Dynamics Of Biological Networks Research Articles

Charting cellular differentiation trajectories with Ricci flow

Complex biological processes, such as cellular differentiation, require intricate rewiring of intra-cellular signalling networks. Previous characterisations revealed a raised network entropy underlies less differentiated and malignant cell states. A connection between entropy and Ricci curvature led to applications of discrete curvatures to biological networks. However, predicting dynamic biological network rewiring remains an open problem. Here we apply Ricci curvature and Ricci flow to biological network rewiring. By investigating the relationship between network entropy and Forman-Ricci curvature, theoretically and empirically on single-cell RNA-sequencing data, we demonstrate that the two measures do not always positively correlate, as previously suggested, and provide complementary rather than interchangeable information. We next employ Ricci flow to derive network rewiring trajectories from stem cells to differentiated cells, accurately predicting true intermediate time points in gene expression time courses. In summary, we present a differential geometry toolkit for understanding dynamic network rewiring during cellular differentiation and cancer.

Cusp bifurcation in a metastatic regulatory network

Understanding the potential for cancers to metastasize is still relatively unknown. While many predictive methods may use deep learning or stochastic processes, we highlight a long standing mathematical concept that may be useful for modeling metastatic breast cancer systems. Ordinary differential equations (ODEs) can model cell state transitions by considering the pertinent environmental variables as well as the paths systems take over time. Bifurcation theory is a branch of dynamical systems which studies changes in the behavior of an ODE system while one or more parameters are varied. Many studies have applied concepts in one-parameter bifurcation theory to model biological network dynamics, and cell division. However, studies of two-parameter bifurcations are much more rare. Two-parameter bifurcations have not been studied in metastatic systems. Here we show how a specific two-parameter bifurcation phenomenon called a cusp bifurcation separates two qualitatively different metastatic cell state transitions modalities and propose a new perspective on defining such transitions based on mathematical theory. We hope the observations and verification methods detailed here may help in the understanding of metastatic potential from a basic biological perspective and in clinical settings.

Efficient Intracellular MicroRNA Imaging Based on the Localized and Self-Sustainable Catalytic DNA Assembly Circuit.

Building dynamic biological networks, especially DNA circuits, has provided a powerful prospect for exploring the intrinsic regulation processes of live cells. Nevertheless, for efficient intracellular microRNA analysis, the available multi-component circuits are constrained by their limited operating speed and efficiency due to the free diffusion of reactants. Herein, we developed an accelerated Y-shaped DNA catalytic (YDC) circuit for high-efficiency intracellular imaging of microRNA. By grafting the catalytic hairpin assembly (CHA) reactants into an integrated Y-shaped scaffold, the CHA probes were concentrated in a compact space, thus achieving high signal amplification. Profiting from the spatially confined reaction and the self-sustainably assembled DNA products, the YDC system facilitated reliable and in situ microRNA imaging in live cells. Compared with the homogeneously dispersed CHA reactants, the integrated YDC system could efficiently promote the reaction kinetics as well as the uniform delivery of CHA probes, thus providing a robust and reliable analytical tool for disease diagnosis and monitoring.

A Survey On Gene Regulatory Network With Optimization Techniques

Recognizing the connections between genes is essential to comprehending bio- logical processes in all living things with cells. Gene regulatory network is the blueprint of the connections between the genes. Understanding fundamental cellular processes and the dynamic behavior of biological systems is the primary goal of research with gene regulatory networks. In conventional biology, it is difficult to reconstruct such regulatory networks from time-series gene expression data, and it has not yet been possible to perfectly reconstruct a network that is biologically accurate. The behavior of a genome can be expressed by a biological system, but computational biology sheds light on its underlying causes. To infer the genetic relationships from the biological network dynamics obtained from the experimental time series gene expression data set, researchers have used various methods from decades. Many researchers prefer the power law-based methods like s-systems, half-systems and recurrent neural networks whereas some of them consider the probabilistic approaches like Bayesian networks or Boolean. Nowadays a new approach to graph signal processing also plays an important role in terms of reconstruction of the gene regulatory network. The objective of this paper is to give a proper overview for the recreation of the gene regulatory network from the time series datasets or from the micro array data sequences. The approaches that the researchers have employed to recreate the gene regulatory network are thoroughly surveyed in this publication. Additionally, it provides future researchers with an understanding of the advantages and disadvantages of each approach, encouraging them to think creatively and beyond the box to increase the network’s prediction accuracy. This paper also includes comparative studies regarding the inference accuracy of the regulatory network which is going to help the researchers to understand the most prominent and significant approach for this work.

Collectively canalizing Boolean functions

This paper studies the mathematical properties of collectively canalizing Boolean functions, a class of functions that has arisen from applications in systems biology. Boolean networks are an increasingly popular modeling framework for regulatory networks, and the class of functions studied here captures a key feature of biological network dynamics, namely that a subset of one or more variables, under certain conditions, can dominate the value of a Boolean function, to the exclusion of all others. These functions have rich mathematical properties to be explored. The paper shows how the number and type of such sets influence a function's behavior and define a new measure for the canalizing strength of any Boolean function. We further connect the concept of collective canalization with the well-studied concept of the average sensitivity of a Boolean function. The relationship between Boolean functions and the dynamics of the networks they form is important in a wide range of applications beyond biology, such as computer science, and has been studied with statistical and simulation-based methods. But the rich relationship between structure and dynamics remains largely unexplored, and this paper is intended as a contribution to its mathematical foundation.

Logical computation with self-assembling electric circuits.

Inspired by self-assembled biological growth, the Circuit Tile Assembly Model (cTAM) was developed to provide insights into signal propagation, information processing, and computation in bioelectric networks. The cTAM is an abstract model that produces a family of circuits of different sizes that is amenable to exact analysis. Here, the cTAM is extended to the Boolean Circuit Tile Assembly Model (bcTAM) that implements a computationally complete set of Boolean gates through self-assembled and self-controlled growth. The proposed model approximates axonal growth in neural networks and thus, investigates the computational capability of dynamic biological networks, for example, in growing networks of axons. Thus, the bcTAM models the effect of electrical activity on growth and shows how that growth might implement Boolean computations. In this sense, given a set of input voltages, the bcTAM is a system that is able to monitor and make decisions about its own growth.

A preference for link operator functions can drive Boolean biological networks towards critical dynamics

Boolean modelling is a powerful framework to understand the operating principles of biological networks. The regulatory logic between biological entities in these networks is expressed as Boolean functions (BFs). There exist various types of BFs (and thus regulatory logic rules) which are meaningful in the biological context. In this contribution, we explore one such type, known as link operator functions (LOFs). We theoretically enumerate these functions and show that, among all BFs and even within the biologically consistent effective and unate functions (EUFs), the LOFs form a tiny subset. We then find that the AND-NOT LOFs are particularly abundant in reconstructed biological Boolean networks. By leveraging these facts, namely, the tiny representation of LOFs in the space of EUFs and their presence in the biological dataset, we show that the space of acceptable models can be shrunk by applying steady-state constraints to BFs, followed by the choice of LOFs which satisfy those constraints. Finally, we demonstrate that among a wide range of BFs, the LOFs drive biological network dynamics towards criticality.

Boolean function metrics can assist modelers to check and choose logical rules

Computational models of biological processes provide one of the most powerful methods for a detailed analysis of the mechanisms that drive the behavior of complex systems. Logic-based modeling has enhanced our understanding and interpretation of those systems. Defining rules that determine how the output activity of biological entities is regulated by their respective inputs has proven to be challenging. Partly this is because of the inherent noise in data that allows multiple model parameterizations to fit the experimental observations, but some of it is also due to the fact that models become increasingly larger, making the use of automated tools to assemble the underlying rules indispensable. We present several Boolean function metrics that provide modelers with the appropriate framework to analyze the impact of a particular model parameterization. We demonstrate the link between a semantic characterization of a Boolean function and its consistency with the model’s underlying regulatory structure. We further define the properties that outline such consistency and show that several of the Boolean functions under study violate them, questioning their biological plausibility and subsequent use. We also illustrate that regulatory functions can have major differences with regard to their asymptotic output behavior, with some of them being biased towards specific Boolean outcomes when others are dependent on the ratio between activating and inhibitory regulators. Application results show that in a specific signaling cancer network, the function bias can be used to guide the choice of logical operators for a model that matches data observations. Moreover, graph analysis indicates that commonly used Boolean functions become more biased with increasing numbers of regulators, supporting the idea that rule specification can effectively determine regulatory outcome despite the complex dynamics of biological networks.

Self-Assembled Biophotonic Lasing Network Driven by Amyloid Fibrils in Microcavities

Self-assembled biological structures have played a significant role in many living systems for its functionality and distinctiveness. Here, we experimentally demonstrate that the random dynamic behavior of strong light-matter interactions in complex biological structures can provide hidden information on optical coupling in a network. The concept of biophotonic lasing network is therefore introduced, where a self-assembled human amyloid fibril network was confined in a Fabry-Perot optical cavity. Distinctive lasing patterns were discovered from self-assembled amyloids with different structural dimensions (0D, 1D, 2D, and 3D) confined in a microcavity. Network laser emission exhibiting evidence of light coupling at different wavelengths and locations was spectrally resolved. Dynamic changes of lasing patterns can therefore be interpreted into a graph to reveal the optical correlation in biophotonic networks. Our findings indicate that each graph represents the highly unclonable features of a self-assembled network which can sensitively respond to environmental stimulus. This study offers the potential for studying dynamic biological networks through amplified interactions, shedding light on the development of biologically controlled photonic devices, biosensing, and information encryption.

The ecological network approach to algal-bacterial relationships: Review and prospects

<p indent=0mm>Algae and bacteria numerically dominate oceanic and freshwater planktonic communities. They play a central biogeochemical role in the marine ecosystem, including producing biomass to support aquatic food webs, cycling nutrients and trace elements, and decomposing organic matter. Algae and bacteria synergistically affect each other’s physiology and metabolism and have coexisted ever since the early stages of evolution that revolutionized many aspects of life on Earth. The relationship between algae and bacteria influences ecosystems and represents all conceivable modes of interaction from mutualism to parasitism. The interactions between these two groups of plankton, and the influence of their interaction on each other and on a global scale have, therefore, become the focus of recent research interest. Previous studies have summarized a variety of algal-bacterial interactions and aimed to reveal the essence of those interactions. However, it is clear that their interactions are diverse and not static, and can be initiated and broken in response to environmental and developmental cues. Traditional research methods have been unable to reveal the complexity behind algal-bacterial symbiosis. As microbial omics technology has developed and the influence of global change on marine ecosystems has become apparent, the research perspective on algal-bacterial relationships has gradually risen to the level of systemic ecology. The rapid-blooming of high-throughput sequencing technology and the ability to analyze big data offer new opportunities for a thorough study of algal-bacterial interaction. Ecological networks are prominent among these new methods: They can integrate multiple types of information and might represent systems-level behavior. Network theory methods are powerful approaches for quantifying relationships between biological components and their relevance to phenotypes, environmental conditions or other external variables within a system. In this paper, we review the research advances in the algal-bacterial ecological network based on big data. We begin by introducing the network parameters and attributes commonly used in ecological network analysis and review the existing network modeling methods in microbial studies and algorithm features and application scenarios. By comparing some common algorithms or software, researchers can choose appropriate network construction methods when confronted with different data characteristics. Next, the ecological network analysis used in the study of algal-bacterial relationships is presented at multiple layers from taxonomy to function (e.g., molecular and metabolic networks). The problems and experiences encountered during research into algal-bacterial relationships are then discussed. For example, when focusing on the interaction between host and microorganism, the time/space shift correlations among the variables will lead to wrong conclusions, including false-positive or false-negative results. We also attempt to introduce metabolic and dynamic biological networks into the study of the algal-bacterial relationship to reveal further the mechanism of their interaction from the perspectives of function and causality. Finally, our novel proposal to establish a knowledge network database of algal-bacterial interactions and a graphic database of photosphere biological profiles is discussed. We highlight the need for microbial ecological network inference and suggest strategies to infer networks more reliably. Our study aimed to explore the holistic information behind algal-bacterial relationships and provide new cues for further revealing the molecular mechanisms of algal-bacterial interactions.

Advances in Drug Resistance of Esophageal Cancer: From the Perspective of Tumor Microenvironment.

Drug resistance represents the major obstacle to get the maximum therapeutic benefit for patients with esophageal cancer since numerous patients are inherently or adaptively resistant to therapeutic agents. Notably, increasing evidence has demonstrated that drug resistance is closely related to the crosstalk between tumor cells and the tumor microenvironment (TME). TME is a dynamic and ever-changing complex biological network whose diverse cellular and non-cellular components influence hallmarks and fates of tumor cells from the outside, and this is responsible for the development of resistance to conventional therapeutic agents to some extent. Indeed, the formation of drug resistance in esophageal cancer should be considered as a multifactorial process involving not only cancer cells themselves but cancer stem cells, tumor-associated stromal cells, hypoxia, soluble factors, extracellular vesicles, etc. Accordingly, combination therapy targeting tumor cells and tumor-favorable microenvironment represents a promising strategy to address drug resistance and get better therapeutic responses for patients with esophageal cancer. In this review, we mainly focus our discussion on molecular mechanisms that underlie the role of TME in drug resistance in esophageal cancer. We also discuss the opportunities and challenges for therapeutically targeting tumor-favorable microenvironment, such as membrane proteins, pivotal signaling pathways, and cytokines, to attenuate drug resistance in esophageal cancer.

ANCA: Alignment-Based Network Construction Algorithm.

Dynamic biological networks model changes in the network topology over time. However, often the topologies of these networks are not available at specific time points. Existing algorithms for studying dynamic networks often ignore this problem and focus only on the time points at which experimental data is available. In this paper, we develop a novel alignment based network construction algorithm, ANCA, that constructs the dynamic networks at the missing time points by exploiting the information from a reference dynamic network. Our experiments on synthetic and real networks demonstrate that ANCA predicts the missing target networks accurately, and scales to large-scale biological networks in practical time. Our analysis of an E. coli protein-protein interaction network shows that ANCA successfully identifies key temporal changes in the biological networks. Our analysis also suggests that by focusing on the topological differences in the network, our method can be used to find important genes and temporal functional changes in the biological networks.

Using linkage logic theory to control dynamics of a gene regulatory network of a chordate embryo

Linkage logic theory provides a mathematical criterion to control network dynamics by manipulating activities of a subset of network nodes, which are collectively called a feedback vertex set (FVS). Because many biological functions emerge from dynamics of biological networks, this theory provides a promising tool for controlling biological functions. By manipulating the activity of FVS molecules identified in a gene regulatory network (GRN) for fate specification of seven tissues in ascidian embryos, we previously succeeded in reproducing six of the seven cell types. Simultaneously, we discovered that the experimentally reconstituted GRN lacked information sufficient to reproduce muscle cells. Here, we utilized linkage logic theory as a tool to find missing edges in the GRN. Then, we identified a FVS from an updated version of the GRN and confirmed that manipulating the activity of this FVS was sufficient to induce all seven cell types, even in a multi-cellular environment. Thus, linkage logic theory provides tools to find missing edges in experimentally reconstituted networks, to determine whether reconstituted networks contain sufficient information to fulfil expected functions, and to reprogram cell fate.

Boolean Feedforward Neural Network Modeling of Molecular Regulatory Networks for Cellular State Conversion.

The molecular regulatory network (MRN) within a cell determines cellular states and transitions between them. Thus, modeling of MRNs is crucial, but this usually requires extensive analysis of time-series measurements, which is extremely difficult to obtain from biological experiments. However, single-cell measurement data such as single-cell RNA-sequencing databases have recently provided a new insight into resolving this problem by ordering thousands of cells in pseudo-time according to their differential gene expressions. Neural network modeling can be employed by using temporal data as learning data. In contrast, Boolean network modeling of MRNs has a growing interest, as it is a parameter-free logical modeling and thereby robust to noisy data while still capturing essential dynamics of biological networks. In this study, we propose a Boolean feedforward neural network (FFN) modeling by combining neural network and Boolean network modeling approach to reconstruct a practical and useful MRN model from large temporal data. Furthermore, analyzing the reconstructed MRN model can enable us to identify control targets for potential cellular state conversion. Here, we show the usefulness of Boolean FFN modeling by demonstrating its applicability through a toy model and biological networks.

Role of modularity in self-organization dynamics in biological networks.

Interconnected ensembles of biological entities are perhaps some of the most complex systems that modern science has encountered so far. In particular, scientists have concentrated on understanding how the complexity of the interacting structure between different neurons, proteins, or species influences the functioning of their respective systems. It is well established that many biological networks are constructed in a highly hierarchical way with two main properties: short average paths that join two apparently distant nodes (neuronal, species, or protein patches) and a high proportion of nodes in modular aggregations. Although several hypotheses have been proposed so far, still little is known about the relation of the modules with the dynamical activity in such biological systems. Here we show that network modularity is a key ingredient for the formation of self-organizing patterns of functional activity, independently of the topological peculiarities of the structure of the modules. In particular, we propose a self-organizing mechanism which explains the formation of macroscopic spatial patterns, which are homogeneous within modules. This may explain how spontaneous order in biological networks follows their modular structural organization. We test our results on real-world networks to confirm the important role of modularity in creating macroscale patterns.

Physically-interpretable classification of biological network dynamics for complex collective motions

Understanding biological network dynamics is a fundamental issue in various scientific and engineering fields. Network theory is capable of revealing the relationship between elements and their propagation; however, for complex collective motions, the network properties often transiently and complexly change. A fundamental question addressed here pertains to the classification of collective motion network based on physically-interpretable dynamical properties. Here we apply a data-driven spectral analysis called graph dynamic mode decomposition, which obtains the dynamical properties for collective motion classification. Using a ballgame as an example, we classified the strategic collective motions in different global behaviours and discovered that, in addition to the physical properties, the contextual node information was critical for classification. Furthermore, we discovered the label-specific stronger spectra in the relationship among the nearest agents, providing physical and semantic interpretations. Our approach contributes to the understanding of principles of biological complex network dynamics from the perspective of nonlinear dynamical systems.

Comprehensive pharmacogenomic characterization of gastric cancer

BackgroundGastric cancer is among the most lethal human malignancies. Previous studies have identified molecular aberrations that constitute dynamic biological networks and genomic complexities of gastric tumors. However, the clinical translation of molecular-guided targeted therapy is hampered by challenges. Notably, solid tumors often harbor multiple genetic alterations, complicating the development of effective treatments.MethodsTo address such challenges, we established a comprehensive dataset of molecularly annotated patient derivatives coupled with pharmacological profiles for 60 targeted agents to explore dynamic pharmacogenomic interactions in gastric cancers.ResultsWe identified lineage-specific drug sensitivities based on histopathological and molecular subclassification, including substantial sensitivities toward VEGFR and EGFR inhibition therapies in diffuse- and signet ring-type gastric tumors, respectively. We identified potential therapeutic opportunities for WNT pathway inhibitors in ALK-mutant tumors, a significant association between PIK3CA-E542K mutation and AZD5363 response, and transcriptome expression of RNF11 as a potential predictor of response to gefitinib.ConclusionsCollectively, our results demonstrate the feasibility of drug screening combined with tumor molecular characterization to facilitate personalized therapeutic regimens for gastric tumors.

Bifurcation analysis of bistable and oscillatory dynamics in biological networks using the root-locus method.

Most of the biological systems including gene regulatory networks can be described well by ordinary differential equation models with rational non-linearities. These models are derived either based on the reaction kinetics or by curve fitting to experimental data. This study demonstrates the applicability of the root-locus-based bifurcation analysis method for studying the complex dynamics of such models. The effectiveness of the bifurcation analysis in determining the exact parameter regions in each of which the system shows a certain dynamical behaviour, such as bistability, oscillation, and asymptotically equilibrium dynamics is shown by considering two mostly studied gene regulatory networks, namely Gardner's genetic toggle switch and p53 gene network possessing two-phase (mono-stable/oscillation) dynamics.

Systems NMR: single-sample quantification of RNA, proteins and metabolites for biomolecular network analysis.

Cellular behavior is controlled by the interplay of diverse biomolecules. Most experimental methods, however, can monitor only a single molecule class or reaction type at a time. We developed an in vitro Nuclear Magnetic Resonance spectroscopy (NMR) approach, which permitted dynamic quantification of an entire “heterotypic” network – simultaneously monitoring three distinct molecule classes (metabolites, proteins, RNA) and all elementary reaction types (bimolecular interactions, catalysis, unimolecular changes). Focusing on an 8-reaction co-transcriptional RNA folding network, in a single sample we recorded over 35 time-points with over 170 observables each, and accurately determined 5 core reaction constants in multiplex. This reconstruction revealed unexpected cross-talk between the different reactions. We further observed dynamic phase-separation in a system of five distinct RNA binding domains in the course of the RNA transcription reaction. Our Systems NMR approach provides a deeper understanding of biological network dynamics by combining the dynamic resolution of biochemical assays and the multiplexing ability of “omics”.

Representing dynamic biological networks with multi-scale probabilistic models

Dynamic models analyzing gene regulation and metabolism face challenges when adapted to modeling signal transduction networks. During signal transduction, molecular reactions and mechanisms occur in different spatial and temporal frames and involve feedbacks. This impedes the straight-forward use of methods based on Boolean networks, Bayesian approaches, and differential equations. We propose a new approach, ProbRules, that combines probabilities and logical rules to represent the dynamics of a system across multiple scales. We demonstrate that ProbRules models can represent various network motifs of biological systems. As an example of a comprehensive model of signal transduction, we provide a Wnt network that shows remarkable robustness under a range of phenotypical and pathological conditions. Its simulation allows the clarification of controversially discussed molecular mechanisms of Wnt signaling by predicting wet-lab measurements. ProbRules provides an avenue in current computational modeling by enabling systems biologists to integrate vast amounts of available data on different scales.