Modeling the dynamic behavior of biochemical regulatory networks

Optimisation of gene expression noise for cellular persistence against lethal events

Bacterial cell persistence, crucial for survival under adverse conditions like antibiotic exposure, is intrinsically linked to stochastic fluctuations in gene expression. Certain genes, while inhibiting growth under normal circumstances, confer tolerance to antibiotics at elevated expression levels. The occurrence of antibiotic events lead to instantaneous cellular responses with varied survival probabilities correlated with gene expression levels. Notably, cells with lower protein concentrations face higher mortality rates. This study aims to elucidate an optimal strategy for protein expression conducive to cellular survival. Through comprehensive mathematical analysis, we determine the optimal burst size and frequency that maximise cell proliferation. Furthermore, we explore how the optimal expression distribution changes as the cost of protein expression to growth escalates. Our model reveals a hysteresis phenomenon, characterised by discontinuous transitions between deterministic and stochastic optima. Intriguingly, stochastic optima possess a noise floor, representing the minimal level of fluctuations essential for optimal cellular resilience.

Stochastic Boolean model of normal and aberrant cell cycles in budding yeast

The cell cycle of budding yeast is governed by an intricate protein regulatory network whose dysregulation can lead to lethal mistakes or aberrant cell division cycles. In this work, we model this network in a Boolean framework for stochastic simulations. Our model is sufficiently detailed to account for the phenotypes of 40 mutant yeast strains (83% of the experimentally characterized strains that we simulated) and also to simulate an endoreplicating strain (multiple rounds of DNA synthesis without mitosis) and a strain that exhibits 'Cdc14 endocycles' (periodic transitions between metaphase and anaphase). Because our model successfully replicates the observed properties of both wild-type yeast cells and many mutant strains, it provides a reasonable, validated starting point for more comprehensive stochastic-Boolean models of cell cycle controls. Such models may provide a better understanding of cell cycle anomalies in budding yeast and ultimately in mammalian cells.

Multiscale Modeling of Bistability in the Yeast Polarity Circuit

Cell polarity refers to the asymmetric distribution of proteins and other molecules along a specified axis within a cell. Polarity establishment is the first step in many cellular processes. For example, directed growth or migration requires the formation of a cell front and back. In many cases, polarity occurs in the absence of spatial cues. That is, the cell undergoes symmetry breaking. Understanding the molecular mechanisms that allow cells to break symmetry and polarize requires computational models that span multiple spatial and temporal scales. Here, we apply a multiscale modeling approach to examine the polarity circuit of yeast. In addition to symmetry breaking, experiments revealed two key features of the yeast polarity circuit: bistability and rapid dismantling of the polarity site following a loss of signal. We used modeling based on ordinary differential equations (ODEs) to investigate mechanisms that generate these behaviors. Our analysis revealed that a model involving positive and negative feedback acting on different time scales captured both features. We then extend our ODE model into a coarse-grained reaction-diffusion equation (RDE) model to capture the spatial profiles of polarity factors. After establishing that the coarse-grained RDE model qualitatively captures key features of the polarity circuit, we expand it to more accurately capture the biochemical reactions involved in the system. We convert the expanded model to a particle-based model that resolves individual molecules and captures fluctuations that arise from the stochastic nature of biochemical reactions. Our models assume that negative regulation results from negative feedback. However, experimental observations do not rule out the possibility that negative regulation occurs through an incoherent feedforward loop. Therefore, we conclude by using our RDE model to suggest how negative feedback might be distinguished from incoherent feedforward regulation.

Exploring gene regulation and biological processes in insects: Insights from omics data using gene regulatory network models

Gene regulatory network (GRN) comprises complicated yet intertwined gene-regulator relationships. Understanding the GRN dynamics will unravel the complexity behind the observed gene expressions. Insect gene regulation is often complicated due to their complex life cycles and diverse ecological adaptations. The main interest of this review is to have an update on the current mathematical modelling methods of GRNs to explain insect science. Several popular GRN architecture models are discussed, together with examples of applications in insect science. In the last part of this review, each model is compared from different aspects, including network scalability, computation complexity, robustness to noise and biological relevancy.

Integrative modeling uncovers p21-driven drug resistance and prioritizes therapies for PIK3CA-mutant breast cancer

Utility of PI3Kα inhibitors like BYL719 is limited by the acquisition of genetic and non-genetic mechanisms of resistance which cause disease recurrence. Several combination therapies based on PI3K inhibition have been proposed, but a way to systematically prioritize them for breast cancer treatment is still missing. By integrating published and in-house studies, we have developed in silico models that quantitatively capture dynamics of PI3K signaling at the network-level under a BYL719-sensitive versus BYL719 resistant-cell state. Computational predictions show that signal rewiring to alternative components of the PI3K pathway promote resistance to BYL719 and identify PDK1 as the most effective co-target with PI3Kα rescuing sensitivity of resistant cells to BYL719. To explore whether PI3K pathway-independent mechanisms further contribute to BYL719 resistance, we performed phosphoproteomics and found that selection of high levels of the cell cycle regulator p21 unexpectedly promoted drug resistance in T47D cells. Functionally, high p21 levels favored repair of BYL719-induced DNA damage and bypass of the associated cellular senescence. Importantly, targeted inhibition of the check-point inhibitor CHK1 with MK-8776 effectively caused death of p21-high T47D cells, thus establishing a new vulnerability of BYL719-resistant breast cancer cells. Together, our integrated studies uncover hidden molecular mediators causing resistance to PI3Kα inhibition and provide a framework to prioritize combination therapies for PI3K-mutant breast cancer.

Modeling transcriptional regulation of the cell cycle using a novel cybernetic-inspired approach

Quantitative understanding of cellular processes, such as cell cycle and differentiation, is impeded by various forms of complexity ranging from myriad molecular players and their multilevel regulatory interactions, cellular evolution with multiple intermediate stages, lack of elucidation of cause-effect relationships among the many system players, and the computational complexity associated with the profusion of variables and parameters. In this paper, we present a modeling framework based on the cybernetic concept that biological regulation is inspired by objectives embedding rational strategies for dimension reduction, process stage specification through the system dynamics, and innovative causal association of regulatory events with the ability to predict the evolution of the dynamical system. The elementary step of the modeling strategy involves stage-specific objective functions that are computationally determined from experiments, augmented with dynamical network computations involving endpoint objective functions, mutual information, change-point detection, and maximal clique centrality. We demonstrate the power of the method through application to the mammalian cell cycle, which involves thousands of biomolecules engaged in signaling, transcription, and regulation. Starting with a fine-grained transcriptional description obtained from RNA sequencing measurements, we develop an initial model, which is then dynamically modeled using the cybernetic-inspired method, based on the strategies described above. The cybernetic-inspired method is able to distill the most significant interactions from a multitude of possibilities. In addition to capturing the complexity of regulatory processes in a mechanistically causal and stage-specific manner, we identify the functional network modules, including novel cell cycle stages. Our model is able to predict future cell cycles consistent with experimental measurements. We posit that this innovative framework has the promise to extend to the dynamics of other biological processes, with a potential to provide novel mechanistic insights.

Iron Homeostatic Regulation in Saccharomyces cerevisiae: Introduction to a Computational Modeling Method

Over the past 30 years, much has been learned regarding iron homeostatic regulation in budding yeast, S. cerevisiae, including the identity of many of the proteins and molecular-level regulatory mechanisms involved. Most advances have involved inferring such mechanisms based on the analysis of iron-dysregulation phenotypes arising in various genetic mutant strains. Still lacking is a cellular- or system-level understanding of iron homeostasis. These experimental advances are summarized in this review, and a method for developing cellular-level regulatory mechanisms in yeast is presented. The method employs the results of Mössbauer spectroscopy of whole cells and organelles, iron quantification of the same, and ordinary differential equation-based mathematical models. Current models are simplistic when compared to the complexity of iron homeostasis in real cells, yet they hold promise as a useful, perhaps even required, complement to the popular genetics-based approach. The fundamental problem in comprehending cellular regulatory mechanisms is that, given the complexities involved, different molecular-level mechanisms can often give rise to virtually indistinguishable cellular phenotypes. Mathematical models cannot eliminate this problem, but they can minimize it.

A kinetic model of iron trafficking in growing Saccharomyces cerevisiae cells; applying mathematical methods to minimize the problem of sparse data and generate viable autoregulatory mechanisms

Iron is an essential transition metal for all eukaryotic cells, and its trafficking throughout the cell is highly regulated. However, the overall cellular mechanism of regulation is poorly understood despite knowing many of the molecular players involved. Here, an ordinary-differential-equations (ODE) based kinetic model of iron trafficking within a growing yeast cell was developed that included autoregulation. The 9-reaction 8-component in-silico cell model was solved under both steady-state and time-dependent dynamical conditions. The ODE for each component included a dilution term due to cell growth. Conserved rate relationships were obtained from the null space of the stoichiometric matrix, and the reduced-row-echelon-form was used to distinguish independent from dependent rates. Independent rates were determined from experimentally estimated component concentrations, cell growth rates, and the literature. Simple rate-law expressions were assumed, allowing rate-constants for each reaction to be estimated. Continuous Heaviside logistical functions were used to regulate rate-constants. These functions acted like valves, opening or closing depending on component "sensor" concentrations. Two cellular regulatory mechanisms were selected from 134,217,728 possibilities using a novel approach involving 6 mathematically-defined filters. Three cellular states were analyzed including healthy wild-type cells, iron-deficient wild-type cells, and a frataxin-deficient strain of cells characterizing the disease Friedreich's Ataxia. The model was stable toward limited perturbations, as determined by the eigenvalues of Jacobian matrices. Autoregulation allowed healthy cells to transition to the diseased state when triggered by a mutation in frataxin, and to the iron-deficient state when cells are placed in iron-deficient growth medium. The in-silico phenotypes observed during these transitions were similar to those observed experimentally. The model also predicted the observed effects of hypoxia on the diseased condition. A similar approach could be used to solve ODE-based kinetic models associated with other biochemical processes operating within growing cells.

Fluorescent biosensor imaging meets deterministic mathematical modelling: quantitative investigation of signalling compartmentalization

Cells execute specific responses to diverse environmental cues by encoding information in distinctly compartmentalized biochemical signalling reactions. Genetically encoded fluorescent biosensors enable the spatial and temporal monitoring of signalling events in live cells. Temporal and spatiotemporal computational models can be used to interpret biosensor experiments in complex biochemical networks and to explore hypotheses that are difficult to test experimentally. In this review, we first provide brief discussions of the experimental toolkit of fluorescent biosensors as well as computational basics with a focus on temporal and spatiotemporal deterministic models. We then describe how we used this combined approach to identify and investigate a protein kinase A (PKA) - cAMP - Ca2+ oscillatory circuit in MIN6 β cells, a mouse pancreatic β cell system. We describe the application of this combined approach to interrogate how this oscillatory circuit is differentially regulated in a nano-compartment formed at the plasma membrane by the scaffolding protein A kinase anchoring protein 79/150. We leveraged both temporal and spatiotemporal deterministic models to identify the key regulators of this oscillatory circuit, which we confirmed with further experiments. The powerful approach of combining live-cell biosensor imaging with quantitative modelling, as discussed here, should find widespread use in the investigation of spatiotemporal regulation of cell signalling.

Biology-inspired graph neural network encodes reactome and reveals biochemical reactions of disease

Functional heterogeneity of healthy human tissues complicates interpretation of molecular studies, impeding precision therapeutic target identification and treatment. Considering this, we generated a graph neural network with Reactome-based architecture and trained it using 9,115 samples from Genotype-Tissue Expression (GTEx). Our graph neural network (GNN) achieves adjusted Rand index (ARI) = 0.7909, while a Resnet18 control model achieves ARI = 0.7781, on 370 held-out healthy human tissue samples from The Cancer Genome Atlas (TCGA), despite the Resnet18 using over 600 times the parameters. Our GNN also succeeds in separating 83 healthy skin samples from 95 lesional psoriasis samples, revealing that upregulation of 26S- and NUB1-mediated degradation of NEDD8, UBD, and their conjugates is central to the largest perturbed reaction network component in psoriasis. We show that our results are not discoverable using traditional differential expression and hypergeometric pathway enrichment analyses yet are supported by separate human multi-omics and small-molecule mouse studies, suggesting future molecular disease studies may benefit from similar GNN analytical approaches.

Modeling transcriptional regulation of the cell cycle using a novel cybernetic-inspired approach

Quantitative understanding of cellular processes, such as cell cycle and differentiation, is impeded by various forms of complexity ranging from myriad molecular players and their multilevel regulatory interactions, cellular evolution with multiple intermediate stages, lack of elucidation of cause-effect relationships among the many system players, and the computational complexity associated with the profusion of variables and parameters. In this paper, we present an elegant modeling framework based on the cybernetic concept that biological regulation is inspired by objectives embedding entirely novel strategies for dimension reduction, process stage specification through the system dynamics, and innovative causal association of regulatory events with the ability to predict the evolution of the dynamical system. The elementary step of the modeling strategy involves stage-specific objective functions that are computationally-determined from experiments, augmented with dynamical network computations involving end point objective functions, mutual information, change point detection, and maximal clique centrality. We demonstrate the power of the method through application to the mammalian cell cycle, which involves thousands of biomolecules engaged in signaling, transcription, and regulation. Starting with a fine-grained transcriptional description obtained from RNA sequencing measurements, we develop an initial model, which is then dynamically modeled using the cybernetic-inspired method (CIM), utilizing the strategies described above. The CIM is able to distill the most significant interactions from a multitude of possibilities. In addition to capturing the complexity of regulatory processes in a mechanistically causal and stage-specific manner, we identify the functional network modules, including novel cell cycle stages. Our model is able to predict future cell cycles consistent with experimental measurements. We posit that this state-of-the-art framework has the promise to extend to the dynamics of other biological processes, with a potential to provide novel mechanistic insights.

STATEMENT OF SIGNIFICANCE

Cellular processes like cell cycle are overly complex, involving multiple players interacting at multiple levels, and explicit modeling of such systems is challenging. The availability of longitudinal RNA measurements provides an opportunity to "reverse-engineer" for novel regulatory models. We develop a novel framework, inspired using goal-oriented cybernetic model, to implicitly model transcriptional regulation by constraining the system using inferred temporal goals. A preliminary causal network based on information-theory is used as a starting point, and our framework is used to distill the network to temporally-based networks containing essential molecular players. The strength of this approach is its ability to dynamically model the RNA temporal measurements. The approach developed paves the way for inferring regulatory processes in many complex cellular processes.

Mathematical modeling of regulatory networks of intracellular processes - Aims and selected methods

Regulatory networks structure and signaling pathways dynamics are uncovered in time- and resource consuming experimental work. However, it is increasingly supported by modeling, analytical and computational techniques as well as discrete mathematics and artificial intelligence applied to to extract knowledge from existing databases. This review is focused on mathematical modeling used to analyze dynamics and robustness of these networks. This paper presents a review of selected modeling methods that facilitate advances in molecular biology.

Mathematical Models of Death Signaling Networks

This review provides an overview of the progress made by computational and systems biologists in characterizing different cell death regulatory mechanisms that constitute the cell death network. We define the cell death network as a comprehensive decision-making mechanism that controls multiple death execution molecular circuits. This network involves multiple feedback and feed-forward loops and crosstalk among different cell death-regulating pathways. While substantial progress has been made in characterizing individual cell death execution pathways, the cell death decision network is poorly defined and understood. Certainly, understanding the dynamic behavior of such complex regulatory mechanisms can be only achieved by applying mathematical modeling and system-oriented approaches. Here, we provide an overview of mathematical models that have been developed to characterize different cell death mechanisms and intend to identify future research directions in this field.

Leveraging network structure in nonlinear control

Over the last twenty years, dynamic modeling of biomolecular networks has exploded in popularity. Many of the classical tools for understanding dynamical systems are unwieldy in the highly nonlinear, poorly constrained, high-dimensional systems that often arise from these modeling efforts. Understanding complex biological systems is greatly facilitated by purpose-built methods that leverage common features of such models, such as local monotonicity, interaction graph sparsity, and sigmoidal kinetics. Here, we review methods for controlling the systems of ordinary differential equations used to model biomolecular networks. We focus on methods that make use of the structure of the network of interactions to help inform, which variables to target for control, and highlight the computational and experimental advantages of such approaches. We also discuss the importance of nonperturbative methods in biomedical and experimental molecular biology applications, where finely tuned interventions can be difficult to implement. It is well known that feedback loops, and positive feedback loops in particular, play a major determining role in the dynamics of biomolecular networks. In many of the methods we cover here, control over system trajectories is realized by overriding the behavior of key feedback loops.

Current State and Challenges of the Global Outcomes of Dental Caries Research in the Meta-Omics Era

Despite significant healthcare advances in the 21st century, the exact etiology of dental caries remains unsolved. The past two decades have witnessed a tremendous growth in our understanding of dental caries amid the advent of revolutionary omics technologies. Accordingly, a consensus has been reached that dental caries is a community-scale metabolic disorder, and its etiology is beyond a single causative organism. This conclusion was based on a variety of microbiome studies following the flow of information along the central dogma of biology from genomic data to the end products of metabolism. These studies were facilitated by the unprecedented growth of the next- generation sequencing tools and omics techniques, such as metagenomics and metatranscriptomics, to estimate the community composition of oral microbiome and its functional potential. Furthermore, the rapidly evolving proteomics and metabolomics platforms, including nuclear magnetic resonance spectroscopy and/or mass spectrometry coupled with chromatography, have enabled precise quantification of the translational outcomes. Although the majority supports 'conserved functional changes' as indicators of dysbiosis, it remains unclear how caries dynamics impact the microbiota functions and vice versa, over the course of disease onset and progression. What compounds the situation is the host-microbiota crosstalk. Genome-wide association studies have been undertaken to elucidate the interaction of host genetic variation with the microbiome. However, these studies are challenged by the complex interaction of host genetics and environmental factors. All these complementary approaches need to be orchestrated to capture the key players in this multifactorial disease. Herein, we critically review the milestones in caries research focusing on the state-of-art singular and integrative omics studies, supplemented with a bibliographic network analysis to address the oral microbiome, the host factors, and their interactions. Additionally, we highlight gaps in the dental literature and shed light on critical future research questions and study designs that could unravel the complexities of dental caries, the most globally widespread disease.

A Dynamic Mechanistic Model of Perceptual Binding

The brain’s ability to create a unified conscious representation of an object by integrating information from multiple perception pathways is called perceptual binding. Binding is crucial for normal cognitive function. Some perceptual binding errors and disorders have been linked to certain neurological conditions, brain lesions, and conditions that give rise to illusory conjunctions. However, the mechanism of perceptual binding remains elusive. Here, I present a computational model of binding using two sets of coupled oscillatory processes that are assumed to occur in response to two different percepts. I use the model to study the dynamic behavior of coupled processes to characterize how these processes can modulate each other and reach a temporal synchrony. I identify different oscillatory dynamic regimes that depend on coupling mechanisms and parameter values. The model can also discriminate different combinations of initial inputs that are set by initial states of coupled processes. Decoding brain signals that are formed through perceptual binding is a challenging task, but my modeling results demonstrate how crosstalk between two systems of processes can possibly modulate their outputs. Therefore, my mechanistic model can help one gain a better understanding of how crosstalk between perception pathways can affect the dynamic behavior of the systems that involve perceptual binding.

Patient-specific Boolean models of signalling networks guide personalised treatments

Prostate cancer is the second most occurring cancer in men worldwide. To better understand the mechanisms of tumorigenesis and possible treatment responses, we developed a mathematical model of prostate cancer which considers the major signalling pathways known to be deregulated. We personalised this Boolean model to molecular data to reflect the heterogeneity and specific response to perturbations of cancer patients. A total of 488 prostate samples were used to build patient-specific models and compared to available clinical data. Additionally, eight prostate cell line-specific models were built to validate our approach with dose-response data of several drugs. The effects of single and combined drugs were tested in these models under different growth conditions. We identified 15 actionable points of interventions in one cell line-specific model whose inactivation hinders tumorigenesis. To validate these results, we tested nine small molecule inhibitors of five of those putative targets and found a dose-dependent effect on four of them, notably those targeting HSP90 and PI3K. These results highlight the predictive power of our personalised Boolean models and illustrate how they can be used for precision oncology.

Can Systems Biology Advance Clinical Precision Oncology?

Precision oncology is perceived as a way forward to treat individual cancer patients. However, knowing particular cancer mutations is not enough for optimal therapeutic treatment, because cancer genotype-phenotype relationships are nonlinear and dynamic. Systems biology studies the biological processes at the systems' level, using an array of techniques, ranging from statistical methods to network reconstruction and analysis, to mathematical modeling. Its goal is to reconstruct the complex and often counterintuitive dynamic behavior of biological systems and quantitatively predict their responses to environmental perturbations. In this paper, we review the impact of systems biology on precision oncology. We show examples of how the analysis of signal transduction networks allows to dissect resistance to targeted therapies and inform the choice of combinations of targeted drugs based on tumor molecular alterations. Patient-specific biomarkers based on dynamical models of signaling networks can have a greater prognostic value than conventional biomarkers. These examples support systems biology models as valuable tools to advance clinical and translational oncological research.

The finding and researching algorithm for potentially oscillating enzymatic systems

Many processes in living organisms are subject to periodic oscillations at different hierarchical levels of their organization: from molecular-genetic to population and ecological. Oscillatory processes are responsible for cell cycles in both prokaryotes and eukaryotes, for circadian rhythms, for synchronous coupling of respiration with cardiac contractions, etc. Fluctuations in the numbers of organisms in natural populations can be caused by the populations' own properties, their age structure, and ecological relationships with other species. Along with experimental approaches, mathematical and computer modeling is widely used to study oscillating biological systems. This paper presents classical mathematical models that describe oscillatory behavior in biological systems. Methods for the search for oscillatory molecular-genetic systems are presented by the example of their special case - oscillatory enzymatic systems. Factors influencing the cyclic dynamics in living systems, typical not only of the molecular-genetic level, but of higher levels of organization as well, are considered. Application of different ways to describe gene networks for modeling oscillatory molecular-genetic systems is considered, where the most important factor for the emergence of cyclic behavior is the presence of feedback. Techniques for finding potentially oscillatory enzymatic systems are presented. Using the method described in the article, we present and analyze, in a step-by-step manner, first the structural models (graphs) of gene networks and then the reconstruction of the mathematical models and computational experiments with them. Structural models are ideally suited for the tasks of an automatic search for potential oscillating contours (linked subgraphs), whose structure can correspond to the mathematical model of the molecular-genetic system that demonstrates oscillatory behavior in dynamics. At the same time, it is the numerical study of mathematical models for the selected contours that makes it possible to confirm the presence of stable limit cycles in them. As an example of application of the technology, a network of 300 metabolic reactions of the bacterium Escherichia coli was analyzed using mathematical and computer modeling tools. In particular, oscillatory behavior was shown for a loop whose reactions are part of the tryptophan biosynthesis pathway.

Crosstalk between Plk1, p53, cell cycle, and G2/M DNA damage checkpoint regulation in cancer: computational modeling and analysis

Different cancer cell lines can have varying responses to the same perturbations or stressful conditions. Cancer cells that have DNA damage checkpoint-related mutations are often more sensitive to gene perturbations including altered Plk1 and p53 activities than cancer cells without these mutations. The perturbations often induce a cell cycle arrest in the former cancer, whereas they only delay the cell cycle progression in the latter cancer. To study crosstalk between Plk1, p53, and G2/M DNA damage checkpoint leading to differential cell cycle regulations, we developed a computational model by extending our recently developed model of mitotic cell cycle and including these key interactions. We have used the model to analyze the cancer cell cycle progression under various gene perturbations including Plk1-depletion conditions. We also analyzed mutations and perturbations in approximately 1800 different cell lines available in the Cancer Dependency Map and grouped lines by genes that are represented in our model. Our model successfully explained phenotypes of various cancer cell lines under different gene perturbations. Several sensitivity analysis approaches were used to identify the range of key parameter values that lead to the cell cycle arrest in cancer cells. Our resulting model can be used to predict the effect of potential treatments targeting key mitotic and DNA damage checkpoint regulators on cell cycle progression of different types of cancer cells.

A frequency-amplitude coordinator and its optimal energy consumption for biological oscillators

Biorhythm including neuron firing and protein-mRNA interaction are fundamental activities with diffusive effect. Their well-balanced spatiotemporal dynamics are beneficial for healthy sustainability. Therefore, calibrating both anomalous frequency and amplitude of biorhythm prevents physiological dysfunctions or diseases. However, many works were devoted to modulate frequency exclusively whereas amplitude is usually ignored, although both quantities are equally significant for coordinating biological functions and outputs. Especially, a feasible method coordinating the two quantities concurrently and precisely is still lacking. Here, for the first time, we propose a universal approach to design a frequency-amplitude coordinator rigorously via dynamical systems tools. We consider both spatial and temporal information. With a single well-designed coordinator, they can be calibrated to desired levels simultaneously and precisely. The practical usefulness and efficacy of our method are demonstrated in representative neuronal and gene regulatory models. We further reveal its fundamental mechanism and optimal energy consumption providing inspiration for biorhythm regulation in future.

Implications of Noise on Neural Correlates of Consciousness: A Computational Analysis of Stochastic Systems of Mutually Connected Processes

Random fluctuations in neuronal processes may contribute to variability in perception and increase the information capacity of neuronal networks. Various sources of random processes have been characterized in the nervous system on different levels. However, in the context of neural correlates of consciousness, the robustness of mechanisms of conscious perception against inherent noise in neural dynamical systems is poorly understood. In this paper, a stochastic model is developed to study the implications of noise on dynamical systems that mimic neural correlates of consciousness. We computed power spectral densities and spectral entropy values for dynamical systems that contain a number of mutually connected processes. Interestingly, we found that spectral entropy decreases linearly as the number of processes within the system doubles. Further, power spectral density frequencies shift to higher values as system size increases, revealing an increasing impact of negative feedback loops and regulations on the dynamics of larger systems. Overall, our stochastic modeling and analysis results reveal that large dynamical systems of mutually connected and negatively regulated processes are more robust against inherent noise than small systems.

Gene regulatory networks exhibit several kinds of memory: quantification of memory in biological and random transcriptional networks

Gene regulatory networks (GRNs) process important information in developmental biology and biomedicine. A key knowledge gap concerns how their responses change over time. Hypothesizing long-term changes of dynamics induced by transient prior events, we created a computational framework for defining and identifying diverse types of memory in candidate GRNs. We show that GRNs from a wide range of model systems are predicted to possess several types of memory, including Pavlovian conditioning. Associative memory offers an alternative strategy for the biomedical use of powerful drugs with undesirable side effects, and a novel approach to understanding the variability and time-dependent changes of drug action. We find evidence of natural selection favoring GRN memory. Vertebrate GRNs overall exhibit more memory than invertebrate GRNs, and memory is most prevalent in differentiated metazoan cell networks compared with undifferentiated cells. Timed stimuli are a powerful alternative for biomedical control of complex in vivo dynamics without genomic editing or transgenes.

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Gene regulatory networks' dynamics are modified by transient stimuli

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GRNs have several different types of memory, including associative conditioning

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Evolution favored GRN memory, and differentiated cells have the most memory capacity

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Training GRNs offers a novel biomedical strategy not dependent on genetic rewiring

Finding new edges: systems approaches to MTOR signaling

Cells have evolved highly intertwined kinase networks to finely tune cellular homeostasis to the environment. The network converging on the mechanistic target of rapamycin (MTOR) kinase constitutes a central hub that integrates metabolic signals and adapts cellular metabolism and functions to nutritional changes and stress. Feedforward and feedback loops, crosstalks and a plethora of modulators finely balance MTOR-driven anabolic and catabolic processes. This complexity renders it difficult — if not impossible — to intuitively decipher signaling dynamics and network topology. Over the last two decades, systems approaches have emerged as powerful tools to simulate signaling network dynamics and responses. In this review, we discuss the contribution of systems studies to the discovery of novel edges and modulators in the MTOR network in healthy cells and in disease.

Overcoming the Challenges to Enhancing Experimental Plant Biology With Computational Modeling

The study of complex biological systems necessitates computational modeling approaches that are currently underutilized in plant biology. Many plant biologists have trouble identifying or adopting modeling methods to their research, particularly mechanistic mathematical modeling. Here we address challenges that limit the use of computational modeling methods, particularly mechanistic mathematical modeling. We divide computational modeling techniques into either pattern models (e.g., bioinformatics, machine learning, or morphology) or mechanistic mathematical models (e.g., biochemical reactions, biophysics, or population models), which both contribute to plant biology research at different scales to answer different research questions. We present arguments and recommendations for the increased adoption of modeling by plant biologists interested in incorporating more modeling into their research programs. As some researchers find math and quantitative methods to be an obstacle to modeling, we provide suggestions for easy-to-use tools for non-specialists and for collaboration with specialists. This may especially be the case for mechanistic mathematical modeling, and we spend some extra time discussing this. Through a more thorough appreciation and awareness of the power of different kinds of modeling in plant biology, we hope to facilitate interdisciplinary, transformative research.

A systems biology approach to discovering pathway signaling dysregulation in metastasis

Total metastatic burden is the primary cause of death for many cancer patients. While the process of metastasis has been studied widely, much remains to be understood. Moreover, few agents have been developed that specifically target the major steps of the metastatic cascade. Many individual genes and pathways have been implicated in metastasis but a holistic view of how these interact and cooperate to regulate and execute the process remains somewhat rudimentary. It is unclear whether all of the signaling features that regulate and execute metastasis are yet fully understood. Novel features of a complex system such as metastasis can often be discovered by taking a systems-based approach. We introduce the concepts of systems modeling and define some of the central challenges facing the application of a multidisciplinary systems-based approach to understanding metastasis and finding actionable targets therein. These challenges include appreciating the unique properties of the high-dimensional omics data often used for modeling, limitations in knowledge of the system (metastasis), tumor heterogeneity and sampling bias, and some of the issues key to understanding critical features of molecular signaling in the context of metastasis. We also provide a brief introduction to integrative modeling that focuses on both the nodes and edges of molecular signaling networks. Finally, we offer some observations on future directions as they relate to developing a systems-based model of the metastatic cascade.

Applications of personalised signalling network models in precision oncology

As our ability to provide in-depth, patient-specific characterisation of the molecular alterations within tumours rapidly improves, it is becoming apparent that new approaches will be required to leverage the power of this data and derive the full benefit for each individual patient. Systems biology approaches are beginning to emerge within this field as a potential method of incorporating large volumes of network level data and distilling a coherent, clinically-relevant prediction of drug response. However, the initial promise of this developing field is yet to be realised. Here we argue that in order to develop these precise models of individual drug response and tailor treatment accordingly, we will need to develop mathematical models capable of capturing both the dynamic nature of drug-response signalling networks and key patient-specific information such as mutation status or expression profiles. We also review the modelling approaches commonly utilised within this field, and outline recent examples of their use in furthering the application of systems biology for a precision medicine approach to cancer treatment.

Disentangling a complex response in cell reprogramming and probing the Waddington landscape by automatic construction of Petri nets

We analyzed the developmental switch to sporulation of a multinucleate Physarum polycephalum plasmodial cell, a complex response to phytochrome photoreceptor activation. Automatic construction of Petri nets representing finite state machines assembled from trajectories of differential gene expression in single cells revealed alternative, genotype-dependent interconnected developmental routes and identified reversible steps, metastable states, commitment points, and subsequent irreversible steps together with molecular signatures associated with cell fate decision and differentiation. Formation of cyclic transits identified by transition invariants in mutants that are locked in a proliferative state is remarkable considering the view that oncogenic alterations may cause the formation of cancer attractors. We conclude that the Petri net approach is useful to probe the Waddington landscape of cellular reprogramming, to disentangle developmental routes for the reconstruction of the gene regulatory network, and to understand how genetic alterations or physiological conditions reshape the landscape eventually creating new basins of attraction. Unraveling the complexity of pathogenesis, disease progression, drug response or the analysis of attractor landscapes in other complex systems of uncertain structure might be additional fields of application.

Systems biology: perspectives on multiscale modeling in research on endocrine-related cancers

Drawing on concepts from experimental biology, computer science, informatics, mathematics and statistics, systems biologists integrate data across diverse platforms and scales of time and space to create computational and mathematical models of the integrative, holistic functions of living systems. Endocrine-related cancers are well suited to study from a systems perspective because of the signaling complexities arising from the roles of growth factors, hormones and their receptors as critical regulators of cancer cell biology and from the interactions among cancer cells, normal cells and signaling molecules in the tumor microenvironment. Moreover, growth factors, hormones and their receptors are often effective targets for therapeutic intervention, such as estrogen biosynthesis, estrogen receptors or HER2 in breast cancer and androgen receptors in prostate cancer. Given the complexity underlying the molecular control networks in these cancers, a simple, intuitive understanding of how endocrine-related cancers respond to therapeutic protocols has proved incomplete and unsatisfactory. Systems biology offers an alternative paradigm for understanding these cancers and their treatment. To correctly interpret the results of systems-based studies requires some knowledge of how in silico models are built, and how they are used to describe a system and to predict the effects of perturbations on system function. In this review, we provide a general perspective on the field of cancer systems biology, and we explore some of the advantages, limitations and pitfalls associated with using predictive multiscale modeling to study endocrine-related cancers.

Ensembles, dynamics, and cell types: Revisiting the statistical mechanics perspective on cellular regulation

Genetic regulatory networks control ontogeny. For fifty years Boolean networks have served as models of such systems, ranging from ensembles of random Boolean networks as models for generic properties of gene regulation to working dynamical models of a growing number of sub-networks of real cells. At the same time, their statistical mechanics has been thoroughly studied. Here we recapitulate their original motivation in the context of current theoretical and empirical research. We discuss ensembles of random Boolean networks whose dynamical attractors model cell types. A sub-ensemble is the critical ensemble. There is now strong evidence that genetic regulatory networks are dynamically critical, and that evolution is exploring the critical sub-ensemble. The generic properties of this sub-ensemble predict essential features of cell differentiation. In particular, the number of attractors in such networks scales as the DNA content raised to the 0.63 power. Data on the number of cell types as a function of the DNA content per cell shows a scaling relationship of 0.88. Thus, the theory correctly predicts a power law relationship between the number of cell types and the DNA contents per cell, and a comparable slope. We discuss these new scaling values and show prospects for new research lines for Boolean networks as a base model for systems biology.