Hepatic cholesterol biosynthesis and dioxin-induced dysregulation: A multiscale computational approach.

Humans are constantly exposed to lipophilic persistent organic pollutants (POPs) that accumulate in fatty foods. Among the numerous POPs, dioxins, in particular 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD), can impact several organ systems. While the hazard is clearly recognized, it is still difficult to develop a comprehensive understanding of the overall health impacts of dioxins. As chemical toxicity testing is steadily adopting new approach methodologies (NAMs), it becomes imperative to develop computational models that can bridge the data gaps between in vitro testing and in vivo outcomes. As an effort to address this challenge, we propose a multiscale computational approach using a "template-and-anchor" (T&A) structure. A template is a high-level umbrella model that permits the integration of information from various, detailed anchor models. In the present study, we use this T&A approach to describe the effect of TCDD on cholesterol dynamics. Specifically, we represent hepatic cholesterol biosynthesis as an anchor model that is perturbed by TCDD, leading to steatosis, along with alterations of plasma cholesterol. In the future, incorporating pertinent information from all anchor models into the template model will allow the characterization of the global effects of dioxin, which can subsequently be translated into overall - and ultimately personalized - human health risk assessment.

Mathematical models of cystic fibrosis as a systemic disease.

Cystic fibrosis (CF) is widely known as a disease of the lung, even though it is in truth a systemic disease, whose symptoms typically manifest in gastrointestinal dysfunction first. CF ultimately impairs not only the pancreas and intestine but also the lungs, gonads, liver, kidneys, bones, and the cardiovascular system. It is caused by one of several mutations in the gene of the epithelial ion channel protein CFTR. Intense research and improved antimicrobial treatments during the past eight decades have steadily increased the predicted life expectancy of a person with CF (pwCF) from a few weeks to over 50 years. Moreover, several drugs ameliorating the sequelae of the disease have become available in recent years, and notable treatments of the root cause of the disease have recently generated substantial improvements in health for some but not all pwCF. Yet, numerous fundamental questions remain unanswered. Complicating CF, for instance in the lung, is the fact that the associated insufficient chloride secretion typically perturbs the electrochemical balance across epithelia and, in the airways, leads to the accumulation of thick, viscous mucus and mucus plaques that cannot be cleared effectively and provide a rich breeding ground for a spectrum of bacterial and fungal communities. The subsequent infections often become chronic and respond poorly to antibiotic treatments, with outcomes sometimes only weakly correlated with the drug susceptibility of the target pathogen. Furthermore, in contrast to rapidly resolved acute infections with a single target pathogen, chronic infections commonly involve multi-species bacterial communities, called "infection microbiomes," that develop their own ecological and evolutionary dynamics. It is presently impossible to devise mathematical models of CF in its entirety, but it is feasible to design models for many of the distinct drivers of the disease. Building upon these growing yet isolated modeling efforts, we discuss in the following the feasibility of a multi-scale modeling framework, known as template-and-anchor modeling, that allows the gradual integration of refined sub-models with different granularity. The article first reviews the most important biomedical aspects of CF and subsequently describes mathematical modeling approaches that already exist or have the potential to deepen our understanding of the multitude aspects of the disease and their interrelationships. The conceptual ideas behind the approaches proposed here do not only pertain to CF but are translatable to other systemic diseases. This article is categorized under: Congenital Diseases > Computational Models.

A dynamic compartment model for xylem loading and long-distance transport of iron explains the effect of kanamycin on metal uptake in Arabidopsis.

Arabidopsis plants exposed to the antibiotic kanamycin (Kan) display altered metal homeostasis. Further, mutation of the WBC19 gene leads to increased sensitivity to kanamycin and changes in iron (Fe) and zinc (Zn) uptake. Here we propose a model that explain this surprising relationship between metal uptake and exposure to Kan. We first use knowledge about the metal uptake phenomenon to devise a transport and interaction diagram on which we base the construction of a dynamic compartment model. The model has three pathways for loading Fe and its chelators into the xylem. One pathway, involving an unknown transporter, loads Fe as a chelate with citrate (Ci) into the xylem. This transport step can be significantly inhibited by Kan. In parallel, FRD3 transports Ci into the xylem where it can chelate with free Fe. A third critical pathway involves WBC19, which transports metal-nicotianamine (NA), mainly as Fe-NA chelate, and possibly NA itself. To permit quantitative exploration and analysis, we use experimental time series data to parameterize this explanatory and predictive model. Its numerical analysis allows us to predict responses by a double mutant and explain the observed differences between data from wildtype, mutants and Kan inhibition experiments. Importantly, the model provides novel insights into metal homeostasis by permitting the reverse-engineering of mechanistic strategies with which the plant counteracts the effects of mutations and of the inhibition of iron transport by kanamycin.

MaHPIC malaria systems biology data from Plasmodium cynomolgi sporozoite longitudinal infections in macaques.

Plasmodium cynomolgi causes zoonotic malarial infections in Southeast Asia and this parasite species is important as a model for Plasmodium vivax and Plasmodium ovale. Each of these species produces hypnozoites in the liver, which can cause relapsing infections in the blood. Here we present methods and data generated from iterative longitudinal systems biology infection experiments designed and performed by the Malaria Host-Pathogen Interaction Center (MaHPIC) to delve deeper into the biology, pathogenesis, and immune responses of P. cynomolgi in the Macaca mulatta host. Infections were initiated by sporozoite inoculation. Blood and bone marrow samples were collected at defined timepoints for biological and computational experiments and integrative analyses revolving around primary illness, relapse illness, and subsequent disease and immune response patterns. Parasitological, clinical, haematological, immune response, and -omic datasets (transcriptomics, proteomics, metabolomics, and lipidomics) including metadata and computational results have been deposited in public repositories. The scope and depth of these datasets are unprecedented in studies of malaria, and they are projected to be a F.A.I.R., reliable data resource for decades.

Plasmodium knowlesi Cytoadhesion Involves SICA Variant Proteins.

Plasmodium knowlesi poses a health threat throughout Southeast Asian communities and currently causes most cases of malaria in Malaysia. This zoonotic parasite species has been studied in Macaca mulatta (rhesus monkeys) as a model for severe malarial infections, chronicity, and antigenic variation. The phenomenon of Plasmodium antigenic variation was first recognized during rhesus monkey infections. Plasmodium-encoded variant proteins were first discovered in this species and found to be expressed at the surface of infected erythrocytes, and then named the Schizont-Infected Cell Agglutination (SICA) antigens. SICA expression was shown to be spleen dependent, as SICA expression is lost after P. knowlesi is passaged in splenectomized rhesus. Here we present data from longitudinal P. knowlesi infections in rhesus with the most comprehensive analysis to date of clinical parameters and infected red blood cell sequestration in the vasculature of tissues from 22 organs. Based on the histopathological analysis of 22 tissue types from 11 rhesus monkeys, we show a comparative distribution of parasitized erythrocytes and the degree of margination of the infected erythrocytes with the endothelium. Interestingly, there was a significantly higher burden of parasites in the gastrointestinal tissues, and extensive margination of the parasites along the endothelium, which may help explain gastrointestinal symptoms frequently reported by patients with P. knowlesi malarial infections. Moreover, this margination was not observed in splenectomized rhesus that were infected with parasites not expressing the SICA proteins. This work provides data that directly supports the view that a subpopulation of P. knowlesi parasites cytoadheres and sequesters, likely via SICA variant antigens acting as ligands. This process is akin to the cytoadhesive function of the related variant antigen proteins, namely Erythrocyte Membrane Protein-1, expressed by Plasmodium falciparum.

Discrete Biochemical Systems Theory.

Almost every biomedical systems analysis requires early decisions regarding the choice of the most suitable representations to be used. De facto the most prevalent choice is a system of ordinary differential equations (ODEs). This framework is very popular because it is flexible and fairly easy to use. It is also supported by an enormous array of stand-alone programs for analysis, including many distinct numerical solvers that are implemented in the main programming languages. Having selected ODEs, the modeler must then choose a mathematical format for the equations. This selection is not trivial as nearly unlimited options exist and there is seldom objective guidance. The typical choices include ad hoc representations, default models like mass-action or Lotka-Volterra equations, and generic approximations. Within the realm of approximations, linear models are typically successful for analyses of engineered systems, but they are not as appropriate for biomedical phenomena, which often display nonlinear features such as saturation, threshold effects or limit cycle oscillations, and possibly even chaos. Power-law approximations are simple but overcome these limitations. They are the key ingredient of Biochemical Systems Theory (BST), which uses ODEs exclusively containing power-law representations for all processes within a model. BST models cover a vast repertoire of nonlinear responses and, at the same time, have structural properties that are advantageous for a wide range of analyses. Nonetheless, as all ODE models, the BST approach has limitations. In particular, it is not always straightforward to account for genuine discreteness, time delays, and stochastic processes. As a new option, we therefore propose here an alternative to BST in the form of discrete Biochemical Systems Theory (dBST). dBST models have the same generality and practicality as their BST-ODE counterparts, but they are readily implemented even in situations where ODEs struggle. As a case study, we illustrate dBST applied to the dynamics of the aryl hydrocarbon receptor (AhR), a signal transduction system that simultaneously involves time delays and stochasticity.

Inference of dynamic interaction networks: A comparison between Lotka-Volterra and multivariate autoregressive models.

Networks are ubiquitous throughout biology, spanning the entire range from molecules to food webs and global environmental systems. Yet, despite substantial efforts by the scientific community, the inference of these networks from data still presents a problem that is unsolved in general. One frequent strategy of addressing the structure of networks is the assumption that the interactions among molecular or organismal populations are static and correlative. While often successful, these static methods are no panacea. They usually ignore the asymmetry of relationships between two species and inferences become more challenging if the network nodes represent dynamically changing quantities. Overcoming these challenges, two very different network inference approaches have been proposed in the literature: Lotka-Volterra (LV) models and Multivariate Autoregressive (MAR) models. These models are computational frameworks with different mathematical structures which, nevertheless, have both been proposed for the same purpose of inferring the interactions within coexisting population networks from observed time-series data. Here, we assess these dynamic network inference methods for the first time in a side-by-side comparison, using both synthetically generated and ecological datasets. Multivariate Autoregressive and Lotka-Volterra models are mathematically equivalent at the steady state, but the results of our comparison suggest that Lotka-Volterra models are generally superior in capturing the dynamics of networks with non-linear dynamics, whereas Multivariate Autoregressive models are better suited for analyses of networks of populations with process noise and close-to linear behavior. To the best of our knowledge, this is the first study comparing LV and MAR approaches. Both frameworks are valuable tools that address slightly different aspects of dynamic networks.

Clinical recovery of Macaca fascicularis infected with Plasmodium knowlesi.

BACKGROUND: Kra monkeys (Macaca fascicularis), a natural host of Plasmodium knowlesi, control parasitaemia caused by this parasite species and escape death without treatment. Knowledge of the disease progression and resilience in kra monkeys will aid the effective use of this species to study mechanisms of resilience to malaria. This longitudinal study aimed to define clinical, physiological and pathological changes in kra monkeys infected with P. knowlesi, which could explain their resilient phenotype. METHODS: Kra monkeys (n = 15, male, young adults) were infected intravenously with cryopreserved P. knowlesi sporozoites and the resulting parasitaemias were monitored daily. Complete blood counts, reticulocyte counts, blood chemistry and physiological telemetry data (n = 7) were acquired as described prior to infection to establish baseline values and then daily after inoculation for up to 50 days. Bone marrow aspirates, plasma samples, and 22 tissue samples were collected at specific time points to evaluate longitudinal clinical, physiological and pathological effects of P. knowlesi infections during acute and chronic infections. RESULTS: As expected, the kra monkeys controlled acute infections and remained with low-level, persistent parasitaemias without anti-malarial intervention. Unexpectedly, early in the infection, fevers developed, which ultimately returned to baseline, as well as mild to moderate thrombocytopenia, and moderate to severe anaemia. Mathematical modelling and the reticulocyte production index indicated that the anaemia was largely due to the removal of uninfected erythrocytes and not impaired production of erythrocytes. Mild tissue damage was observed, and tissue parasite load was associated with tissue damage even though parasite accumulation in the tissues was generally low. CONCLUSIONS: Kra monkeys experimentally infected with P. knowlesi sporozoites presented with multiple clinical signs of malaria that varied in severity among individuals. Overall, the animals shared common mechanisms of resilience characterized by controlling parasitaemia 3-5 days after patency, and controlling fever, coupled with physiological and bone marrow responses to compensate for anaemia. Together, these responses likely minimized tissue damage while supporting the establishment of chronic infections, which may be important for transmission in natural endemic settings. These results provide new foundational insights into malaria pathogenesis and resilience in kra monkeys, which may improve understanding of human infections.

Emergence and Enhancement of Ultrasensitivity through Posttranslational Modulation of Protein Stability.

Signal amplification in biomolecular networks converts a linear input to a steeply sigmoid output and is central to a number of cellular functions including proliferation, differentiation, homeostasis, adaptation, and biological rhythms. One canonical signal amplifying motif is zero-order ultrasensitivity that is mediated through the posttranslational modification (PTM) cycle of signaling proteins. The functionality of this signaling motif has been examined conventionally by supposing that the total amount of the protein substrates remains constant, as by the classical Koshland-Goldbeter model. However, covalent modification of signaling proteins often results in changes in their stability, which affects the abundance of the protein substrates. Here, we use mathematical models to explore the signal amplification properties in such scenarios and report some novel aspects. Our analyses indicate that PTM-induced protein stabilization brings the enzymes closer to saturation. As a result, ultrasensitivity may emerge or is greatly enhanced, with a steeper sigmoidal response, higher magnitude, and generally longer response time. In cases where PTM destabilizes the protein, ultrasensitivity can be regained through changes in the activities of the involved enzymes or from increased protein synthesis. Importantly, ultrasensitivity is not limited to modified or unmodified protein substrates-when protein turnover is considered, the total free protein substrate can also exhibit ultrasensitivity under several conditions. When full enzymatic reactions are used instead of Michaelis-Menten kinetics for the modeling, the total free protein substrate can even exhibit nonmonotonic dose-response patterns. It is conceivable that cells use inducible protein stabilization as a strategy in the signaling network to boost signal amplification while saving energy by keeping the protein substrate levels low at basal conditions.

Dramatic transcriptomic differences in Macaca mulatta and Macaca fascicularis with Plasmodium knowlesi infections.

Plasmodium knowlesi, a model malaria parasite, is responsible for a significant portion of zoonotic malaria cases in Southeast Asia and must be controlled to avoid disease severity and fatalities. However, little is known about the host-parasite interactions and molecular mechanisms in play during the course of P. knowlesi malaria infections, which also may be relevant across Plasmodium species. Here we contrast P. knowlesi sporozoite-initiated infections in Macaca mulatta and Macaca fascicularis using whole blood RNA-sequencing and transcriptomic analysis. These macaque hosts are evolutionarily close, yet malaria-naïve M. mulatta will succumb to blood-stage infection without treatment, whereas malaria-naïve M. fascicularis controls parasitemia without treatment. This comparative analysis reveals transcriptomic differences as early as the liver phase of infection, in the form of signaling pathways that are activated in M. fascicularis, but not M. mulatta. Additionally, while most immune responses are initially similar during the acute stage of the blood infection, significant differences arise subsequently. The observed differences point to prolonged inflammation and anti-inflammatory effects of IL10 in M. mulatta, while M. fascicularis undergoes a transcriptional makeover towards cell proliferation, consistent with its recovery. Together, these findings suggest that timely detection of P. knowlesi in M. fascicularis, coupled with control of inflammation while initiating the replenishment of key cell populations, helps contain the infection. Overall, this study points to specific genes and pathways that could be investigated as a basis for new drug targets that support recovery from acute malaria.

A model of dopamine and serotonin-kynurenine metabolism in cortisolemia: Implications for depression.

A major factor contributing to the etiology of depression is a neurochemical imbalance of the dopaminergic and serotonergic systems, which is caused by persistently high levels of circulating stress hormones. Here, a computational model is proposed to investigate the interplay between dopaminergic and serotonergic-kynurenine metabolism under cortisolemia and its consequences for the onset of depression. The model was formulated as a set of nonlinear ordinary differential equations represented with power-law functions. Parameter values were obtained from experimental data reported in the literature, biological databases, and other general information, and subsequently fine-tuned through optimization. Model simulations predict that changes in the kynurenine pathway, caused by elevated levels of cortisol, can increase the risk of neurotoxicity and lead to increased levels of 3,4-dihydroxyphenylaceltahyde (DOPAL) and 5-hydroxyindoleacetaldehyde (5-HIAL). These aldehydes contribute to alpha-synuclein aggregation and may cause mitochondrial fragmentation. Further model analysis demonstrated that the inhibition of both serotonin transport and kynurenine-3-monooxygenase decreased the levels of DOPAL and 5-HIAL and the neurotoxic risk often associated with depression. The mathematical model was also able to predict a novel role of the dopamine and serotonin metabolites DOPAL and 5-HIAL in the ethiology of depression, which is facilitated through increased cortisol levels. Finally, the model analysis suggests treatment with a combination of inhibitors of serotonin transport and kynurenine-3-monooxygenase as a potentially effective pharmacological strategy to revert the slow-down in monoamine neurotransmission that is often triggered by inflammation.

Dynamic Control Balancing Cell Proliferation and Inflammation is Crucial for an Effective Immune Response to Malaria.

Malaria has a complex pathology with varying manifestations and symptoms, effects on host tissues, and different degrees of severity and ultimate outcome, depending on the causative Plasmodium pathogen and host species. Previously, we compared the peripheral blood transcriptomes of two macaque species (Macaca mulatta and Macaca fascicularis) in response to acute primary infection by Plasmodium knowlesi. Although these two species are very closely related, the infection in M. mulatta is fatal, unless aggressively treated, whereas M. fascicularis develops a chronic, but tolerable infection in the blood. As a reason for this stark difference, our analysis suggests delayed pathogen detection in M. mulatta followed by extended inflammation that eventually overwhelms this monkey's immune response. By contrast, the natural host M. fascicularis detects the pathogen earlier and controls the inflammation. Additionally, M. fascicularis limits cell proliferation pathways during the log phase of infection, presumably in an attempt to control inflammation. Subsequent cell proliferation suggests a cell-mediated adaptive immune response. Here, we focus on molecular mechanisms underlying the key differences in the host and parasite responses and their coordination. SICAvar Type 1 surface antigens are highly correlated with pattern recognition receptor signaling and important inflammatory genes for both hosts. Analysis of pathogen detection pathways reveals a similar signaling mechanism, but with important differences in the glutamate G-protein coupled receptor (GPCR) signaling pathway. Furthermore, differences in inflammasome assembly processes suggests an important role of S100 proteins in balancing inflammation and cell proliferation. Both differences point to the importance of Ca2+ homeostasis in inflammation. Additionally, the kynurenine-to-tryptophan ratio, a known inflammatory biomarker, emphasizes higher inflammation in M. mulatta during log phase. Transcriptomics-aided metabolic modeling provides a functional method for evaluating these changes and understanding downstream changes in NAD metabolism and aryl hydrocarbon receptor (AhR) signaling, with enhanced NAD metabolism in M. fascicularis and stronger AhR signaling in M. mulatta. AhR signaling controls important immune genes like IL6, IFNγ and IDO1. However, direct changes due to AhR signaling could not be established due to complicated regulatory feedback mechanisms associated with the AhR repressor (AhRR). A complete understanding of the exact dynamics of the immune response is difficult to achieve. Nonetheless, our comparative analysis provides clear suggestions of processes that underlie an effective immune response. Thus, our study identifies multiple points of intervention that are apparently responsible for a balanced and effective immune response and thereby paves the way toward future immune strategies for treating malaria.

Mechanistic Model of Signaling Dynamics Across an Epithelial Mesenchymal Transition.

Intracellular signaling pathways are at the core of cellular information processing. The states of these pathways and their inputs determine signaling dynamics and drive cell function. Within a cancerous tumor, many combinations of cell states and microenvironments can lead to dramatic variations in responses to treatment. Network rewiring has been thought to underlie these context-dependent differences in signaling; however, from a biochemical standpoint, rewiring of signaling networks should not be a prerequisite for heterogeneity in responses to stimuli. Here we address this conundrum by analyzing an in vitro model of the epithelial mesenchymal transition (EMT), a biological program implicated in increased tumor invasiveness, heterogeneity, and drug resistance. We used mass cytometry to measure EGF signaling dynamics in the ERK and AKT signaling pathways before and after induction of EMT in Py2T murine breast cancer cells. Analysis of the data with standard network inference methods suggested EMT-dependent network rewiring. In contrast, use of a modeling approach that adequately accounts for single-cell variation demonstrated that a single reaction-based pathway model with constant structure and near-constant parameters is sufficient to represent differences in EGF signaling across EMT. This result indicates that rewiring of the signaling network is not necessary for heterogeneous responses to a signal and that unifying reaction-based models should be employed for characterization of signaling in heterogeneous environments, such as cancer.

ENaC regulation by phospholipids and DGK explained through mathematical modeling.

Cystic fibrosis is a condition caused by mutations in the cystic fibrosis transmembrane conductance regulator (CFTR). It is also thought to increase the activity of epithelial sodium channels (ENaC). The altered function of these ion channels is one of the causes of the thick dehydrated mucus that characterizes the disease and is partially responsible for recurrent pulmonary infections and inflammation events that ultimately destroy the lungs of affected subjects. Phosphoinositides are signaling lipids that regulate numerous cellular processes and membrane proteins, including ENaC. Inhibition of diacylglycerol kinase (DGK), an enzyme of the phosphoinositide pathway, reduces ENaC function. We propose a computational analysis that is based on the combination of two existing mathematical models: one representing the dynamics of phosphoinositides and the other explaining how phosphatidylinositol 4,5-bisphosphate (PI(4,5)P2) influences ENaC activity and, consequently, airway surface liquid. This integrated model permits, for the first time, a detailed assessment of the intricate interactions between DGK and ENaC and is consistent with available literature data. In particular, the computational approach allows comparisons of two competing hypotheses regarding the regulation of ENaC. The results strongly suggest that the regulation of ENaC is primarily exerted through the control of PI(4,5)P2 production by type-I phosphatidylinositol-4-phosphate 5-kinase (PIP5KI), which in turn is controlled by phosphatidic acid (PA), the product of the DGK reaction.

Comparison of physical examination and laboratory data between a clinical study and electronic health records.

Research based on secondary analysis of data stored in electronic health records (EHR) has gained popularity, but whether the data are consistent with those collected under a study setting is unknown. The objective is to assess the agreement between data obtained in a prospective study and routine-care data extracted retrospectively from the EHR. We compared the data collected in a longitudinal lifestyle intervention study with those recorded in the EHR system over 5 years. A total of 225 working adults were recruited at an academic institution between 2008-2012, whose EHR data were also available during the same time period. After aligning the participants' study visit dates with their hospital encounter dates, data on blood pressure, body mass index (BMI), and laboratory measurements (including high-density lipoprotein (HDL), low-density lipoprotein (LDL), triglycerides, and total cholesterol) were compared via a paired t-test for equivalence with pre-specified margins. Summary statistics were used to compare smoking status and medication prescriptions. Overall, data were consistent between the two sources (i.e., BMI, smoking status, medication prescriptions), whereas some differences were found in cholesterol measurements (i.e., HDL and total cholesterol), possibly due to different lab assays and subject's fasting status. In conclusion, some EHR data are fairly consistent with those collected in a clinical study, whereas others may require further examination. Researchers should evaluate the consistency and quality of EHR data and compare them with other sources of data when possible.

Agent-Based Modeling and Simulation in Mathematics and Biology Education.

With advances in computing, agent-based models (ABMs) have become a feasible and appealing tool to study biological systems. ABMs are seeing increased incorporation into both the biology and mathematics classrooms as powerful modeling tools to study processes involving substantial amounts of stochasticity, nonlinear interactions, and/or heterogeneous spatial structures. Here we present a brief synopsis of the agent-based modeling approach with an emphasis on its use to simulate biological systems, and provide a discussion of its role and limitations in both the biology and mathematics classrooms.

Model-based Comparisons of the Abundance Dynamics of Bacterial Communities in Two Lakes.

Lake Lanier (Georgia, USA) is home to more than 11,000 microbial Operational Taxonomic Units (OTUs), many of which exhibit clear annual abundance patterns. To assess the dynamics of this microbial community, we collected time series data of 16S and 18S rRNA gene sequences, recovered from 29 planktonic shotgun metagenomic datasets. Based on these data, we constructed a dynamic mathematical model of bacterial interactions in the lake and used it to analyze changes in the abundances of OTUs. The model accounts for interactions among 14 sub-communities (SCs), which are composed of OTUs blooming at the same time of the year, and three environmental factors. It captures the seasonal variations in abundances of the SCs quite well. Simulation results suggest that changes in water temperature affect the various SCs differentially and that the timing of perturbations is critical. We compared the model results with published results from Lake Mendota (Wisconsin, USA). These comparative analyses between lakes in two very different geographical locations revealed substantially more cooperation and less competition among species in the warmer Lake Lanier than in Lake Mendota.

Separable Nonlinear Least-Squares Parameter Estimation for Complex Dynamic Systems.

Nonlinear dynamic models are widely used for characterizing processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data collected via high-throughput experiments using methods from molecular biology. While these data are very beneficial, they are typically incomplete and noisy, which renders the inference of parameter values for complex dynamic models challenging. Fortunately, many biological systems have embedded linear mathematical features, which may be exploited, thereby improving fits and leading to better convergence of optimization algorithms. In this paper, we explore options of inference for dynamic models using a novel method of separable nonlinear least-squares optimization and compare its performance to the traditional nonlinear least-squares method. The numerical results from extensive simulations suggest that the proposed approach is at least as accurate as the traditional nonlinear least-squares, but usually superior, while also enjoying a substantial reduction in computational time.

Perspective: Dimensions of the scientific method.

The scientific method has been guiding biological research for a long time. It not only prescribes the order and types of activities that give a scientific study validity and a stamp of approval but also has substantially shaped how we collectively think about the endeavor of investigating nature. The advent of high-throughput data generation, data mining, and advanced computational modeling has thrown the formerly undisputed, monolithic status of the scientific method into turmoil. On the one hand, the new approaches are clearly successful and expect the same acceptance as the traditional methods, but on the other hand, they replace much of the hypothesis-driven reasoning with inductive argumentation, which philosophers of science consider problematic. Intrigued by the enormous wealth of data and the power of machine learning, some scientists have even argued that significant correlations within datasets could make the entire quest for causation obsolete. Many of these issues have been passionately debated during the past two decades, often with scant agreement. It is proffered here that hypothesis-driven, data-mining-inspired, and "allochthonous" knowledge acquisition, based on mathematical and computational models, are vectors spanning a 3D space of an expanded scientific method. The combination of methods within this space will most certainly shape our thinking about nature, with implications for experimental design, peer review and funding, sharing of result, education, medical diagnostics, and even questions of litigation.