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

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.

A Neuron-Glial Model of Exosomal Release in the Onset and Progression of Alzheimer's Disease

Exosomes are nano-sized extracellular vesicles that perform a variety of biological functions linked to the pathogenesis of various neurodegenerative disorders. In Alzheimer's disease (AD), for examples, exosomes are responsible for the release of Aβ oligomers, and their extracellular accumulation, although the underpinning molecular machinery remains elusive. We propose a novel model for Alzheimer's Aβ accumulation based on Ca²⁺-dependent exosome release from astrocytes. Moreover, we exploit our model to assess how temperature dependence of exosome release could interact with Aβ neurotoxicity. We predict that voltage-gated Ca²⁺ channels (VGCCs) along with the transient-receptor potential M8 (TRPM8) channel are crucial molecular components in Alzheimer's progression.

Targeted Drug Delivery for Cardiovascular Disease: Modeling of Modulated Extracellular Vesicle Release Rates

Invasive and medical therapy has led to major improvements in cardiovascular disease management, but important challenges remain open. The discovery of a nano-sized system of extracellular vesicles (EVs) is opening new possibilities for reprogramming malfunctioning cells and indicates that EVs can be employed in therapeutic biomedical applications as engineered drug vehicles. Molecular communication (MC) has applications for treating cells with directed drug delivery, employing special targeting transmembrane proteins. In this paper, we propose a novel drug delivery system for cardiovascular diseases using an EV-mediated MC platform and exemplify the potential use in hypertrophic cardiomyopathy. We utilize intracellular calcium signaling as a natural mediator of EVs released from synthetic cells and model the release rate. We propose to use the cells as a therapeutic release system with a control signal input which modulates the EVs release rate as the output signal. We also study the frequency domain of the proposed model and estimate the transfer function of the therapeutic release system model numerically where the root-mean-square error for two separate estimated output signals are 0.0353 and 0.0124. The proposed EV-mediated targeted drug delivery system can make breakthroughs in future healthcare, in cardiovascular and other diseases where targeting is required.

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 β-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/β-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.

Modeling of Modulated Exosome Release From Differentiated Induced Neural Stem Cells for Targeted Drug Delivery

A novel implantable and externally controllable stem-cell-based platform for the treatment of Glioblastoma brain cancer has been proposed to bring hope to patients who suffer from this devastating cancer type. Induced Neural Stem Cells (iNSCs), known to have potent therapeutic effects through exosomes-based molecular communication, play a pivotal role in this platform. Transplanted iNSCs demonstrate long-term survival and differentiation into neurons and glia which then fully functionally integrate with the existing neural network. Recent studies have shown that specific types of calcium channels in differentiated neurons and astrocytes are inhibited or activated upon cell depolarization leading to the increased intracellular calcium concentration levels which, in turn, interact with mobilization of multivesicular bodies and exosomal release. In order to provide a platform towards treating brain cancer with the optimum therapy dosage, we propose mathematical models to compute the therapeutic exosomal release rate that is modulated by cell stimulation patterns applied from the external wearable device. This study serves as an initial and required step in the evaluation of controlled exosomal secretion and release via induced stimulation with electromagnetic, optical and/or ultrasonic waves.

Modelling of energy-driven switch for glucagon and insulin secretion

We present a mathematical model of the energy-driven metabolic switch for glucagon and insulin secretion from pancreatic alpha and beta cells, respectively. The energy status related to hormone secretion is studied for various glucose concentrations. Additionally, the physiological response is studied with regards to the presence of other metabolites, particularly the free-fatty acids. At low glucose, the ATP production in alpha cells is high due to free-fatty acids oxidation in mitochondria, which enables glucagon secretion. When the glucose concentration is elevated above the threshold value, the glucagon secretion is switched off due to the contribution of glycolytic ATP production, representing an "anaerobic switch". On the other hand, during hypoglycemia, the ATP production in beta cells is low, reflecting a "waiting state" for glucose as the main metabolite. When glucose is elevated above the threshold value, the oxidative fate of glucose in mitochondria is the main source of energy required for effective insulin secretion, i.e. the "aerobic switch". Our results show the importance of well-regulated and fine-tuned energetic processes in pancreatic alpha and beta cells required for efficient hormone secretion and hence effective blood glucose regulation. These energetic processes have to be appropriately switched on and off based on the sensing of different metabolites by alpha and beta cells. Our computational results indicate that disturbances in cell energetics (e.g. mitochondrial dysfunction), and dysfunctional metabolite sensing and distribution throughout the cell might be related to pathologies such as metabolic syndrome and diabetes.

Cytoplasmic Calcium Buffering: An Integrative Crosstalk

Calcium (Ca²⁺) buffering is part of an integrative crosstalk between different mechanisms and elements involved in the control of free Ca²⁺ ions persistence in the cytoplasm and hence, in the Ca²⁺-dependence of many intracellular processes. Alterations of Ca²⁺ homeostasis and signaling from systemic to subcellular levels also play a pivotal role in the pathogenesis of many diseases.Compared with Ca²⁺ sequestration towards intracellular Ca²⁺ stores, Ca²⁺ buffering is a rapid process occurring in a subsecond scale. Any molecule (or binding site) with the ability to bind Ca²⁺ ions could be considered, at least in principle, as a buffer. However, the term Ca²⁺ buffer is applied only to a small subset of Ca²⁺ binding proteins containing acidic side-chain residues.Ca²⁺ buffering in the cytoplasm mainly relies on mobile and immobile or fixed buffers controlling the diffusion of free Ca²⁺ ions inside the cytosol both temporally and spatially. Mobility of buffers depends on their molecular weight, but other parameters as their concentration, affinity for Ca²⁺ or Ca²⁺ binding and dissociation kinetics next to their diffusional mobility also contribute to make Ca²⁺ signaling one of the most complex signaling activities of the cell.The crosstalk between all the elements involved in the intracellular Ca²⁺ dynamics is a process of extreme complexity due to the diversity of structural and molecular elements involved but permit a highly regulated spatiotemporal control of the signal mediated by Ca²⁺ ions. The basis of modeling tools to study Ca²⁺ dynamics are also presented.

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 BK_Ca potassium currents, and hence BK_Ca–CaV complexes controlled locally by CaVs via Ca²⁺ nanodomains. We showed how different CaV types and BK_Ca–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 BK_Ca–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.