Data-driven Mathematical Modeling Research Articles

Data-Driven Mathematical Model of Osteosarcoma.

Simple SummaryOsteosarcoma is the most common primary bone tumor and has a poor prognosis. Therefore, it is important to understand the mechanism of the development of osteosarcoma to overcome therapy resistance. Several mathematical models have been developed to study the initiation and progression of many cancer types. However, there are currently no mathematical models for the progression of osteosarcoma, to the best of our knowledge. In this work, we develop a data-driven mathematical model to analyze the impact of the immune cell interactions on the growth of osteosarcoma tumors that have distinct immune patterns. Our model provides a foundation for investigating the effect of various treatments on the dynamics of key players in the primary tumor, including immune cells and cytokines, and ultimately the whole tumor.As the immune system has a significant role in tumor progression, in this paper, we develop a data-driven mathematical model to study the interactions between immune cells and the osteosarcoma microenvironment. Osteosarcoma tumors are divided into three clusters based on their relative abundance of immune cells as estimated from their gene expression profiles. We then analyze the tumor progression and effects of the immune system on cancer growth in each cluster. Cluster 3, which had approximately the same number of naive and M2 macrophages, had the slowest tumor growth, and cluster 2, with the highest population of naive macrophages, had the highest cancer population at the steady states. We also found that the fastest growth of cancer occurred when the anti-tumor immune cells and cytokines, including dendritic cells, helper T cells, cytotoxic cells, and IFN-, switched from increasing to decreasing, while the dynamics of regulatory T cells switched from decreasing to increasing. Importantly, the most impactful immune parameters on the number of cancer and total cells were the activation and decay rates of the macrophages and regulatory T cells for all clusters. This work presents the first osteosarcoma progression model, which can be later extended to investigate the effectiveness of various osteosarcoma treatments.

Modeling multi-sensory feedback control of zebrafish in a flow.

Understanding how animals navigate complex environments is a fundamental challenge in biology and a source of inspiration for the design of autonomous systems in engineering. Animal orientation and navigation is a complex process that integrates multiple senses, whose function and contribution are yet to be fully clarified. Here, we propose a data-driven mathematical model of adult zebrafish engaging in counter-flow swimming, an innate behavior known as rheotaxis. Zebrafish locomotion in a two-dimensional fluid flow is described within the finite-dipole model, which consists of a pair of vortices separated by a constant distance. The strength of these vortices is adjusted in real time by the fish to afford orientation and navigation control, in response to of the multi-sensory input from vision, lateral line, and touch. Model parameters for the resulting stochastic differential equations are calibrated through a series of experiments, in which zebrafish swam in a water channel under different illumination conditions. The accuracy of the model is validated through the study of a series of measures of rheotactic behavior, contrasting results of real and in-silico experiments. Our results point at a critical role of hydromechanical feedback during rheotaxis, in the form of a gradient-following strategy.

A generic approach to decipher the mechanistic pathway of heterogeneous protein aggregation kinetics.

Amyloid formation is a generic property of many protein/polypeptide chains. A broad spectrum of proteins, despite having diversity in the inherent precursor sequence and heterogeneity present in the mechanism of aggregation produces a common cross β-spine structure that is often associated with several human diseases. However, a general modeling framework to interpret amyloid formation remains elusive. Herein, we propose a data-driven mathematical modeling approach that elucidates the most probable interaction network for the aggregation of a group of proteins (α-synuclein, Aβ42, Myb, and TTR proteins) by considering an ensemble set of network models, which include most of the mechanistic complexities and heterogeneities related to amyloidogenesis. The best-fitting model efficiently quantifies various timescales involved in the process of amyloidogenesis and explains the mechanistic basis of the monomer concentration dependency of amyloid-forming kinetics. Moreover, the present model reconciles several mutant studies and inhibitor experiments for the respective proteins, making experimentally feasible non-intuitive predictions, and provides further insights about how to fine-tune the various microscopic events related to amyloid formation kinetics. This might have an application to formulate better therapeutic measures in the future to counter unwanted amyloidogenesis. Importantly, the theoretical method used here is quite general and can be extended for any amyloid-forming protein.

Modal decompositions of the kinematics of Crevalle jack and the fluid–caudal fin interaction

To understand the governing mechanisms of bio-inspired swimming has always been challenging due to intense interactions between flexible bodies of natural aquatic species and water around them. Advanced modal decomposition techniques provide us with tools to develop more in-depth understating about these complex dynamical systems. In this paper, we employ proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) techniques to extract energetically strongest spatio-temporal orthonormal components of complex kinematics of a Crevalle jack (Caranx hippos) fish. Then, we present a computational framework for handling fluid–structure interaction related problems in order to investigate their contributions towards the overall dynamics of highly nonlinear systems. We find that the undulating motion of this fish can be described by only two standing-wave like spatially orthonormal modes. Constructing the data set from our numerical simulations for flows over the membranous caudal fin of the jack fish, our modal analyses reveal that only the first few modes receive energy from both the fluid and structure, but the contribution of the structure in the remaining modes is minimal. For the viscous and transitional flow conditions considered here, both spatially and temporally orthonormal modes show strikingly similar coherent flow structures. Our investigations are expected to assist in developing data-driven reduced-order mathematical models to examine the dynamics of bio-inspired swimming robots and develop new and effective control strategies to bring their performance closer to real fish species.

An experimental design tool to optimize inference precision in data-driven mathematical models of bacterial infections in vivo.

The management of bacterial diseases calls for a detailed knowledge about the dynamic changes in host-bacteria interactions. Biological insights are gained by integrating experimental data with mechanistic mathematical models to infer experimentally unobservable quantities. This inter-disciplinary field would benefit from experiments with maximal information content yielding high-precision inference. Here, we present a computationally efficient tool for optimizing experimental design in terms of parameter inference in studies using isogenic-tagged strains. We study the effect of three experimental design factors: number of biological replicates, sampling timepoint selection and number of copies per tagged strain. We conduct a simulation study to establish the relationship between our optimality criterion and the size of parameter estimate confidence intervals, and showcase its application in a range of biological scenarios reflecting different dynamics patterns observed in experimental infections. We show that in low-variance systems with low killing and replication rates, predicting high-precision experimental designs is consistently achieved; higher replicate sizes and strategic timepoint selection yield more precise estimates. Finally, we address the question of resource allocation under constraints; given a fixed number of host animals and a constraint on total inoculum size per host, infections with fewer strains at higher copies per strain lead to higher-precision inference.

Guiding Students to Understand Functional Responses: Holling's Disc Experiment Revisited

ABSTRACT Inspired by the approach first employed by C.S. Holling in his classic “disc experiment,” this article provides a sequence of learning activities that increase students' understanding of the mechanisms behind saturating effects in predator-prey scenarios. The proposed lesson is recommended for inclusion in courses that address mathematical biology or modeling from introductory to advanced levels. The featured activities include a theoretical derivation of Holling's type II functional response model, a hands-on experiment for data gathering, and tools for further exploration through individual-based computer simulations. This multi-faceted approach gives students the opportunity to gather different sets of data in order to meet multiple learning objectives. Classroom trials conducted in Spring 2019 indicate that the proposed instructional resources and activities are effective for improving students' understanding of the mechanisms in Holling's type II functional response equation, and deepen students' appreciation of authentic data-driven mathematical modeling in ecology.

A new data-driven mathematical model dissociates attractiveness from sexual dimorphism of human faces

Human facial attractiveness is evaluated by using multiple cues. Among others, sexual dimorphism (i.e. masculinity for male faces/femininity for female faces) is an influential factor of perceived attractiveness. Since facial attractiveness is judged by incorporating sexually dimorphic traits as well as other cues, it is theoretically possible to dissociate sexual dimorphism from facial attractiveness. This study tested this by using a data-driven mathematical modelling approach. We first analysed the correlation between perceived masculinity/femininity and attractiveness ratings for 400 computer-generated male and female faces (Experiment 1) and found positive correlations between perceived femininity and attractiveness for both male and female faces. Using these results, we manipulated a set of faces along the attractiveness dimension while controlling for sexual dimorphism by orthogonalisation with data-driven mathematical models (Experiment 2). Our results revealed that perceived attractiveness and sexual dimorphism are dissociable, suggesting that there are as yet unidentified facial cues other than sexual dimorphism that contribute to facial attractiveness. Future studies can investigate the true preference of sexual dimorphism or the genuine effects of attractiveness by using well-controlled facial stimuli like those that this study generated. The findings will be of benefit to the further understanding of what makes a face attractive.

Application of the group method of data handling and variable importance analysis for prediction and modelling of saltwater intrusion processes in coastal aquifers

Data-driven mathematical models are powerful prediction tools, which are utilized to approximate solution responses obtained using numerical saltwater intrusion simulation models. Employing data-driven prediction models as a replacement of the complex groundwater flow and transport models enables prediction of future scenarios. Most important, it also helps save computational time, effort and requirements when developing optimal coastal aquifer management methodologies using complex and large-scale coupled simulation-optimization models. In this study, a new data-driven mathematical model, namely group method of data handling (GMDH)-based prediction models, is developed and utilized to predict salinity concentration in a coastal aquifer by mimicking the responses of a variable-density flow and solute transport numerical simulation model. For comparison and evaluation purpose, the prediction performances of GMDH models were compared with well-established support vector machine regression and genetic programming based models. In addition, one important characteristic of the GMDH models is explored and evaluated, i.e. the ability to identify a set of most influential input predictor variables (pumping rates) that had the most significant impact on the outcomes (salinity concentration at monitoring locations). To confirm variable importance, 3 tests are conducted in which new GMDH models are constructed using subsets of the original datasets. In TEST 1, new GMDH models are constructed using a set of most influential variables (consisting of pumping rates at selected locations) only. In TEST 2, a subset of 20 variables (10 most and least influential variables) is used to develop new GMDH models. In TEST 3, a subset of the least influential variables is used to develop GMDH models. The performance evaluation results demonstrate that GMDH models developed using the entire dataset had reasonable prediction accuracy and efficiency. The comparison performance evaluation results for the three test scenarios highlighted the importance of the appropriate selection of relevant input pumping rates when developing accurate prediction models. The results suggested that incorporating the least influential variables deteriorate the accuracy of the prediction models; thus, considering the most influential pumping rates it is possible to develop more accurate and efficient salinity prediction models. Overall, the evaluation results from this study establish that the GMDH models and the inherent input variable ranking capability can be utilized as accurate and efficient coastal saltwater intrusion prediction models. Hence, GMDH models are viable saltwater intrusion modelling tools, which can be employed in future regional-scale saltwater intrusion prediction and management investigations.

Characterization of multicellular breast tumor spheroids using image data-driven biophysical mathematical modeling

Multicellular tumor spheroid (MCTS) systems provide an in vitro cell culture model system which mimics many of the complexities of an in vivo solid tumor and tumor microenvironment, and are often used to study cancer cell growth and drug efficacy. Here, we present a coupled experimental-computational framework to estimate phenotypic growth and biophysical tumor microenvironment properties. This novel framework utilizes standard microscopy imaging of MCTS systems to drive a biophysical mathematical model of MCTS growth and mechanical interactions. By extending our previous in vivo mechanically-coupled reaction–diffusion modeling framework we developed a microscopy image processing framework capable of mechanistic characterization of MCTS systems. Using MDA-MB-231 breast cancer MCTS, we estimated biophysical parameters of cellular diffusion, rate of cellular proliferation, and cellular tractions forces. We found significant differences in these model-based biophysical parameters throughout the treatment time course between untreated and treated MCTS systems, whereas traditional size-based morphometric parameters were inconclusive. The proposed experimental-computational framework estimates mechanistic MCTS growth and invasion parameters with significant potential to assist in better and more precise assessment of in vitro drug efficacy through the development of computational analysis methodologies for three-dimensional cell culture systems to improve the development and evaluation of antineoplastic drugs.

Personalized surveillance for hepatocellular carcinoma in cirrhosis – using machine learning adapted to HCV status

Refining hepatocellular carcinoma (HCC) surveillance programs requires improved individual risk prediction. Thus, we aimed to develop algorithms based on machine learning approaches to predict the risk of HCC more accurately in patients with HCV-related cirrhosis, according to their virological status. Patients with compensated biopsy-proven HCV-related cirrhosis from the French ANRS CO12 CirVir cohort were included in a semi-annual HCC surveillance program. Three prognostic models for HCC occurrence were built, using (i) Fine-Gray regression as a benchmark, (ii) single decision tree (DT), and (iii) random survival forest for competing risks survival (RSF). Model performance was evaluated from C-indexes validated externally in the ANRS CO22 Hepather cohort (n= 668 enrolled between 08/2012-01/2014). Out of 836 patients analyzed, 156 (19%) developed HCC and 434 (52%) achieved sustained virological response (SVR) (median follow-up 63 months). Fine-Gray regression models identified 6 independent predictors of HCC occurrence in patients before SVR (past excessive alcohol intake, genotype 1, elevated AFP and GGT, low platelet count and albuminemia) and 3 in patients after SVR (elevated AST, low platelet count and shorter prothrombin time). DT analysis confirmed these associations but revealed more complex interactions, yielding 8 patient groups with varying cancer risks and predictors depending on SVR achievement. On RSF analysis, the most important predictors of HCC varied by SVR status (non-SVR: platelet count, GGT, AFP and albuminemia; SVR: prothrombin time, ALT, age and platelet count). Externally validated C-indexes before/after SVR were 0.64/0.64 [Fine-Gray], 0.60/62 [DT] and 0.71/0.70 [RSF]. Risk factors for hepatocarcinogenesis differ according to SVR status. Machine learning algorithms can refine HCC risk assessment by revealing complex interactions between cancer predictors. Such approaches could be used to develop more cost-effective tailored surveillance programs. Patients with HCV-related cirrhosis must be included in liver cancer surveillance programs, which rely on ultrasound examination every 6 months. Hepatocellular carcinoma (HCC) screening is hampered by sensitivity issues, leading to late cancer diagnoses in a substantial number of patients. Refining surveillance periodicity and modality using more sophisticated imaging techniques such as MRI may only be cost-effective in patients with the highest HCC incidence. Herein, we demonstrate how machine learning algorithms (i.e. data-driven mathematical models to make predictions or decisions), can refine individualized risk prediction.

Research Spotlights

We are fortunate to have three topically diverse papers featured in Research Spotlights in the current issue. The first of these, “Stochastic Sensitivity: A Computable Lagrangian Uncertainty Measure for Unsteady Flows," deals with modeling uncertainties in velocity data for the purpose of quantifying their influence when computing Lagrangian particle trajectories of fluids. One application that author Sanjeeva Balasuriya gives for pursuing this line of research is climate and environmental modeling: ocean and atmospheric models utilize velocity data to understand the movement of such quantities of interest as pollutants and plankton, and the trajectories of these quantities of interest have an impact on the environment and climate. This paper fills a gap in the current literature by addressing specifically the impact of velocity uncertainties---including those due to measurement error, turbulence at subgrid levels, or other effects uncaptured by the model---on trajectories. It offers the reader a “set of rigorous computational tools" to quantify the resulting Lagrangian uncertainties as a “physically interpretable field." The final section contains an extensive discussion in which the author considers connections of this work to uncertainty quantification and illuminates important remaining research directions. The second article, coauthored by Yuanzhao Zhang and Adilson E. Motter, is entitled “Symmetric-Independent Stability Analysis of Synchronization Patterns." The stability of synchronization patterns in complex networks is important to understand because of the “significant ramifications in various biological and technical systems" in the absence of such analysis. The key innovation in the present work is the introduction of a new algorithm to find the finest simultaneous block diagonalization (SBD) for any given set of self-adjoint matrices. This permits the extension of the master stability function (MSF) formalism since the proposed method now allows for the optimal separation of perturbation modes from which the stability of arbitrary synchronization patterns can then be undertaken. The authors provide a convincing demonstration of the strength of the new approach by applying their method to characterize permanently stable chimera-like states in multilayer networks. The paper includes a gentle introduction to matrix $*$-algebras and their relevance in developing the new algorithm; code for the latter is available on a GitHub repository, along with test problems. Importantly, the reader should note the potential for SBD in applications beyond the topic considered here---indeed, the authors suggest it may be relevant in other applications that involve many matrices such as control of network systems and semidefinite programming. The subject of the last of the three articles is extremely timely, as the title “Forecasting Elections Using Compartmental Models of Infection" itself suggests. Authors Alexandria Volkening, Daniel F. Linder, Mason A. Porter, and Grzegorz A. Rempala propose a data-driven mathematical model of the temporal evolution of political opinions during U.S. elections. Key features include the explicit modeling of how states influence each other through a compartmental model of disease dynamics, treating “voting intentions as contagions” that spread between states. Data fitting with polling data is used to specify the values of the parameters in the model, and the model predictions are compared to election outcomes from several recent U.S. elections. The initial model is expanded to a stochastic differential equations model in an effort to capture and quantify uncertainty in a given race. The authors are clear in describing their simplifications in modeling, yet the comparison reveals their forecasting method “performs as well as popular analysts." In the interest of transparency and in an effort to encourage more readers to become engaged in the remaining research questions, all codes and data associated with the article are available to the public. And yes, the authors also provide a link where the reader can find their model's forecast for the 2020 U.S. election!

Accelerating river blindness elimination by supplementing MDA with a vegetation \u201cslash and clear\u201d vector control strategy: a data-driven modeling analysis

Attention is increasingly focusing on how best to accelerate progress toward meeting the WHO’s 2030 goals for neglected tropical diseases (NTDs). For river blindness, a major NTD targeted for elimination, there is a long history of using vector control to suppress transmission, but traditional larvicide-based approaches are limited in their utility. One innovative and sustainable approach, “slash and clear”, involves clearing vegetation from breeding areas, and recent field trials indicate that this technique very effectively reduces the biting density of Simulium damnosum s.s. In this study, we use a Bayesian data-driven mathematical modeling approach to investigate the potential impact of this intervention on human onchocerciasis infection. We developed a novel “slash and clear” model describing the effect of the intervention on seasonal black fly biting rates and coupled this with our population dynamics model of Onchocerca volvulus transmission. Our results indicate that supplementing annual drug treatments with “slash and clear” can significantly accelerate the achievement of onchocerciasis elimination. The efficacy of the intervention is not very sensitive to the timing of implementation, and the impact is meaningful even if vegetation is cleared only once per year. As such, this community-driven technique will represent an important option for achieving and sustaining O. volvulus elimination.

Application of machine learning to accidents detection at directional drilling

We present a data-driven algorithm and mathematical model for anomaly alarming at directional drilling. The algorithm is based on machine learning. It compares the real-time drilling telemetry with one corresponding to past accidents and analyses the level of similarity. The model performs a time-series comparison using aggregated statistics and Gradient Boosting classification. It is trained on historical data containing the drilling telemetry of 80 wells drilled within 19 oilfields. The model can detect an anomaly and identify its type by comparing the real-time measurements while drilling with the ones from the database of past accidents. Validation tests show that our algorithm identifies half of the anomalies with about 0.53 false alarms per day on average. The model performance ensures sufficient time and cost savings as it enables partial prevention of the failures and accidents at the well construction.

Data-driven mathematical model of East-Asian facial attractiveness: the relative contributions of shape and reflectance to attractiveness judgements.

Facial attractiveness is judged through a combination of multiple cues including morphology (facial shape) and skin properties (facial reflectance). While several studies have examined the way in which people in Western cultures judge facial attractiveness, there have been fewer investigations into non-Western attitudes. This is because stimuli that quantitatively vary the attractiveness of non-Western faces are rare. In the present study, we built a model of the attractiveness of East-Asian faces, judged by East-Asian observers. Therefore, 400 computer-generated East-Asian faces were created and attractiveness rating scores were collected from Japanese observers. Data-driven mathematical calculations were used to identify quantitative links between facial attractiveness and shape and reflectance properties, with no prior hypothesis. Results indicate that faces with larger eyes, smaller noses and brighter skin are judged as more attractive, regardless of the sex of the faces, possibly reflecting a general preference for femininity. Shape is shown to be a strong determinant of attractiveness for both male and female faces, while reflectance properties are less important in judging male facial attractiveness. Our model provides a tool to effectively produce East-Asian face stimuli that quantitatively varies attractiveness and can be used to elucidate visual processes related to attractiveness judgements.

Bacteria display optimal transport near surfaces

The near-surface swimming patterns of bacteria are determined by hydrodynamic interactions between the bacteria and the surface, which trap the bacteria in smooth circular trajectories that lead to inefficient surface exploration. Here, we combine experiments with a data-driven mathematical model to show that the surface exploration of a pathogenic strain of Escherichia coli results from a complex interplay between motility and transient surface adhesion events. These events allow the bacteria to break the smooth circular trajectories and regulate their transport properties by exploiting stop events that are facilitated by surface adhesion and lead to characteristic intermittent motion on surfaces. We find that the experimentally measured frequency of these stop-adhesion events coincides with the value that maximizes bacterial surface diffusivity according to our mathematical model. We discuss the applicability of our experimental and theoretical results to other bacterial strains on different surfaces. Our findings suggest that swimming bacteria use transient adhesion as a generic mechanism to regulate surface motion. Bacteria swimming near surfaces can get trapped in circular trajectories that lead nowhere, hindering efficient surface exploration. A harmful strain of bacteria is now shown to circumvent the problem by exploiting transient surface adhesion events.

Single-cell data-driven mathematical model reveals possible molecular mechanisms of embryonic stem-cell differentiation.

Embryonic development is widely studied due to its application in disease treatment. The published literature demonstrated that Krüppel-like factor 8(KLF8) plays an important role in modulating mesendoderm to definitive endoderm (DE) differentiation. However, it is not clear how KLF8 interacts with other key genes and affects the differentiation process. To qualitatively and quantitatively explore the molecular mechanisms of KLF8 during the differentiation of human embryonic stem cells (hESCs) in detail, we developed a mathematical model to describe the dynamics between KLF8 and two other significant genes, E-cadherin(CDH1) and Zinc-finger E-box-binding homeobox1(ZEB1). Based on the single-cell RNA-seq data, the model structure and parameters were obtained using particle swarm optimization (PSO). The bifurcation analysis and simulation results reveal that the system can exhibit a complex tristable transition, which corresponds to the three states of embryonic development at the single-cell level. We further predict that the novel important gene KLF8 promotes the formation of DE cells by reciprocal inhibition between CDH1 and KLF8 and promotion of the expression of ZEB1. These results may help to shed light on the biological mechanism in the differentiation process of hESCs.

Serum biomarkers of drug-induced liver injury: Current status and future directions.

Drug-induced liver injury (DILI), which is caused by drugs and herbal or dietary supplements, remains a serious concern for drug developers, regulators, and clinicians; however, serum biomarkers utilized to detect and monitor DILI have not changed in decades and have limitations. Data-driven mathematical modeling that incorporates the release and clearance kinetics of traditional biomarkers has improved their use in the prediction of liver safety liabilities for new drug candidates. Several newer biomarkers have shown promise in terms of liver specificity, predicting the outcome of DILI events, and providing insight into its underlying mechanisms. For these new biomarkers to be qualified for regulatory acceptance, it will require their assessment in large numbers of patients who are receiving a wide range of compounds and who develop a broad spectrum of liver injuries. The ongoing and evolving international biomarker consortia should play a major role in this effort, which is likely to transform the assessment of liver safety in clinical trials and in the clinic.

Differential induction of interferon stimulated genes between type I and type III interferons is independent of interferon receptor abundance.

It is currently believed that type I and III interferons (IFNs) have redundant functions. However, the preferential distribution of type III IFN receptor on epithelial cells suggests functional differences at epithelial surfaces. Here, using human intestinal epithelial cells we could show that although both type I and type III IFNs confer an antiviral state to the cells, they do so with distinct kinetics. Type I IFN signaling is characterized by an acute strong induction of interferon stimulated genes (ISGs) and confers fast antiviral protection. On the contrary, the slow acting type III IFN mediated antiviral protection is characterized by a weaker induction of ISGs in a delayed manner compared to type I IFN. Moreover, while transcript profiling revealed that both IFNs induced a similar set of ISGs, their temporal expression strictly depended on the IFNs, thereby leading to unique antiviral environments. Using a combination of data-driven mathematical modeling and experimental validation, we addressed the molecular reason for this differential kinetic of ISG expression. We could demonstrate that these kinetic differences are intrinsic to each signaling pathway and not due to different expression levels of the corresponding IFN receptors. We report that type III IFN is specifically tailored to act in specific cell types not only due to the restriction of its receptor but also by providing target cells with a distinct antiviral environment compared to type I IFN. We propose that this specific environment is key at surfaces that are often challenged with the extracellular environment.

Event-Based Modeling and Analysis of Sensor Enabled Networked Manufacturing Systems

Mathematical models are often required in process modeling, control, and evaluation. To meet the increasing demand of production system real-time performance evaluation and improvement, in this paper: 1) an innovative event-based, data-driven mathematical model is established for network structured manufacturing systems; 2) important properties of network structured manufacturing systems are obtained through the concept development of a virtual ideal clean system; and 3) a system performance diagnostic method is developed based on the mathematical model and system properties, as well as available sensor data. The mathematical model and system performance identification methodology are studied analytically and validated by simulation studies. This data-driven mathematical framework and system real-time performance diagnostic methodology are invaluable for real-time production control to improve system responsiveness and efficiency. Note to Practitioners —For production systems with complex networked structure layouts, the dependence relationship between machines and buffers is more complicated compared with serial production lines. Therefore, it is more difficult to analyze and evaluate their real-time production performance such as permanent production loss. Such information is critical for real-time production management and control to achieve higher system responsiveness and efficiency. This paper establishes an event-based data-driven mathematical model to describe the real-time dynamic behavior of manufacturing systems with complex networked structures. Furthermore, an analysis method for networked manufacturing system properties and a data-driven system performance diagnostic method are proposed. The methods provide a quantitative solution to evaluate production capacity and production constraints of complex networked manufacturing systems, and to evaluate the system real-time performance such as permanent production loss and its attribution to each disruption event and machine.

Data-driven dynamical model indicates that the heat shock response in Chlamydomonas reinhardtii is tailored to handle natural temperature variation.

Global warming exposes plants to severe heat stress, with consequent crop yield reduction. Organisms exposed to high temperature stresses typically protect themselves with a heat shock response (HSR), where accumulation of unfolded proteins initiates the synthesis of heat shock proteins through the heat shock transcription factor HSF1. While the molecular mechanisms are qualitatively well characterized, our quantitative understanding of the underlying dynamics is still very limited. Here, we study the dynamics of HSR in the photosynthetic model organism Chlamydomonas reinhardtii with a data-driven mathematical model of HSR. We based our dynamical model mostly on mass action kinetics, with a few nonlinear terms. The model was parametrized and validated by several independent datasets obtained from the literature. We demonstrate that HSR quantitatively and significantly differs if an increase in temperature of the same magnitude occurs abruptly, as often applied under laboratory conditions, or gradually, which would rather be expected under natural conditions. In contrast to rapid temperature increases, under gradual changes only negligible amounts of misfolded proteins accumulate, indicating that the HSR of C. reinhardtii efficiently avoids the accumulation of misfolded proteins under conditions most likely to prevail in nature. The mathematical model we developed is a flexible tool to simulate the HSR to different conditions and complements the current experimental approaches.