Cellular Automata Modeling of Stem-Cell-Driven Development of Tissue in the Nervous System

Bridging systems biology and tissue engineering: Unleashing the full potential of complex 3D in vitro tissue models of disease

Rapid advances in tissue engineering have resulted in more complex and physiologically relevant 3D in vitro tissue models with applications in fundamental biology and therapeutic development. However, the complexity provided by these models is often not leveraged fully due to the reductionist methods used to analyze them. Computational and mathematical models developed in the field of systems biology can address this issue. Yet, traditional systems biology has been mostly applied to simpler in vitro models with little physiological relevance and limited cellular complexity. Therefore, integrating these two inherently interdisciplinary fields can result in new insights and move both disciplines forward. In this review, we provide a systematic overview of how systems biology has been integrated with 3D in vitro tissue models and discuss key application areas where the synergies between both fields have led to important advances with potential translational impact. We then outline key directions for future research and discuss a framework for further integration between fields.

Hybrid electrospun polyhydroxybutyrate/gelatin/laminin/polyaniline scaffold for nerve tissue engineering application: Preparation, characterization, and in vitro assay

Despite the widespread central nervous system injuries, treatment of these disorders is still an issue of concern due to the complexities. Natural recovery in these patients is rarely observed, which calls for developing new methods that address these problems. In this study, natural polymers of polyhydroxybutyrate (PHB) and gelatin were electrospun into scaffolds and cross-linked. In order to modify the PHB-based scaffold for nerve tissue engineering, the scaffold surface was modified by exposure to the ammonium gas plasma under controlled conditions, and the laminin as a promoter for neural cells was coated on the sample surface. Then, polyaniline nanoparticles were inkjet-printed on a sample surface as parallel lines to induce the differentiation of stem cells into neural cells. Infrared spectroscopy, absorption of PBS, AFM, degradation rate, contact angle, electron microscopy and optical microscopy, thermal and mechanical behavior, and analysis of the viability of L929 cells were investigated for the scaffolds. The results showed gelatin decreased the contact angle from 106.2° to 38° and increased the residual weight after PBS incubation from 82 % to 38 %. The moduli of the scaffold increased from 8.78 MPa for pure PHB to 28.74 for the modified scaffold. In addition, performed methods increased cell viability from 69 % for PHB to 89 % for modified scaffold and also had a favorable effect on cell adhesion. Investigation of culturing P19 stem cells demonstrated that they successfully differentiated into neural cells. Results show that the scaffolds prepared in this study were promising for nerve tissue engineering.

Travelling-Wave and Asymptotic Analysis of a Multiphase Moving Boundary Model for Engineered Tissue Growth

We derive a multiphase, moving boundary model to represent the development of tissue in vitro in a porous tissue engineering scaffold. We consider a cell, extra-cellular liquid and a rigid scaffold phase, and adopt Darcy’s law to relate the velocity of the cell and liquid phases to their respective pressures. Cell–cell and cell–scaffold interactions which can drive cellular motion are accounted for by utilising relevant constitutive assumptions for the pressure in the cell phase. We reduce the model to a nonlinear reaction–diffusion equation for the cell phase, coupled to a moving boundary condition for the tissue edge, the diffusivity being dependent on the cell and scaffold volume fractions, cell and liquid viscosities and parameters that relate to cellular motion. Numerical simulations reveal that the reduced model admits three regimes for the evolution of the tissue edge at large time: linear, logarithmic and stationary. Employing travelling-wave and asymptotic analysis, we characterise these regimes in terms of parameters related to cellular production and motion. The results of our investigation allow us to suggest optimal values for the governing parameters, so as to stimulate tissue growth in an engineering scaffold.

A computational model of organism development and carcinogenesis resulting from cells' bioelectric properties and communication

A sound theory of biological organization is clearly missing for a better interpretation of observational results and faster progress in understanding life complexity. The availability of such a theory represents a fundamental progress in explaining both normal and pathological organism development. The present work introduces a computational implementation of some principles of a theory of organism development, namely that the default state of cells is proliferation and motility, and includes the principle of variation and organization by closure of constraints. In the present model, the bioelectric context of cells and tissue is the field responsible for organization, as it regulates cell proliferation and the level of communication driving the system’s evolution. Starting from a depolarized (proliferative) cell, the organism grows to a certain size, limited by the increasingly polarized state after successive proliferation events. The system reaches homeostasis, with a depolarized core (proliferative cells) surrounded by a rim of polarized cells (non-proliferative in this condition). This state is resilient to cell death (random or due to injure) and to limited depolarization (potentially carcinogenic) events. Carcinogenesis is introduced through a localized event (a spot of depolarized cells) or by random depolarization of cells in the tissue, which returns cells to their initial proliferative state. The normalization of the bioelectric condition can reverse this out-of-equilibrium state to a new homeostatic one. This simplified model of embryogenesis, tissue organization and carcinogenesis, based on non-excitable cells’ bioelectric properties, can be made more realistic with the introduction of other components, like biochemical fields and mechanical interactions, which are fundamental for a more faithful representation of reality. However, even a simple model can give insight for new approaches in complex systems and suggest new experimental tests, focused in its predictions and interpreted under a new paradigm.

Integrative lymph node-mimicking models created with biomaterials and computational tools to study the immune system

The lymph node (LN) is a vital organ of the lymphatic and immune system that enables timely detection, response, and clearance of harmful substances from the body. Each LN comprises of distinct substructures, which host a plethora of immune cell types working in tandem to coordinate complex innate and adaptive immune responses. An improved understanding of LN biology could facilitate treatment in LN-associated pathologies and immunotherapeutic interventions, yet at present, animal models, which often have poor physiological relevance, are the most popular experimental platforms. Emerging biomaterial engineering offers powerful alternatives, with the potential to circumvent limitations of animal models, for in-depth characterization and engineering of the lymphatic and adaptive immune system. In addition, mathematical and computational approaches, particularly in the current age of big data research, are reliable tools to verify and complement biomaterial works. In this review, we first discuss the importance of lymph node in immunity protection followed by recent advances using biomaterials to create in vitro/vivo LN-mimicking models to recreate the lymphoid tissue microstructure and microenvironment, as well as to describe the related immuno-functionality for biological investigation. We also explore the great potential of mathematical and computational models to serve as in silico supports. Furthermore, we suggest how both in vitro/vivo and in silico approaches can be integrated to strengthen basic patho-biological research, translational drug screening and clinical personalized therapies. We hope that this review will promote synergistic collaborations to accelerate progress of LN-mimicking systems to enhance understanding of immuno-complexity.

Seven challenges in the multiscale modeling of multicellular tissues

The growth and dynamics of multicellular tissues involve tightly regulated and coordinated morphogenetic cell behaviors, such as shape changes, movement, and division, which are governed by subcellular machinery and involve coupling through short- and long-range signals. A key challenge in the fields of developmental biology, tissue engineering and regenerative medicine is to understand how relationships between scales produce emergent tissue-scale behaviors. Recent advances in molecular biology, live-imaging and ex vivo techniques have revolutionized our ability to study these processes experimentally. To fully leverage these techniques and obtain a more comprehensive understanding of the causal relationships underlying tissue dynamics, computational modeling approaches are increasingly spanning multiple spatial and temporal scales, and are coupling cell shape, growth, mechanics, and signaling. Yet such models remain challenging: modeling at each scale requires different areas of technical skills, while integration across scales necessitates the solution to novel mathematical and computational problems. This review aims to summarize recent progress in multiscale modeling of multicellular tissues and to highlight ongoing challenges associated with the construction, implementation, interrogation, and validation of such models. This article is categorized under: Reproductive System Diseases > Computational Models Metabolic Diseases > Computational Models Cancer > Computational Models.

Mathematical modeling of Notch dynamics in Drosophila neural development

Notch signalling is a well-conserved signalling pathway that regulates cell fate through cell-cell communication. A typical feature of Notch signalling is ‘lateral inhibition’, whereby two neighbouring cells of equivalent state of differentiation acquire different cell fates. Recently, mathematical and computational approaches have addressed the Notch dynamics in Drosophila neural development. Typical examples of lateral inhibition are observed in the specification of neural stem cells in the embryo and sensory organ precursors in the thorax. In eye disc development, Notch signalling cooperates with other signalling pathways to define the evenly spaced positioning of the photoreceptor cells. The interplay between Notch and epidermal growth factor receptor signalling regulates the timing of neural stem cell differentiation in the optic lobe. In this review, we summarize the theoretical studies that have been conducted to elucidate the Notch dynamics in these systems and discuss the advantages of combining mathematical models with biological experiments.

Modeling and Analysis of Cardiac Hybrid Cellular Automata via GPU-Accelerated Monte Carlo Simulation

The heart consists of a complex network of billions of cells. Under physiological conditions, cardiac cells propagate electrical signals in space, generating the heartbeat in a synchronous and coordinated manner. When such a synchronization fails, life-threatening events can arise. The inherent complexity of the underlying nonlinear dynamics and the large number of biological components involved make the modeling and the analysis of electrophysiological properties in cardiac tissue still an open challenge. We consider here a Hybrid Cellular Automata (HCA) approach modeling the cardiac cell-cell membrane resistance with a free variable. We show that the modeling approach can reproduce important and complex spatiotemporal properties paving the ground for promising future applications. We show how GPU-based technology can considerably accelerate the simulation and the analysis. Furthermore, we study the cardiac behavior within a unidimensional domain considering inhomogeneous resistance and we perform a Monte Carlo analysis to evaluate our approach.

The Neurosphere Simulator: An educational online tool for modeling neural stem cell behavior and tissue growth

Until very recently, distance education, including digital science labs, served a rather small portion of postsecondary students in the United States and many other countries. This situation has, however, dramatically changed in 2020 in the wake of the COVID-19 pandemic, which forced colleges to rapidly transit from face-to-face instructions to online classes. Here, we report the development of an interactive simulator that is freely available on the web (http://neurosphere.cos.northeastern.edu/) for teaching lab classes in developmental biology. This simulator is based on cellular automata models of neural-stem-cell-driven tissue growth in the neurosphere assay. By modifying model parameters, users can explore the role in tissue growth of several developmental mechanisms, such as regulation of mitosis or apoptotic cell death by contact inhibition. Besides providing an instantaneous animation of the simulated development of neurospheres, the Neurosphere Simulator tool offers also the possibility to download data for detailed analysis. The simulator function is complemented by a tutorial that introduces students to computational modeling of developmental processes.

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We developed an interactive neurosphere simulator.

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Simulations are based on cellular automata models of neurosphere growth.

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This educational tool is freely available on the web.

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The simulator can be used for online lab classes in developmental biology.

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Students explore through exercises mechanisms of stem-cell-driven tissue growth.

A continuation method for spatially discretized models with nonlocal interactions conserving size and shape of cells and lattices

In this paper, we introduce a continuation method for the spatially discretized models, while conserving the size and shape of the cells and lattices. This proposed method is realized using the shift operators and nonlocal operators of convolution types. Through this method and using the shift operator, the nonlinear spatially discretized model on the uniform and nonuniform lattices can be systematically converted into a spatially continuous model; this renders both models point-wisely equivalent. Moreover, by the convolution with suitable kernels, we mollify the shift operator and approximate the spatially discretized models using the nonlocal evolution equations, rendering suitable for the application in both experimental and mathematical analyses. We also demonstrate that this approximation is supported by the singular limit analysis, and that the information of the lattice and cells is expressed in the shift and nonlocal operators. The continuous models designed using our method can successfully replicate the patterns corresponding to those of the original spatially discretized models obtained from the numerical simulations. Furthermore, from the observations of the isotropy of the Delta–Notch signaling system in a developing real fly brain, we propose a radially symmetric kernel for averaging the cell shape using our continuation method. We also apply our method for cell division and proliferation to spatially discretized models of the differentiation wave and describe the discrete models on the sphere surface. Finally, we demonstrate an application of our method in the linear stability analysis of the planar cell polarity model.

The recent advances in the mathematical modelling of human pluripotent stem cells

Human pluripotent stem cells hold great promise for developments in regenerative medicine and drug design. The mathematical modelling of stem cells and their properties is necessary to understand and quantify key behaviours and develop non-invasive prognostic modelling tools to assist in the optimisation of laboratory experiments. Here, the recent advances in the mathematical modelling of hPSCs are discussed, including cell kinematics, cell proliferation and colony formation, and pluripotency and differentiation.