Mathematical Modeling of Complex Regulatory Networks

Are There Biomimetic Lessons from Genetic Regulatory Networks for Developing a Lunar Industrial Ecology?

We examine the prospect for employing a bio-inspired architecture for a lunar industrial ecology based on genetic regulatory networks. The lunar industrial ecology resembles a metabolic system in that it comprises multiple chemical processes interlinked through waste recycling. Initially, we examine lessons from factory organisation which have evolved into a bio-inspired concept, the reconfigurable holonic architecture. We then examine genetic regulatory networks and their application in the biological cell cycle. There are numerous subtleties that would be challenging to implement in a lunar industrial ecology but much of the essence of biological circuitry (as implemented in synthetic biology, for example) is captured by traditional electrical engineering design with emphasis on feedforward and feedback loops to implement robustness.

Multiscale modeling meets machine learning: What can we learn?

Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incredibly successful in image recognition with immediate applications in diagnostics including electrophysiology, radiology, or pathology, where we have access to massive amounts of annotated data. However, machine learning often performs poorly in prognosis, especially when dealing with sparse data. This is a field where classical physics-based simulation seems to remain irreplaceable. In this review, we identify areas in the biomedical sciences where machine learning and multiscale modeling can mutually benefit from one another: Machine learning can integrate physics-based knowledge in the form of governing equations, boundary conditions, or constraints to manage ill-posted problems and robustly handle sparse and noisy data; multiscale modeling can integrate machine learning to create surrogate models, identify system dynamics and parameters, analyze sensitivities, and quantify uncertainty to bridge the scales and understand the emergence of function. With a view towards applications in the life sciences, we discuss the state of the art of combining machine learning and multiscale modeling, identify applications and opportunities, raise open questions, and address potential challenges and limitations. We anticipate that it will stimulate discussion within the community of computational mechanics and reach out to other disciplines including mathematics, statistics, computer science, artificial intelligence, biomedicine, systems biology, and precision medicine to join forces towards creating robust and efficient models for biological systems.

Transformative Impact of Proteomics on Cardiovascular Health and Disease: A Scientific Statement From the American Heart Association

The year 2014 marked the 20th anniversary of the coining of the term proteomics. The purpose of this scientific statement is to summarize advances over this period that have catalyzed our capacity to address the experimental, translational, and clinical implications of proteomics as applied to cardiovascular health and disease and to evaluate the current status of the field. Key successes that have energized the field are delineated; opportunities for proteomics to drive basic science research, facilitate clinical translation, and establish diagnostic and therapeutic healthcare algorithms are discussed; and challenges that remain to be solved before proteomic technologies can be readily translated from scientific discoveries to meaningful advances in cardiovascular care are addressed. Proteomics is the result of disruptive technologies, namely, mass spectrometry and database searching, which drove protein analysis from 1 protein at a time to protein mixture analyses that enable large-scale analysis of proteins and facilitate paradigm shifts in biological concepts that address important clinical questions. Over the past 20 years, the field of proteomics has matured, yet it is still developing rapidly. The scope of this statement will extend beyond the reaches of a typical review article and offer guidance on the use of next-generation proteomics for future scientific discovery in the basic research laboratory and clinical settings.

Validation of signalling pathways: Case study of the p16-mediated pathway

p16 is recognized as a tumor suppressor gene due to the prevalence of its genetic inactivation in all types of human cancers. Additionally, p16 gene plays a critical role in controlling aging, regulating cellular senescence, detection and maintenance of DNA damage. The molecular mechanism behind these events involves p16-mediated signaling pathway (or p16- Rb pathway), the focus of our study. Understanding functional dependence between dynamic behavior of biological components involved in the p16-mediated pathway and aforesaid molecular-level events might suggest possible implications in the diagnosis, prognosis and treatment of human cancer. In the present work, we employ reverse-engineering approach to construct the most detailed computational model of p16-mediated pathway in higher eukaryotes. We implement experimental data from the literature to validate the model, and under various assumptions predict the dynamic behavior of p16 and other biological components by interpreting the simulation results. The quantitative model of p16-mediated pathway is created in a systematic manner in terms of Petri net technologies.

Using systems biology approaches to understand cardiac inflammation and extracellular matrix remodeling in the setting of myocardial infarction

Inflammation and extracellular matrix (ECM) remodeling are important components regulating the response of the left ventricle to myocardial infarction (MI). Significant cellular- and molecular-level contributors can be identified by analyzing data acquired through high-throughput genomic and proteomic technologies that provide expression levels for thousands of genes and proteins. Large-scale data provide both temporal and spatial information that need to be analyzed and interpreted using systems biology approaches in order to integrate this information into dynamic models that predict and explain mechanisms of cardiac healing post-MI. In this review, we summarize the systems biology approaches needed to computationally simulate post-MI remodeling, including data acquisition, data analysis for biomarker classification and identification, data integration to build dynamic models, and data interpretation for biological functions. An example for applying a systems biology approach to ECM remodeling is presented as a reference illustration.

State estimation for genetic regulatory networks with mode-dependent leakage delays, time-varying delays, and Markovian jumping parameters

This paper considers the state estimation problem for Markovian jumping genetic regulatory networks (GRNs) with mode-dependent leakage and time-varying delays. In order to approximate the true concentrations of the mRNA and protein, the state estimator is designed using available measurement outputs. The GRNs are composed of N modes. The system switches from one mode to another according to a Markovian chain with known transition probabilities. Based on the Lyapunov functionals, including triple integral terms, some inequalities, and a time-varying delay partitioning approach, delay-dependent criteria which employ all upper bounds of time delays of each mode are obtained in terms of linear matrix inequalities (LMIs). This guarantees that the estimation error dynamics can be globally asymptotically stable from solutions of LMIs. Finally, a numerical example is presented to demonstrate the efficiency of the proposed estimation scheme.

Mathematical models in biology: from molecules to life

A vexing question in the biological sciences is the following: can biological phenotypes be explained with mathematical models of molecules that interact according to physical laws? At the crux of the matter lies the doubt that humans can develop physically faithful mathematical representations of living organisms. We discuss advantages that synthetic biological systems confer that may help us describe life's distinctiveness with tractable mathematics that are grounded on universal laws of thermodynamics and molecular biology.

Development of a quantitative model of pregnane X receptor (PXR) mediated xenobiotic metabolizing enzyme induction

The pregnane X receptor plays an integral role in the regulation of hepatic metabolism. It has been shown to regulate CYP3A4, which is the most abundant cytochrome P450 in the human liver. With its large and flexible ligand-binding domain, PXR can be activated by an enormous range of relatively small, hydrophobic, exogenous compounds. Upon activation, PXR partners with the retinoid X receptor (RXR) to form a heterodimer. The newly formed heterodimer binds to an appropriate DNA response element, causing increased transcription. This leads to an induction in the level of CYP3A4. These mechanistic steps are included into a biologically-based mathematical model. The quantitative model predicts fold level inductions of CYP3A4 mRNA and protein in response to PXR activation. Model parameter values have been taken from literature when appropriate. Unknown parameter values are estimated by optimizing the model results to published in vivo and in vitro data sets. A sensitivity analysis is performed to evaluate the model structure and identify future data needs which would be critical to revising the model.

Systems-level engineering of nonfermentative metabolism in yeast

We designed and experimentally validated an in silico gene deletion strategy for engineering endogenous one-carbon (C1) metabolism in yeast. We used constraint-based metabolic modeling and computer-aided gene knockout simulations to identify five genes (ALT2, FDH1, FDH2, FUM1, and ZWF1), which, when deleted in combination, predicted formic acid secretion in Saccharomyces cerevisiae under aerobic growth conditions. Once constructed, the quintuple mutant strain showed the predicted increase in formic acid secretion relative to a formate dehydrogenase mutant (fdh1 fdh2), while formic acid secretion in wild-type yeast was undetectable. Gene expression and physiological data generated post hoc identified a retrograde response to mitochondrial deficiency, which was confirmed by showing Rtg1-dependent NADH accumulation in the engineered yeast strain. Formal pathway analysis combined with gene expression data suggested specific modes of regulation that govern C1 metabolic flux in yeast. Specifically, we identified coordinated transcriptional regulation of C1 pathway enzymes and a positive flux control coefficient for the branch point enzyme 3-phosphoglycerate dehydrogenase (PGDH). Together, these results demonstrate that constraint-based models can identify seemingly unrelated mutations, which interact at a systems level across subcellular compartments to modulate flux through nonfermentative metabolic pathways.

Computational systems biology of the cell cycle

One of the early success stories of computational systems biology was the work done on cell-cycle regulation. The earliest mathematical descriptions of cell-cycle control evolved into very complex, detailed computational models that describe the regulation of cell division in many different cell types. On the way these models predicted several dynamical properties and unknown components of the system that were later experimentally verified/identified. Still, research on this field is far from over. We need to understand how the core cell-cycle machinery is controlled by internal and external signals, also in yeast cells and in the more complex regulatory networks of higher eukaryotes. Furthermore, there are many computational challenges what we face as new types of data appear thanks to continuing advances in experimental techniques. We have to deal with cell-to-cell variations, revealed by single cell measurements, as well as the tremendous amount of data flowing from high throughput machines. We need new computational concepts and tools to handle these data and develop more detailed, more precise models of cell-cycle regulation in various organisms. Here we review past and present of computational modeling of cell-cycle regulation, and discuss possible future directions of the field.

Modeling the effects of cell cycle M-phase transcriptional inhibition on circadian oscillation

Circadian clocks are endogenous time-keeping systems that temporally organize biological processes. Gating of cell cycle events by a circadian clock is a universal observation that is currently considered a mechanism serving to protect DNA from diurnal exposure to ultraviolet radiation or other mutagens. In this study, we put forward another possibility: that such gating helps to insulate the circadian clock from perturbations induced by transcriptional inhibition during the M phase of the cell cycle. We introduced a periodic pulse of transcriptional inhibition into a previously published mammalian circadian model and simulated the behavior of the modified model under both constant darkness and light–dark cycle conditions. The simulation results under constant darkness indicated that periodic transcriptional inhibition could entrain/lock the circadian clock just as a light–dark cycle does. At equilibrium states, a transcriptional inhibition pulse of certain periods was always locked close to certain circadian phases where inhibition on Per and Bmal1 mRNA synthesis was most balanced. In a light–dark cycle condition, inhibitions imposed at different parts of a circadian period induced different degrees of perturbation to the circadian clock. When imposed at the middle- or late-night phase, the transcriptional inhibition cycle induced the least perturbations to the circadian clock. The late-night time window of least perturbation overlapped with the experimentally observed time window, where mitosis is most frequent. This supports our hypothesis that the circadian clock gates the cell cycle M phase to certain circadian phases to minimize perturbations induced by the latter. This study reveals the hidden effects of the cell division cycle on the circadian clock and, together with the current picture of genome stability maintenance by circadian gating of cell cycle, provides a more comprehensive understanding of the phenomenon of circading gating of cell cycle.

Circadian clock and cell cycle are two important biological processes that are essential for nearly all eukaryotes. The circadian clock governs day and night 24 h periodic molecular processes and physiological behaviors, while cell cycle controls cell division process. It has been widely observed that cell division does not occur randomly across day and night, but instead is normally confined to specific times during day and night. These observations suggest that cell cycle events are gated by the circadian clock. Regarding the biological benefit and rationale for this intriguing gating phenomena, it has been postulated that circadian gating helps to maintain genome stability by confining radiation-sensitive cell cycle phases to night. Bearing in mind the facts that global transcriptional inhibition occurs at cell division and transcriptional inhibition shifts circadian phases and periods, we postulate that confining cell division to specific circadian times benefits the circadian clock by removing or minimizing the side effects of cell division on the circadian clock. Our results based on computational simulation in this study show that periodic transcriptional inhibition can perturb the circadian clock by altering circadian phases and periods, and the magnitude of the perturbation is clearly circadian phase dependent. Specifically, transcriptional inhibition initiated at certain circadian phases induced minimal perturbation to the circadian clock. These results provide support for our postulation. Our postulation and results point to the importance of the effect of cell division on the circadian clock in the interaction between circadian and cell cycle and suggest that it should be considered together with other factors in the exploitation of circadian cell cycle interaction, especially the phenomena of circadian gating of cell cycle.

Accelerated search for biomolecular network models to interpret high-throughput experimental data

BACKGROUND

The functions of human cells are carried out by biomolecular networks, which include proteins, genes, and regulatory sites within DNA that encode and control protein expression. Models of biomolecular network structure and dynamics can be inferred from high-throughput measurements of gene and protein expression. We build on our previously developed fuzzy logic method for bridging quantitative and qualitative biological data to address the challenges of noisy, low resolution high-throughput measurements, i.e., from gene expression microarrays. We employ an evolutionary search algorithm to accelerate the search for hypothetical fuzzy biomolecular network models consistent with a biological data set. We also develop a method to estimate the probability of a potential network model fitting a set of data by chance. The resulting metric provides an estimate of both model quality and dataset quality, identifying data that are too noisy to identify meaningful correlations between the measured variables.

RESULTS

Optimal parameters for the evolutionary search were identified based on artificial data, and the algorithm showed scalable and consistent performance for as many as 150 variables. The method was tested on previously published human cell cycle gene expression microarray data sets. The evolutionary search method was found to converge to the results of exhaustive search. The randomized evolutionary search was able to converge on a set of similar best-fitting network models on different training data sets after 30 generations running 30 models per generation. Consistent results were found regardless of which of the published data sets were used to train or verify the quantitative predictions of the best-fitting models for cell cycle gene dynamics.

CONCLUSION

Our results demonstrate the capability of scalable evolutionary search for fuzzy network models to address the problem of inferring models based on complex, noisy biomolecular data sets. This approach yields multiple alternative models that are consistent with the data, yielding a constrained set of hypotheses that can be used to optimally design subsequent experiments.

The sorting direct method for stochastic simulation of biochemical systems with varying reaction execution behavior

A key to advancing the understanding of molecular biology in the post-genomic age is the development of accurate predictive models for genetic regulation, protein interaction, metabolism, and other biochemical processes. To facilitate model development, simulation algorithms must provide an accurate representation of the system, while performing the simulation in a reasonable amount of time. Gillespie's stochastic simulation algorithm (SSA) accurately depicts spatially homogeneous models with small populations of chemical species and properly represents noise, but it is often abandoned when modeling larger systems because of its computational complexity. In this work, we examine the performance of different versions of the SSA when applied to several biochemical models. Through our analysis, we discover that transient changes in reaction execution frequencies, which are typical of biochemical models with gene induction and repression, can dramatically affect simulator performance. To account for these shifts, we propose a new algorithm called the sorting direct method that maintains a loosely sorted order of the reactions as the simulation executes. Our measurements show that the sorting direct method performs favorably when compared to other well-known exact stochastic simulation algorithms.

Circuit topology and the evolution of robustness in two-gene circadian oscillators

Many parameters driving the behavior of biochemical circuits vary extensively and are thus not fine-tuned. Therefore, the topology of such circuits (the who-interacts-with-whom) is key to understanding their central properties. I here explore several hundred different topologies of a simple biochemical model of circadian oscillations to ask two questions: Do different circuits differ dramatically in their robustness to parameter change? If so, can a process of gradual molecular evolution find highly robust topologies when starting from less robust topologies? I find that the distribution of robustness among different circuit topologies is highly skewed: Most show low robustness, whereas very few topologies are highly robust. To address the second evolutionary question, I define a topology graph, each of whose nodes corresponds to one circuit topology that shows circadian oscillations. Two nodes in this graph are connected if they differ by only one regulatory interaction within the circuit. For the circadian oscillator I study, most topologies are connected in this graph, making evolutionary transitions from low to high robustness easy. A similar approach has been used to study the evolution of robustness in biological macromolecules, with similar results. This suggests that the same principles govern the evolution of robustness on different levels of biological organization. The regulatory interlocking of several oscillating gene products in biological circadian oscillators may exist because it provides robustness.