Cell-cell interaction and diversity of emergent behaviours

Cell-Cell Interactions: How Coupled Boolean Networks Tend to Criticality

Biological cells are usually operating in conditions characterized by intercellular signaling and interaction, which are supposed to strongly influence individual cell dynamics. In this work, we study the dynamics of interacting random Boolean networks, focusing on attractor properties and response to perturbations. We observe that the properties of isolated critical Boolean networks are substantially maintained also in interaction settings, while interactions bias the dynamics of chaotic and ordered networks toward that of critical cells. The increase in attractors observed in multicellular scenarios, compared to single cells, allows us to hypothesize that biological processes, such as ontogeny and cell differentiation, leverage interactions to modulate individual and collective cell responses.

Cellular signaling pathways as plastic, proto-cognitive systems: Implications for biomedicine

Many aspects of health and disease are modeled using the abstraction of a "pathway"-a set of protein or other subcellular activities with specified functional linkages between them. This metaphor is a paradigmatic case of a deterministic, mechanistic framework that focuses biomedical intervention strategies on altering the members of this network or the up-/down-regulation links between them-rewiring the molecular hardware. However, protein pathways and transcriptional networks exhibit interesting and unexpected capabilities such as trainability (memory) and information processing in a context-sensitive manner. Specifically, they may be amenable to manipulation via their history of stimuli (equivalent to experiences in behavioral science). If true, this would enable a new class of biomedical interventions that target aspects of the dynamic physiological "software" implemented by pathways and gene-regulatory networks. Here, we briefly review clinical and laboratory data that show how high-level cognitive inputs and mechanistic pathway modulation interact to determine outcomes in vivo. Further, we propose an expanded view of pathways from the perspective of basal cognition and argue that a broader understanding of pathways and how they process contextual information across scales will catalyze progress in many areas of physiology and neurobiology. We argue that this fuller understanding of the functionality and tractability of pathways must go beyond a focus on the mechanistic details of protein and drug structure to encompass their physiological history as well as their embedding within higher levels of organization in the organism, with numerous implications for data science addressing health and disease. Exploiting tools and concepts from behavioral and cognitive sciences to explore a proto-cognitive metaphor for the pathways underlying health and disease is more than a philosophical stance on biochemical processes; at stake is a new roadmap for overcoming the limitations of today's pharmacological strategies and for inferring future therapeutic interventions for a wide range of disease states.

Characterizing the Impact of Communication on Cellular and Collective Behavior Using a Three-Dimensional Multiscale Cellular Model

Communication between cells enables the coordination that drives structural and functional complexity in biological systems. Both single and multicellular organisms have evolved diverse communication systems for a range of purposes, including synchronization of behavior, division of labor, and spatial organization. Synthetic systems are also increasingly being engineered to utilize cell-cell communication. While research has elucidated the form and function of cell-cell communication in many biological systems, our knowledge is still limited by the confounding effects of other biological phenomena at play and the bias of the evolutionary background. In this work, our goal is to push forward the context-free understanding of what impact cell-cell communication can have on cellular and population behavior to more fully understand the extent to which cell-cell communication systems can be utilized, modified, and engineered. We use an in silico model of 3D multiscale cellular populations, with dynamic intracellular networks interacting via diffusible signals. We focus on two key communication parameters: the effective interaction distance at which cells are able to interact and the receptor activation threshold. We found that cell-cell communication can be divided into six different forms along the parameter axes, three asocial and three social. We also show that cellular behavior, tissue composition, and tissue diversity are all highly sensitive to both the general form and specific parameters of communication even when the cellular network has not been biased towards that behavior.

Emergent Criticality in Coupled Boolean Networks

Early embryonic development involves forming all specialized cells from a fluid-like mass of identical stem cells. The differentiation process consists of a series of symmetry-breaking events, starting from a high-symmetry state (stem cells) to a low-symmetry state (specialized cells). This scenario closely resembles phase transitions in statistical mechanics. To theoretically study this hypothesis, we model embryonic stem cell (ESC) populations through a coupled Boolean network (BN) model. The interaction is applied using a multilayer Ising model that considers paracrine and autocrine signaling, along with external interventions. It is demonstrated that cell-to-cell variability can be interpreted as a mixture of steady-state probability distributions. Simulations have revealed that such models can undergo a series of first- and second-order phase transitions as a function of the system parameters that describe gene expression noise and interaction strengths. These phase transitions result in spontaneous symmetry-breaking events that generate new types of cells characterized by various steady-state distributions. Coupled BNs have also been shown to self-organize in states that allow spontaneous cell differentiation.

Behavior-related gene regulatory networks: A new level of organization in the brain

Neuronal networks are the standard heuristic model today for describing brain activity associated with animal behavior. Recent studies have revealed an extensive role for a completely distinct layer of networked activities in the brain-the gene regulatory network (GRN)-that orchestrates expression levels of hundreds to thousands of genes in a behavior-related manner. We examine emerging insights into the relationships between these two types of networks and discuss their interplay in spatial as well as temporal dimensions, across multiple scales of organization. We discuss properties expected of behavior-related GRNs by drawing inspiration from the rich literature on GRNs related to animal development, comparing and contrasting these two broad classes of GRNs as they relate to their respective phenotypic manifestations. Developmental GRNs also represent a third layer of network biology, playing out over a third timescale, which is believed to play a crucial mediatory role between neuronal networks and behavioral GRNs. We end with a special emphasis on social behavior, discuss whether unique GRN organization and cis-regulatory architecture underlies this special class of behavior, and review literature that suggests an affirmative answer.

Players acting as leaders in turn improve cooperation

Cooperation behaviour is an important topic in society as well as in the biological field, and many factors yield cooperation. Many social phenomena constitute Stackelberg games, but there is little literature on the relationship between Stackelberg games and cooperation. This article shows that in the repeated dynamic Stackelberg games, players acting as leaders in turn yields cooperation. Moreover, social welfare is improved correspondingly when players act as leaders in turn. Therefore, for dynamic Stackelberg games, this paper proposes that the institution of players acting as leaders in turn promotes cooperation.

Integration of single-cell RNA-seq data into population models to characterize cancer metabolism

Metabolic reprogramming is a general feature of cancer cells. Regrettably, the comprehensive quantification of metabolites in biological specimens does not promptly translate into knowledge on the utilization of metabolic pathways. By estimating fluxes across metabolic pathways, computational models hold the promise to bridge this gap between data and biological functionality. These models currently portray the average behavior of cell populations however, masking the inherent heterogeneity that is part and parcel of tumorigenesis as much as drug resistance. To remove this limitation, we propose single-cell Flux Balance Analysis (scFBA) as a computational framework to translate single-cell transcriptomes into single-cell fluxomes. We show that the integration of single-cell RNA-seq profiles of cells derived from lung adenocarcinoma and breast cancer patients into a multi-scale stoichiometric model of a cancer cell population: significantly 1) reduces the space of feasible single-cell fluxomes; 2) allows to identify clusters of cells with different growth rates within the population; 3) points out the possible metabolic interactions among cells via exchange of metabolites. The scFBA suite of MATLAB functions is available at https://github.com/BIMIB-DISCo/scFBA, as well as the case study datasets.

Cytotoxicity of chemotherapeutic agents and resistance to targeted treatments are the main reasons why cancer is still one of the top causes of death. As tumor cells are intrinsically resistant to therapies that target signaling pathways, targeting the metabolic hallmarks of cancer holds promise for more incisive treatments. Regrettably, the heterogeneity of cancer metabolism hinders the identification of effective treatments. To fully uncover the metabolic heterogeneity within tumors, characterization of metabolic programs (metabolic flux distributions) at the single-cell level is required. To fill the gap between current technologies for genomics and future technologies for fluxomics, both at the single-cell and the genome-wide scale, we propose to integrate cancer data from: 1) single-cell transcriptomics and 2) bulk metabolomics, into a multi-scale stoichiometric model, to deliver for the first time metabolic fluxomes at the single-cell level. To this end, we introduce a new paradigm for flux balance analysis and data integration in cancer metabolism to: 1) characterize metabolic heterogeneity, not only at the inter-, but also at the intra-tumor level 2) identify the metabolic interactions between cancer populations, whose role in resistance to metabolic treatments has been recently recognized 3) predict the collective response to drug targeting of metabolism.

Flexibility of Boolean Network Reservoir Computers in Approximating Arbitrary Recursive and Non-Recursive Binary Filters

Reservoir computers (RCs) are biology-inspired computational frameworks for signal processing that are typically implemented using recurrent neural networks. Recent work has shown that Boolean networks (BN) can also be used as reservoirs. We analyze the performance of BN RCs, measuring their flexibility and identifying the factors that determine the effective approximation of Boolean functions applied in a sliding-window fashion over a binary signal, both non-recursively and recursively. We train and test BN RCs of different sizes, signal connectivity, and in-degree to approximate three-bit, five-bit, and three-bit recursive binary functions, respectively. We analyze how BN RC parameters and function average sensitivity, which is a measure of function smoothness, affect approximation accuracy as well as the spread of accuracies for a single reservoir. We found that approximation accuracy and reservoir flexibility are highly dependent on RC parameters. Overall, our results indicate that not all reservoirs are equally flexible, and RC instantiation and training can be more efficient if this is taken into account. The optimum range of RC parameters opens up an angle of exploration for understanding how biological systems might be tuned to balance system restraints with processing capacity.

Emergence of diversity in homogeneous coupled Boolean networks

The origin of multicellularity in metazoa is one of the fundamental questions of evolutionary biology. We have modeled the generic behaviors of gene regulatory networks in isogenic cells as stochastic nonlinear dynamical systems-coupled Boolean networks with perturbation. Model simulations under a variety of dynamical regimes suggest that the central characteristic of multicellularity, permanent spatial differentiation (diversification), indeed can arise. Additionally, we observe that diversification is more likely to occur near the critical regime of Lyapunov stability.

How Criticality of Gene Regulatory Networks Affects the Resulting Morphogenesis under Genetic Perturbations

Whereas the relationship between criticality of gene regulatory networks (GRNs) and dynamics of GRNs at a single-cell level has been vigorously studied, the relationship between the criticality of GRNs and system properties at a higher level has not been fully explored. Here we aim at revealing a potential role of criticality of GRNs in morphogenesis, which is hard to uncover through the single-cell-level studies, especially from an evolutionary viewpoint. Our model simulated the growth of a cell population from a single seed cell. All the cells were assumed to have identical intracellular GRNs. We induced genetic perturbations to the GRN of the seed cell by adding, deleting, or switching a regulatory link between a pair of genes. From numerical simulations, we found that the criticality of GRNs facilitated the formation of nontrivial morphologies when the GRNs were critical in the presence of the evolutionary perturbations. Moreover, the criticality of GRNs produced topologically homogeneous cell clusters by adjusting the spatial arrangements of cells, which led to the formation of nontrivial morphogenetic patterns. Our findings correspond to an epigenetic viewpoint that heterogeneous and complex features emerge from homogeneous and less complex components through the interactions among them. Thus, our results imply that highly structured tissues or organs in morphogenesis of multicellular organisms might stem from the criticality of GRNs.

Angiogenic activity of breast cancer patients' monocytes reverted by combined use of systems modeling and experimental approaches

Angiogenesis plays a key role in tumor growth and cancer progression. TIE-2-expressing monocytes (TEM) have been reported to critically account for tumor vascularization and growth in mouse tumor experimental models, but the molecular basis of their pro-angiogenic activity are largely unknown. Moreover, differences in the pro-angiogenic activity between blood circulating and tumor infiltrated TEM in human patients has not been established to date, hindering the identification of specific targets for therapeutic intervention. In this work, we investigated these differences and the phenotypic reversal of breast tumor pro-angiogenic TEM to a weak pro-angiogenic phenotype by combining Boolean modelling and experimental approaches. Firstly, we show that in breast cancer patients the pro-angiogenic activity of TEM increased drastically from blood to tumor, suggesting that the tumor microenvironment shapes the highly pro-angiogenic phenotype of TEM. Secondly, we predicted in silico all minimal perturbations transitioning the highly pro-angiogenic phenotype of tumor TEM to the weak pro-angiogenic phenotype of blood TEM and vice versa. In silico predicted perturbations were validated experimentally using patient TEM. In addition, gene expression profiling of TEM transitioned to a weak pro-angiogenic phenotype confirmed that TEM are plastic cells and can be reverted to immunological potent monocytes. Finally, the relapse-free survival analysis showed a statistically significant difference between patients with tumors with high and low expression values for genes encoding transitioning proteins detected in silico and validated on patient TEM. In conclusion, the inferred TEM regulatory network accurately captured experimental TEM behavior and highlighted crosstalk between specific angiogenic and inflammatory signaling pathways of outstanding importance to control their pro-angiogenic activity. Results showed the successful in vitro reversion of such an activity by perturbation of in silico predicted target genes in tumor derived TEM, and indicated that targeting tumor TEM plasticity may constitute a novel valid therapeutic strategy in breast cancer.

Investigating the relation between stochastic differentiation, homeostasis and clonal expansion in intestinal crypts via multiscale modeling

Colorectal tumors originate and develop within intestinal crypts. Even though some of the essential phenomena that characterize crypt structure and dynamics have been effectively described in the past, the relation between the differentiation process and the overall crypt homeostasis is still only partially understood. We here investigate this relation and other important biological phenomena by introducing a novel multiscale model that combines a morphological description of the crypt with a gene regulation model: the emergent dynamical behavior of the underlying gene regulatory network drives cell growth and differentiation processes, linking the two distinct spatio-temporal levels. The model relies on a few a priori assumptions, yet accounting for several key processes related to crypt functioning, such as: dynamic gene activation patterns, stochastic differentiation, signaling pathways ruling cell adhesion properties, cell displacement, cell growth, mitosis, apoptosis and the presence of biological noise. We show that this modeling approach captures the major dynamical phenomena that characterize the regular physiology of crypts, such as cell sorting, coordinate migration, dynamic turnover, stem cell niche correct positioning and clonal expansion. All in all, the model suggests that the process of stochastic differentiation might be sufficient to drive the crypt to homeostasis, under certain crypt configurations. Besides, our approach allows to make precise quantitative inferences that, when possible, were matched to the current biological knowledge and it permits to investigate the role of gene-level perturbations, with reference to cancer development. We also remark the theoretical framework is general and may be applied to different tissues, organs or organisms.

Control of cellular automata

We study the problem of master-slave synchronization and control of totalistic cellular automata. The synchronization mechanism is that of setting a fraction of sites of the slave system equal to those of the master one (pinching synchronization). The synchronization observable is the distance between the two configurations. We present three control strategies that exploit local information (the number of nonzero first-order Boolean derivatives) in order to choose the sites to be synchronized. When no local information is used, we speak of simple pinching synchronization. We find the critical properties of control and discuss the best control strategy compared with simple synchronization.

A review of spatial computational models for multi-cellular systems, with regard to intestinal crypts and colorectal cancer development

Colon rectal cancers (CRC) are the result of sequences of mutations which lead the intestinal tissue to develop in a carcinoma following a "progression" of observable phenotypes. The actual modeling and simulation of the key biological structures involved in this process is of interest to biologists and physicians and, at the same time, it poses significant challenges from the mathematics and computer science viewpoints. In this report we give an overview of some mathematical models for cell sorting (a basic phenomenon that underlies several dynamical processes in an organism), intestinal crypt dynamics and related problems and open questions. In particular, major attention is devoted to the survey of so-called in-lattice (or grid) models and off-lattice (off-grid) models. The current work is the groundwork for future research on semi-automated hypotheses formation and testing about the behavior of the various actors taking part in the adenoma-carcinoma progression, from regulatory processes to cell-cell signaling pathways.

A review of spatial computational models for multi-cellular systems, with regard to intestinal crypts and colorectal cancer development

Colon rectal cancers (CRC) are the result of sequences of mutations which lead the intestinal tissue to develop in a carcinoma following a "progression" of observable phenotypes. The actual modeling and simulation of the key biological structures involved in this process is of interest to biologists and physicians and, at the same time, it poses significant challenges from the mathematics and computer science viewpoints. In this report we give an overview of some mathematical models for cell sorting (a basic phenomenon that underlies several dynamical processes in an organism), intestinal crypt dynamics and related problems and open questions. In particular, major attention is devoted to the survey of so-called in-lattice (or grid) models and off-lattice (off-grid) models. The current work is the groundwork for future research on semi-automated hypotheses formation and testing about the behavior of the various actors taking part in the adenoma-carcinoma progression, from regulatory processes to cell-cell signaling pathways.

Integration of Boolean models exemplified on hepatocyte signal transduction

The number of mathematical models for biological pathways is rapidly growing. In particular, Boolean modelling proved to be suited to describe large cellular signalling networks. Systems biology is at the threshold to holistic understanding of comprehensive networks. In order to reach this goal, connection and integration of existing models of parts of cellular networks into more comprehensive network models is necessary. We discuss model combination approaches for Boolean models. Boolean modelling is qualitative rather than quantitative and does not require detailed kinetic information. We show that these models are useful precursors for large-scale quantitative models and that they are comparatively easy to combine. We propose modelling standards for Boolean models as a prerequisite for smooth model integration. Using these standards, we demonstrate the coupling of two logical models on two different examples concerning cellular interactions in the liver. In the first example, we show the integration of two Boolean models of two cell types in order to describe their interaction. In the second example, we demonstrate the combination of two models describing different parts of the network of a single cell type. Combination of partial models into comprehensive network models will take systems biology to the next level of understanding. The combination of logical models facilitated by modelling standards is a valuable example for the next step towards this goal.