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The polarisation of cells and tissues is fundamental for tissue morphogenesis during biological development and regeneration. A deeper understanding of biological polarity pattern formation can be gained from the consideration of pattern…
Recent advances in high-resolution experimental methods have highlighted the significance of cell signal pathway crosstalk and localised signalling activity in the development and disease of numerous biological systems. The investigation of…
Rhythmic and sequential segmentation of the embryonic body plan is a vital developmental patterning process in all vertebrate species. However, a theoretical framework capturing the emergence of dynamic patterns of gene expression from the…
Stem cell regeneration is a crucial biological process for most self-renewing tissues during the development and maintenance of tissue homeostasis. In developing the mathematical models of stem cell regeneration and tissue development, cell…
Spatially annotated single-cell datasets provide unprecedented opportunities to dissect cell-cell communication in development and disease. Heterotypic signaling includes interactions between different cell types and is well established in…
Life presents fascinating examples of self-organization and emergent phenomena. In multi-cellular organisms, a multitude of cells interact to form and maintain highly complex body plans of well-defined size. In this thesis, we investigate…
Understanding the activity of large populations of neurons is difficult due to the combinatorial complexity of possible cell-cell interactions. To reduce the complexity, coarse-graining had been previously applied to experimental neural…
Cell lineage decisions occur in three-dimensional spatial patterns that are difficult to identify by eye. There is an ongoing effort to replicate such patterns using mathematical modeling. One approach uses long ranging cell-cell…
Ordered polarity alignment of a cell population plays a vital role in biology, such as in hair follicle alignment and asymmetric cell division. Here, we propose a theoretical framework for the understanding of generic dynamical properties…
Recovering 3D phase features of complex, multiple-scattering biological samples traditionally sacrifices computational efficiency and processing time for physical model accuracy and reconstruction quality. This trade-off hinders the rapid…
To explain the differentiation of stem cells in terms of dynamical systems theory, models of interacting cells with intracellular protein expression dynamics are analyzed and simulated. Simulations were carried out for all possible protein…
Cells are constantly exposed to diverse stimuli-chemical, mechanical, or electrical-that guide their movement. In physiological conditions, these signals often overlap, as seen during infections, where neutrophils and dendritic cells…
Biological patterns generated during development and regeneration often scale with organism size. Some organisms, e.g., flatworms, can regenerate a rescaled body plan from tissue fragments of varying sizes. Inspired by these examples, we…
Recent experimental studies have demonstrated that cellular motion can be directed by topographical gradients, such as those resulting from spatial variations in the features of a micropatterned substrate. This phenomenon, known as…
We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…
Modeling biological networks serves as both a major goal and an effective tool of systems biology in studying mechanisms that orchestrate the activities of gene products in cells. Biological networks are context specific and dynamic in…
We consider a quantum system with a time-independent Hamiltonian parametrized by a set of unknown parameters $\alpha$. The system is prepared in a general quantum state by an evolution operator that depends on a set of unknown parameters…
The processes taking place inside the living cell are now understood to the point where predictive computational models can be used to gain detailed understanding of important biological phenomena. A key challenge is to extrapolate this…
Interactions between neighboring cells are essential for generating or refining patterns in a number of biological systems. We propose a discrete filtering approach to predict how networks of cells modulate spatially varying input signals…
Cell polarity and movement are fundamental to many biological functions. Experimental and theoretically studies have indicated that interactions of certain proteins lead to the cell polarization which plays a key role in controlling the…