Mathematical model of adult stem cell regeneration with cross-talk between genetic and epigenetic regulation

Homeostatic regulation of renewing tissue cell populations via crowding control: stability, robustness and quasi-dedifferentiation

To maintain renewing epithelial tissues in a healthy, homeostatic state, cell divisions and differentiation need to be tightly regulated. Mechanisms of homeostatic regulation often rely on crowding feedback control: cells are able to sense the cell density in their environment, via various molecular and mechanosensing pathways, and respond by adjusting division, differentiation, and cell state transitions appropriately. Here, we determine, via a mathematically rigorous framework, which general conditions for the crowding feedback regulation (i) must be minimally met, and (ii) are sufficient, to allow the maintenance of homeostasis in renewing tissues. We show that those conditions naturally allow for a degree of robustness toward disruption of regulation. Furthermore, intrinsic to this feedback regulation is that stem cell identity is established collectively by the cell population, not by individual cells, which implies the possibility of 'quasi-dedifferentiation', in which cells committed to differentiation may reacquire stem cell properties upon depletion of the stem cell pool. These findings can guide future experimental campaigns to identify specific crowding feedback mechanisms.

Dynamics of cell-type transition mediated by epigenetic modifications

Maintaining tissue homeostasis requires appropriate regulation of stem cell differentiation. The Waddington landscape posits that gene circuits in a cell form a potential landscape of different cell types, wherein cells follow attractors of the probability landscape to develop into distinct cell types. However, how adult stem cells achieve a delicate balance between self-renewal and differentiation remains unclear. We propose that random inheritance of epigenetic states plays a pivotal role in stem cell differentiation and present a hybrid model of stem cell differentiation induced by epigenetic modifications. Our comprehensive model integrates gene regulation networks, epigenetic state inheritance, and cell regeneration, encompassing multi-scale dynamics ranging from transcription regulation to cell population. Through model simulations, we demonstrate that random inheritance of epigenetic states during cell divisions can spontaneously induce cell differentiation, dedifferentiation, and transdifferentiation. Furthermore, we investigate the influences of interfering with epigenetic modifications and introducing additional transcription factors on the probabilities of dedifferentiation and transdifferentiation, revealing the underlying mechanism of cell reprogramming. This in silico model provides valuable insights into the intricate mechanism governing stem cell differentiation and cell reprogramming and offers a promising path to enhance the field of regenerative medicine.

Nanotoxicity of multifunctional stoichiometric cobalt oxide nanoparticles (SCoONPs) with repercussions toward apoptosis, necrosis, and cancer necrosis factor (TNF-α) at nano-biointerfaces

Introduction

Apoptosis, necrosis, and cancer necrosis factor (TNF-a) are all impacted by the nanotoxicity of multifunctional stoichiometric cobalt oxide nanoparticles (SCoONPs) at nano-biointerfaces. The creation of multi-functional nanoparticles has had a considerable impact on the transport of drugs and genes, nanotheranostics (in-vivo imaging, concurrent diagnostics), interventions for external healing, the creation of nano-bio interfaces, and the instigation of desired changes in nanotherapeutics.

Objectives

The quantitative structure-activity relationships, chemical transformations, biological interactions as well as toxicological analyses are considered as main objectives. Discrete dimensions of SCoNPs-cell interaction interfaces, their characteristic physical features (size, shape, shell structure, and surface chemistry), impact on cell proliferation and differentiation are the key factors responsible for nanotoxicity.

Methods

The development of multi-functional nanoparticles has been significant in drug/gene delivery, nanotheranostics (in-vivo imaging, coinciding diagnostics), and external healing interventions, designing a nano-bio interface, as well as inciting desired alterations in nanotherapeutics. Every so often, the cellular uptake of multi-functional cobalt [Co, CoO, Co2(CO)8 and Co3O4] nanoparticles (SCoONPs) influences cellular mechanics and initiates numerous repercussions (oxidative stress, DNA damage, cytogenotoxicity, and chromosomal damage) in pathways, including the generation of dysregulating factors involved in biochemical transformations.

Results

The concerns and influences of multifunctional SCoNPs on different cell mechanisms (mitochondria impermeability, hydrolysis of ATP, the concentration of Ca2+, impaired calcium clearance, defective autophagy, apoptosis, and necrosis), and interlinked properties (adhesion, motility, and internalization dynamics, role in toxicity, surface hydrophilic and hydrophobicity, biokinetics and biomimetic behaviors of biochemical reactions) have also been summarized. SCoONPs have received a lot of interest among the nanocarriers family because of its advantageous qualities such as biodegradability, biocompatibility, nontoxicity, and nonimmunogenicity.

Conclusion

Various applications, such as bio-imaging, cell labeling, gene delivery, enhanced chemical stability, and increased biocompatibility, concerning apoptosis, necrosis, and nano-bio interfaces, along with suitable examples. In this analysis, the multi-functional cobalt [Co, CoO, Co2(CO)8 and Co3O4] nanoparticles (SCoNPs) intricacies (cytogenotoxicity, clastogenicity, and immunomodulatory), nanotoxicity, and associated repercussions have been highlighted and explained.

Modelling cell adaptation using internal variables: Accounting for cell plasticity in continuum mathematical biology

Cellular adaptation is the ability of cells to change in response to different stimuli and environmental conditions. It occurs via phenotypic plasticity, that is, changes in gene expression derived from changes in the physiological environment. This phenomenon is important in many biological processes, in particular in cancer evolution and its treatment. Therefore, it is crucial to understand the mechanisms behind it. Specifically, the emergence of the cancer stem cell phenotype, showing enhanced proliferation and invasion rates, is an essential process in tumour progression. We present a mathematical framework to simulate phenotypic heterogeneity in different cell populations as a result of their interaction with chemical species in their microenvironment, through a continuum model using the well-known concept of internal variables to model cell phenotype. The resulting model, derived from conservation laws, incorporates the relationship between the phenotype and the history of the stimuli to which cells have been subjected, together with the inheritance of that phenotype. To illustrate the model capabilities, it is particularised for glioblastoma adaptation to hypoxia. A parametric analysis is carried out to investigate the impact of each model parameter regulating cellular adaptation, showing that it permits reproducing different trends reported in the scientific literature. The framework can be easily adapted to any particular problem of cell plasticity, with the main limitation of having enough cells to allow working with continuum variables. With appropriate calibration and validation, it could be useful for exploring the underlying processes of cellular adaptation, as well as for proposing favourable/unfavourable conditions or treatments.

Stem Cell Homing in Intrathecal Applications and Inspirations for Improvement Paths

A transplanted stem cell homing is a directed migration from the application site to the targeted tissue. Intrathecal application of stem cells is their direct delivery to cerebrospinal fluid, which defines the homing path from the point of injection to the brain. In the case of neurodegenerative diseases, this application method has the advantage of no blood–brain barrier restriction. However, the homing efficiency still needs improvement and homing mechanisms elucidation. Analysis of current research results on homing mechanisms in the light of intrathecal administration revealed a discrepancy between in vivo and in vitro results and a gap between preclinical and clinical research. Combining the existing research with novel insights from cutting-edge biochips, nano, and other technologies and computational models may bridge this gap faster.

Optimal control model of tumor treatment in the context of cancer stem cell

We consider cancer cytotoxic drugs as an optimal control problem to stabilize a heterogeneous tumor by attacking not the most abundant cancer cells, but those that are crucial in the tumor ecosystem. We propose a mathematical cancer stem cell model that translates the hierarchy and heterogeneity of cancer cell types by including highly structured tumorigenic cancer stem cells that yield low differentiated cancer cells. With respect to the optimal control problem, under a certain admissibility hypothesis, the optimal controls of our problem are bang-bang controls. These control treatments can retain the entire tumor in the neighborhood of an equilibrium. We simulate the bang-bang control numerically and demonstrate that the optimal drug scheduling should be administered continuously over long periods with short rest periods. Moreover, our simulations indicate that combining multidrug therapies and monotherapies is more efficient for heterogeneous tumors than using each one separately.

A 3D Mathematical Model of Coupled Stem Cell-Nutrient Dynamics in Myocardial Regeneration Therapy

Stem cell therapy is a promising treatment for the regeneration of myocardial tissue injured by an ischemic event. Mathematical modeling of myocardial regeneration via stem cell therapy is a challenging task, since the mechanisms underlying the processes involved in the treatment are not yet fully understood. Many aspects must be accounted for, such as the spread of stem cells and nutrients, chemoattraction, cell proliferation, stages of cell maturation, differentiation, angiogenesis, stochastic effects, just to name a few. In this paper we propose a 3D mathematical model with a free boundary that aims to provide a qualitative description of some main aspects of the stem cell regenerative therapy in a simplified scenario. The paper mainly focuses on the description of the shrinking of the necrotic core during treatment. The stem cell and nutrients dynamics are described through coupled reaction-diffusion problems. Proliferation, chemoattraction, tissue regeneration and nutrient consumption are included in the model.

Decidualization Potency and Epigenetic Changes in Human Endometrial Origin Stem Cells During Propagation

Human endometrium derived mesenchymal stem cells (hEndSCs) offer a great promise for regenerative medicine and reproductive system disorders treatment methods based on cell therapy due to their broad differentiation potential and highly efficient proliferation. In our study, we investigated the characteristics of hEndSCs that were isolated from two sources: endometrium and menstrual blood, which both contain endometrial origin stem cells. Changes in gene and protein expression levels during long-term cultivation and decidualization potential were examined in endometrial stem cells (EndSCs) and menstrual blood stem cells (MenSCs). The decidualization process was induced on early and late passages of hEndSCs using dibutyryl cyclic-AMP (db-cAMP) and medroxyprogesterone acetate (MPA) agents. We demonstrated that after long-term cultivation of hEndSCs the expression of typical mesenchymal stromal cell surface markers such as CD44, CD73, CD90, CD105 and perivascular marker CD146 remains at a similar level throughout long-term cultivation. Additionally, hematopoietic and endothelial markers CD34, CD45 were also tested, they were negative in all cases. Analyzed stem cells gene markers, such as OCT4, SOX2, NANOG, KLF4, showed similar expression in all passages of hEndSCs. RT-qPCR results demonstrated that the expression of cell cycle control associated genes - CDK2, CCNA2, CCNE2, p21, p53 and Rb, among all groups was very similar. Expression of genes associated with senescence (ATM, JUND, TOP2A, MYC) was maintained at a similar level throughout passaging. In addition, Western blot analysis was used to assess changes in proteins’ levels associated to epigenetics (EZH2, SUZ12, H3K27me3) and cell cycle control (cyclinE1, p53) during long-term cultivation. The levels of proteins associated with epigenetic changes were fluctuated slightly depending on the patient. Also, we demonstrated that in all induced hEndSCs the expression of decidualization markers Prolactin (PRL), IGFBP1 and WNT4 was upregulated. In conclusion, we demonstrated successful decidualization of stem cells derived from two reproductive system resources: endometrium and menstrual blood by using db-cAMP and MPA regardless of the length of the stem cell passaging. According these findings, we suppose that endometrium derived stem cells and menstrual blood derived stem cells could have a potency not only for endometrium tissue regeneration, but could also become a successful therapy for reproductive system disorders, including infertility or recurrent pregnancy loss.

Integrative Analysis of Biomarkers Through Machine Learning Identifies Stemness Features in Colorectal Cancer

Background: Cancer stem cells (CSCs), which are characterized by self-renewal and plasticity, are highly correlated with tumor metastasis and drug resistance. To fully understand the role of CSCs in colorectal cancer (CRC), we evaluated the stemness traits and prognostic value of stemness-related genes in CRC.

Methods: In this study, the data from 616 CRC patients from The Cancer Genome Atlas (TCGA) were assessed and subtyped based on the mRNA expression-based stemness index (mRNAsi). The correlations of cancer stemness with the immune microenvironment, tumor mutational burden (TMB), and N6-methyladenosine (m6A) RNA methylation regulators were analyzed. Weighted gene co-expression network analysis (WGCNA) was performed to identify the crucial stemness-related genes and modules. Furthermore, a prognostic expression signature was constructed using the Lasso-penalized Cox regression analysis. The signature was validated via multiplex immunofluorescence staining of tissue samples in an independent cohort of 48 CRC patients.

Results: This study suggests that high-mRNAsi scores are associated with poor overall survival in stage IV CRC patients. Moreover, the levels of TMB and m6A RNA methylation regulators were positively correlated with mRNAsi scores, and low-mRNAsi scores were characterized by increased immune activity in CRC. The analysis identified 34 key genes as candidate prognosis biomarkers. Finally, a three-gene prognostic signature (PARPBP, KNSTRN, and KIF2C) was explored together with specific clinical features to construct a nomogram, which was successfully validated in an external cohort.

Conclusion: There is a unique correlation between CSCs and the prognosis of CRC patients, and the novel biomarkers related to cell stemness could accurately predict the clinical outcomes of these patients.

Cancer Niches and Their Kikuchi Free Energy

Biological forms depend on a progressive specialization of pluripotent stem cells. The differentiation of these cells in their spatial and functional environment defines the organism itself; however, cellular mutations may disrupt the mutual balance between a cell and its niche, where cell proliferation and specialization are released from their autopoietic homeostasis. This induces the construction of cancer niches and maintains their survival. In this paper, we characterise cancer niche construction as a direct consequence of interactions between clusters of cancer and healthy cells. Explicitly, we evaluate these higher-order interactions between niches of cancer and healthy cells using Kikuchi approximations to the free energy. Kikuchi's free energy is measured in terms of changes to the sum of energies of baseline clusters of cells (or nodes) minus the energies of overcounted cluster intersections (and interactions of interactions, etc.). We posit that these changes in energy node clusters correspond to a long-term reduction in the complexity of the system conducive to cancer niche survival. We validate this formulation through numerical simulations of apoptosis, local cancer growth, and metastasis, and highlight its implications for a computational understanding of the etiopathology of cancer.

Stochastic intracellular regulation can remove oscillations in a model of tissue growth

The work is devoted to the analysis of cell population dynamics where cells make a choice between differentiation and apoptosis. This choice is based on the values of intracellular proteins whose concentrations are described by a system of ordinary differential equations with bistable dynamics. Intracellular regulation and cell fate are controlled by the extracellular regulation through the number of differentiated cells. It is shown that the total cell number necessarily oscillates if the initial condition in the intracellular regulation is fixed. These oscillations can be suppressed if the initial condition is a random variable with a sufficiently large variation. Thus, the result of the work suggests a possible answer to the question about the role of stochasticity in the intracellular regulation.

A General Theoretical Framework to Study the Influence of Electrical Fields on Mesenchymal Stem Cells

Mesenchymal stem cell dynamics involve cell proliferation and cell differentiation into cells of distinct functional type, such as osteoblasts, adipocytes, or chondrocytes. Electrically active implants influence these dynamics for the regeneration of the cells in damaged tissues. How applied electric field influences processes of individual stem cells is a problem mostly unaddressed. The mathematical approaches to study stem cell dynamics have focused on the stem cell population as a whole, without resolving individual cells and intracellular processes. In this paper, we present a theoretical framework to describe the dynamics of a population of stem cells, taking into account the processes of the individual cells. We study the influence of the applied electric field on the cellular processes. We test our mean-field theory with the experiments from the literature, involving in vitro electrical stimulation of stem cells. We show that a simple model can quantitatively describe the experimentally observed time-course behavior of the total number of cells and the total alkaline phosphate activity in a population of mesenchymal stem cells. Our results show that the stem cell differentiation rate is dependent on the applied electrical field, confirming published experimental findings. Moreover, our analysis supports the cell density-dependent proliferation rate. Since the experimental results are averaged over many cells, our theoretical framework presents a robust and sensitive method for determining the effect of applied electric fields at the scale of the individual cell. These results indicate that the electric field stimulation may be effective in promoting bone regeneration by accelerating osteogenic differentiation.

Modelling stem cell ageing: a multi-compartment continuum approach

Stem cells are important to generate all specialized tissues at an early life stage, and in some systems, they also have repair functions to replenish the adult tissues. Repeated cell divisions lead to the accumulation of molecular damage in stem cells, which are commonly recognized as drivers of ageing. In this paper, a novel model is proposed to integrate stem cell proliferation and differentiation with damage accumulation in the stem cell ageing process. A system of two structured PDEs is used to model the population densities of stem cells (including all multiple progenitors) and terminally differentiated (TD) cells. In this system, cell cycle progression and damage accumulation are modelled by continuous dynamics, and damage segregation between daughter cells is considered at each division. Analysis and numerical simulations are conducted to study the steady-state populations and stem cell damage distributions under different damage segregation strategies. Our simulations suggest that equal distribution of the damaging substance between stem cells in a symmetric renewal and less damage retention in stem cells in the asymmetric division are favourable strategies, which reduce the death rate of the stem cells and increase the TD cell populations. Moreover, asymmetric damage segregation in stem cells leads to less concentrated damage distribution in the stem cell population, which may be more robust to the stochastic changes in the damage. The feedback regulation from stem cells can reduce oscillations and population overshoot in the process, and improve the fitness of stem cells by increasing the percentage of cells with less damage in the stem cell population.

Bone regeneration strategies: Engineered scaffolds, bioactive molecules and stem cells current stage and future perspectives

Bone fractures are the most common traumatic injuries in humans. The repair of bone fractures is a regenerative process that recapitulates many of the biological events of embryonic skeletal development. Most of the time it leads to successful healing and the recovery of the damaged bone. Unfortunately, about 5-10% of fractures will lead to delayed healing or non-union, more so in the case of co-morbidities such as diabetes. In this article, we review the different strategies to heal bone defects using synthetic bone graft substitutes, biologically active substances and stem cells. The majority of currently available reviews focus on strategies that are still at the early stages of development and use mostly in vitro experiments with cell lines or stem cells. Here, we focus on what is already implemented in the clinics, what is currently in clinical trials, and what has been tested in animal models. Treatment approaches can be classified in three major categories: i) synthetic bone graft substitutes (BGS) whose architecture and surface can be optimized; ii) BGS combined with bioactive molecules such as growth factors, peptides or small molecules targeting bone precursor cells, bone formation and metabolism; iii) cell-based strategies with progenitor cells combined or not with active molecules that can be injected or seeded on BGS for improved delivery. We review the major types of adult stromal cells (bone marrow, adipose and periosteum derived) that have been used and compare their properties. Finally, we discuss the remaining challenges that need to be addressed to significantly improve the healing of bone defects.

Single cell analysis reveals a biophysical aspect of collective cell-state transition in embryonic stem cell differentiation

In the stem cell research field, the molecular regulatory network used to define cellular states has been extensively studied, however, the general driving force guiding the collective state dynamics remains to be identified from biophysical aspects. Here we monitored the time-development of the cell-state transition at the single-cell and colony levels, simultaneously, during the early differentiation process in mouse embryonic stem cells. Our quantitative analyses revealed that cellular heterogeneity was a result of spontaneous fluctuation of cellular state and cell-cell cooperativity. We considered that the cell state is like a ball fluctuating on a potential landscape, and found that the cooperativity affects the fluctuation. Importantly, the cooperativity temporarily decreased and increased in the intermediate state of cell differentiation, leading to cell-state transition in unison. This process can be explained using the mathematical equation of flashing-ratchet behaviour, which suggests that a general mechanism is driving the collective decision-making of stem cells.

A mathematical model of stem cell regeneration with epigenetic state transitions

In this paper, we study a mathematical model of stem cell regeneration with epigenetic state transitions. In the model, the heterogeneity of stem cells is considered through the epigenetic state of each cell, and each epigenetic state defines a subpopulation of stem cells. The dynamics of the subpopulations are modeled by a set of ordinary differential equations in which epigenetic state transition in cell division is given by the transition probability. We present analysis for the existence and linear stability of the equilibrium state. As an example, we apply the model to study the dynamics of state transition in breast cancer stem cells.

Exploring intermediate cell states through the lens of single cells

As our catalog of cell states expands, appropriate characterization of these states and the transitions between them is crucial. Here we discuss the roles of intermediate cell states (ICSs) in this growing collection. We begin with definitions and discuss evidence for the existence of ICSs and their relevance in various tissues. We then provide a list of possible functions for ICSs with examples. Finally, we describe means by which ICSs and their functional roles can be identified from single-cell data or predicted from models.

Process System Engineering Methodologies Applied to Tissue Development and Regenerative Medicine

Tissue engineering and the manufacturing of regenerative medicine products demand strict control over the production process and product quality monitoring. In this chapter, the application of process systems engineering (PSE) approaches in the production of cell-based products has been discussed. Mechanistic, empirical, continuum and discrete models are compared and their use in describing cellular phenomena is reviewed. In addition, model-based optimization strategies employed in the field of tissue engineering and regenerative medicine are discussed. An introduction to process control theory is given and the main applications of classical and advanced methods in cellular production processes are described. Finally, new nondestructive and noninvasive monitoring techniques have been reviewed, focusing on large-scale manufacturing systems for cell-based constructs and therapeutic products. The application of the PSE methodologies presented here offers a promising alternative to overcome the main challenges in manufacturing engineered tissue and regeneration products.

Multiscale Modeling of Inflammation-Induced Tumorigenesis Reveals Competing Oncogenic and Oncoprotective Roles for Inflammation

Chronic inflammation is a serious risk factor for cancer; however, the routes from inflammation to cancer are poorly understood. On the basis of the processes implicated by frequently mutated genes associated with inflammation and cancer in three organs (stomach, colon, and liver) extracted from the Gene Expression Omnibus, The Cancer Genome Atlas, and Gene Ontology databases, we present a multiscale model of the long-term evolutionary dynamics leading from inflammation to tumorigenesis. The model incorporates cross-talk among interactions on several scales, including responses to DNA damage, gene mutation, cell-cycle behavior, population dynamics, inflammation, and metabolism-immune balance. Model simulations revealed two stages of inflammation-induced tumorigenesis: a precancerous state and tumorigenesis. The precancerous state was mainly caused by mutations in the cell proliferation pathway; the transition from the precancerous to tumorigenic states was induced by mutations in pathways associated with apoptosis, differentiation, and metabolism-immune balance. We identified opposing effects of inflammation on tumorigenesis. Mild inflammation removed cells with DNA damage through DNA damage-induced cell death, whereas severe inflammation accelerated accumulation of mutations and hence promoted tumorigenesis. These results provide insight into the evolutionary dynamics of inflammation-induced tumorigenesis and highlight the combinatorial effects of inflammation and metabolism-immune balance. This approach establishes methods for quantifying cancer risk, for the discovery of driver pathways in inflammation-induced tumorigenesis, and has direct relevance for early detection and prevention and development of new treatment regimes. Cancer Res; 77(22); 6429-41. ©2017 AACR.

Synthesizing developmental trajectories

Dynamical processes in biology are studied using an ever-increasing number of techniques, each of which brings out unique features of the system. One of the current challenges is to develop systematic approaches for fusing heterogeneous datasets into an integrated view of multivariable dynamics. We demonstrate that heterogeneous data fusion can be successfully implemented within a semi-supervised learning framework that exploits the intrinsic geometry of high-dimensional datasets. We illustrate our approach using a dataset from studies of pattern formation in Drosophila. The result is a continuous trajectory that reveals the joint dynamics of gene expression, subcellular protein localization, protein phosphorylation, and tissue morphogenesis. Our approach can be readily adapted to other imaging modalities and forms a starting point for further steps of data analytics and modeling of biological dynamics.

A wide range of problems in biology require analysis of multivariable dynamics in space and time. As a rule, the multiscale nature and complexity of real systems precludes simultaneous monitoring of all the relevant variables, and multivariable dynamics must be synthesized from partial views provided by different experimental techniques. We present a formal framework for accomplishing this task in the context of imaging studies of pattern formation in developing tissues.

Reprogramming to developmental plasticity in cancer stem cells

During development and throughout adult life, sub-populations of cells exist that exhibit phenotypic plasticity - the ability to differentiate into multiple lineages. This behaviour is important in embryogenesis, is exhibited in a more limited context by adult stem cells, and can be re-activated in cancer cells to drive important processes underlying tumour progression. A well-studied mechanism of phenotypic plasticity is the epithelial-to-mesenchymal transition (EMT), a process which has been observed in both normal and cancerous cells. The epigenetic and metabolic modifications necessary to facilitate phenotypic plasticity are first seen in development and can be re-activated both in normal regeneration and in cancer. In cancer, the re-activation of these mechanisms enables tumour cells to acquire a cancer stem cell (CSC) phenotype with enhanced ability to survive in hostile environments, resist therapeutic interventions, and undergo metastasis. However, recent research has suggested that plasticity may also expose weaknesses in cancer cells that could be exploited for future therapeutic development. More research is needed to identify developmental mechanisms that are active in cancer, so that these may be targeted to reduce tumour growth and metastasis and overcome therapeutic resistance.

Decoding early myelopoiesis from dynamics of core endogenous network

A decade ago mainstream molecular biologists regarded it impossible or biologically ill-motivated to understand the dynamics of complex biological phenomena, such as cancer genesis and progression, from a network perspective. Indeed, there are numerical difficulties even for those who were determined to explore along this direction. Undeterred, seven years ago a group of Chinese scientists started a program aiming to obtain quantitative connections between tumors and network dynamics. Many interesting results have been obtained. In this paper we wish to test such idea from a different angle: the connection between a normal biological process and the network dynamics. We have taken early myelopoiesis as our biological model. A standard roadmap for the cell-fate diversification during hematopoiesis has already been well established experimentally, yet little was known for its underpinning dynamical mechanisms. Compounding this difficulty there were additional experimental challenges, such as the seemingly conflicting hematopoietic roadmaps and the cell-fate inter-conversion events. With early myeloid cell-fate determination in mind, we constructed a core molecular endogenous network from well-documented gene regulation and signal transduction knowledge. Turning the network into a set of dynamical equations, we found computationally several structurally robust states. Those states nicely correspond to known cell phenotypes. We also found the states connecting those stable states. They reveal the developmental routes-how one stable state would most likely turn into another stable state. Such interconnected network among stable states enabled a natural organization of cell-fates into a multi-stable state landscape. Accordingly, both the myeloid cell phenotypes and the standard roadmap were explained mechanistically in a straightforward manner. Furthermore, recent challenging observations were also explained naturally. Moreover, the landscape visually enables a prediction of a pool of additional cell states and developmental routes, including the non-sequential and cross-branch transitions, which are testable by future experiments. In summary, the endogenous network dynamics provide an integrated quantitative framework to understand the heterogeneity and lineage commitment in myeloid progenitors.

Identifying niche-mediated regulatory factors of stem cell phenotypic state: a systems biology approach

Understanding how the cellular niche controls the stem cell phenotype is often hampered due to the complexity of variegated niche composition, its dynamics, and nonlinear stem cell–niche interactions. Here, we propose a systems biology view that considers stem cell–niche interactions as a many‐body problem amenable to simplification by the concept of mean field approximation. This enables approximation of the niche effect on stem cells as a constant field that induces sustained activation/inhibition of specific stem cell signaling pathways in all stem cells within heterogeneous populations exhibiting the same phenotype (niche determinants). This view offers a new basis for the development of single cell‐based computational approaches for identifying niche determinants, which has potential applications in regenerative medicine and tissue engineering.

A systems biology approach to identify niche determinants of cellular phenotypes

Recent reports indicate a dominant role for cellular microenvironment or niche for stably maintaining cellular phenotypic states. Identification of key niche mediated signaling that maintains stem cells in specific phenotypic states remains a challenge, mainly due to the complex and dynamic nature of stem cell-niche interactions. In order to overcome this, we consider that stem cells maintain their phenotypic state by experiencing a constant effect created by the niche by integrating its signals via signaling pathways. Such a constant niche effect should induce sustained activation/inhibition of specific stem cell signaling pathways that controls the gene regulatory program defining the cellular phenotypic state. Based on this view, we propose a computational approach to identify the most likely receptor mediated signaling responsible for transmitting niche signals to the transcriptional regulatory network that maintain cell-specific gene expression patterns, termed as niche determinants. We demonstrate the utility of our method in different stem cell systems by identifying several known and novel niche determinants. Given the key role of niche in several degenerative diseases, identification of niche determinants can aid in developing strategies for potential applications in regenerative medicine.

Controlling Stochasticity in Epithelial-Mesenchymal Transition Through Multiple Intermediate Cellular States

Epithelial-mesenchymal transition (EMT) is an instance of cellular plasticity that plays critical roles in development, regeneration and cancer progression. Recent studies indicate that the transition between epithelial and mesenchymal states is a multi-step and reversible process in which several intermediate phenotypes might coexist. These intermediate states correspond to various forms of stem-like cells in the EMT system, but the function of the multi-step transition or the multiple stem cell phenotypes is unclear. Here, we use mathematical models to show that multiple intermediate phenotypes in the EMT system help to attenuate the overall fluctuations of the cell population in terms of phenotypic compositions, thereby stabilizing a heterogeneous cell population in the EMT spectrum. We found that the ability of the system to attenuate noise on the intermediate states depends on the number of intermediate states, indicating the stem-cell population is more stable when it has more sub-states. Our study reveals a novel advantage of multiple intermediate EMT phenotypes in terms of systems design, and it sheds light on the general design principle of heterogeneous stem cell population.

Near Equilibrium Calculus of Stem Cells in Application to the Airway Epithelium Lineage

Homeostatic maintenance of tissues is orchestrated by well tuned networks of cellular signaling. Such networks regulate, in a stochastic manner, fates of all cells within the respective lineages. Processes such as symmetric and asymmetric divisions, differentiation, de-differentiation, and death have to be controlled in a dynamic fashion, such that the cell population is maintained at a stable equilibrium, has a sufficiently low level of stochastic variation, and is capable of responding efficiently to external damage. Cellular lineages in real tissues may consist of a number of different cell types, connected by hierarchical relationships, albeit not necessarily linear, and engaged in a number of different processes. Here we develop a general mathematical methodology for near equilibrium studies of arbitrarily complex hierarchical cell populations, under regulation by a control network. This methodology allows us to (1) determine stability properties of the network, (2) calculate the stochastic variance, and (3) predict how different control mechanisms affect stability and robustness of the system. We demonstrate the versatility of this tool by using the example of the airway epithelium lineage. Recent research shows that airway epithelium stem cells divide mostly asymmetrically, while the so-called secretory cells divide predominantly symmetrically. It further provides quantitative data on the recovery dynamics of the airway epithelium, which can include secretory cell de-differentiation. Using our new methodology, we demonstrate that while a number of regulatory networks can be compatible with the observed recovery behavior, the observed division patterns of cells are the most optimal from the viewpoint of homeostatic lineage stability and minimizing the variation of the cell population size. This not only explains the observed yet poorly understood features of airway tissue architecture, but also helps to deduce the information on the still largely hypothetical regulatory mechanisms governing tissue turnover, and lends insight into how different control loops influence the stability and variance properties of cell populations.

Tissue stability is the basic property of healthy organs, and yet the mechanisms governing the stable, long-term maintenance of cell numbers in tissues are poorly understood. While more and more signaling pathways are being discovered, for the most part it remains unknown how they are being put together by different cell types into complex, nonlinear, hierarchical control networks that, on the one hand, reliably maintain constant cell numbers, and on the other hand, quickly adjust to oversee the robust response to tissue damage. Theoretical approaches can fill the gap by being able to reconstruct the underlying control network, based on the observations about the aspects of cellular dynamics. We argue that while many hypothetical networks may be capable of basic cell lineage maintenance, some are much more efficient from the viewpoint of variance minimization. Thus, we developed a new methodology that can test various control networks for stability, variance, and robustness. In the example of the airway epithelium that we highlight, it turns out that the evolutionary selected, actual architecture coincides with the mathematically optimal solution that minimizes the fluctuations of cell numbers at homeostasis.

Mathematical Modeling Reveals That Changes to Local Cell Density Dynamically Modulate Baseline Variations in Cell Growth and Drug Response

Cell-to-cell variations contribute to drug resistance with consequent therapy failure in cancer. Experimental techniques have been developed to monitor tumor heterogeneity, but estimates of cell-to-cell variation typically fail to account for the expected spatiotemporal variations during the cell growth process. To fully capture the extent of such dynamic variations, we developed a mechanistic mathematical model supported by in vitro experiments with an ovarian cancer cell line. We introduce the notion of dynamic baseline cell-to-cell variation, showing how the emerging spatiotemporal heterogeneity of one cell population can be attributed to differences in local cell density and cell cycle. Manipulation of the geometric arrangement and spatial density of cancer cells revealed that given a fixed global cell density, significant differences in growth, proliferation, and paclitaxel-induced apoptosis rates were observed based solely on cell movement and local conditions. We conclude that any statistical estimate of changes in the level of heterogeneity should be integrated with the dynamics and spatial effects of the baseline system. This approach incorporates experimental and theoretical methods to systematically analyze biologic phenomena and merits consideration as an underlying reference model for cell biology studies that investigate dynamic processes affecting cancer cell behavior. Cancer Res; 76(10); 2882-90. ©2016 AACR.

Feedback control in planarian stem cell systems

Background

In planarian flatworms, the mechanisms underlying the activity of collectively pluripotent adult stem cells (neoblasts) and their descendants can now be studied from the level of the individual gene to the entire animal. Flatworms maintain startling developmental plasticity and regenerative capacity in response to variable nutrient conditions or injury. We develop a model for cell dynamics in such animals, assuming that fully differentiated cells exert feedback control on neoblast activity.

Results

Our model predicts a number of whole organism level and general cell biological and behaviours, some of which have been empirically observed or inferred in planarians and others that have not. As previously observed empirically we find: 1) a curvilinear relationship between external food and planarian steady state size; 2) the fraction of neoblasts in the steady state is constant regardless of planarian size; 3) a burst of controlled apoptosis during regeneration after amputation as the number of differentiated cells are adjusted towards their homeostatic/steady state level. In addition our model describes the following properties that can inform and be tested by future experiments: 4) the strength of feedback control from differentiated cells to neoblasts (i.e. the activity of the signalling system) and from neoblasts on themselves in relation to absolute number depends upon the level of food in the environment; 5) planarians adjust size when food level reduces initially through increased apoptosis and then through a reduction in neoblast self-renewal activity; 6) following wounding or excision of differentiated cells, different time scales characterize both recovery of size and the two feedback functions; 7) the temporal pattern of feedback controls differs noticeably during recovery from a removal or neoblasts or a removal of differentiated cells; 8) the signaling strength for apoptosis of differentiated cells depends upon both the absolute and relative deviations of the number of differentiated cells from their homeostatic level; and 9) planaria prioritize resource use for cell divisions.

Conclusions

We offer the first analytical framework for organizing experiments on planarian flatworm stem cell dynamics in a form that allows models to be compared with quantitative cell data based on underlying molecular mechanisms and thus facilitate the interplay between empirical studies and modeling. This framework is the foundation for studying cell migration during wound repair, the determination of homeostatic levels of differentiated cells by natural selection, and stochastic effects.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0261-8) contains supplementary material, which is available to authorized users.

Entropy, Ergodicity, and Stem Cell Multipotency

Populations of mammalian stem cells commonly exhibit considerable cell-cell variability. However, the functional role of this diversity is unclear. Here, we analyze expression fluctuations of the stem cell surface marker Sca1 in mouse hematopoietic progenitor cells using a simple stochastic model and find that the observed dynamics naturally lie close to a critical state, thereby producing a diverse population that is able to respond rapidly to environmental changes. We propose an information-theoretic interpretation of these results that views cellular multipotency as an instance of maximum entropy statistical inference.

Cellular population dynamics control the robustness of the stem cell niche

Within populations of cells, fate decisions are controlled by an indeterminate combination of cell-intrinsic and cell-extrinsic factors. In the case of stem cells, the stem cell niche is believed to maintain ‘stemness’ through communication and interactions between the stem cells and one or more other cell-types that contribute to the niche conditions. To investigate the robustness of cell fate decisions in the stem cell hierarchy and the role that the niche plays, we introduce simple mathematical models of stem and progenitor cells, their progeny and their interplay in the niche. These models capture the fundamental processes of proliferation and differentiation and allow us to consider alternative possibilities regarding how niche-mediated signalling feedback regulates the niche dynamics. Generalised stability analysis of these stem cell niche systems enables us to describe the stability properties of each model. We find that although the number of feasible states depends on the model, their probabilities of stability in general do not: stem cell–niche models are stable across a wide range of parameters. We demonstrate that niche-mediated feedback increases the number of stable steady states, and show how distinct cell states have distinct branching characteristics. The ecological feedback and interactions mediated by the stem cell niche thus lend (surprisingly) high levels of robustness to the stem and progenitor cell population dynamics. Furthermore, cell–cell interactions are sufficient for populations of stem cells and their progeny to achieve stability and maintain homeostasis. We show that the robustness of the niche – and hence of the stem cell pool in the niche – depends only weakly, if at all, on the complexity of the niche make-up: simple as well as complicated niche systems are capable of supporting robust and stable stem cell dynamics.

Summary: Stem cell niche dynamics are very robust to external and physiological perturbations because proliferation and differentiation are naturally balanced and controlled by the reliance on a shared niche environment.

Geometry of the Gene Expression Space of Individual Cells

There is a revolution in the ability to analyze gene expression of single cells in a tissue. To understand this data we must comprehend how cells are distributed in a high-dimensional gene expression space. One open question is whether cell types form discrete clusters or whether gene expression forms a continuum of states. If such a continuum exists, what is its geometry? Recent theory on evolutionary trade-offs suggests that cells that need to perform multiple tasks are arranged in a polygon or polyhedron (line, triangle, tetrahedron and so on, generally called polytopes) in gene expression space, whose vertices are the expression profiles optimal for each task. Here, we analyze single-cell data from human and mouse tissues profiled using a variety of single-cell technologies. We fit the data to shapes with different numbers of vertices, compute their statistical significance, and infer their tasks. We find cases in which single cells fill out a continuum of expression states within a polyhedron. This occurs in intestinal progenitor cells, which fill out a tetrahedron in gene expression space. The four vertices of this tetrahedron are each enriched with genes for a specific task related to stemness and early differentiation. A polyhedral continuum of states is also found in spleen dendritic cells, known to perform multiple immune tasks: cells fill out a tetrahedron whose vertices correspond to key tasks related to maturation, pathogen sensing and communication with lymphocytes. A mixture of continuum-like distributions and discrete clusters is found in other cell types, including bone marrow and differentiated intestinal crypt cells. This approach can be used to understand the geometry and biological tasks of a wide range of single-cell datasets. The present results suggest that the concept of cell type may be expanded. In addition to discreet clusters in gene-expression space, we suggest a new possibility: a continuum of states within a polyhedron, in which the vertices represent specialists at key tasks.

In the past, biological experiments usually pooled together millions of cells, masking the differences between individual cells. Current technology takes a big step forward by measuring gene expression from individual cells. Interpreting this data is challenging because we need to understand how cells are arranged in a high dimensional gene expression space. Here we test recent theory that suggests that cells facing multiple tasks should be arranged in simple low dimensional polygons or polyhedra (generally called polytopes). The vertices of the polytopes are gene expression profiles optimal for each of the tasks. We find evidence for such simplicity in a variety of tissues—spleen, bone marrow, intestine—analyzed by different single-cell technologies. We find that cells are distributed inside polytopes, such as tetrahedrons or four-dimensional simplexes, with cells closest to each vertex responsible for a different key task. For example, intestinal progenitor cells that give rise to the other cell types show a continuous distribution in a tetrahedron whose vertices correspond to several key sub-tasks. Immune dendritic cells likewise are continuously distributed between key immune tasks. This approach of testing whether data falls in polytopes may be useful for interpreting a variety of single-cell datasets in terms of biological tasks.

Emergence of drug tolerance in cancer cell populations: an evolutionary outcome of selection, nongenetic instability, and stress-induced adaptation

In recent experiments on isogenetic cancer cell lines, it was observed that exposure to high doses of anticancer drugs can induce the emergence of a subpopulation of weakly proliferative and drug-tolerant cells, which display markers associated with stem cell-like cancer cells. After a period of time, some of the surviving cells were observed to change their phenotype to resume normal proliferation and eventually repopulate the sample. Furthermore, the drug-tolerant cells could be drug resensitized following drug washout. Here, we propose a theoretical mechanism for the transient emergence of such drug tolerance. In this framework, we formulate an individual-based model and an integro-differential equation model of reversible phenotypic evolution in a cell population exposed to cytotoxic drugs. The outcomes of both models suggest that nongenetic instability, stress-induced adaptation, selection, and the interplay between these mechanisms can push an actively proliferating cell population to transition into a weakly proliferative and drug-tolerant state. Hence, the cell population experiences much less stress in the presence of the drugs and, in the long run, reacquires a proliferative phenotype, due to phenotypic fluctuations and selection pressure. These mechanisms can also reverse epigenetic drug tolerance following drug washout. Our study highlights how the transient appearance of the weakly proliferative and drug-tolerant cells is related to the use of high-dose therapy. Furthermore, we show how stem-like characteristics can act to stabilize the transient, weakly proliferative, and drug-tolerant subpopulation for a longer time window. Finally, using our models as in silico laboratories, we propose new testable hypotheses that could help uncover general principles underlying the emergence of cancer drug tolerance.

Understanding, treating and avoiding hematological disease: better medicine through mathematics?

This paper traces the experimental, clinical and mathematical modeling efforts to understand a periodic hematological disease-cyclical neutropenia. It is primarily a highly personal account by two scientists from quite different backgrounds of their interactions over almost 40 years and their attempts to understand this intriguing disease. It's also a story of their efforts to offer effective treatments for the patients who suffer from cyclic neutropenia and other conditions causing neutropenia and infections.

The diversity of small non-coding RNAs in the diatom Phaeodactylum tricornutum

Background

Marine diatoms constitute a major component of eukaryotic phytoplankton and stand at the crossroads of several evolutionary lineages. These microalgae possess peculiar genomic features and novel combinations of genes acquired from bacterial, animal and plant ancestors. Furthermore, they display both DNA methylation and gene silencing activities. Yet, the biogenesis and regulatory function of small RNAs (sRNAs) remain ill defined in diatoms.

Results

Here we report the first comprehensive characterization of the sRNA landscape and its correlation with genomic and epigenomic information in Phaeodactylum tricornutum. The majority of sRNAs is 25 to 30 nt-long and maps to repetitive and silenced Transposable Elements marked by DNA methylation. A subset of this population also targets DNA methylated protein-coding genes, suggesting that gene body methylation might be sRNA-driven in diatoms. Remarkably, 25-30 nt sRNAs display a well-defined and unprecedented 180 nt-long periodic distribution at several highly methylated regions that awaits characterization. While canonical miRNAs are not detectable, other 21-25 nt sRNAs of unknown origin are highly expressed. Besides, non-coding RNAs with well-described function, namely tRNAs and U2 snRNA, constitute a major source of 21-25 nt sRNAs and likely play important roles under stressful environmental conditions.

Conclusions

P. tricornutum has evolved diversified sRNA pathways, likely implicated in the regulation of largely still uncharacterized genetic and epigenetic processes. These results uncover an unexpected complexity of diatom sRNA population and previously unappreciated features, providing new insights into the diversification of sRNA-based processes in eukaryotes.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2164-15-698) contains supplementary material, which is available to authorized users.