This thesis provides a physics account of the ability of cells to integrate environmental information to make complex decisions, a process commonly known as signaling. It strives to address the following questions: (i) How do cells relate the state of the environment (e.g. presence/absence of specific molecules) to a desired response such as gene expression? (ii) How can cells robustly transfer information? (iii) Is there a biophysical limit to a cells' ability to process information? (iv) Can we use the answers to the above questions to formulate biophysical principles that inform us about the evolution of signaling? Throughout, I borrow techniques from non-equilibrium statistical physics, statistical learning theory, information theory and information geometry to construct biophysical models capable of making quantitative experimental predictions. Finally, I address the connection of energy expenditure and biological efficiency by zeroing in on a process unique to eukaryotic cells-- nuclear transport. The thesis concludes with a discussion of our theory and its implications for synthetic biology.

<p>Embryonic development is a complicated phenomenon influenced by genetic regulation and biomechanical cellular behaviors. However, the relative influence of these factors on spatiotemporal morphogen distributions is not well understood. Bone Morphogenetic Proteins (BMPs) are the primary morphogen guiding the dorsal-ventral (DV) patterning of the early zebrafish embryo, and BMP signaling is regulated by a network of extracellular and intracellular factors that impact the range and signaling of BMP ligands.  Recent advances in understanding the mechanism of pattern formation support a source-sink mechanism, however, it is not clear how the source-sink mechanism shapes patterns in 3D, nor how sensitive the pattern is to biophysical rates and boundary conditions along both the anteroposterior (AP) and DV axes of the embryo.</p><p> Throughout blastulation and gastrulation, major cell movement, known as epiboly, happens along with the BMP mediated DV patterning. The layer of epithelial cells begins to thin as it spreads toward the vegetal pole of the embryo until it has completely engulfed the yolk cell. This dynamic domain may influence the distributions of BMP network members. This project aims to investigate the multiscale regulatory network of the BMP signaling dynamics along with the biophysical deformation of the embryo tissue during epiboly. </p><p> In this study, we present a three-dimensional (3D) growing domain mathematical modeling framework to simulate the BMP patterning and epiboly process during the blastula to gastrula stage zebrafish embryo, with both finite difference and finite element approaching. These models provide a starting point to elucidate how different mechanisms and components work together in 3D to create and maintain the BMP gradient in the zebrafish embryo. We are interested in how the cellular movements impact the formation of gradients by contributing an advective term whereby the morphogens are swept with the moving cells as they move vegetally. Dynamic cell imaging data are used to quantify the cell movement during the epiboly. We evaluated the accuracy of the mesh updating compared to the advection caused by cell movement and its role in embryonic patterning. Quantitative whole-mount RNA scope data of BMP2b, Chordin, Noggin, Sizzled, and phosphorylated-SMAD data are collected and analyzed precisely to test the hypotheses of the gradient formation mechanism in our model. We also present a novel approach of Neuro Network model to accelerate the computationally intensive PDE simulations. Our goal is to develop a complete advection-diffusion-reaction model that incorporates all stages of zebrafish embryonic development data. By combining the biophysics of epiboly with the regulatory dynamics of the BMP network, we can test complex models to investigate the consistent spatiotemporal DV patterning in the early zebrafish embryo.</p>

AMP-activated protein kinase (AMPK) is a key regulator of energy homeostasis in cells. It has been implicated as a therapeutic target for various metabolic diseases like type II diabetes and obesity. However, its role in cancer is context-dependent and therefore warrants further studies to explore its possible use as a therapeutic target. AMPK can either promote or retard the growth of cancer cells depending on other cues and stresses in the milieu of the cancer cells. This study aims to understand AMPK signalling in response to extracellular cues of matrix deprivation and matrix stiffness that are important determinants of metastasis. 1) Calcium-Oxidant Signalling Network Regulates AMPK Activation upon Matrix Deprivation. Recent work from our lab, as well as others, has identified a novel role for the cellular energy sensor AMP-activated protein kinase in epithelial cancer cell survival under matrix deprivation. However, the molecular mechanisms that activate AMPK upon matrix-detachment remain unexplored. In this study, we show that AMPK activation is a rapid and sustained phenomenon upon matrix deprivation, while re-attachment to the matrix leads to its dephosphorylating and inactivation. Since matrix-detachment leads to loss of integrin signalling, we investigate whether integrin signalling negatively regulates AMPK activation. However, modulation of FAK or Src, the major downstream components of integrin signalling, fails to cause a corresponding change in AMPK signalling. Further investigations reveal that the upstream AMPK kinases, LKB1 and CaMKKβ, contribute to AMPK activation upon detachment. Additionally, we show LKB1 phosphorylation and cytosolic translocation upon matrix deprivation, which might also contribute to AMPK activation. In LKB1-deficient cells, we find AMPK activation to be predominantly dependent on Caskβ. We observe no change in ATP levels under detached conditions at early time points suggesting that rapid AMPK activation upon detachment is not triggered by energy stress. We demonstrate that matrix deprivation leads to a spike in intracellular calcium as well as oxidant signalling and both these intracellular messengers contribute to rapid AMPK activation upon detachment. We further show that ER calcium release induced store-operated calcium entry (SOCE) contributes to intracellular calcium increase, leading to ROS production, and AMPK activation. We additionally show that the LKB1/CaMKK-AMPK axis and intracellular calcium levels play a critical role in anchorage-independent cancer sphere formation. We find a significant increase in LKB1 as well as pACC levels in breast tumour tissues in comparison to normal tissues. Further, we observe a significant correlation between LKB1 and pACC levels in breast tumour tissues suggesting that LKB1-AMPK signaling pathway is active in vivo in breast cancers. Thus, the Ca2+/ROS triggered LKB1/CaMKK-AMPK signalling cascade may provide a quick, adaptable switch to promote survival of metastasising cancer cells. 2) Extracellular Matrix Stiffness Regulates Stemless through AMPK. Cancer cells experience changes in extracellular matrix stiffness during cancer progression. However, the signalling pathways utilised in sensing matrix stiffness are poorly understood. In this study, we identify AMPK pathway as a possible mechanosensory pathway in response to matrix stiffness. AMPK activity, as measured by downstream target phosphorylation, is found to be higher in soft matrix conditions. We additionally show that compared to stiff matrices, soft matrices increase stemless properties, as evidenced by the increased expression of stemless markers, which is dependent on AMPK activity. Thus, we elucidate a novel mechanotransduction pathway triggered by matrix stiffness that contributes to stemness of cancer cells by regulating AMPK activity. Taken together, our study identifies a novel calcium-oxidant signaling network in the rapid modulation of AMPK signaling in the context of matrix detachment. This pathway is especially relevant in the context of metastasising cancer cells that may not face energy stress in the blood stream but are matrix-deprived. Inhibition of AMPK might compromise the viability of these circulating cells thereby reducing the metastatic spread of cancer. Our study further suggests that varying stiffnesses experienced by cancer cells can modulate AMPK activity and this, in turn, regulates stem-like properties. Thus our study provides novel insights into various extracellular cues that regulate this kinase and contribute to cell survival and metastasis. This knowledge can be utilised in the stage-specific use of AMPK inhibitors in the treatment of breast cancer patients.

Neste trabalho estudamos os type-dependent stochastic spin models propostos por Fernández et al., os que chamaremos de modelos de spins estocástico dependentes de tipo, e que foram usados para modelar redes de sinalização biológica. A modelagem original descreve a evolução macroscópica de um modelo de spin-flip de tamanho finito com k tipos de spins, possuindo um número arbitrário de estados internos, que interagem através de uma dinâmica estocástica não reversível. No limite termodinânico foi provado que, em um intervalo de tempo finito as trajetórias convergem quase certamente para uma trajetória determinística, dada por uma equação diferencial de primeira ordem. Os comportamentos destes sistemas dinâmicos podem incluir bifurcações, relacionadas às transições de fase do modelo. O nosso objetivo principal foi de estender os modelos de spins com dinâmica de Glauber utiliza- dos pelos autores, permitindo trocas múltiplas dos spins. No contexto biológico tentamos incluir situações nas quais moléculas de tipos diferentes trocam simultaneamente os seus estados internos. Utilizando diversas técnicas, como as de grandes desvíos e acoplamento, tem sido possível demonstrar a convergência para o sistema dinâmico associado. / We study type-dependent stochastic spin models proposed by Fernández et al., which were used to model biological signaling networks. The original modeling setup describes the macroscopic evolution of a finite-size spin-flip model with k types of spins with arbitrary number of internal states interacting through a non-reversible stochastic dynamics. In the thermodynamic limit it was proved that, within arbitrary finite time-intervals, the path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation. The behavior of the associated dynamical system may include bifurcations, associated to phase transitions in the statistical mechanical setting. Our aim is to extend the spin model with Glauber dynamics, to allow multiple spin-flips. In the biological context we included situations in which molecules of different types simultaneously change their internal states. Using several methods, such as large deviations and coupling, we prove the convergence theorem.

Neste trabalho estudamos os type-dependent stochastic spin models propostos por Fernández et al., os que chamaremos de modelos de spins estocástico dependentes de tipo, e que foram usados para modelar redes de sinalização biológica. A modelagem original descreve a evolução macroscópica de um modelo de spin-flip de tamanho finito com k tipos de spins, possuindo um número arbitrário de estados internos, que interagem através de uma dinâmica estocástica não reversível. No limite termodinânico foi provado que, em um intervalo de tempo finito as trajetórias convergem quase certamente para uma trajetória determinística, dada por uma equação diferencial de primeira ordem. Os comportamentos destes sistemas dinâmicos podem incluir bifurcações, relacionadas às transições de fase do modelo. O nosso objetivo principal foi de estender os modelos de spins com dinâmica de Glauber utiliza- dos pelos autores, permitindo trocas múltiplas dos spins. No contexto biológico tentamos incluir situações nas quais moléculas de tipos diferentes trocam simultaneamente os seus estados internos. Utilizando diversas técnicas, como as de grandes desvíos e acoplamento, tem sido possível demonstrar a convergência para o sistema dinâmico associado. / We study type-dependent stochastic spin models proposed by Fernández et al., which were used to model biological signaling networks. The original modeling setup describes the macroscopic evolution of a finite-size spin-flip model with k types of spins with arbitrary number of internal states interacting through a non-reversible stochastic dynamics. In the thermodynamic limit it was proved that, within arbitrary finite time-intervals, the path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation. The behavior of the associated dynamical system may include bifurcations, associated to phase transitions in the statistical mechanical setting. Our aim is to extend the spin model with Glauber dynamics, to allow multiple spin-flips. In the biological context we included situations in which molecules of different types simultaneously change their internal states. Using several methods, such as large deviations and coupling, we prove the convergence theorem.