Mathematical modeling of the heat-shock response in HeLa cells.

The heat-shock response is a key factor in diverse stress scenarios, ranging from hyperthermia to protein folding diseases. However, the complex dynamics of this physiological response have eluded mathematical modeling efforts. Although several computational models have attempted to characterize the heat-shock response, they were unable to model its dynamics across diverse experimental datasets. To address this limitation, we mined the literature to obtain a compendium of in vitro hyperthermia experiments investigating the heat-shock response in HeLa cells. We identified mechanisms previously discussed in the experimental literature, such as temperature-dependent transcription, translation, and heat-shock factor (HSF) oligomerization, as well as the role of heat-shock protein mRNA, and constructed an expanded mathematical model to explain the temperature-varying DNA-binding dynamics, the presence of free HSF during homeostasis and the initial phase of the heat-shock response, and heat-shock protein dynamics in the long-term heat-shock response. In addition, our model was able to consistently predict the extent of damage produced by different combinations of exposure temperatures and durations, which were validated against known cellular-response patterns. Our model was also in agreement with experiments showing that the number of HSF molecules in a HeLa cell is roughly 100 times greater than the number of stress-activated heat-shock element sites, further confirming the model's ability to reproduce experimental results not used in model calibration. Finally, a sensitivity analysis revealed that altering the homeostatic concentration of HSF can lead to large changes in the stress response without significantly impacting the homeostatic levels of other model components, making it an attractive target for intervention. Overall, this model represents a step forward in the quantitative understanding of the dynamics of the heat-shock response.

Predicting critical transitions in a model of systemic inflammation.

The human body can be viewed as a dynamical system, with physiological states such as health and disease broadly representing steady states. From this perspective, and given inter- and intra-individual heterogeneity, an important task is identifying the propensity to transition from one steady state to another, which in practice can occur abruptly. Detecting impending transitions between steady states is of significant importance in many fields, and thus a variety of methods have been developed for this purpose, but lack of data has limited applications in physiology. Here, we propose a model-based approach towards identifying critical transitions in systemic inflammation based on a minimal amount of assumptions about the availability of data and the structure of the system. We derived a warning signal metric to identify forthcoming abrupt transitions occurring in a mathematical model of systemic inflammation with a gradually increasing bacterial load. Intervention to remove the inflammatory stimulus was successful in restoring homeostasis if undertaken when the warning signal was elevated rather than waiting for the state variables of the system themselves to begin moving to a new steady state. The proposed combination of data and model-based analysis for predicting physiological transitions represents a step forward towards the quantitative study of complex biological systems.

Translational applications of evaluating physiologic variability in human endotoxemia.

Dysregulation of the inflammatory response is a critical component of many clinically challenging disorders such as sepsis. Inflammation is a biological process designed to lead to healing and recovery, ultimately restoring homeostasis; however, the failure to fully achieve those beneficial results can leave a patient in a dangerous persistent inflammatory state. One of the primary challenges in developing novel therapies in this area is that inflammation is comprised of a complex network of interacting pathways. Here, we discuss our approaches towards addressing this problem through computational systems biology, with a particular focus on how the presence of biological rhythms and the disruption of these rhythms in inflammation may be applied in a translational context. By leveraging the information content embedded in physiologic variability, ranging in scale from oscillations in autonomic activity driving short-term heart rate variability to circadian rhythms in immunomodulatory hormones, there is significant potential to gain insight into the underlying physiology.

Transcriptional implications of ultradian glucocorticoid secretion in homeostasis and in the acute stress response.

Endogenous glucocorticoids are secreted by the hypothalamic-pituitary-adrenal (HPA) axis in response to a wide range of stressors. Glucocorticoids exert significant downstream effects, including the regulation of many inflammatory genes. The HPA axis functions such that glucocorticoids are released in a pulsatile manner, producing ultradian rhythms in plasma glucocorticoid levels. It is becoming increasingly evident that this ultradian pulsatility is important in maintaining proper homeostatic regulation and responsiveness to stress. This is particularly interesting from a clinical perspective given that pathological dysfunctions of the HPA axis produce altered ultradian patterns. Modeling this system facilitates the understanding of how glucocorticoid pulsatility arises, how it can be lost, and the transcriptional implications of ultradian rhythms. To approach these questions, we developed a mathematical model that integrates the cyclic production of glucocorticoids by the HPA axis and their downstream effects by integrating existing models of the HPA axis and glucocorticoid pharmacodynamics. This combined model allowed us to evaluate the implications of pulsatility in homeostasis as well as in response to acute stress. The presence of ultradian rhythms allows the system to maintain a lower response to homeostatic levels of glucocorticoids, but diminished feedback within the HPA axis leads to a loss of glucocorticoid rhythmicity. Furthermore, the loss of HPA pulsatility in homeostasis correlates with a decrease in the peak output in response to an acute stressor. These results are important in understanding how cyclic glucocorticoid secretion helps maintain the responsiveness of the HPA axis.

Entrainment of peripheral clock genes by cortisol.

Circadian rhythmicity in mammals is primarily driven by the suprachiasmatic nucleus (SCN), often called the central pacemaker, which converts the photic information of light and dark cycles into neuronal and hormonal signals in the periphery of the body. Cells of peripheral tissues respond to these centrally mediated cues by adjusting their molecular function to optimize organism performance. Numerous systemic cues orchestrate peripheral rhythmicity, such as feeding, body temperature, the autonomic nervous system, and hormones. We propose a semimechanistic model for the entrainment of peripheral clock genes by cortisol as a representative entrainer of peripheral cells. This model demonstrates the importance of entrainer's characteristics in terms of the synchronization and entrainment of peripheral clock genes, and predicts the loss of intercellular synchrony when cortisol moves out of its homeostatic amplitude and frequency range, as has been observed clinically in chronic stress and cancer. The model also predicts a dynamic regime of entrainment, when cortisol has a slightly decreased amplitude rhythm, where individual clock genes remain relatively synchronized among themselves but are phase shifted in relation to the entrainer. The model illustrates how the loss of communication between the SCN and peripheral tissues could result in desynchronization of peripheral clocks.

Modeling physiologic variability in human endotoxemia.

The control and management of inflammation is a key aspect of clinical care for critical illnesses such as sepsis. In an ideal reaction to injury, the inflammatory response provokes a strong enough response to heal the injury and then restores homeostasis. When inflammation becomes dysregulated, a persistent inflammatory state can lead to significant deleterious effects and clinical challenges. Thus, gaining a better biological understanding of the mechanisms driving the inflammatory response is of the utmost importance. In this review, we discuss our work with the late Stephen F. Lowry to investigate systemic inflammation through systems biology of human endotoxemia. We present our efforts in modeling the human endotoxemia response with a particular focus on physiologic variability. Through modeling, with a focus ultimately on translational applications, we obtain more fundamental understanding of relevant physiological processes. And by taking advantage of the information embedded in biological rhythms, ranging in time scale from high-frequency autonomic oscillations reflected in heart rate variability to circadian rhythms in inflammatory mediators, we gain insight into the underlying physiology.

Modeling autonomic regulation of cardiac function and heart rate variability in human endotoxemia.

Heart rate variability (HRV), the quantification of beat-to-beat variability, has been studied as a potential prognostic marker in inflammatory diseases such as sepsis. HRV normally reflects significant levels of variability in homeostasis, which can be lost under stress. Much effort has been placed in interpreting HRV from the perspective of quantitatively understanding how stressors alter HRV dynamics, but the molecular and cellular mechanisms that give rise to both homeostatic HRV and changes in HRV have received less focus. Here, we develop a mathematical model of human endotoxemia that incorporates the oscillatory signals giving rise to HRV and their signal transduction to the heart. Connections between processes at the cellular, molecular, and neural levels are quantitatively linked to HRV. Rhythmic signals representing autonomic oscillations and circadian rhythms converge to modulate the pattern of heartbeats, and the effects of these oscillators are diminished in the acute endotoxemia response. Based on the semimechanistic model developed herein, homeostatic and acute stress responses of HRV are studied in terms of these oscillatory signals. Understanding the loss of HRV in endotoxemia serves as a step toward understanding changes in HRV observed clinically through translational applications of systems biology based on the relationship between biological processes and clinical outcomes.

Assessment of pharmacologic area under the curve when baselines are variable.

PURPOSE: The area under the curve (AUC) is commonly used to assess the extent of exposure of a drug. The same concept can be applied to generally assess pharmacodynamic responses and the deviation of a signal from its baseline value. When the initial condition for the response of interest is not zero, there is uncertainty in the true value of the baseline measurement. This necessitates the consideration of the AUC relative to baseline to account for this inherent uncertainty and variability in baseline measurements. METHODS: An algorithm to calculate the AUC with respect to a variable baseline is developed by comparing the AUC of the response curve with the AUC of the baseline while taking into account uncertainty in both measurements. Furthermore, positive and negative components of AUC (above and below baseline) are calculated separately to allow for the identification of biphasic responses. RESULTS: This algorithm is applied to gene expression data to illustrate its ability to capture transcriptional responses to a drug that deviate from baseline and to synthetic data to quantitatively test its performance. CONCLUSIONS: The variable nature of the baseline is an important aspect to consider when calculating the AUC.

Modeling the influence of circadian rhythms on the acute inflammatory response.

A wide variety of modeling techniques have been applied towards understanding inflammation. These models have broad potential applications, from optimizing clinical trials to improving clinical care. Models have been developed to study specific systems and diseases, but the effect of circadian rhythms on the inflammatory response has not been modeled. Circadian rhythms are normal biological variations obeying the 24-h light/dark cycle and have been shown to play a critical role in the treatment and progression of many diseases. Several of the key components of the inflammatory response, including cytokines and hormones, have been observed to undergo significant diurnal variations in plasma concentration. It is hypothesized that these diurnal rhythms are entrained by the cyclic production of the hormones cortisol and melatonin, as stimulated by the central clock in the suprachiasmatic nucleus. Based on this hypothesis, a mathematical model of the interplay between inflammation and circadian rhythms is developed. The model is validated by its ability to reproduce diverse sets of experimental data and clinical observations concerning the temporal sensitivity of the inflammatory response.

A late-binding, distributed, NoSQL warehouse for integrating patient data from clinical trials.

Clinical trial data are typically collected through multiple systems developed by different vendors using different technologies and data standards. That data need to be integrated, standardized and transformed for a variety of monitoring and reporting purposes. The need to process large volumes of often inconsistent data in the presence of ever-changing requirements poses a significant technical challenge. As part of a comprehensive clinical data repository, we have developed a data warehouse that integrates patient data from any source, standardizes it and makes it accessible to study teams in a timely manner to support a wide range of analytic tasks for both in-flight and completed studies. Our solution combines Apache HBase, a NoSQL column store, Apache Phoenix, a massively parallel relational query engine and a user-friendly interface to facilitate efficient loading of large volumes of data under incomplete or ambiguous specifications, utilizing an extract-load-transform design pattern that defers data mapping until query time. This approach allows us to maintain a single copy of the data and transform it dynamically into any desirable format without requiring additional storage. Changes to the mapping specifications can be easily introduced and multiple representations of the data can be made available concurrently. Further, by versioning the data and the transformations separately, we can apply historical maps to current data or current maps to historical data, which simplifies the maintenance of data cuts and facilitates interim analyses for adaptive trials. The result is a highly scalable, secure and redundant solution that combines the flexibility of a NoSQL store with the robustness of a relational query engine to support a broad range of applications, including clinical data management, medical review, risk-based monitoring, safety signal detection, post hoc analysis of completed studies and many others.

On heart rate variability and autonomic activity in homeostasis and in systemic inflammation.

Analysis of heart rate variability (HRV) is a promising diagnostic technique due to the noninvasive nature of the measurements involved and established correlations with disease severity, particularly in inflammation-linked disorders. However, the complexities underlying the interpretation of HRV complicate understanding the mechanisms that cause variability. Despite this, such interpretations are often found in literature. In this paper we explored mathematical modeling of the relationship between the autonomic nervous system and the heart, incorporating basic mechanisms such as perturbing mean values of oscillating autonomic activities and saturating signal transduction pathways to explore their impacts on HRV. We focused our analysis on human endotoxemia, a well-established, controlled experimental model of systemic inflammation that provokes changes in HRV representative of acute stress. By contrasting modeling results with published experimental data and analyses, we found that even a simple model linking the autonomic nervous system and the heart confound the interpretation of HRV changes in human endotoxemia. Multiple plausible alternative hypotheses, encoded in a model-based framework, equally reconciled experimental results. In total, our work illustrates how conventional assumptions about the relationships between autonomic activity and frequency-domain HRV metrics break down, even in a simple model. This underscores the need for further experimental work towards unraveling the underlying mechanisms of autonomic dysfunction and HRV changes in systemic inflammation. Understanding the extent of information encoded in HRV signals is critical in appropriately analyzing prior and future studies.

Linking Inflammation, Cardiorespiratory Variability, and Neural Control in Acute Inflammation via Computational Modeling.

Acute inflammation leads to organ failure by engaging catastrophic feedback loops in which stressed tissue evokes an inflammatory response and, in turn, inflammation damages tissue. Manifestations of this maladaptive inflammatory response include cardio-respiratory dysfunction that may be reflected in reduced heart rate and ventilatory pattern variabilities. We have developed signal-processing algorithms that quantify non-linear deterministic characteristics of variability in biologic signals. Now, coalescing under the aegis of the NIH Computational Biology Program and the Society for Complexity in Acute Illness, two research teams performed iterative experiments and computational modeling on inflammation and cardio-pulmonary dysfunction in sepsis as well as on neural control of respiration and ventilatory pattern variability. These teams, with additional collaborators, have recently formed a multi-institutional, interdisciplinary consortium, whose goal is to delineate the fundamental interrelationship between the inflammatory response and physiologic variability. Multi-scale mathematical modeling and complementary physiological experiments will provide insight into autonomic neural mechanisms that may modulate the inflammatory response to sepsis and simultaneously reduce heart rate and ventilatory pattern variabilities associated with sepsis. This approach integrates computational models of neural control of breathing and cardio-respiratory coupling with models that combine inflammation, cardiovascular function, and heart rate variability. The resulting integrated model will provide mechanistic explanations for the phenomena of respiratory sinus-arrhythmia and cardio-ventilatory coupling observed under normal conditions, and the loss of these properties during sepsis. This approach holds the potential of modeling cross-scale physiological interactions to improve both basic knowledge and clinical management of acute inflammatory diseases such as sepsis and trauma.

Pulsatile glucocorticoid secretion: origins and downstream effects.

Glucocorticoids are steroid hormones which, among other functions, exert an antiinflammatory effect. Endogenous glucocorticoids are normally secreted by the adrenal gland in discrete bursts. It is becoming increasingly evident that this pulsatile secretion pattern, leading to ultradian rhythms of plasma glucocorticoid levels, may have important downstream regulatory effects on glucocorticoid-responsive genes. Mathematical modeling of this system can compliment recent experimental data and quantitatively evaluate hypothesized mechanistic underpinnings of differential pulsatile signal transduction. In this paper, we describe an integrated model of pulsatile secretion of glucocorticoids by the hypothalamic-pituitary-adrenal (HPA) axis and the pharmacodynamic effect of glucocorticoids. This model is used to investigate the difference in transcriptional responses to pulsatile and constant glucocorticoid exposure. Nonlinearity in ligand-receptor kinetics leads to the differential expression of glucocorticoid-responsive genes in response to different patterns of glucocorticoid secretion, even when the total amount of glucocorticoid exposure is held constant. Understanding the implications of ultradian rhythms in glucocorticoids is important in studying the dysregulation of HPA axis function leading to altered glucocorticoid secretion patterns in disease.

A new symbolic representation for the identification of informative genes in replicated microarray experiments.

Microarray experiments generate massive amounts of data, necessitating innovative algorithms to distinguish biologically relevant information from noise. Because the variability of gene expression data is an important factor in determining which genes are differentially expressed, analysis techniques that take into account repeated measurements are critically important. Additionally, the selection of informative genes is typically done by searching for the individual genes that vary the most across conditions. Yet because genes tend to act in groups rather than individually, it may be possible to glean more information from the data by searching specifically for concerted behavior in a set of genes. Applying a symbolic transformation to the gene expression data allows the detection overrepresented patterns in the data, in contrast to looking only for genes that exhibit maximal differential expression. These challenges are approached by introducing an algorithm based on a new symbolic representation that searches for concerted gene expression patterns; furthermore, the symbolic representation takes into account the variance in multiple replicates and can be applied to long time series data. The proposed algorithm's ability to discover biologically relevant signals in gene expression data is exhibited by applying it to three datasets that measure gene expression in the rat liver.