Multiscale models of angiogenesis

Probing phosphorylation events in biological membranes: The transducer function

The extracellular environment is sensed by receptors in the plasma membrane. Some of these receptors initiate cytoplasmic signaling cascades involving phosphorylation: the addition of a phosphate group to a specific amino acid, such as tyrosine, in a protein. Receptor Tyrosine Kinases (RTKs) are one large class of membrane receptors that can directly initiate signaling cascades through their intracellular kinase domains, which both catalyze tyrosine phosphorylation and get phosphorylated. In the first step of signaling, the ligands stabilize phosphorylation-competent RTK dimers and oligomers, which leads to the phosphorylation of specific tyrosine residues in the activation loop of the kinases. Here we discuss quantitative measurements of tyrosine phosphorylation efficiencies for RTKs, described by the "transducer function". The transducer function links the phosphorylation (the response) and the binding of the activating ligand to the receptor (the stimulus). We overview a methodology that allows such measurements in direct response to ligand binding. We discuss experiments which demonstrate that EGF is a partial agonist, and that two tyrosines in the intracellular domain of EGFR, Y1068 and Y1173, are differentially phosphorylated in the EGF-bound EGFR dimers.

Agent-based model demonstrates the impact of nonlinear, complex interactions between cytokinces on muscle regeneration

Muscle regeneration is a complex process due to dynamic and multiscale biochemical and cellular interactions, making it difficult to identify microenvironmental conditions that are beneficial to muscle recovery from injury using experimental approaches alone. To understand the degree to which individual cellular behaviors impact endogenous mechanisms of muscle recovery, we developed an agent-based model (ABM) using the Cellular-Potts framework to simulate the dynamic microenvironment of a cross-section of murine skeletal muscle tissue. We referenced more than 100 published studies to define over 100 parameters and rules that dictate the behavior of muscle fibers, satellite stem cells (SSCs), fibroblasts, neutrophils, macrophages, microvessels, and lymphatic vessels, as well as their interactions with each other and the microenvironment. We utilized parameter density estimation to calibrate the model to temporal biological datasets describing cross-sectional area (CSA) recovery, SSC, and fibroblast cell counts at multiple timepoints following injury. The calibrated model was validated by comparison of other model outputs (macrophage, neutrophil, and capillaries counts) to experimental observations. Predictions for eight model perturbations that varied cell or cytokine input conditions were compared to published experimental studies to validate model predictive capabilities. We used Latin hypercube sampling and partial rank correlation coefficient to identify in silico perturbations of cytokine diffusion coefficients and decay rates to enhance CSA recovery. This analysis suggests that combined alterations of specific cytokine decay and diffusion parameters result in greater fibroblast and SSC proliferation compared to individual perturbations with a 13% increase in CSA recovery compared to unaltered regeneration at 28 days. These results enable guided development of therapeutic strategies that similarly alter muscle physiology (i.e. converting extracellular matrix [ECM]-bound cytokines into freely diffusible forms as studied in cancer therapeutics or delivery of exogenous cytokines) during regeneration to enhance muscle recovery after injury.

Review of cardiac-coronary interaction and insights from mathematical modeling

Cardiac-coronary interaction is fundamental to the function of the heart. As one of the highest metabolic organs in the body, the cardiac oxygen demand is met by blood perfusion through the coronary vasculature. The coronary vasculature is largely embedded within the myocardial tissue which is continually contracting and hence squeezing the blood vessels. The myocardium-coronary vessel interaction is two-ways and complex. Here, we review the different types of cardiac-coronary interactions with a focus on insights gained from mathematical models. Specifically, we will consider the following: (1) myocardial-vessel mechanical interaction; (2) metabolic-flow interaction and regulation; (3) perfusion-contraction matching, and (4) chronic interactions between the myocardium and coronary vasculature. We also provide a discussion of the relevant experimental and clinical studies of different types of cardiac-coronary interactions. Finally, we highlight knowledge gaps, key challenges, and limitations of existing mathematical models along with future research directions to understand the unique myocardium-coronary coupling in the heart. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Cardiovascular Diseases > Molecular and Cellular Physiology.

Agent-based model demonstrates the impact of nonlinear, complex interactions between cytokines on muscle regeneration

Muscle regeneration is a complex process due to dynamic and multiscale biochemical and cellular interactions, making it difficult to identify microenvironmental conditions that are beneficial to muscle recovery from injury using experimental approaches alone. To understand the degree to which individual cellular behaviors impact endogenous mechanisms of muscle recovery, we developed an agent-based model (ABM) using the Cellular Potts framework to simulate the dynamic microenvironment of a cross-section of murine skeletal muscle tissue. We referenced more than 100 published studies to define over 100 parameters and rules that dictate the behavior of muscle fibers, satellite stem cells (SSC), fibroblasts, neutrophils, macrophages, microvessels, and lymphatic vessels, as well as their interactions with each other and the microenvironment. We utilized parameter density estimation to calibrate the model to temporal biological datasets describing cross-sectional area (CSA) recovery, SSC, and fibroblast cell counts at multiple time points following injury. The calibrated model was validated by comparison of other model outputs (macrophage, neutrophil, and capillaries counts) to experimental observations. Predictions for eight model perturbations that varied cell or cytokine input conditions were compared to published experimental studies to validate model predictive capabilities. We used Latin hypercube sampling and partial rank correlation coefficient to identify in silico perturbations of cytokine diffusion coefficients and decay rates to enhance CSA recovery. This analysis suggests that combined alterations of specific cytokine decay and diffusion parameters result in greater fibroblast and SSC proliferation compared to individual perturbations with a 13% increase in CSA recovery compared to unaltered regeneration at 28 days. These results enable guided development of therapeutic strategies that similarly alter muscle physiology (i.e. converting ECM-bound cytokines into freely diffusible forms as studied in cancer therapeutics or delivery of exogenous cytokines) during regeneration to enhance muscle recovery after injury.

Computational modeling of angiogenesis: The importance of cell rearrangements during vascular growth

Angiogenesis is the process wherein endothelial cells (ECs) form sprouts that elongate from the pre-existing vasculature to create new vascular networks. In addition to its essential role in normal development, angiogenesis plays a vital role in pathologies such as cancer, diabetes and atherosclerosis. Mathematical and computational modeling has contributed to unraveling its complexity. Many existing theoretical models of angiogenic sprouting are based on the "snail-trail" hypothesis. This framework assumes that leading ECs positioned at sprout tips migrate toward low-oxygen regions while other ECs in the sprout passively follow the leaders' trails and proliferate to maintain sprout integrity. However, experimental results indicate that, contrary to the snail-trail assumption, ECs exchange positions within developing vessels, and the elongation of sprouts is primarily driven by directed migration of ECs. The functional role of cell rearrangements remains unclear. This review of the theoretical modeling of angiogenesis is the first to focus on the phenomenon of cell mixing during early sprouting. We start by describing the biological processes that occur during early angiogenesis, such as phenotype specification, cell rearrangements and cell interactions with the microenvironment. Next, we provide an overview of various theoretical approaches that have been employed to model angiogenesis, with particular emphasis on recent in silico models that account for the phenomenon of cell mixing. Finally, we discuss when cell mixing should be incorporated into theoretical models and what essential modeling components such models should include in order to investigate its functional role. This article is categorized under: Cardiovascular Diseases > Computational Models Cancer > Computational Models.

Numerical investigation of the pharmacokinetics and pharmacodynamics of the chemotherapeutic drug in avascular and vascular stages of a brain tumor

One of the most commonly used approaches for treating solid tumors is the systemic delivery of chemotherapeutic drugs. However, our understanding of the factors influencing treatment efficacy through this method is still limited. This study presents a comprehensive and realistic mathematical model that incorporates the dynamics of tumor growth, capillary network extension, and drug delivery in a coupled and simultaneous manner. The model covers two stages of tumor growth: avascular and vascular. For tumor growth, a continuum model is employed using the phase field interface-capturing method. The neo-vascularization process is modeled using a hybrid discrete-continuum approach. Additionally, a multi-scale model is used to describe the pharmacokinetics of doxorubicin, considering various agents. The study investigates the effect of haptotaxis and reveals that a higher haptotaxis coefficient leads to faster tumor growth (up to 2.6 times) and a quicker progression to angiogenesis. The impact of tumor-related and drug-related parameters is also examined, including tumor size, tumor sensitivity to the drug, chemotherapy initialization, treatment cycle duration, drug affinity to cells, and drug dose. The findings indicate that chemotherapy is more effective during the angiogenesis stage when active loops have formed. Other clinical methods such as radiotherapy and surgery may be more appropriate during the avascular stage or the transition period between angiogenesis initialization and loop formation. The penetration depth of the drug decreases by approximately 50% with an increase in the drug binding rate to surface-cell receptors. As a result, high-associate-rate drugs are preferred for chemotherapy after active loops have formed, while low-associate-rate drugs are suitable for earlier stages.

Soliton approximation in continuum models of leader-follower behavior

Complex biological processes involve collective behavior of entities (bacteria, cells, animals) over many length and time scales and can be described by discrete models that track individuals or by continuum models involving densities and fields. We consider hybrid stochastic agent-based models of branching morphogenesis and angiogenesis (new blood vessel creation from preexisting vasculature), which treat cells as individuals that are guided by underlying continuous chemical and/or mechanical fields. In these descriptions, leader (tip) cells emerge from existing branches and follower (stalk) cells build the new sprout in their wake. Vessel branching and fusion (anastomosis) occur as a result of tip and stalk cell dynamics. Coarse graining these hybrid models in appropriate limits produces continuum partial differential equations (PDEs) for endothelial cell densities that are more analytically tractable. While these models differ in nonlinearity, they produce similar equations at leading order when chemotaxis is dominant. We analyze this leading order system in a simple quasi-one-dimensional geometry and show that the numerical solution of the leading order PDE is well described by a soliton wave that evolves from vessel to source. This wave is an attractor for intermediate times until it arrives at the hypoxic region releasing the growth factor. The mathematical techniques used here thus identify common features of discrete and continuum approaches and provide insight into general biological mechanisms governing their collective dynamics.

External mechanical loading overrules cell-cell mechanical communication in sprouting angiogenesis during early bone regeneration

Sprouting angiogenesis plays a key role during bone regeneration. For example, insufficient early revascularization of the injured site can lead to delayed or non-healing. During sprouting, endothelial cells are known to be mechano-sensitive and respond to local mechanical stimuli. Endothelial cells interact and communicate mechanically with their surroundings, such as outer-vascular stromal cells, through cell-induced traction forces. In addition, external physiological loads act at the healing site, resulting in tissue deformations and impacting cellular arrangements. How these two distinct mechanical cues (cell-induced and external) impact angiogenesis and sprout patterning in early bone healing remains however largely unknown. Therefore, the aim of this study was to investigate the relative role of externally applied and cell-induced mechanical signals in driving sprout patterning at the onset of bone healing. To investigate cellular self-organisation in early bone healing, an in silico model accounting for the mechano-regulation of sprouting angiogenesis and stromal cell organization was developed. Computer model predictions were compared to in vivo experiments of a mouse osteotomy model stabilized with a rigid or a semirigid fixation system. We found that the magnitude and orientation of principal strains within the healing region can explain experimentally observed sprout patterning, under both fixation conditions. Furthermore, upon simulating the selective inhibition of either cell-induced or externally applied mechanical cues, external mechanical signals appear to overrule the mechanical communication acting on a cell-cell interaction level. Such findings illustrate the relevance of external mechanical signals over the local cell-mediated mechanical cues and could be used in the design of fracture treatment strategies for bone regeneration.

Multi-scale model of lumen formation via inverse membrane blebbing mechanism during sprouting angiogenesis process

Cancer is one of the leading causes of mortality and morbidity among people worldwide. Cancer appears as solid tumors in many cases. Angiogenesis is the growth of blood vessels from the existing vasculature and is one of the imperative processes in tumor growth. Another vital phenomenon for formation and functionality of this vasculature network is lumen formation. The results of recent studies indicate the importance of blood pressure in this mechanism. Computational modeling can study these processes in different scales. Hence, wide varieties of these models have been proposed during recent years. In this research, a multi-scale model is developed for the angiogenesis process. In the extracellular scale, the growth factor concentration is calculated via the reaction diffusion equation. At the cellular scale, growth, migration, and the adhesion of endothelial cells are modeled by the Potts cellular model. At the intra-cellular scale by considering biochemical signals, a Boolean network model describes migration, division, or apoptosis of endothelial cells. A stochastic model developed for lumen formation via inverse membrane blebbing mechanism. A CFD simulation was also used to investigate the role of pulsated blood pressure in the inverse membrane blebbing mechanism. The lumen formation model shows stochastic behavior in blebs expansion and lumen expansion. Comparing the stochastic model's results with the CFD simulation also shows the vital role of pressure pulse and the topology of the blebs in bleb retraction.

A global method for fast simulations of molecular dynamics in multiscale agent-based models of biological tissues

Agent-based models (ABMs) are a natural platform for capturing the multiple time and spatial scales in biological processes. However, these models are computationally expensive, especially when including molecular-level effects. The traditional approach to simulating this type of multiscale ABM is to solve a system of ordinary differential equations for the molecular events per cell. This significantly adds to the computational cost of simulations as the number of agents grows, which contributes to many ABMs being limited to around10 5 cells. We propose an approach that requires the same computational time independent of the number of agents. This speeds up the entire simulation by orders of magnitude, allowing for more thorough explorations of ABMs with even larger numbers of agents. We use two systems to show that the new method strongly agrees with the traditionally used approach. This computational strategy can be applied to a wide range of biological investigations.

In silico optimization of heparin microislands in microporous annealed particle (MAP) hydrogel for endothelial cell migration

Biomaterials capable of generating growth factor gradients have shown success in guiding tissue regeneration, as growth factor gradients are a physiologic driver of cell migration. Of particular importance, a focus on promoting endothelial cell migration is vital to angiogenesis and new tissue formation. Microporous Annealed Particle (MAP) scaffolds represent a unique niche in the field of regenerative biomaterials research as an injectable biomaterial with an open porosity that allows cells to freely migrate independent of material degradation. Recently, we have used the MAP platform to heterogeneously include spatially isolated heparin-modified microgels (heparin microislands) which can sequester growth factors and guide cell migration. In in vitro sprouting angiogenesis assays, we observed a parabolic relationship between the percentage of heparin microislands and cell migration, where 10% heparin microislands had more endothelial cell migration compared to 1% and 100%. Due to the low number of heparin microisland ratios tested, we hypothesize the spacing between microgels can be further optimized. Rather than use purely empirical methods, which are both expensive and time intensive, we believe this challenge represents an opportunity to use computational modeling. Here we present the first agent-based model of a MAP scaffold to optimize the ratio of heparin microislands. Specifically, we develop a two-dimensional model in Hybrid Automata Library (HAL) of endothelial cell migration within the unique MAP scaffold geometry. Finally, we present how our model can accurately predict cell migration trends in vitro, and these studies provide insight on how computational modeling can be used to design particle-based biomaterials. STATEMENT OF SIGNIFICANCE: : While the combination of experimental and computational approaches is increasingly being used to gain a better understanding of cellular processes, their combination in biomaterials development has been relatively limited. Heparin microislands are spatially isolated heparin microgels; when located within a microporous annealed particle (MAP) scaffold, they can sequester and release growth factors. Importantly, we present the first agent-based model of MAP scaffolds to optimize the ratio of heparin microislands within the scaffold to promote endothelial cell migration. We demonstrate this model can accurately predict trends in vitro, thus opening a new avenue of research to aid in the design of MAP scaffolds.

In Vitro, In Vivo, and In Silico Models of Lymphangiogenesis in Solid Malignancies

Lymphangiogenesis (LA) is the formation of new lymphatic vessels by lymphatic endothelial cells (LECs) sprouting from pre-existing lymphatic vessels. It is increasingly recognized as being involved in many diseases, such as in cancer and secondary lymphedema, which most often results from cancer treatments. For some cancers, excessive LA is associated with cancer progression and metastatic dissemination to the lymph nodes (LNs) through lymphatic vessels. The study of LA through in vitro, in vivo, and, more recently, in silico models is of paramount importance in providing novel insights and identifying the key molecular actors in the biological dysregulation of this process under pathological conditions. In this review, the different biological (in vitro and in vivo) models of LA, especially in a cancer context, are explained and discussed, highlighting their principal modeled features as well as their advantages and drawbacks. Imaging techniques of the lymphatics, complementary or even essential to in vivo models, are also clarified and allow the establishment of the link with computational approaches. In silico models are introduced, theoretically described, and illustrated with examples specific to the lymphatic system and the LA. Together, these models constitute a toolbox allowing the LA research to be brought to the next level.

A multiscale cell-based model of tumor growth for chemotherapy assessment and tumor-targeted therapy through a 3D computational approach

OBJECTIVES

Computational modeling of biological systems is a powerful tool to clarify diverse processes contributing to cancer. The aim is to clarify the complex biochemical and mechanical interactions between cells, the relevance of intracellular signaling pathways in tumor progression and related events to the cancer treatments, which are largely ignored in previous studies.

MATERIALS AND METHODS

A three-dimensional multiscale cell-based model is developed, covering multiple time and spatial scales, including intracellular, cellular, and extracellular processes. The model generates a realistic representation of the processes involved from an implementation of the signaling transduction network.

RESULTS

Considering a benign tumor development, results are in good agreement with the experimental ones, which identify three different phases in tumor growth. Simulating tumor vascular growth, results predict a highly vascularized tumor morphology in a lobulated form, a consequence of cells' motile behavior. A novel systematic study of chemotherapy intervention, in combination with targeted therapy, is presented to address the capability of the model to evaluate typical clinical protocols. The model also performs a dose comparison study in order to optimize treatment efficacy and surveys the effect of chemotherapy initiation delays and different regimens.

CONCLUSIONS

Results not only provide detailed insights into tumor progression, but also support suggestions for clinical implementation. This is a major step toward the goal of predicting the effects of not only traditional chemotherapy but also tumor-targeted therapies.

Systems biology of angiogenesis signaling: Computational models and omics

Angiogenesis is a highly regulated multiscale process that involves a plethora of cells, their cellular signal transduction, activation, proliferation, differentiation, as well as their intercellular communication. The coordinated execution and integration of such complex signaling programs is critical for physiological angiogenesis to take place in normal growth, development, exercise, and wound healing, while its dysregulation is critically linked to many major human diseases such as cancer, cardiovascular diseases, and ocular disorders; it is also crucial in regenerative medicine. Although huge efforts have been devoted to drug development for these diseases by investigation of angiogenesis‐targeted therapies, only a few therapeutics and targets have proved effective in humans due to the innate multiscale complexity and nonlinearity in the process of angiogenic signaling. As a promising approach that can help better address this challenge, systems biology modeling allows the integration of knowledge across studies and scales and provides a powerful means to mechanistically elucidate and connect the individual molecular and cellular signaling components that function in concert to regulate angiogenesis. In this review, we summarize and discuss how systems biology modeling studies, at the pathway‐, cell‐, tissue‐, and whole body‐levels, have advanced our understanding of signaling in angiogenesis and thereby delivered new translational insights for human diseases.

This article is categorized under:

Cardiovascular Diseases > Computational Models

Cancer > Computational Models

Capillary network formation and structure in a modified discrete mathematical model of angiogenesis

Angiogenesis, as part of cancer development, involves hierarchical complicated events and processes. Multiple studies have revealed the significance of the formation and structure of tumor-induced capillary networks. In this study, a discrete mathematical model of angiogenesis is studied and modified to capture the realistic physics of capillary network formation. Modifications are performed on the mathematical foundations of an existing discrete model of angiogenesis. The main modifications are the imposition of the matrix density effect, implementation of realistic boundary and initial conditions, and improvement of the method of governing equations based on physical observation. Results show that endothelial cells accelerate angiogenesis and capillary formation as they migrate toward the tumor and clearly exhibit the physical concept of haptotactic movement. On the other hand, consideration of blood flow-induced stress leads to a dynamic adaptive vascular network of capillaries which intelligibly reflects the brush border effect . The present modified model of capillary network formation is based on the physical rationale that defines a clear mathematical and physical interpretation of angiogenesis, which is likely to be used in cancer development modeling and anti-angiogenic therapies.

How can we fully realize the potential of mathematical and biological models to reintegrate biology?

Both mathematical models and biological model systems stand as tractable representations of complex biological systems or behaviors. They facilitate research and provide insights, and they can describe general rules. Models that represent biological processes or formalize general hypotheses are essential to any broad understanding. Mathematical or biological models necessarily omit details of the natural systems and thus may ultimately be "incorrect" representations. A key challenge is that tractability requires relatively simple models but simplification can result in models that are incorrect in their qualitative, broad implications if the abstracted details matter. Our paper discusses this tension, and how we can improve our inferences from models. We advocate for further efforts dedicated to model development, improvement, and acceptance by the scientific community, all of which may necessitate a more explicit discussion of the purpose and power of models. We argue that models should play a central role in reintegrating biology as a way to test our integrated understanding of how molecules, cells, organs, organisms, populations, and ecosystems function.

Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data

Tumor-associated vasculature is responsible for the delivery of nutrients, removal of waste, and allowing growth beyond 2-3 mm3. Additionally, the vascular network, which is changing in both space and time, fundamentally influences tumor response to both systemic and radiation therapy. Thus, a robust understanding of vascular dynamics is necessary to accurately predict tumor growth, as well as establish optimal treatment protocols to achieve optimal tumor control. Such a goal requires the intimate integration of both theory and experiment. Quantitative and time-resolved imaging methods have emerged as technologies able to visualize and characterize tumor vascular properties before and during therapy at the tissue and cell scale. Parallel to, but separate from those developments, mathematical modeling techniques have been developed to enable in silico investigations into theoretical tumor and vascular dynamics. In particular, recent efforts have sought to integrate both theory and experiment to enable data-driven mathematical modeling. Such mathematical models are calibrated by data obtained from individual tumor-vascular systems to predict future vascular growth, delivery of systemic agents, and response to radiotherapy. In this review, we discuss experimental techniques for visualizing and quantifying vascular dynamics including magnetic resonance imaging, microfluidic devices, and confocal microscopy. We then focus on the integration of these experimental measures with biologically based mathematical models to generate testable predictions.

Modular microenvironment components reproduce vascular dynamics de novo in a multi-scale agent-based model

Cells do not exist in isolation; they continuously act within and react to their environment. And this environment is not static; it continuously adapts and responds to cells. Here, we investigate how vascular structure and function impact emergent cell population behavior using an agent-based model (ABM). Our ABM enables researchers to "mix and match" cell agents, subcellular modules, and microenvironment components ranging from simple nutrient sources to complex, realistic vascular architectures that accurately capture hemodynamics. We use this ABM to highlight the bilateral relationship between cells and nearby vasculature, demonstrate the effect of vascular structure on environmental heterogeneity, and emphasize the non-linear, non-intuitive relationship between vascular function and the behavior of cell populations over time. Our ABM is well suited to characterizing in vitro and in vivo studies, with applications from basic science to translational synthetic biology and medicine. The model is freely available at https://github.com/bagherilab/ARCADE. A record of this paper's transparent peer review process is included in the supplemental information.

Multiscale modeling of tumor growth and angiogenesis: Evaluation of tumor-targeted therapy

The dynamics of tumor growth and associated events cover multiple time and spatial scales, generally including extracellular, cellular and intracellular modifications. The main goal of this study is to model the biological and physical behavior of tumor evolution in presence of normal healthy tissue, considering a variety of events involved in the process. These include hyper and hypoactivation of signaling pathways during tumor growth, vessels' growth, intratumoral vascularization and competition of cancer cells with healthy host tissue. The work addresses two distinctive phases in tumor development-the avascular and vascular phases-and in each stage two cases are considered-with and without normal healthy cells. The tumor growth rate increases considerably as closed vessel loops (anastomoses) form around the tumor cells resulting from tumor induced vascularization. When taking into account the host tissue around the tumor, the results show that competition between normal cells and cancer cells leads to the formation of a hypoxic tumor core within a relatively short period of time. Moreover, a dense intratumoral vascular network is formed throughout the entire lesion as a sign of a high malignancy grade, which is consistent with reported experimental data for several types of solid carcinomas. In comparison with other mathematical models of tumor development, in this work we introduce a multiscale simulation that models the cellular interactions and cell behavior as a consequence of the activation of oncogenes and deactivation of gene signaling pathways within each cell. Simulating a therapy that blocks relevant signaling pathways results in the prevention of further tumor growth and leads to an expressive decrease in its size (82% in the simulation).

Interpretation of wave reflections in the umbilical arterial segment of the feto-placental circulation: computational modeling of the feto-placental arterial tree

Placental vascular abnormalities are associated with a host of pregnancy complications including placenta mediated fetal growth restriction (FGR). Umbilical arterial (UA) Doppler ultrasound velocity waveforms are widely used in the diagnosis of underlying placental vascular abnormalities in pregnancies with suspected FGR, which greatly help prevent stillbirth via ongoing fetal monitoring and timely delivery. However, the sensitivity of UA Doppler diagnosis diminishes late in gestation. Our goal was to present a generalized wave decomposition method to compute forward and reflected components from UA waveforms. A detailed anatomical based model was also developed to explain observed UA flow waveform and to explore how vascular properties affect the shape of flow wave components. Using pregnant mice and high frequency ultrasound microscopy, we obtained in utero Doppler and M- mode ultrasound measurements in 15 fetuses UA. Following ultrasound, the placentas were collected and perfused with contrast agent to obtain high-resolution 3D images of the feto-placental arteries. Model results indicate the significant role of terminal load impedance (capillary and/or veins) in creating positive or negative reflected waveforms. A negative reflected waveform is obtained when terminal impedance increases. This is consistent with the elongated and non-branching terminal villi that are proposed cause the highly abnormal UA waveforms found in early-onset FGR. The significance of these findings for the diagnostic utility of UA Doppler in human pregnancy is that the identification and measurement of wave reflections may aid in discriminating between healthy and abnormal placental vasculature in pregnancies with suspected late-onset FGR.

VEGF-A splice variants bind VEGFRs with differential affinities

Vascular endothelial growth factor A (VEGF-A) and its binding to VEGFRs is an important angiogenesis regulator, especially the earliest-known isoform, VEGF-A165a. Yet several additional splice variants play prominent roles in regulating angiogenesis in health and in vascular disease, including VEGF-A121 and an anti-angiogenic variant, VEGF-A165b. Few studies have attempted to distinguish these forms from their angiogenic counterparts, experimentally. Previous studies of VEGF-A:VEGFR binding have measured binding kinetics for VEGFA165 and VEGF-A121, but binding kinetics of the other two pro- and all anti-angiogenic splice variants are not known. We measured the binding kinetics for VEGF-A165, -A165b, and -A121 with VEGFR1 and VEGF-R2 using surface plasmon resonance. We validated our methods by reproducing the known affinities between VEGF-A165a:VEGFR1 and VEGF-A165a:VEGFR2, 1.0 pM and 10 pM respectively, and validated the known affinity VEGF-A121:VEGFR2 as KD = 0.66 nM. We found that VEGF-A121 also binds VEGFR1 with an affinity KD = 3.7 nM. We further demonstrated that the anti-angiogenic variant, VEGF-A165b selectively prefers VEGFR2 binding at an affinity = 0.67 pM while binding VEGFR1 with a weaker affinity-KD = 1.4 nM. These results suggest that the - A165b anti-angiogenic variant would preferentially bind VEGFR2. These discoveries offer a new paradigm for understanding VEGF-A, while further stressing the need to take care in differentiating the splice variants in all future VEGF-A studies.

Understanding the Principles of Pattern Formation Driven by Notch Signaling by Integrating Experiments and Theoretical Models

Notch signaling is an evolutionary conserved cell-cell communication pathway. Besides regulating cell-fate decisions at an individual cell level, Notch signaling coordinates the emergent spatiotemporal patterning in a tissue through ligand-receptor interactions among transmembrane molecules of neighboring cells, as seen in embryonic development, angiogenesis, or wound healing. Due to its ubiquitous nature, Notch signaling is also implicated in several aspects of cancer progression, including tumor angiogenesis, stemness of cancer cells and cellular invasion. Here, we review experimental and computational models that help understand the operating principles of cell patterning driven by Notch signaling. First, we discuss the basic mechanisms of spatial patterning via canonical lateral inhibition and lateral induction mechanisms, including examples from angiogenesis, inner ear development and cancer metastasis. Next, we analyze additional layers of complexity in the Notch pathway, including the effect of varying cell sizes and shapes, ligand-receptor binding within the same cell, variable binding affinity of different ligand/receptor subtypes, and filopodia. Finally, we discuss some recent evidence of mechanosensitivity in the Notch pathway in driving collective epithelial cell migration and cardiovascular morphogenesis.

The Convergence of Cell-Based Surface Plasmon Resonance and Biomaterials: The Future of Quantifying Bio-molecular Interactions-A Review

Cell biology is driven by complex networks of biomolecular interactions. Characterizing the kinetic and thermodynamic properties of these interactions is crucial to understanding their role in different physiological processes. Surface plasmon resonance (SPR)-based approaches have become a key tool in quantifying biomolecular interactions, however conventional approaches require isolating the interacting components from the cellular system. Cell-based SPR approaches have recently emerged, promising to enable precise measurements of biomolecular interactions within their normal biological context. Two major approaches have been developed, offering their own advantages and limitations. These approaches currently lack a systematic exploration of 'best practices' like those existing for traditional SPR experiments. Toward this end, we describe the two major approaches, and identify the experimental parameters that require exploration, and discuss the experimental considerations constraining the optimization of each. In particular, we discuss the requirements of future biomaterial development needed to advance the cell-based SPR technique.

Sex differences in cancer mechanisms

We now know that cancer is many different diseases, with great variation even within a single histological subtype. With the current emphasis on developing personalized approaches to cancer treatment, it is astonishing that we have not yet systematically incorporated the biology of sex differences into our paradigms for laboratory and clinical cancer research. While some sex differences in cancer arise through the actions of circulating sex hormones, other sex differences are independent of estrogen, testosterone, or progesterone levels. Instead, these differences are the result of sexual differentiation, a process that involves genetic and epigenetic mechanisms, in addition to acute sex hormone actions. Sexual differentiation begins with fertilization and continues beyond menopause. It affects virtually every body system, resulting in marked sex differences in such areas as growth, lifespan, metabolism, and immunity, all of which can impact on cancer progression, treatment response, and survival. These organismal level differences have correlates at the cellular level, and thus, males and females can fundamentally differ in their protections and vulnerabilities to cancer, from cellular transformation through all stages of progression, spread, and response to treatment. Our goal in this review is to cover some of the robust sex differences that exist in core cancer pathways and to make the case for inclusion of sex as a biological variable in all laboratory and clinical cancer research. We finish with a discussion of lab- and clinic-based experimental design that should be used when testing whether sex matters and the appropriate statistical models to apply in data analysis for rigorous evaluations of potential sex effects. It is our goal to facilitate the evaluation of sex differences in cancer in order to improve outcomes for all patients.

Spiral Wave Propagation in Communities with Spatially Correlated Heterogeneity

Many multicellular communities propagate signals in a directed manner via excitable waves. Cell-to-cell heterogeneity is a ubiquitous feature of multicellular communities, but the effects of heterogeneity on wave propagation are still unclear. Here, we use a minimal FitzHugh-Nagumo-type model to investigate excitable wave propagation in a two-dimensional heterogeneous community. The model shows three dynamic regimes in which waves either propagate directionally, die out, or spiral indefinitely, and we characterize how these regimes depend on the heterogeneity parameters. We find that in some parameter regimes, spatial correlations in the heterogeneity enhance directional propagation and suppress spiraling. However, in other regimes, spatial correlations promote spiraling, a surprising feature that we explain by demonstrating that these spirals form by a second, distinct mechanism. Finally, we characterize the dynamics using techniques from percolation theory. Despite the fact that percolation theory does not completely describe the dynamics quantitatively because it neglects the details of the excitable propagation, we find that it accounts for the transitions between the dynamic regimes and the general dependency of the spiral period on the heterogeneity and thus provides important insights. Our results reveal that the spatial structure of cell-to-cell heterogeneity can have important consequences for signal propagation in cellular communities.

A Computational Model of the Endothelial to Mesenchymal Transition

Endothelial cells (ECs) form the lining of lymph and blood vessels. Changes in tissue requirements or wounds may cause ECs to behave as tip or stalk cells. Alternatively, they may differentiate into mesenchymal cells (MCs). These processes are known as EC activation and endothelial-to-mesenchymal transition (EndMT), respectively. EndMT, Tip, and Stalk EC behaviors all require SNAI1, SNAI2, and Matrix metallopeptidase (MMP) function. However, only EndMT inhibits the expression of VE-cadherin, PECAM1, and VEGFR2, and also leads to EC detachment. Physiologically, EndMT is involved in heart valve development, while a defective EndMT regulation is involved in the physiopathology of cardiovascular malformations, congenital heart disease, systemic and organ fibrosis, pulmonary arterial hypertension, and atherosclerosis. Therefore, the control of EndMT has many promising potential applications in regenerative medicine. Despite the fact that many molecular components involved in EC activation and EndMT have been characterized, the system-level molecular mechanisms involved in this process have not been elucidated. Toward this end, hereby we present Boolean network model of the molecular involved in the regulation of EC activation and EndMT. The simulated dynamic behavior of our model reaches fixed and cyclic patterns of activation that correspond to the expected EC and MC cell types and behaviors, recovering most of the specific effects of simple gain and loss-of-function mutations as well as the conditions associated with the progression of several diseases. Therefore, our model constitutes a theoretical framework that can be used to generate hypotheses and guide experimental inquiry to comprehend the regulatory mechanisms behind EndMT. Our main findings include that both the extracellular microevironment and the pattern of molecular activity within the cell regulate EndMT. EndMT requires a lack of VEGFA and sufficient oxygen in the extracellular microenvironment as well as no FLI1 and GATA2 activity within the cell. Additionally Tip cells cannot undergo EndMT directly. Furthermore, the specific conditions that are sufficient to trigger EndMT depend on the specific pattern of molecular activation within the cell.

Single-Cell Receptor Quantification of an In Vitro Coculture Angiogenesis Model Reveals VEGFR, NRP1, Tie2, and PDGFR Regulation and Endothelial Heterogeneity

Angiogenesis, the formation of new blood vessels from pre-existing ones, is essential for both normal development and numerous pathologies. Systems biology has offered a unique approach to study angiogenesis by profiling tyrosine kinase receptors (RTKs) that regulate angiogenic processes and computationally modeling RTK signaling pathways. Historically, this systems biology approach has been applied on ex vivo angiogenesis assays, however, these assays are difficult to quantify and limited in their potential of temporal analysis. In this study, we adopted a simple two-dimensional angiogenesis assay comprised of human umbilical vein endothelial cells (HUVECs) and human dermal fibroblasts (HDFs) and examined temporal dynamics of a panel of six RTKs and cell heterogeneity up to 17 days. We observed ~2700 VEGFR1 (vascular endothelial growth factor receptor 1) per cell on 24-h-old cocultured HDF plasma membranes, which do not express VEGFR when cultured alone. We observed 4000–8100 VEGFR2 per cell on cocultured HUVEC plasma membranes throughout endothelial tube formation. We showed steady increase of platelet-derived growth factor receptors (PDGFRs) on cocultured HDF plasma membranes, and more interestingly, 1900–2900 PDGFRβ per plasma membrane were found on HUVECs within the first six hours of coculturing. These quantitative findings will offer us insights into molecular regulation during angiogenesis and help assess in vitro tube formation models and their physiological relevance.

The RTK Interactome: Overview and Perspective on RTK Heterointeractions

Receptor tyrosine kinases (RTKs) play important roles in cell growth, motility, differentiation, and survival. These single-pass membrane proteins are grouped into subfamilies based on the similarity of their extracellular domains. They are generally thought to be activated by ligand binding, which promotes homodimerization and then autophosphorylation in trans. However, RTK interactions are more complicated, as RTKs can interact in the absence of ligand and heterodimerize within and across subfamilies. Here, we review the known cross-subfamily RTK heterointeractions and their possible biological implications, as well as the methodologies which have been used to study them. Moreover, we demonstrate how thermodynamic models can be used to study RTKs and to explain many of the complicated biological effects which have been described in the literature. Finally, we discuss the concept of the RTK interactome: a putative, extensive network of interactions between the RTKs. This RTK interactome can produce unique signaling outputs; can amplify, inhibit, and modify signaling; and can allow for signaling backups. The existence of the RTK interactome could provide an explanation for the irreproducibility of experimental data from different studies and for the failure of some RTK inhibitors to produce the desired therapeutic effects. We argue that a deeper knowledge of RTK interactome thermodynamics can lead to a better understanding of fundamental RTK signaling processes in health and disease. We further argue that there is a need for quantitative, thermodynamic studies that probe the strengths of the interactions between RTKs and their ligands and between different RTKs.

A multiscale model for heterogeneous tumor spheroid in vitro

In this paper, a novel multiscale method is proposed for the study of heterogeneous tumor spheroid growth in vitro. The entire tumor spheroid is described by an ellipsoid-based model while nutrient and other environmental factors are treated as continua. The ellipsoid-based discrete component is capable of incorporating mechanical effects and deformability, while keeping a minimum set of free variables to describe complex shape variations. Moreover, our purely cell-based description of tumor avoids the complex mutual conversion between a cell-based model and continuum model within a tumor, such as force and mass transformation. This advantage makes it highly suitable for the study of tumor spheroids in vitro whose size are normally less than 800 μm in diameter. In addition, our numerical scheme provides two computational options depending on tumor size. For a small or medium tumor spheroid, a three-dimensional (3D) numerical model can be directly applied. For a large spheroid, we suggest the use of a 3D-adapted 2D cross section configuration, which has not yet been explored in the literature, as an alternative for the theoretical investigation to bridge the gap between the 2D and 3D models. Our model and its implementations have been validated and applied to various studies given in the paper. The simulation results fit corresponding in vitro experimental observations very well.

The temporal basis of angiogenesis

The process of new blood vessel growth (angiogenesis) is highly dynamic, involving complex coordination of multiple cell types. Though the process must carefully unfold over time to generate functional, well-adapted branching networks, we seldom hear about the time-based properties of angiogenesis, despite timing being central to other areas of biology. Here, we present a novel, time-based formulation of endothelial cell behaviour during angiogenesis and discuss a flurry of our recent, integrated in silico/in vivo studies, put in context to the wider literature, which demonstrate that tissue conditions can locally adapt the timing of collective cell behaviours/decisions to grow different vascular network architectures. A growing array of seemingly unrelated ‘temporal regulators’ have recently been uncovered, including tissue derived factors (e.g. semaphorins or the high levels of VEGF found in cancer) and cellular processes (e.g. asymmetric cell division or filopodia extension) that act to alter the speed of cellular decisions to migrate. We will argue that ‘temporal adaptation’ provides a novel account of organ/disease-specific vascular morphology and reveals ‘timing’ as a new target for therapeutics. We therefore propose and explain a conceptual shift towards a ‘temporal adaptation’ perspective in vascular biology, and indeed other areas of biology where timing remains elusive.

This article is part of the themed issue ‘Systems morphodynamics: understanding the development of tissue hardware’.

A Network Model to Explore the Effect of the Micro-environment on Endothelial Cell Behavior during Angiogenesis

Angiogenesis is an important adaptation mechanism of the blood vessels to the changing requirements of the body during development, aging, and wound healing. Angiogenesis allows existing blood vessels to form new connections or to reabsorb existing ones. Blood vessels are composed of a layer of endothelial cells (ECs) covered by one or more layers of mural cells (smooth muscle cells or pericytes). We constructed a computational Boolean model of the molecular regulatory network involved in the control of angiogenesis. Our model includes the ANG/TIE, HIF, AMPK/mTOR, VEGF, IGF, FGF, PLCγ/Calcium, PI3K/AKT, NO, NOTCH, and WNT signaling pathways, as well as the mechanosensory components of the cytoskeleton. The dynamical behavior of our model recovers the patterns of molecular activation observed in Phalanx, Tip, and Stalk ECs. Furthermore, our model is able to describe the modulation of EC behavior due to extracellular micro-environments, as well as the effect due to loss- and gain-of-function mutations. These properties make our model a suitable platform for the understanding of the molecular mechanisms underlying some pathologies. For example, it is possible to follow the changes in the activation patterns caused by mutations that promote Tip EC behavior and inhibit Phalanx EC behavior, that lead to the conditions associated with retinal vascular disorders and tumor vascularization. Moreover, the model describes how mutations that promote Phalanx EC behavior are associated with the development of arteriovenous and venous malformations. These results suggest that the network model that we propose has the potential to be used in the study of how the modulation of the EC extracellular micro-environment may improve the outcome of vascular disease treatments.

Discovery of High-Affinity PDGF-VEGFR Interactions: Redefining RTK Dynamics

Nearly all studies of angiogenesis have focused on uni-family ligand-receptor binding, e.g., VEGFs bind to VEGF receptors, PDGFs bind to PDGF receptors, etc. The discovery of VEGF-PDGFRs binding challenges this paradigm and calls for investigation of other ligand-receptor binding possibilities. We utilized surface plasmon resonance to identify and measure PDGF-to-VEGFR binding rates, establishing cut-offs for binding and non-binding interactions. We quantified the kinetics of the recent VEGF-A:PDGFRβ interaction for the first time with K_D = 340 pM. We discovered new PDGF:VEGFR2 interactions with PDGF-AA:R2 K_D = 530 nM, PDGF-AB:R2 K_D = 110 pM, PDGF-BB:R2 K_D = 40 nM, and PDGF-CC:R2 K_D = 70 pM. We computationally predict that cross-family PDGF binding could contribute up to 96% of VEGFR2 ligation in healthy conditions and in cancer. Together the identification, quantification, and simulation of these novel cross-family interactions posits new mechanisms for understanding anti-angiogenic drug resistance and presents an expanded role of growth factor signaling with significance in health and disease.

Immunophysical analysis of corneal neovascularization: mechanistic insights and implications for pharmacotherapy

The cornea lacks adaptive immune cells and vasculature under healthy conditions, but is populated by both cell types under pathologic conditions and after transplantation. Here we propose an immunophysical approach to describe postoperative neovascularization in corneal grafts. We develop a simple dynamic model that captures not only the well-established interactions between innate immunity and vascular dynamics but also incorporates the contributions of adaptive immunity to vascular growth. We study how these interactions determine dynamic changes and steady states of the system as well as the clinical outcome, i.e. graft survival. The model allows us to systematically explore the impact of pharmacological inhibitors of vascular growth on the function and survival of transplanted corneas and search for the optimal time to initiatetherapy. Predictions from our models will help ongoing efforts to design therapeutic approaches to modulate alloimmunity and suppress allograft rejection.

Modelling Tumor-induced Angiogenesis: Combination of Stochastic Sprout Spacing and Sprout Progression

BACKGROUND

Angiogenesis initiated by cancerous cells is the process by which new blood vessels are formed to enhance oxygenation and growth of tumor.

OBJECTIVE

In this paper, we present a new multiscale mathematical model for the formation of a vascular network in tumor angiogenesis process.

METHODS

Our model couples an improved sprout spacing model as a stochastic mathematical model of sprouting along an existing parent blood vessel, with a mathematical model of sprout progression in the extracellular matrix (ECM) in response to some tumor angiogenic factors (TAFs). We perform simulations of the siting of capillary sprouts on an existing blood vessel using finite difference approximation of the dynamic equations of some angiogenesis activators and inhibitors. Angiogenesis activators are chemicals secreted by hypoxic tumor cells for initiating angiogenesis, and inhibitors of the angiogenesis are chemicals that are produced around every new sprout during tumor angiogenesis to inhibit the formation of further sprouts as a feedback of sprouting in angiogenesis. Moreover, for modelling sprout progression in ECM, we use three equations for the motility of endothelial cells at the tip of the activated sprouts, the consumption of TAF and the production and uptake of Fibronectin by endothelial cells.

RESULTS

Coupling these two basic models not only does provide a better time estimation of angiogenesis process, but also it is more compatible with reality.

CONCLUSION

This model can be used to provide basic information for angiogenesis in the related studies. Related simulations can estimate the position and number of sprouts along parent blood vessel during the initial steps of angiogenesis and models the process of sprout progression in ECM until they vascularize a tumor.

Hypoxic behavior in cells under controlled microfluidic environment

BACKGROUND

Depleted oxygen levels, known as hypoxia, causes considerable changes in the cellular metabolism. Hypoxia-inducible factors (HIF) act as the major protagonist in orchestrating manifold hypoxic responses by escaping cellular degradation mechanisms. These complex and dynamic intracellular responses are significantly dependent on the extracellular environment. In this study, we present a detailed model of a hypoxic cellular microenvironment in a microfluidic setting involving HIF hydroxylation.

METHODS

We have modeled the induction of hypoxia in a microfluidic chip by an unsteady permeation of oxygen from the microchannel through a porous polydimethylsiloxane channel wall. Extracellular and intracellular interactions were modeled with two different mathematical descriptions. Intracellular space is directly coupled to the extracellular environment through uptake and consumption of oxygen and ascorbate similar to cells in vivo.

RESULTS

Our results indicate a sharp switch in HIF hydroxylation behavior with changing prolyl hydroxylase levels from 0.1 to 4.0μM. Furthermore, we studied the effects of extracellular ascorbate concentration, using a new model, to predict its accumulation inside the cell over a relevant physiological range. In different hypoxic conditions, the cellular environment showed a significant dependence on oxygen levels in resulting intracellular response.

CONCLUSIONS

Change in hydroxylation behavior and nutrient supplementation can have significant potential in designing novel therapeutic interventions in cancer and ischemia/reperfusion injuries.

GENERAL SIGNIFICANCE

The hybrid mathematical model can effectively predict intracellular behavior due to external influences providing valuable directions in designing future experiments.

Multi-scale Modeling in Clinical Oncology: Opportunities and Barriers to Success

Hierarchical processes spanning several orders of magnitude of both space and time underlie nearly all cancers. Multi-scale statistical, mathematical, and computational modeling methods are central to designing, implementing and assessing treatment strategies that account for these hierarchies. The basic science underlying these modeling efforts is maturing into a new discipline that is close to influencing and facilitating clinical successes. The purpose of this review is to capture the state-of-the-art as well as the key barriers to success for multi-scale modeling in clinical oncology. We begin with a summary of the long-envisioned promise of multi-scale modeling in clinical oncology, including the synthesis of disparate data types into models that reveal underlying mechanisms and allow for experimental testing of hypotheses. We then evaluate the mathematical techniques employed most widely and present several examples illustrating their application as well as the current gap between pre-clinical and clinical applications. We conclude with a discussion of what we view to be the key challenges and opportunities for multi-scale modeling in clinical oncology.

3D-printed fluidic networks as vasculature for engineered tissue

Fabrication of vascular networks within engineered tissue remains one of the greatest challenges facing the fields of biomaterials and tissue engineering. Historically, the structural complexity of vascular networks has limited their fabrication in tissues engineered in vitro. Recently, however, key advances have been made in constructing fluidic networks within biomaterials, suggesting a strategy for fabricating the architecture of the vasculature. These techniques build on emerging technologies within the microfluidics community as well as on 3D printing. The freeform fabrication capabilities of 3D printing are allowing investigators to fabricate fluidic networks with complex architecture inside biomaterial matrices. In this review, we examine the most exciting 3D printing-based techniques in this area. We also discuss opportunities for using these techniques to address open questions in vascular biology and biophysics, as well as for engineering therapeutic tissue substitutes in vitro.

VEGFR-2 conformational switch in response to ligand binding

VEGFR-2 is the primary regulator of angiogenesis, the development of new blood vessels from pre-existing ones. VEGFR-2 has been hypothesized to be monomeric in the absence of bound ligand, and to undergo dimerization and activation only upon ligand binding. Using quantitative FRET and biochemical analysis, we show that VEGFR-2 forms dimers also in the absence of ligand when expressed at physiological levels, and that these dimers are phosphorylated. Ligand binding leads to a change in the TM domain conformation, resulting in increased kinase domain phosphorylation. Inter-receptor contacts within the extracellular and TM domains are critical for the establishment of the unliganded dimer structure, and for the transition to the ligand-bound active conformation. We further show that the pathogenic C482R VEGFR-2 mutant, linked to infantile hemangioma, promotes ligand-independent signaling by mimicking the structure of the ligand-bound wild-type VEGFR-2 dimer.

Augmenting Surgery via Multi-scale Modeling and Translational Systems Biology in the Era of Precision Medicine: A Multidisciplinary Perspective

In this era of tremendous technological capabilities and increased focus on improving clinical outcomes, decreasing costs, and increasing precision, there is a need for a more quantitative approach to the field of surgery. Multiscale computational modeling has the potential to bridge the gap to the emerging paradigms of Precision Medicine and Translational Systems Biology, in which quantitative metrics and data guide patient care through improved stratification, diagnosis, and therapy. Achievements by multiple groups have demonstrated the potential for (1) multiscale computational modeling, at a biological level, of diseases treated with surgery and the surgical procedure process at the level of the individual and the population; along with (2) patient-specific, computationally-enabled surgical planning, delivery, and guidance and robotically-augmented manipulation. In this perspective article, we discuss these concepts, and cite emerging examples from the fields of trauma, wound healing, and cardiac surgery.

Integrating Multiscale Modeling with Drug Effects for Cancer Treatment

In this paper, we review multiscale modeling for cancer treatment with the incorporation of drug effects from an applied system's pharmacology perspective. Both the classical pharmacology and systems biology are inherently quantitative; however, systems biology focuses more on networks and multi factorial controls over biological processes rather than on drugs and targets in isolation, whereas systems pharmacology has a strong focus on studying drugs with regard to the pharmacokinetic (PK) and pharmacodynamic (PD) relations accompanying drug interactions with multiscale physiology as well as the prediction of dosage-exposure responses and economic potentials of drugs. Thus, it requires multiscale methods to address the need for integrating models from the molecular levels to the cellular, tissue, and organism levels. It is a common belief that tumorigenesis and tumor growth can be best understood and tackled by employing and integrating a multifaceted approach that includes in vivo and in vitro experiments, in silico models, multiscale tumor modeling, continuous/discrete modeling, agent-based modeling, and multiscale modeling with PK/PD drug effect inputs. We provide an example application of multiscale modeling employing stochastic hybrid system for a colon cancer cell line HCT-116 with the application of Lapatinib drug. It is observed that the simulation results are similar to those observed from the setup of the wet-lab experiments at the Translational Genomics Research Institute.

Retinal Artery-Vein Classification via Topology Estimation

We propose a novel, graph-theoretic framework for distinguishing arteries from veins in a fundus image. We make use of the underlying vessel topology to better classify small and midsized vessels. We extend our previously proposed tree topology estimation framework by incorporating expert, domain-specific features to construct a simple, yet powerful global likelihood model. We efficiently maximize this model by iteratively exploring the space of possible solutions consistent with the projected vessels. We tested our method on four retinal datasets and achieved classification accuracies of 91.0%, 93.5%, 91.7%, and 90.9%, outperforming existing methods. Our results show the effectiveness of our approach, which is capable of analyzing the entire vasculature, including peripheral vessels, in wide field-of-view fundus photographs. This topology-based method is a potentially important tool for diagnosing diseases with retinal vascular manifestation.

Agent-based modeling of porous scaffold degradation and vascularization: Optimal scaffold design based on architecture and degradation dynamics

A multi-layer agent-based model (ABM) of biomaterial scaffold vascularization is extended to consider the effects of scaffold degradation kinetics on blood vessel formation. A degradation model describing the bulk disintegration of porous hydrogels is incorporated into the ABM. The combined degradation-angiogenesis model is used to investigate growing blood vessel networks in the presence of a degradable scaffold structure. Simulation results indicate that higher porosity, larger mean pore size, and rapid degradation allow faster vascularization when not considering the structural support of the scaffold. However, premature loss of structural support results in failure for the material. A strategy using multi-layer scaffold with different degradation rates in each layer was investigated as a way to address this issue. Vascularization was improved with the multi-layered scaffold model compared to the single-layer model. The ABM developed provides insight into the characteristics that influence the selection of optimal geometric parameters and degradation behavior of scaffolds, and enables easy refinement of the model as new knowledge about the underlying biological phenomena becomes available.

STATEMENT OF SIGNIFICANCE

This paper proposes a multi-layer agent-based model (ABM) of biomaterial scaffold vascularization integrated with a structural-kinetic model describing bulk degradation of porous hydrogels to consider the effects of scaffold degradation kinetics on blood vessel formation. This enables the assessment of scaffold characteristics and in particular the disintegration characteristics of the scaffold on angiogenesis. Simulation results indicate that higher porosity, larger mean pore size, and rapid degradation allow faster vascularization when not considering the structural support of the scaffold. However, premature loss of structural support by scaffold disintegration results in failure of the material and disruption of angiogenesis. A strategy using multi-layer scaffold with different degradation rates in each layer was investigated as away to address this issue. Vascularization was improved with the multi-layered scaffold model compared to the single-layer model. The ABM developed provides insight into the characteristics that influence the selection of optimal geometric and degradation characteristics of tissue engineering scaffolds.

Mathematical Model of Oxygen Transport in Tuberculosis Granulomas

Pulmonary granulomas--the hallmark of Mycobacterium tuberculosis (MTB) infection--are dense cellular lesions that often feature regions of hypoxia and necrosis, partially due to limited transport of oxygen. Low oxygen in granulomas can impair the host immune response, while MTB are able to adapt and persist in hypoxic environments. Here, we used a physiologically based mathematical model of oxygen diffusion and consumption to calculate oxygen profiles within the granuloma, assuming Michaelis-Menten kinetics. An approximate analytical solution--using a priori and newly estimated parameters from experimental data in a rabbit model of tuberculosis--was able to predict the size of hypoxic and necrotic regions in agreement with experimental results from the animal model. Such quantitative understanding of transport limitations can inform future tuberculosis therapeutic strategies that may include adjunct host-directed therapies that facilitate oxygen and drug delivery for more effective treatment.

The Vital Role of Blood Flow-Induced Proliferation and Migration in Capillary Network Formation in a Multiscale Model of Angiogenesis

Sprouting angiogenesis and capillary network formation are tissue scale phenomena. There are also sub-scale phenomena involved in angiogenesis including at the cellular and intracellular (molecular) scales. In this work, a multiscale model of angiogenesis spanning intracellular, cellular, and tissue scales is developed in detail. The key events that are considered at the tissue scale are formation of closed flow path (that is called loop in this article) and blood flow initiation in the loop. At the cellular scale, growth, migration, and anastomosis of endothelial cells (ECs) are important. At the intracellular scale, cell phenotype determination as well as alteration due to blood flow is included, having pivotal roles in the model. The main feature of the model is to obtain the physical behavior of a closed loop at the tissue scale, relying on the events at the cellular and intracellular scales, and not by imposing physical behavior upon it. Results show that, when blood flow is considered in the loop, the anastomosed sprouts stabilize and elongate. By contrast, when the loop is modeled without consideration of blood flow, the loop collapses. The results obtained in this work show that proper determination of EC phenotype is the key for its survival.

Assessing the carcinogenic potential of low-dose exposures to chemical mixtures in the environment: focus on the cancer hallmark of tumor angiogenesis

One of the important 'hallmarks' of cancer is angiogenesis, which is the process of formation of new blood vessels that are necessary for tumor expansion, invasion and metastasis. Under normal physiological conditions, angiogenesis is well balanced and controlled by endogenous proangiogenic factors and antiangiogenic factors. However, factors produced by cancer cells, cancer stem cells and other cell types in the tumor stroma can disrupt the balance so that the tumor microenvironment favors tumor angiogenesis. These factors include vascular endothelial growth factor, endothelial tissue factor and other membrane bound receptors that mediate multiple intracellular signaling pathways that contribute to tumor angiogenesis. Though environmental exposures to certain chemicals have been found to initiate and promote tumor development, the role of these exposures (particularly to low doses of multiple substances), is largely unknown in relation to tumor angiogenesis. This review summarizes the evidence of the role of environmental chemical bioactivity and exposure in tumor angiogenesis and carcinogenesis. We identify a number of ubiquitous (prototypical) chemicals with disruptive potential that may warrant further investigation given their selectivity for high-throughput screening assay targets associated with proangiogenic pathways. We also consider the cross-hallmark relationships of a number of important angiogenic pathway targets with other cancer hallmarks and we make recommendations for future research. Understanding of the role of low-dose exposure of chemicals with disruptive potential could help us refine our approach to cancer risk assessment, and may ultimately aid in preventing cancer by reducing or eliminating exposures to synergistic mixtures of chemicals with carcinogenic potential.