A General Approach for the Modelling of Negative Feedback Physiological Control Systems.

Mathematical models can improve the understanding of physiological systems behaviour, which is a fundamental topic in the bioengineering field. Having a reliable model enables researchers to carry out in silico experiments, which require less time and resources compared to their in vivo and in vitro counterparts. This work's objective is to capture the characteristics that a nonlinear dynamical mathematical model should exhibit, in order to describe physiological control systems at different scales. The similarities among various negative feedback physiological systems have been investigated and a unique general framework to describe them has been proposed. Within such a framework, both the existence and stability of equilibrium points are investigated. The model here introduced is based on a closed-loop topology, on which the homeostatic process is based. Finally, to validate the model, three paradigmatic examples of physiological control systems are illustrated and discussed: the ultrasensitivity mechanism for achieving homeostasis in biomolecular circuits, the blood glucose regulation, and the neuromuscular reflex arc (also referred to as muscle stretch reflex). The results show that, by a suitable choice of the modelling functions, the dynamic evolution of the systems under study can be described through the proposed general nonlinear model. Furthermore, the analysis of the equilibrium points and dynamics of the above-mentioned systems are consistent with the literature.

CBRA: Cardiac biomarkers release analyzer.

BACKGROUND AND OBJECTIVES: The most advanced technologies and continuous innovations in the medical field require a necessary interaction between the clinical and the engineering world. In this context, software applications are proposed as a bridge between the two scientific fields and, therefore, as powerful tools, easy to use, and with great analytical skills. In this work, we propose CBRA as an innovative software platform, moving towards personalized medicine, which aims to simplify and speed up the triage of patients and support doctors in the diagnostic and prognostic phase. METHODS: The computational core of the devised software application consists of a model-based identification algorithm, which enables the reconstruction of the cardiac biomarkers release curves in patients with ST-Elevation Acute Myocardial Infarction (STEMI). Identification and parametric optimization techniques allow the application of the proposed approach to each singular patient: based on a few experimental acquisitions, CBRA can extrapolate several quantitative features of high clinical relevance, thus facilitating and rendering more objective the clinical evaluation and therapeutic choices. A dedicated database to collect and manage patients clinical and personal data, as well as a graphical user interface, provides clinicians and researchers with an intuitive and user-friendly environment. RESULTS: In the following work, we present some examples of the possible applications of CBRA, ranging from the management of the cardiac biomarkers time-series, up to the real analysis of the clinical features that CBRA can extract from the reconstructed curve, such as, e.g., maximum concentration values of biomarkers in the plasma and relative times, in the distinct phases of the acute myocardial infarction, or identification of the time to onset of symptoms. CONCLUSIONS: CBRA makes it easy for clinicians to use modeling and parametric identification tools to reconstruct release curves. Furthermore, CBRA provides support to the clinical decision, thanks to its capability to extract information of high clinical relevance, not easily obtainable from the mere visual analysis of experimental samples. Having information about the previously listed clinical parameters could allow, e.g., identify in which stage of AMI the patient is, when She/He goes to the emergency room, with significant benefits in the therapy.

Deciphering the Role of Wnt and Rho Signaling Pathway in iPSC-Derived ARVC Cardiomyocytes by In Silico Mathematical Modeling.

Arrhythmogenic Right Ventricular cardiomyopathy (ARVC) is an inherited cardiac muscle disease linked to genetic deficiency in components of the desmosomes. The disease is characterized by progressive fibro-fatty replacement of the right ventricle, which acts as a substrate for arrhythmias and sudden cardiac death. The molecular mechanisms underpinning ARVC are largely unknown. Here we propose a mathematical model for investigating the molecular dynamics underlying heart remodeling and the loss of cardiac myocytes identity during ARVC. Our methodology is based on three computational models: firstly, in the context of the Wnt pathway, we examined two different competition mechanisms between ß-catenin and Plakoglobin (PG) and their role in the expression of adipogenic program. Secondly, we investigated the role of RhoA-ROCK pathway in ARVC pathogenesis, and thirdly we analyzed the interplay between Wnt and RhoA-ROCK pathways in the context of the ARVC phenotype. We conclude with the following remark: both Wnt/ß-catenin and RhoA-ROCK pathways must be inactive for a significant increase of PPARγ expression, suggesting that a crosstalk mechanism might be responsible for mediating ARVC pathogenesis.

Heterogeneous alpha-cell population modeling of glucose-induced inhibition of electrical activity.

Glucagon release from the pancreatic alpha-cells is regulated by glucose, but the underlying mechanisms are far from understood. It is known that the alpha-cell population is very heterogeneous, but - compared to the insulin-secreting beta-cells - the consequences of this cell-to-cell variation are much less studied. Since the alpha-cells are not electrically coupled, large differences in the single cell responses are to be expected, and this variation may contribute to the confusion regarding the mechanisms of glucose-induced suppression of glucagon release. Using mathematical modeling of alpha-cells with realistic cell-to-cell parameter variation based on recent experimental results, we show that the simulated alpha-cells exhibit great diversity in their electrophysiological behavior. To robustly reproduce experimental recordings from alpha-cell exposed to a rise in glucose levels, we must assume that both intrinsic mechanisms and paracrine signals contribute to glucose-induced changes in electrical activity. Our simulations suggest that the sum of different electrophysiological responses due to alpha-cell heterogeneity is involved in glucose-suppressed glucagon secretion, and that more than one mechanism contribute to control the alpha-cell populations' behavior. Finally, we apply regression analysis to our synthetic alpha-cell population to infer which membrane currents influence electrical activity in alpha-cells at different glucose levels. The results from such statistical modeling suggest possible disturbances underlying defect regulation of alpha-cell electrical behavior in diabetics. Thus, although alpha-cells appear to be inherently complex and heterogeneous as reflected in published data, realistic modeling of the alpha-cells at the population level provides insight into the mechanisms of glucagon release.

From Local to Global Modeling for Characterizing Calcium Dynamics and Their Effects on Electrical Activity and Exocytosis in Excitable Cells.

Electrical activity in neurons and other excitable cells is a result of complex interactions between the system of ion channels, involving both global coupling (e.g., via voltage or bulk cytosolic Ca2+ concentration) of the channels, and local coupling in ion channel complexes (e.g., via local Ca2+ concentration surrounding Ca2+ channels (CaVs), the so-called Ca2+ nanodomains). We recently devised a model of large-conductance BKCa potassium currents, and hence BKCa-CaV complexes controlled locally by CaVs via Ca2+ nanodomains. We showed how different CaV types and BKCa-CaV stoichiometries affect whole-cell electrical behavior. Ca2+ nanodomains are also important for triggering exocytosis of hormone-containing granules, and in this regard, we implemented a strategy to characterize the local interactions between granules and CaVs. In this study, we coupled electrical and exocytosis models respecting the local effects via Ca2+ nanodomains. By simulating scenarios with BKCa-CaV complexes with different stoichiometries in pituitary cells, we achieved two main electrophysiological responses (continuous spiking or bursting) and investigated their effects on the downstream exocytosis process. By varying the number and distance of CaVs coupled with the granules, we found that bursting promotes exocytosis with faster rates than spiking. However, by normalizing to Ca2+ influx, we found that bursting is only slightly more efficient than spiking when CaVs are far away from granules, whereas no difference in efficiency between bursting and spiking is observed with close granule-CaV coupling.

Explicit Theoretical Analysis of How the Rate of Exocytosis Depends on Local Control by Ca2+ Channels.

Hormones and neurotransmitters are released from cells by calcium-regulated exocytosis, and local coupling between Ca2+ channels (CaVs) and secretory granules is a key factor determining the exocytosis rate. Here, we devise a methodology based on Markov chain models that allows us to obtain analytic results for the expected rate. First, we analyze the property of the secretory complex obtained by coupling a single granule with one CaV. Then, we extend our results to a more general case where the granule is coupled with n CaVs. We investigate how the exocytosis rate is affected by varying the location of granules and CaVs. Moreover, we assume that the single granule can form complexes with inactivating or non-inactivating CaVs. We find that increasing the number of CaVs coupled with the granule determines a much higher rise of the exocytosis rate that, in case of inactivating CaVs, is more pronounced when the granule is close to CaVs, while, surprisingly, in case of non-inactivating CaVs, the highest relative increase in rate is obtained when the granule is far from the CaVs. Finally, we exploit the devised model to investigate the relation between exocytosis and calcium influx. We find that the quantities are typically linearly related, as observed experimentally. For the case of inactivating CaVs, our simulations show a change of the linear relation due to near-complete inactivation of CaVs.

Concise Whole-Cell Modeling of BKCa-CaV Activity Controlled by Local Coupling and Stoichiometry.

Large-conductance Ca2+-dependent K+ (BKCa) channels are important regulators of electrical activity. These channels colocalize and form ion channel complexes with voltage-dependent Ca2+ (CaV) channels. Recent stochastic simulations of the BKCa-CaV complex with 1:1 stoichiometry have given important insight into the local control of BKCa channels by fluctuating nanodomains of Ca2+. However, such Monte Carlo simulations are computationally expensive, and are therefore not suitable for large-scale simulations of cellular electrical activity. In this work we extend the stochastic model to more realistic BKCa-CaV complexes with 1:n stoichiometry, and analyze the single-complex model with Markov chain theory. From the description of a single BKCa-CaV complex, using arguments based on timescale analysis, we derive a concise model of whole-cell BKCa currents, which can readily be analyzed and inserted into models of cellular electrical activity. We illustrate the usefulness of our results by inserting our BKCa description into previously published whole-cell models, and perform simulations of electrical activity in various cell types, which show that BKCa-CaV stoichiometry can affect whole-cell behavior substantially. Our work provides a simple formulation for the whole-cell BKCa current that respects local interactions in BKCa-CaV complexes, and indicates how local-global coupling of ion channels may affect cell behavior.

Recent advances in mathematical modeling and statistical analysis of exocytosis in endocrine cells.

Most endocrine cells secrete hormones as a result of Ca2+-regulated exocytosis, i.e., fusion of the membranes of hormone-containing secretory granules with the cell membrane, which allows the hormone molecules to escape to the extracellular space. As in neurons, electrical activity and cell depolarization open voltage-sensitive Ca2+ channels, and the resulting Ca2+ influx elevate the intracellular Ca2+ concentration, which in turn causes exocytosis. Whereas the main molecular components involved in exocytosis are increasingly well understood, quantitative understanding of the dynamical aspects of exocytosis is still lacking. Due to the nontrivial spatiotemporal Ca2+ dynamics, which depends on the particular pattern of electrical activity as well as Ca2+ channel kinetics, exocytosis is dependent on the spatial arrangement of Ca2+ channels and secretory granules. For example, the creation of local Ca2+ microdomains, where the Ca2+ concentration reaches tens of µM, are believed to be important for triggering exocytosis. Spatiotemporal simulations of buffered Ca2+ diffusion have provided important insight into the interplay between electrical activity, Ca2+ channel kinetics, and the location of granules and Ca2+ channels. By confronting simulations with statistical time-to-event (or survival) regression analysis of single granule exocytosis monitored with TIRF microscopy, a direct connection between location and rate of exocytosis can be obtained at the local, single-granule level. To get insight into whole-cell secretion, simplifications of the full spatiotemporal dynamics have shown to be highly helpful. Here, we provide an overview of recent approaches and results for quantitative analysis of Ca2+ regulated exocytosis of hormone-containing granules.

Ultrasensitive Negative Feedback Control: A Natural Approach for the Design of Synthetic Controllers.

Many of the most important potential applications of Synthetic Biology will require the ability to design and implement high performance feedback control systems that can accurately regulate the dynamics of multiple molecular species within the cell. Here, we argue that the use of design strategies based on combining ultrasensitive response dynamics with negative feedback represents a natural approach to this problem that fully exploits the strongly nonlinear nature of cellular information processing. We propose that such feedback mechanisms can explain the adaptive responses observed in one of the most widely studied biomolecular feedback systems-the yeast osmoregulatory response network. Based on our analysis of such system, we identify strong links with a well-known branch of mathematical systems theory from the field of Control Engineering, known as Sliding Mode Control. These insights allow us to develop design guidelines that can inform the construction of feedback controllers for synthetic biological systems.

Implementing Nonlinear Feedback Controllers Using DNA Strand Displacement Reactions.

We show how an important class of nonlinear feedback controllers can be designed using idealized abstract chemical reactions and implemented via DNA strand displacement (DSD) reactions. Exploiting chemical reaction networks (CRNs) as a programming language for the design of complex circuits and networks, we show how a set of unimolecular and bimolecular reactions can be used to realize input-output dynamics that produce a nonlinear quasi sliding mode (QSM) feedback controller. The kinetics of the required chemical reactions can then be implemented as enzyme-free, enthalpy/entropy driven DNA reactions using a toehold mediated strand displacement mechanism via Watson-Crick base pairing and branch migration. We demonstrate that the closed loop response of the nonlinear QSM controller outperforms a traditional linear controller by facilitating much faster tracking response dynamics without introducing overshoots in the transient response. The resulting controller is highly modular and is less affected by retroactivity effects than standard linear designs.

Mathematical modelling of local calcium and regulated exocytosis during inhibition and stimulation of glucagon secretion from pancreatic alpha-cells.

Glucagon secretion from pancreatic alpha-cells is dysregulated in diabetes. Despite decades of investigations of the control of glucagon release by glucose and hormones, the underlying mechanisms are still debated. Recently, mathematical models have been applied to investigate the modification of electrical activity in alpha-cells as a result of glucose application. However, recent studies have shown that paracrine effects such as inhibition of glucagon secretion by glucagon-like peptide 1 (GLP-1) or stimulation of release by adrenaline involve cAMP-mediated effects downstream of electrical activity. In particular, depending of the intracellular cAMP concentration, specific types of Ca(2+) channels are inhibited or activated, which interacts with mobilization of secretory granules. To investigate these aspects of alpha-cell function theoretically, we carefully developed a mathematical model of Ca(2+) levels near open or closed Ca(2+) channels of various types, which was linked to a description of Ca(2+) below the plasma membrane, in the bulk cytosol and in the endoplasmic reticulum. We investigated how the various subcellular Ca(2+) compartments contribute to control of glucagon-exocytosis in response to glucose, GLP-1 or adrenaline. Our studies refine previous modelling studies of alpha-cell function, and provide deeper insight into the control of glucagon secretion.

Biomolecular implementation of a quasi sliding mode feedback controller based on DNA strand displacement reactions.

A fundamental aim of synthetic biology is to achieve the capability to design and implement robust embedded biomolecular feedback control circuits. An approach to realize this objective is to use abstract chemical reaction networks (CRNs) as a programming language for the design of complex circuits and networks. Here, we employ this approach to facilitate the implementation of a class of nonlinear feedback controllers based on sliding mode control theory. We show how a set of two-step irreversible reactions with ultrasensitive response dynamics can provide a biomolecular implementation of a nonlinear quasi sliding mode (QSM) controller. We implement our controller in closed-loop with a prototype of a biological pathway and demonstrate that the nonlinear QSM controller outperforms a traditional linear controller by facilitating faster tracking response dynamics without introducing overshoots in the transient response.