Quantitative Biology

Heart is an electrically-connected network. Spiral wave dynamics of cardiac fibrillation shows chaotic and disintegrated patterns while sinus rhythm shows synchronized excitation patterns. To determine functional interactions between cardiomyocytes during complex fibrillation states, we applied a pairwise maximum entropy model (MEM) to the sequential electrical activity maps acquired from the 2D computational simulation of human atrial fibrillation. Then, we constructed energy landscape and estimated hierarchical structure among the different local minima (attractors) to explain the dynamic properties of cardiac fibrillation. Four types of the wave dynamics were considered: sinus rhythm; single stable rotor; single rotor with wavebreak; and multiple wavelet. The MEM could describe all types of wave dynamics (both accuracy and reliability>0.9) except the multiple random wavelet. Both of the sinus rhythm and the single stable rotor showed relatively high pairwise interaction coefficients among the cardiomyocytes. Also, the local energy minima had relatively large basins and high energy barrier, showing stable attractor properties. However, in the single rotor with wavebreak, there were relatively low pairwise interaction coefficients and a similar number of the local minima separated by a relatively low energy barrier compared with the single stable rotor case. The energy landscape of the multiple wavelet consisted of a large number of the local minima separated by a relatively low energy barrier, showing unstable dynamics. These results indicate that the MEM provides information about local and global coherence among the cardiomyocytes beyond the simple structural connectivity. Energy landscape analysis can explain stability and transitional properties of complex dynamics of cardiac fibrillation, which might be determined by the presence of 'driver' such as sinus node or rotor.

We introduce a continuous modeling approach which combines elastic responds of the trabecular bone structure, the concentration of signaling molecules within the bone and a mechanism how this concentration at the bone surface is used for local bone formation and resorption. In an abstract setting bone can be considered as a shape changing structure. For similar problems in materials science phase field approximations have been established as an efficient computational tool. We adapt such an approach for trabecular bone remodeling. It allows for a smooth representation of the trabecular bone structure and drastically reduces computational costs if compared with traditional micro finite element approaches. We demonstrate the advantage of the approach within a minimal model. We quantitatively compare the results with established micro finite element approaches on simple geometries and consider the bone morphology within a bone segment obtained from μ CT data of a sheep vertebra with realistic parameters.

Uncontrolled, excessive production of pro-inflammatory mediators from immune cells and traumatized tissues can cause systemic inflammatory issues like sepsis, one of the ten leading causes of death in the United States and one of the three leading causes of death in the intensive care unit. Understanding the effects of inflammation on the autonomic control system can improve a patient's chance of recovery after an inflammatory event such as surgery. Though the effects of the autonomic response on the inflammatory system are well defined, there remains a gap in understanding the reverse response. Specifically, the impact of the inflammatory response on the autonomic control system remains unknown. In this study, we investigate hypothesized interactions of the inflammatory system with the thermal and cardiovascular regulatory systems in response to an endotoxin challenge using mathematical modeling. We calibrate the model to data from two independent studies: a) of the inflammatory response in healthy young men and b) a comparative study of the inflammatory response between mice and humans. Simulation analysis is used to explore how the model responds to pathological input and treatment, specifically antibiotics, antipyretics, vasopressors, and combination therapy. Our findings show that multimodal treatment that simultaneously targets both the pathogen and the infection symptoms gives the most favorable recovery outcome.

We propose deterministic and stochastic models for studying the pharmacokinetics of chronic myeloid leukemia (CML), upon administration of IFN- α (the traditional treatment for CML), TKI (the current frontline medication for CML) and Wnt/ β -catenin signaling (the state-of-the art therapeutic breakthrough for CML). To the best of our knowledge, no mathematical model incorporating all these three therapeutic protocols are available in literature. Further, this work introduces a stochastic approach in the study of CML dynamics. The key contributions of this work are: (1) Determination of the patient condition, contingent upon the patient specific model parameters, which leads to prediction of the appropriate patient specific therapeutic dosage. (2) Addressing the question of how the dual therapy of TKI and Wnt/ β -catenin signaling or triple combination of all three, offers potentially improved therapeutic responses, particularly in terms of reduced side effects of TKI or IFN- α . (3) Prediction of the likelihood of CML extinction/remission based on the level of CML stem cells at detection.

Polymer-based hydrogels have been widely applied for chronic wound therapeutics, due to their well-acclaimed wound exudate management capability. At the same time, there is still an unmet clinical need for simple wound diagnostic tools to assist clinical decision-making at the point of care and deliver on the vision of patient-personalised wound management. To explore this challenge, we present a one-step synthetic strategy to realise a redox-responsive, hyaluronic acid (HA)-based hydrogel that is sensitive to wound environment-related variations in glutathione (GSH) concentration. By selecting aminoethyl disulfide (AED) as a GSH-sensitive crosslinker and considering GSH concentration variations in active and non-self-healing wounds, we investigated the impact of GSH-induced AED cleavage on hydrogel dimensions, aiming to build GSH-size relationships for potential point-of-care wound diagnosis. The hydrogel was also found to be non-cytotoxic and aided L929 fibroblast growth and proliferation over seven days in vitro. Such a material offers a very low-cost tool for the visual detection of a target analyte that varies dependent on the status of the cells and tissues (wound detection) and may be further exploited as an implant for fibroblast growth and tissue regeneration (wound repair).

Optimization of fluid transport in the slime mold Physarum polycephalum has been the subject of several modeling efforts in recent literature. Existing models assume that the tube adaptation mechanism in P. polycephalum's tubular network is controlled by the sheer amount of fluid flow through the tubes. We put forward the hypothesis that the controlling variable may instead be the flow's pressure gradient along the tube. We carry out the stability analysis of such a revised mathematical model for a parallel-edge network, proving that the revised model supports the global flow-optimizing behavior of the slime mold for a substantially wider class of response functions compared to previous models. Simulations also suggest that the same conclusion may be valid for arbitrary network topologies.

In this paper, we derive an effective macroscale description suitable to describe the growth of biological tissue within a porous tissue-engineering scaffold. As in our recent work (Holden \textit{et al.} "A multiphase multiscale model for nutrient limited tissue growth", The ANZIAM Journal, 2018, doi:10.1017/S1446181118000044) the underlying tissue dynamics is described as a multiphase mixture, thereby naturally accommodating features such as interstitial growth and active cell motion. Via a linearisation of the underlying multiphase model (whose nonlinearity poses significant challenge for such analyses), we obtain, by means of multiple-scales homogenisation, a simplified macroscale model that nevertheless retains explicit dependence on both the microscale scaffold structure and the tissue dynamics. The model we obtain comprises Darcy flow, and differential equations for the volume fraction of cells within the scaffold and the concentration of nutrient, required for growth. These are coupled to underlying Stokes-type cell problems that provide permeability tensors to parameterise the macroscale description. In Holden \textit{et al.}, the cell problems retain macroscale dependence, posing significant computational challenges; here, we obtain a decoupled system whereby the quasi-steady cell-problems may be solved separately from the macroscale description, thereby greatly reducing the complexity associated with fully-coupled multiscale descriptions. Moreover, we indicate how the formulation is influenced by a set of alternative microscale boundary conditions.S

To predict if developing human embryos are permissive to coronaviruses, we analyzed publicly available single cell RNA-seq datasets of zygotes, 4-cell, 8-cell, morula, inner cell mass, epiblast, primitive endoderm and trophectoderm for the coronavirus receptors (ACE2, BSG, DPP4 and ANPEP), the Spike protein cleavage enzymes (TMPRSS2, CTSL). We also analyzed the presence of host genes involved in viral replication, the endosomal sorting complexes required for transport (ESCRT) and SARS-Cov-2 interactions. The results reveal that ACE2, BSG, DPP4 and ANPEP are expressed in the cells of the zygote, to blastocyst including the trophectodermal lineage. ACE2, TMPRSS, BSG and CTSL are co-transcribed in a proportion of epiblast cells and most cells of the trophectoderm. The embryonic and trophectodermal cells also express genes for proteins ESCRT, viral replication and those that interact with SARS-CoV-2. We identified 1985 genes in epiblast and 1452 genes in the trophectoderm that are enriched in the ACE2 and TMPRSS2 co-expressing cells; 216 genes of these are common in both the cell types. These genes are associated with lipid metabolism, lysosome, peroxisome and oxidative phosphorylation pathways. Together our results suggest that developing human embryos could be permissive to coronavirus entry by both canonical and non-canonical mechanisms and they also express the genes for proteins involved in viral endocytosis and replication. This knowledge will be useful for evidence-based patient management for IVF during the COVID-19 pandemic.

Tumour spheroids have the potential to be used as preclinical chemosensitivity assays. However, the production of three dimensional (3D) tumour spheroids remains challenging as not all tumour cell lines form spheroids with regular morphologies and spheroid transfer often induces disaggregation. In the field of pancreatic cancer, the MiaPaCa-2 cell line is an interesting model for research but it is known for its difficulty to form stable spheroids; also, when formed, spheroids from this cell line are weak and arduous to manage and to harvest for further analyses such as multiple staining and imaging. In this work, we compared different methods (i.e. hanging drop, round bottom wells and Matrigel embedding, each of them with or without methylcellulose in the media) to evaluate which one allowed to better overpass these limitations. Morphometric analysis indicated that hanging drop in presence of methylcellulose leaded to well-organized spheroids; interestingly, quantitative PCR (qPCR) analysis reflected the morphometric characterization, indicating that same spheroids expressed the highest values of CD44, VIMENTIN, TGF beta1 and Ki67. In addition, we investigated the generation of MiaPaCa-2 spheroids when cultured on substrates of different hydrophobicity, in order to minimize the area in contact with the culture media and to further improve spheroid formation.

Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed interface evolving via forced mean curvature flow (together with a `kinetic under-cooling' regularisation) where the forcing depends on the solution of a PDE that holds in the domain enclosed by the interface. We perform linear stability analysis and derive a diffuse-interface approximation of the model. Finite-element discretisations of two closely related models are presented, together with computational results comparing the approximate solutions.