kind of research questions I have liked to ask are often variations of the following: are observed biological processes driven by inherent biological (genetic, chemical) differences, or by physical processes?

The former is easier to test and measure in a wet lab and thus easier to gather data on. The latter is significantly more difficult to measure and test experimentally, but by focussing on the underlying physics, we can abstract these complex processes and tease out the fundamental mechanisms.

Modelling approaches

I use both individual (cell-based) and coarse-grained continuum models to study biological tissue. Neither is inherently ‘better’ than the other and the considered system in question dictates the modelling approach.

Multicellular modelling

The fundamental unit of biology is the cell. Cells continuously update their internal machinery, interact with other cells and the external environment. Multicellular models, also known as individual-based or cell-based models, are defined by this ‘middle out’ paradigm. Taking this approach allows us control the amount of biological detail (and hence model complexity) at three key spatial scales: the subcellular, cellular, and tissue scale. Multicellular models have gained particular traction in recent years thanks to the rapid improvement and availability of computing power.

My experience lies primarily with cell-centre models, where, as the name suggests, cells are defined by the spatial position of their centres. Cell shapes are then modelled using a Voronoï Tessellation or by assuming a fixed shape; when the shape is a circle or sphere, the model is called the Overlapping Spheres model. The models I develop are generally implemented using the Chaste framework, allowing me to readily draw upon its pre-existing functionality and build new models without having to ‘reinvent the wheel’ continually.

Continuum mechanics

Multicellular models are incredibly useful for simulating a wide range of biological phenomena, as one can easily incorporate model complexity. However, with this degree of biological detail, it can become tricky to make sense of model output, which depends on incredibly large parameter spaces. Furthermore, a number of tissue-scale phenomena still elude a current approaches, especially those involving dynamic, deformable geometries. One workaround to ‘impose’ the deformed tissue state. However, numerous biological structures exhibit transitions from ‘flat’ shapes to complex morphologies, such as wrinkles and folds, in both development and pathology. This transition is called buckling and has been well studied for over a century, using the theory of continuum mechanics, and continues to be relevant to biology.

Continuum mechanics models are constructed by applying balance laws that are derived from a first principles approach and physical principles which are fundamentally true across all of nature. Models of biological tissue are constructed by ‘coarse-graining’ the cell population and exploiting a slenderness scale to reduce the geometric dimensionality of the problem. My current research involves using morphoelastic rod theory, an extension of the classic Kirchhoff rod theory that incorporates biological tissue growth. This framework has been incredibly useful in replicating many of the complex morphological structures observed in biology, such as the crypt. My research involves using morphoelastic rod theory to investigate how these structures may have formed initially, by drawing analogies with buckling instabilities, and subsequently how these structures could continue to deform. Numerical solutions were obtained using some form of numerical continuation of solutions for different growth values, using either collocation or shooting methods.

Biological applications

So far, my work has been applied to the gut and skin, the two most rapidly self-renewing organs in and on the body.

Intestinal crypt morphogenesis

The small intestinal and colonic crypts are test-tube-shaped glands that maintain the intestinal epithelium, a single layer of cells that protect the intestines during digestion. An overlooked aspect of crypts is their significantly-deformed morphology; a human colonic crypt can be anywhere from five to eight times as long as its width. Such deformations are often beyond the scope of what is considered in engineering studies, which focus primarily on the initial onset of buckling, which historically indicated structural failure. However, biological systems like the crypt seem to be able to harness these deformations. There is a fundamental link between biological function and form; the population structure across crypts is remarkably robust, with each crypt housing a pool of long-living stem cells that is protected by this invaginated structure.

During my DPhil, we used morphoelastic rod theory and numerical continuation to investigate the underlying bifurcation structure of an abstracted model of crypt formation, revealing a complex boundary separating supercritical pitchfork bifurcations, where the rod transitions continuously from its flat state to a buckled state, and a subcritical pitchfork, where the transition is discontinuous. We also analysed how the bifurcation structure changed due to spatial heterogeneity in growth, material stiffness, and substrate stiffness, drawing analogies with classic imperfection sensitivity analysis.

Intestinal crypt homeostasis

Tissue homeostasis can be defined as the state when cell birth is exactly balanced by cell death. In homeostasis, one observes a static tissue morphology, stress, and velocity profile akin to a ‘steady state’ in mathematics. However, when individual cells are labelled (e.g. with a fluorescent marker) and tracked, a continuous migration of cells out of the crypt can be observed. Therefore, homeostasis is not a steady state in a conventional mathematical sense. Rather, homeostasis is like a river: a rock in the river bed observes the flow from a static position, but a leaf floating on top of the river moves with the water. These two complementary views are referred to in fluid mechanics as the Eulerian (fixed current position) and Lagrangian (fixed initial position) descriptions and describe homeostasis aptly.

One technical challenge is that solid mechanics frameworks, such as morphoelastic rod theory, are more appropriately described using a Lagrangian description, while homeostasis and biological processes in general seem more appropriately described by an Eulerian description in the “lab setting”. During my DPhil, we developed a morphoelastic rod model that reconciled these complementary views in a model of crypt homeostasis. By constructing this model, we also demonstrated that the homeostatic proliferative structure of the crypt can be generated by simple mechanochemical growth coupling WNT, the predominant signalling pathway regulating growth along the crypt, to contact inhibition of cell division due to compression. We showed that under the assumption of homeostasis and mechanochemical growth, we could reduce the fully dynamic homeostasis model to a quasi-static buckling problem. In doing so, we showed that the crypt is stable only at certain morphologies, indicated by invagination length, and only sufficiently “long” crypts exhibit biologically realistic growth and velocity profiles.

Scar formation in skin

Wound healing in skin is an extraordinarily complex process, involving the coordination of numerous biological, chemical, and mechanical processes over various timescales and spatial scales. One hallmark of skin repair in mammals is that scars are left once the wound healing process has completed. Scars can be characterised by the presence of dense, aligned extracellular matrix (collagen) fibres, which results in weaker structural integrity, as well as the loss of function and complexity observed in non-scarred skin, such as hair follicles and dermal papillae. Recently, it has been discovered that in mice, hair follicles sometimes form after the healing of large wounds (>1cm in diameter), while small wounds (<1cm in diameter) always repair by scarring. This suggests that some of the skin functional components lost due to wound healing can be restored, which is indicated by the formation of new hair follicles.

Clearly, the formation of scars relies on production of extracellular matrix components. It is known that fibroblasts are the main cell type that deposit and remodel extracellular matrix during wound healing. As such, it is important to understand how fibroblasts contribute to wound healing and scar formation.

My current work focusses on understanding 1) the influence of fibroblasts on scar formation and 2) why large wounds heal ‘better’ than small wounds in mice. By studying these, we hope to deduce what may be ‘missing’ from human skin repair processes that prevents a more regenerative form of wound healing occuring. I am building an individual-based model of the skin dermis, focussing on the interactions between fibroblasts, the extracellular matrix, immune cells, and the epidermis, that generates in silico equivalents of scars. In the long-run, we aim to add biological detail by incorporating various signalling pathways that are activated during wound healing, which we will infer from single-cell RNA-seq data.