STOCHASTIC DYNAMICS OF CELL LINEAGE IN TISSUE HOMEOSTASIS.

During epithelium tissue maintenance, lineages of cells differentiate and proliferate in a coordinated way to provide the desirable size and spatial organization of different types of cells. While mathematical models through deterministic description have been used to dissect role of feedback regulations on tissue layer size and stratification, how the stochastic effects influence tissue maintenance remains largely unknown. Here we present a stochastic continuum model for cell lineages to investigate how both layer thickness and layer stratification are affected by noise. We find that the cell-intrinsic noise often causes reduction and oscillation of layer size whereas the cell-extrinsic noise increases the thickness, and sometimes, leads to uncontrollable growth of the tissue layer. The layer stratification usually deteriorates as the noise level increases in the cell lineage systems. Interestingly, the morphogen noise, which mixes both cell-intrinsic noise and cell-extrinsic noise, can lead to larger size of layer with little impact on the layer stratification. By investigating different combinations of the three types of noise, we find the layer thickness variability is reduced when cell-extrinsic noise level is high or morphogen noise level is low. Interestingly, there exists a tradeoff between low thickness variability and strong layer stratification due to competition among the three types of noise, suggesting robust layer homeostasis requires balanced levels of different types of noise in the cell lineage systems

A HYBRID METHOD FOR STIFF REACTION-DIFFUSION EQUATIONS.

The second-order implicit integration factor method (IIF2) is effective at solving stiff reaction-diffusion equations owing to its nice stability condition. IIF has previously been applied primarily to systems in which the reaction contained no explicitly time-dependent terms and the boundary conditions were homogeneous. If applied to a system with explicitly time-dependent reaction terms, we find that IIF2 requires prohibitively small time-steps, that are relative to the square of spatial grid sizes, to attain its theoretical second-order temporal accuracy. Although the second-order implicit exponential time differencing (iETD2) method can accurately handle explicitly time-dependent reactions, it is more computationally expensive than IIF2. In this paper, we develop a hybrid approach that combines the advantages of both methods, applying IIF2 to reaction terms that are not explicitly time-dependent and applying iETD2 to those which are. The second-order hybrid IIF-ETD method (hIFE2) inherits the lower complexity of IIF2 and the ability to remain second-order accurate in time for large time-steps from iETD2. Also, it inherits the unconditional stability from IIF2 and iETD2 methods for dealing with the stiffness in reaction-diffusion systems. Through a transformation, hIFE2 can handle nonhomogeneous boundary conditions accurately and efficiently. In addition, this approach can be naturally combined with the compact and array representations of IIF and ETD for systems in higher spatial dimensions. Various numerical simulations containing linear and nonlinear reactions are presented to demonstrate the superior stability, accuracy, and efficiency of the new hIFE method

Noise control and utility: From regulatory network to spatial patterning

Stochasticity (or noise) at cellular and molecular levels has been observed extensively as a universal feature for living systems. However, how living systems deal with noise while performing desirable biological functions remains a major mystery. Regulatory network configurations, such as their topology and timescale, are shown to be critical in attenuating noise, and noise is also found to facilitate cell fate decision. Here we review major recent findings on noise attenuation through regulatory control, the benefit of noise via noise-induced cellular plasticity during developmental patterning, and summarize key principles underlying noise control

SVSBI: Sequence-based virtual screening of biomolecular interactions

Virtual screening (VS) is an essential technique for understanding biomolecular interactions, particularly, drug design and discovery. The best-performing VS models depend vitally on three-dimensional (3D) structures, which are not available in general but can be obtained from molecular docking. However, current docking accuracy is relatively low, rendering unreliable VS models. We introduce sequence-based virtual screening (SVS) as a new generation of VS models for modeling biomolecular interactions. The SVS model utilizes advanced natural language processing (NLP) algorithms and optimizes deep $K$-embedding strategies to encode biomolecular interactions without invoking 3D structure-based docking. We demonstrate the state-of-art performance of SVS for four regression datasets involving protein-ligand binding, protein-protein, protein-nucleic acid binding, and ligand inhibition of protein-protein interactions and five classification datasets for the protein-protein interactions in five biological species. SVS has the potential to dramatically change the current practice in drug discovery and protein engineering

A multiscale hybrid mathematical model of epidermal-dermal interactions during skin wound healing.

Following injury, skin activates a complex wound healing programme. While cellular and signalling mechanisms of wound repair have been extensively studied, the principles of epidermal-dermal interactions and their effects on wound healing outcomes are only partially understood. To gain new insight into the effects of epidermal-dermal interactions, we developed a multiscale, hybrid mathematical model of skin wound healing. The model takes into consideration interactions between epidermis and dermis across the basement membrane via diffusible signals, defined as activator and inhibitor. Simulations revealed that epidermal-dermal interactions are critical for proper extracellular matrix deposition in the dermis, suggesting these signals may influence how wound scars form. Our model makes several theoretical predictions. First, basal levels of epidermal activator and inhibitor help to maintain dermis in a steady state, whereas their absence results in a raised, scar-like dermal phenotype. Second, wound-triggered increase in activator and inhibitor production by basal epidermal cells, coupled with fast re-epithelialization kinetics, reduces dermal scar size. Third, high-density fibrin clot leads to a raised, hypertrophic scar phenotype, whereas low-density fibrin clot leads to a hypotrophic phenotype. Fourth, shallow wounds, compared to deep wounds, result in overall reduced scarring. Taken together, our model predicts the important role of signalling across dermal-epidermal interface and the effect of fibrin clot density and wound geometry on scar formation. This hybrid modelling approach may be also applicable to other complex tissue systems, enabling the simulation of dynamic processes, otherwise computationally prohibitive with fully discrete models due to a large number of variables

Chronic Kidney Disease Increases Atrial Fibrillation Inducibility: Involvement of Inflammation, Atrial Fibrosis, and Connexins

Chronic kidney disease (CKD) causes atrial structural remodeling and subsequently increases the incidence of atrial fibrillation (AF). Atrial connexins and inflammatory responses may be involved in this remodeling process. In this study, nephrectomy was used to produce the CKD rat model. Three months post-nephrectomy, cardiac structure, function and AF vulnerability were quantified using echocardiography and electrophysiology methods. The left atrial tissue was tested for quantification of fibrosis and inflammation, and for the distribution and expression of connexin (Cx) 40 and Cx43. An echocardiography showed that CKD resulted in the left atrial enlargement and left ventricular hypertrophy, but had no functional changes. CKD caused a significant increase in the AF inducible rate (91.11% in CKD group vs. 6.67% in sham group, P < 0.001) and the AF duration [107 (0–770) s in CKD vs. 0 (0–70) s in sham, P < 0.001] with prolonged P-wave duration. CKD induced severe interstitial fibrosis, activated the transforming growth factor-β1/Smad2/3 pathway with a massive extracellular matrix deposition of collagen type I and α-smooth muscle actin, and matured the NLR (nucleotide-binding domain leucine-rich repeat-containing receptor) pyrin domain-containing protein 3 (NLRP3) inflammasome with an inflammatory cascade response. CKD resulted in an increase in non-phosphorylated-Cx43, a decrease in Cx40 and phosphorylated-Cx43, and lateralized the distribution of Cx40 and Cx43 proteins with upregulations of Rac-1, connective tissue growth factor and N-cadherin. These findings implicate the transforming growth factor-β1/Smad2/3, the NLRP3 inflammasome and the connexins as potential mediators of increased AF vulnerability in CKD

Multiscale Modeling for Tissue Patterning: Growth and Stochasticity

The spatial organization of tissues is often determined by long-range signals, morphogens, through the concentration-dependent manner. The morphogen-mediated patterning is a great foundation, but inadequate to explain the effects of tissue growth and stochasticity, the two prevalent phenomena, in pattern formation. In this thesis, we use multi-scale models to study those questions. In Chapter 2, we study how pattern scales to tissue size in Drosophila wing disc and find the scaling is through the feedback control on receptors and co-receptors of the morphogen. In Chapter 3, we study how different types of noise affect the dynamics of spatial pattern in the epithelium and we find the balanced levels of different types of noise is essential to the tissue homeostasis. In Chapter 4, we discuss both effects of growth and noise in the zebrafish hindbrain pattern. Despite the noise causes variability, growth improves the precision of the pattern. In Chapter 5, we develop a numerical method for solving stiff reaction-diffusion equations which provides a necessary tool for solving modeling problems