The progression towards Alzheimer's disease described as a bistable switch arising from the positive loop between amyloids and Ca(2+)

A nonlinear meccano for Alzheimer's emergence by amyloid β-mediated glutamatergic hyperactivity

The pathophysiological process of Alzheimer's disease (AD) is believed to begin many years before the formal diagnosis of AD dementia. This protracted preclinical phase offers a crucial window for potential therapeutic interventions, yet its comprehensive characterization remains elusive. Accumulating evidence suggests that amyloid-β (Aβ) may mediate neuronal hyperactivity in circuit dysfunction in the early stages of AD. At the same time, neural activity can also facilitate Aβ accumulation through intricate feed-forward interactions, complicating elucidating the conditions governing Aβ-dependent hyperactivity and its diagnostic utility. In this study, we use biophysical modeling to shed light on such conditions. Our analysis reveals that the inherently nonlinear nature of the underlying molecular interactions can give rise to the emergence of various modes of hyperactivity. This diversity in the mechanisms of hyperactivity may ultimately account for a spectrum of AD manifestations.

Data-driven Stochastic Model for Quantifying the Interplay Between Amyloid-beta and Calcium Levels in Alzheimer's Disease

The abnormal aggregation of extracellular amyloid-β ( A β ) in senile plaques resulting in calcium C a + 2 dyshomeostasis is one of the primary symptoms of Alzheimer's disease (AD). Significant research efforts have been devoted in the past to better understand the underlying molecular mechanisms driving A β deposition and C a + 2 dysregulation. Importantly, synaptic impairments, neuronal loss, and cognitive failure in AD patients are all related to the buildup of intraneuronal A β accumulation. Moreover, increasing evidence show a feed-forward loop between A β and C a + 2 levels, i.e. A β disrupts neuronal C a + 2 levels, which in turn affects the formation of A β . To better understand this interaction, we report a novel stochastic model where we analyze the positive feedback loop between A β and C a + 2 using ADNI data. A good therapeutic treatment plan for AD requires precise predictions. Stochastic models offer an appropriate framework for modelling AD since AD studies are observational in nature and involve regular patient visits. The etiology of AD may be described as a multi-state disease process using the approximate Bayesian computation method. So, utilizing ADNI data from 2-year visits for AD patients, we employ this method to investigate the interplay between A β and C a + 2 levels at various disease development phases. Incorporating the ADNI data in our physics-based Bayesian model, we discovered that a sufficiently large disruption in either A β metabolism or intracellular C a + 2 homeostasis causes the relative growth rate in both C a + 2 and A β , which corresponds to the development of AD. The imbalance of C a + 2 ions causes A β disorders by directly or indirectly affecting a variety of cellular and subcellular processes, and the altered homeostasis may worsen the abnormalities of C a + 2 ion transportation and deposition. This suggests that altering the C a + 2 balance or the balance between A β and C a + 2 by chelating them may be able to reduce disorders associated with AD and open up new research possibilities for AD therapy.

Altered synaptic plasticity at hippocampal CA1-CA3 synapses in Alzheimer's disease: integration of amyloid precursor protein intracellular domain and amyloid beta effects into computational models

Alzheimer's disease (AD) is a progressive memory loss and cognitive dysfunction brain disorder brought on by the dysfunctional amyloid precursor protein (APP) processing and clearance of APP peptides. Increased APP levels lead to the production of AD-related peptides including the amyloid APP intracellular domain (AICD) and amyloid beta (Aβ), and consequently modify the intrinsic excitability of the hippocampal CA1 pyramidal neurons, synaptic protein activity, and impair synaptic plasticity at hippocampal CA1-CA3 synapses. The goal of the present study is to build computational models that incorporate the effect of AD-related peptides on CA1 pyramidal neuron and hippocampal synaptic plasticity under the AD conditions and investigate the potential pharmacological treatments that could normalize hippocampal synaptic plasticity and learning in AD. We employ a phenomenological N-methyl-D-aspartate (NMDA) receptor-based voltage-dependent synaptic plasticity model that includes the separate receptor contributions on long-term potentiation (LTP) and long-term depression (LTD) and embed it into the a detailed compartmental model of CA1 pyramidal neuron. Modeling results show that partial blockade of Glu2NB-NMDAR-gated channel restores intrinsic excitability of a CA1 pyramidal neuron and rescues LTP in AICD and Aβ conditions. The model provides insight into the complex interactions in AD pathophysiology and suggests the conditions under which the synchronous activation of a cluster of synaptic inputs targeting the dendritic tree of CA1 pyramidal neuron leads to restored synaptic plasticity.

Using sensitivity analyses to understand bistable system behavior

BACKGROUND

Bistable systems, i.e., systems that exhibit two stable steady states, are of particular interest in biology. They can implement binary cellular decision making, e.g., in pathways for cellular differentiation and cell cycle regulation. The onset of cancer, prion diseases, and neurodegenerative diseases are known to be associated with malfunctioning bistable systems. Exploring and characterizing parameter spaces in bistable systems, so that they retain or lose bistability, is part of a lot of therapeutic research such as cancer pharmacology.

RESULTS

We use eigenvalue sensitivity analysis and stable state separation sensitivity analysis to understand bistable system behaviors, and to characterize the most sensitive parameters of a bistable system. While eigenvalue sensitivity analysis is an established technique in engineering disciplines, it has not been frequently used to study biological systems. We demonstrate the utility of these approaches on a published bistable system. We also illustrate scalability and generalizability of these methods to larger bistable systems.

CONCLUSIONS

Eigenvalue sensitivity analysis and separation sensitivity analysis prove to be promising tools to define parameter design rules to make switching decisions between either stable steady state of a bistable system and a corresponding monostable state after bifurcation. These rules were applied to the smallest two-component bistable system and results were validated analytically. We showed that with multiple parameter settings of the same bistable system, we can design switching to a desirable state to retain or lose bistability when the most sensitive parameter is varied according to our parameter perturbation recommendations. We propose eigenvalue and stable state separation sensitivity analyses as a framework to evaluate large and complex bistable systems.

Effect of disturbances in neuronal calcium and IP3 dynamics on β-amyloid production and degradation

Overproduction and accumulation of β-amyloid and its improper clearance can cause neurotoxicity leading to Alzheimer's disease. The production and degradation of β-amyloid depend on the calcium ([Ca2+]) and IP3 dynamics in the nerve cells. Thus, there is a need to understand the impacts of disturbances in the processes of [Ca2+] and IP3 dynamics on β-amyloid production and its degradation. Here, a model is proposed to investigate the role of [Ca2+] and IP3 dynamics on β-amyloid production and degradation. The problem is formulated in terms of the initial boundary value problem involving the system of two reaction-diffusion equations respectively for [Ca2+] and IP3 in the nerve cell. The solution is obtained by employing the Finite element approach. The numerical results are used to analyze the impact of various mechanisms of calcium and IP3 dynamics on β-amyloid production and degradation in a neuron cell. The results indicate that disturbances in any of the constitutive processes of interdependent calcium and IP3 dynamics like source influx, buffering, serca pump, and IP3 dynamics, etc. can cause dynamic changes in β-amyloid production and degradation, which in turn can be the cause of neurotoxicity and neuronal disorders like Alzheimer's disease. Thus, the relationships obtained by the proposed model among various mechanisms can be useful in addressing the challenges of identifying specific constitutive processes causing neuronal disorders like Alzheimer's disease, etc., and developing the framework for their diagnosis and treatment.

A general hypothesis of multistable systems in pathophysiology

Despite intensive investigations numerous diseases remain etiologically puzzling and recalcitrant to treatments. A hypothesis is proposed here assuming that these difficulties are due to an unsuitable approach to the mechanisms of life, which is subjugated by an apparent complexity and fails to grasp the uniformity that lays behind. The stability of metabolism, despite the enormous complex of chemical reactions, suggests that reciprocal control is a prerequisite of life. Negative feedback loops have been known for a long time to maintain homeostasis, while more recently, different life processes involved in transitions or changes have been modeled by positive loops giving rise to bistable switches, also including various diseases. The present hypothesis makes a generalization, by assuming that any functional element of a biological system is involved in a positive or a negative feedback loop. Consequently, the hypothesis holds that the starting mechanism of any disease that affects a healthy human can be conceptually reduced to a bistable or multistationary loop system, thus providing a unifying model leading to the discovery of critical therapeutic targets.

A general theory of multistable systems in pathophysiology

Despite intensive investigations numerous diseases remain etiologically puzzling and recalcitrant to treatments. A theory is proposed here assuming that these difficulties are due to an unsuitable approach to the mechanisms of life, which is subjugated by an apparent complexity and fails to grasp the uniformity that lays behind. The stability of metabolism, despite the enormous complex of chemical reactions, suggests that reciprocal control is a prerequisite of life. Negative feedback loops have been known for a long time to maintain homeostasis, while more recently, different life processes involved in transitions or changes have been modeled by positive loops giving rise to bistable switches, also including various diseases. The present theory makes a generalization, by assuming that any functional element of a biological system is involved in a positive or a negative feedback loop. Consequently, the theory holds that the starting mechanism of any disease that affects a healthy human can be conceptually reduced to a bistable or multistationary loop system, thus providing a unifying model leading to the discovery of critical therapeutic targets.

A general hypothesis of multistable systems in pathophysiology

Despite intensive investigations numerous diseases remain etiologically puzzling and recalcitrant to treatments. A hypothesis is proposed here assuming that these difficulties are due to an unsuitable approach to the mechanisms of life, which is subjugated by an apparent complexity and fails to grasp the uniformity that lays behind. The stability of metabolism, despite the enormous complex of chemical reactions, suggests that reciprocal control is a prerequisite of life. Negative feedback loops have been known for a long time to maintain homeostasis, while more recently, different life processes involved in transitions or changes have been modeled by positive loops giving rise to bistable switches, also including various diseases. The present hypothesis makes a generalization, by assuming that any functional element of a biological system is involved in a positive or a negative feedback loop. Consequently, the hypothesis holds that the starting mechanism of any disease that affects a healthy human can be conceptually reduced to a bistable or multistationary loop system, thus providing a unifying model leading to the discovery of critical therapeutic targets.

Model scenarios for cell cycle re-entry in Alzheimer's disease

Alzheimer's disease (AD) is the most prevalent neurodegenerative disease. Aberrant production and aggregation of amyloid beta (Aβ) peptide into plaques is a frequent feature of AD, but therapeutic approaches targeting Aβ accumulation fail to inhibit disease progression. The approved cholinesterase inhibitor drugs are symptomatic treatments. During human brain development, the progenitor cells differentiate into neurons and switch to a postmitotic state. However, cell cycle re-entry often precedes loss of neurons. We developed mathematical models of multiple routes leading to cell cycle re-entry in neurons that incorporate the crosstalk between cell cycle, neuronal, and apoptotic signaling mechanisms. We show that the integration of multiple feedback loops influences disease severity making the switch to pathological state irreversible. We observe that the transcriptional changes associated with this transition are also characteristics of the AD brain. We propose that targeting multiple arms of the feedback loop may bring about disease-modifying effects in AD.

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Developed mathematical models of cell cycle re-entry in Alzheimer's disease (AD)

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Integration of multiple feedback loops drives irreversible transition to AD

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Predicted transcriptional dysregulation is validated using AD gene expression data

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Inhibition of self-amplifying feedback loops brings about disease-modifying effects

Thalamocortical bistable switch as a theoretical model of fibromyalgia pathogenesis inferred from a literature survey

Fibromyalgia (FM) is an unsolved central pain processing disturbance. We aim to provide a unifying model for FM pathogenesis based on a loop network involving thalamocortical regions, i.e., the ventroposterior lateral thalamus (VPL), the somatosensory cortex (SC), and the thalamic reticular nucleus (TRN). The dynamics of the loop have been described by three differential equations having neuron mean firing rates as variables and containing Hill functions to model mutual interactions among the loop elements. A computational analysis conducted with MATLAB has shown a transition from monostability to bistability of the loop behavior for a weakening of GABAergic transmission between TRN and VPL. This involves the appearance of a high-firing-rate steady state, which becomes dominant and is assumed to represent pathogenic pain processing giving rise to chronic pain. Our model is consistent with a bulk of literature evidence, such as neuroimaging and pharmacological data collected on FM patients, and with correlations between FM and immunoendocrine conditions, such as stress, perimenopause, chronic inflammation, obesity, and chronic dizziness. The model suggests that critical targets for FM treatment are to be found among immunoendocrine pathways leading to GABA/glutamate imbalance having an impact on the thalamocortical system.

A kinetic scheme to examine the role of glial cells in the pathogenesis of Alzheimer's disease

Alzheimer's disease (AD) is a complex neurodegenerative disorder that leads to severe impairments in cognitive functions including memory and learning. An improved kinetic model is proposed here to understand the pathogenesis of AD in particular the role of glial cells in the presence of amyloid plaques and neurofibrillary tangles (NFTs). The kinetic model describes the production of activated microglia and astroglia. It involves two rate equations and incorporates the dual role of these glial cells which can function as neuroprotective and as neurotoxic cells. Examination of the steady state solutions of the model predicts an increase in population of these glial cells as (AD) progresses, and that this continues to increase linearly even after the amyloid population has reached a plateau.This is in agreement with experimental data. Limiting AD to the effect of amyloid peptides alone is incorrect and the role of neurofibrillary tangles, clearance rate of dead neurons and neuroinflammation from glial cells are vital and must be included in understanding the pathogenesis of AD. The study shows that increasing the clearance of dead neurons and use of any method to deactivate the glial cells will diminish the progression of AD.

Impact of β-Amyloids Induced Disruption of Ca2+ Homeostasis in a Simple Model of Neuronal Activity

Alzheimer’s disease is characterized by a marked dysregulation of intracellular Ca²⁺ homeostasis. In particular, toxic β-amyloids (Aβ) perturb the activities of numerous Ca²⁺ transporters or channels. Because of the tight coupling between Ca²⁺ dynamics and the membrane electrical activity, such perturbations are also expected to affect neuronal excitability. We used mathematical modeling to systematically investigate the effects of changing the activities of the various targets of Aβ peptides reported in the literature on calcium dynamics and neuronal excitability. We found that the evolution of Ca²⁺ concentration just below the plasma membrane is regulated by the exchanges with the extracellular medium, and is practically independent from the Ca²⁺ exchanges with the endoplasmic reticulum. Thus, disruptions of Ca²⁺ homeostasis interfering with signaling do not affect the electrical properties of the neurons at the single cell level. In contrast, the model predicts that by affecting the activities of L-type Ca²⁺ channels or Ca²⁺-activated K⁺ channels, Aβ peptides promote neuronal hyperexcitability. On the contrary, they induce hypo-excitability when acting on the plasma membrane Ca²⁺ ATPases. Finally, the presence of pores of amyloids in the plasma membrane can induce hypo- or hyperexcitability, depending on the conditions. These modeling conclusions should help with analyzing experimental observations in which Aβ peptides interfere at several levels with Ca²⁺ signaling and neuronal activity.

Unraveling Aβ-Mediated Multi-Pathway Calcium Dynamics in Astrocytes: Implications for Alzheimer's Disease Treatment From Simulations

The accumulation of amyloid β peptide (Aβ) in the brain is hypothesized to be the major factor driving Alzheimer's disease (AD) pathogenesis. Mounting evidence suggests that astrocytes are the primary target of Aβ neurotoxicity. Aβ is known to interfere with multiple calcium fluxes, thus disrupting the calcium homeostasis regulation of astrocytes, which are likely to produce calcium oscillations. Ca²⁺ dyshomeostasis has been observed to precede the appearance of clinical symptoms of AD; however, it is experimentally very difficult to investigate the interactions of many mechanisms. Given that Ca²⁺ disruption is ubiquitously involved in AD progression, it is likely that focusing on Ca²⁺ dysregulation may serve as a potential therapeutic approach to preventing or treating AD, while current hypotheses concerning AD have so far failed to yield curable therapies. For this purpose, we derive and investigate a concise mathematical model for Aβ-mediated multi-pathway astrocytic intracellular Ca²⁺ dynamics. This model accounts for how Aβ affects various fluxes contributions through voltage-gated calcium channels, Aβ-formed channels and ryanodine receptors. Bifurcation analysis of Aβ level, which reflected the corresponding progression of the disease, revealed that Aβ significantly induced the increasing [Ca²⁺] _i and frequency of calcium oscillations. The influence of inositol 1,4,5-trisphosphate production (IP₃) is also investigated in the presence of Aβ as well as the impact of changes in resting membrane potential. In turn, the Ca²⁺ flux can be considerably changed by exerting specific interventions, such as ion channel blockers or receptor antagonists. By doing so, a "combination therapy" targeting multiple pathways simultaneously has finally been demonstrated to be more effective. This study helps to better understand the effect of Aβ, and our findings provide new insight into the treatment of AD.

Modeling Neurotransmission: Computational Tools to Investigate Neurological Disorders

The investigation of synaptic functions remains one of the most fascinating challenges in the field of neuroscience and a large number of experimental methods have been tuned to dissect the mechanisms taking part in the neurotransmission process. Furthermore, the understanding of the insights of neurological disorders originating from alterations in neurotransmission often requires the development of (i) animal models of pathologies, (ii) invasive tools and (iii) targeted pharmacological approaches. In the last decades, additional tools to explore neurological diseases have been provided to the scientific community. A wide range of computational models in fact have been developed to explore the alterations of the mechanisms involved in neurotransmission following the emergence of neurological pathologies. Here, we review some of the advancements in the development of computational methods employed to investigate neuronal circuits with a particular focus on the application to the most diffuse neurological disorders.

Bridging Scales in Alzheimer's Disease: Biological Framework for Brain Simulation With The Virtual Brain

Despite the acceleration of knowledge and data accumulation in neuroscience over the last years, the highly prevalent neurodegenerative disease of AD remains a growing problem. Alzheimer's Disease (AD) is the most common cause of dementia and represents the most prevalent neurodegenerative disease. For AD, disease-modifying treatments are presently lacking, and the understanding of disease mechanisms continues to be incomplete. In the present review, we discuss candidate contributing factors leading to AD, and evaluate novel computational brain simulation methods to further disentangle their potential roles. We first present an overview of existing computational models for AD that aim to provide a mechanistic understanding of the disease. Next, we outline the potential to link molecular aspects of neurodegeneration in AD with large-scale brain network modeling using The Virtual Brain (www.thevirtualbrain.org), an open-source, multiscale, whole-brain simulation neuroinformatics platform. Finally, we discuss how this methodological approach may contribute to the understanding, improved diagnostics, and treatment optimization of AD.

A Statistical View on Calcium Oscillations

Transient rises and falls of the intracellular calcium concentration have been observed in numerous cell types and under a plethora of conditions. There is now a growing body of evidence that these whole-cell calcium oscillations are stochastic, which poses a significant challenge for modelling. In this review, we take a closer look at recently developed statistical approaches to calcium oscillations. These models describe the timing of whole-cell calcium spikes, yet their parametrisations reflect subcellular processes. We show how non-stationary calcium spike sequences, which e.g. occur during slow depletion of intracellular calcium stores or in the presence of time-dependent stimulation, can be analysed with the help of so-called intensity functions. By utilising Bayesian concepts, we demonstrate how values of key parameters of the statistical model can be inferred from single cell calcium spike sequences and illustrate what information whole-cell statistical models can provide about the subcellular mechanistic processes that drive calcium oscillations. In particular, we find that the interspike interval distribution of HEK293 cells under constant stimulation is captured by a Gamma distribution.

Tonic Activation of Extrasynaptic NMDA Receptors Decreases Intrinsic Excitability and Promotes Bistability in a Model of Neuronal Activity

NMDA receptors (NMDA-R) typically contribute to excitatory synaptic transmission in the central nervous system. While calcium influx through NMDA-R plays a critical role in synaptic plasticity, experimental evidence indicates that NMDAR-mediated calcium influx also modifies neuronal excitability through the activation of calcium-activated potassium channels. This mechanism has not yet been studied theoretically. Our theoretical model provides a simple description of neuronal electrical activity that takes into account the tonic activity of extrasynaptic NMDA receptors and a cytosolic calcium compartment. We show that calcium influx mediated by the tonic activity of NMDA-R can be coupled directly to the activation of calcium-activated potassium channels, resulting in an overall inhibitory effect on neuronal excitability. Furthermore, the presence of tonic NMDA-R activity promotes bistability in electrical activity by dramatically increasing the stimulus interval where both a stable steady state and repetitive firing can coexist. These results could provide an intrinsic mechanism for the constitution of memory traces in neuronal circuits. They also shed light on the way by which β-amyloids can alter neuronal activity when interfering with NMDA-R in Alzheimer’s disease and cerebral ischemia.

Mathematical Models to Shed Light on Amyloid-Beta and Tau Protein Dependent Pathologies in Alzheimer's Disease

The number of patients suffering from dementia due to Alzheimer's disease (AD) is constantly rising worldwide. This has accordingly resulted in huge burdens on the health systems and involved families. Lack of profound understanding of neural networking in normal brain and their interruption in AD makes the treatment of this neurodegenerative multifaceted disease a challenging issue. In recent years, mathematical and computational methods have paved the way towards a better understanding of the brain functional connectivity. Thus, much attention has been paid to this matter from both basic science researchers and clinicians with an interdisciplinary approach to determine what is not functioning properly in AD patients and how this malfunctioning can be addressed. In this review, a number of AD-related articles and well-studied pathophysiologic topics (e.g., amyloid-beta, neurofibrillary tangles, Ca²⁺ dysregulation, and synaptic plasticity alterations) has been literally surveyed from a computational and systems biology point of view. The neural networks were discussed from biological and mathematical point of views and their alterations in recent findings were further highlighted. Application of the graph theoretical analysis in the brain imaging was reviewed, depicting the relations between brain structure and function, without diving into mathematical details. Moreover, differential rate equations were briefly articulated, emphasizing the potential use of these equations in simplifying complex processes in relevance to pathologies of AD. Comprehensive insights were given into the AD progression from neural networks perspective, which may lead us towards potential strategies for early diagnosis and effective treatment of AD.

Data-driven modeling of mitochondrial dysfunction in Alzheimer's disease

Intracellular accumulation of oligomeric forms of β amyloid (Aβ) are now believed to play a key role in the earliest phase of Alzheimer's disease (AD) as their rise correlates well with the early symptoms of the disease. Extensive evidence points to impaired neuronal Ca²⁺ homeostasis as a direct consequence of the intracellular Aβ oligomers. However, little is known about the downstream effects of the resulting Ca²⁺ rise on the many intracellular Ca²⁺-dependent pathways. Here we use multiscale modeling in conjunction with patch-clamp electrophysiology of single inositol 1,4,5-trisphosphate (IP₃) receptor (IP₃R) and fluorescence imaging of whole-cell Ca²⁺ response, induced by exogenously applied intracellular Aβ₄₂ oligomers to show that Aβ₄₂ inflicts cytotoxicity by impairing mitochondrial function. Driven by patch-clamp experiments, we first model the kinetics of IP₃R, which is then extended to build a model for the whole-cell Ca²⁺ signals. The whole-cell model is then fitted to fluorescence signals to quantify the overall Ca²⁺ release from the endoplasmic reticulum by intracellular Aβ₄₂ oligomers through G-protein-mediated stimulation of IP₃ production. The estimated IP₃ concentration as a function of intracellular Aβ₄₂ content together with the whole-cell model allows us to show that Aβ₄₂ oligomers impair mitochondrial function through pathological Ca²⁺ uptake and the resulting reduced mitochondrial inner membrane potential, leading to an overall lower ATP and increased production of reactive oxygen species and H₂O₂. We further show that mitochondrial function can be restored by the addition of Ca²⁺ buffer EGTA, in accordance with the observed abrogation of Aβ₄₂ cytotoxicity by EGTA in our live cells experiments.

A mathematical model for the effects of amyloid beta on intracellular calcium

The accumulation of Alzheimer's disease (AD) associated Amyloid beta (Aβ) oligomers can trigger aberrant intracellular calcium (Ca2+) levels by disrupting the intrinsic Ca2+ regulatory mechanism within cells. These disruptions can cause changes in homeostasis levels that can have detrimental effects on cell function and survival. Although studies have shown that Aβ can interfere with various Ca2+ fluxes, the complexity of these interactions remains elusive. We have constructed a mathematical model that simulates Ca2+ patterns under the influence of Aβ. Our simulations shows that Aβ can increase regions of mixed-mode oscillations leading to aberrant signals under various conditions. We investigate how Aβ affects individual flux contributions through inositol triphosphate (IP3) receptors, ryanodine receptors, and membrane pores. We demonstrate that controlling for the ryanodine receptor's maximal kinetic reaction rate may provide a biophysical way of managing aberrant Ca2+ signals. The influence of a dynamic model for IP3 production is also investigated under various conditions as well as the impact of changes in membrane potential. Our model is one of the first to investigate the effects of Aβ on a variety of cellular mechanisms providing a base modeling scheme from which further studies can draw on to better understand Ca2+ regulation in an AD environment.

Dissipative structures in biological systems: bistability, oscillations, spatial patterns and waves

The goal of this review article is to assess how relevant is the concept of dissipative structure for understanding the dynamical bases of non-equilibrium self-organization in biological systems, and to see where it has been applied in the five decades since it was initially proposed by Ilya Prigogine. Dissipative structures can be classified into four types, which will be considered, in turn, and illustrated by biological examples: (i) multistability, in the form of bistability and tristability, which involve the coexistence of two or three stable steady states, or in the form of birhythmicity, which involves the coexistence between two stable rhythms; (ii) temporal dissipative structures in the form of sustained oscillations, illustrated by biological rhythms; (iii) spatial dissipative structures, known as Turing patterns; and (iv) spatio-temporal structures in the form of propagating waves. Rhythms occur with widely different periods at all levels of biological organization, from neural, cardiac and metabolic oscillations to circadian clocks and the cell cycle; they play key roles in physiology and in many disorders. New rhythms are being uncovered while artificial ones are produced by synthetic biology. Rhythms provide the richest source of examples of dissipative structures in biological systems. Bistability has been observed experimentally, but has primarily been investigated in theoretical models in an increasingly wide range of biological contexts, from the genetic to the cell and animal population levels, both in physiological conditions and in disease. Bistable transitions have been implicated in the progression between the different phases of the cell cycle and, more generally, in the process of cell fate specification in the developing embryo. Turing patterns are exemplified by the formation of some periodic structures in the course of development and by skin stripe patterns in animals. Spatio-temporal patterns in the form of propagating waves are observed within cells as well as in intercellular communication. This review illustrates how dissipative structures of all sorts abound in biological systems.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

What can computational modeling offer for studying the Ca2+ dysregulation in Alzheimer's disease: current research and future directions

Ca²⁺ dysregulation is an early event observed in Alzheimer’s disease (AD) patients preceding the presence of its clinical symptoms. Dysregulation of neuronal Ca²⁺ will cause synaptic loss and neuronal death, eventually leading to memory impairments and cognitive decline. Treatments targeting Ca²⁺ signaling pathways are potential therapeutic strategies against AD. The complicated interactions make it challenging and expensive to study the underlying mechanisms as to how Ca²⁺ signaling contributes to the pathogenesis of AD. Computational modeling offers new opportunities to study the signaling pathway and test proposed mechanisms. In this mini-review, we present some computational approaches that have been used to study Ca²⁺ dysregulation of AD by simulating Ca²⁺ signaling at various levels. We also pointed out the future directions that computational modeling can be done in studying the Ca²⁺ dysregulation in AD.

Computational modeling and biomarker studies of pharmacological treatment of Alzheimer's disease (Review)

Alzheimer's disease (AD) is a complex and multifactorial disease. In order to understand the genetic influence in the progression of AD, and to identify novel pharmaceutical agents and their associated targets, the present study discusses computational modeling and biomarker evaluation approaches. Based on mechanistic signaling pathway approaches, various computational models, including biochemical and morphological models, are discussed to explore the strategies that may be used to target AD treatment. Different biomarkers are interpreted on the basis of morphological and functional features of amyloid β plaques and unstable microtubule‑associated tau protein, which is involved in neurodegeneration. Furthermore, imaging and cerebrospinal fluids are also considered to be key methods in the identification of novel markers for AD. In conclusion, the present study reviews various biochemical and morphological computational models and biomarkers to interpret novel targets and agonists for the treatment of AD. This review also highlights several therapeutic targets and their associated signaling pathways in AD, which may have potential to be used in the development of novel pharmacological agents for the treatment of patients with AD. Computational modeling approaches may aid the quest for the development of AD treatments with enhanced therapeutic efficacy and reduced toxicity.

Composite mathematical modeling of calcium signaling behind neuronal cell death in Alzheimer's disease

Background

Alzheimer’s disease (AD) is a progressive neurological disorder, recognized as the most common cause of dementia affecting people aged 65 and above. AD is characterized by an increase in amyloid metabolism, and by the misfolding and deposition of β-amyloid oligomers in and around neurons in the brain. These processes remodel the calcium signaling mechanism in neurons, leading to cell death via apoptosis. Despite accumulating knowledge about the biological processes underlying AD, mathematical models to date are restricted to depicting only a small portion of the pathology.

Results

Here, we integrated multiple mathematical models to analyze and understand the relationship among amyloid depositions, calcium signaling and mitochondrial permeability transition pore (PTP) related cell apoptosis in AD. The model was used to simulate calcium dynamics in the absence and presence of AD. In the absence of AD, i.e. without β-amyloid deposition, mitochondrial and cytosolic calcium level remains in the low resting concentration. However, our in silico simulation of the presence of AD with the β-amyloid deposition, shows an increase in the entry of calcium ions into the cell and dysregulation of Ca ²⁺ channel receptors on the Endoplasmic Reticulum. This composite model enabled us to make simulation that is not possible to measure experimentally.

Conclusions

Our mathematical model depicting the mechanisms affecting calcium signaling in neurons can help understand AD at the systems level and has potential for diagnostic and therapeutic applications.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0529-2) contains supplementary material, which is available to authorized users.

Vitamin D, reactive oxygen species and calcium signalling in ageing and disease

Vitamin D is a hormone that maintains healthy cells. It functions by regulating the low resting levels of cell signalling components such as Ca(2+) and reactive oxygen species (ROS). Its role in maintaining phenotypic stability of these signalling pathways depends on the ability of vitamin D to control the expression of those components that act to reduce the levels of both Ca(2+) and ROS. This regulatory role of vitamin D is supported by both Klotho and Nrf2. A decline in the vitamin D/Klotho/Nrf2 regulatory network may enhance the ageing process, and this is well illustrated by the age-related decline in cognition in rats that can be reversed by administering vitamin D. A deficiency in vitamin D has also been linked to two of the major diseases in man: heart disease and Alzheimer's disease (AD). In cardiac cells, this deficiency alters the Ca(2+) transients to activate the gene transcriptional events leading to cardiac hypertrophy and the failing heart. In the case of AD, it is argued that vitamin D deficiency results in the Ca(2+) landscape that initiates amyloid formation, which then elevates the resting level of Ca(2+) to drive the memory loss that progresses to neuronal cell death and dementia.This article is part of the themed issue 'Evolution brings Ca(2+) and ATP together to control life and death'.

A Bayesian approach to modelling heterogeneous calcium responses in cell populations

Calcium responses have been observed as spikes of the whole-cell calcium concentration in numerous cell types and are essential for translating extracellular stimuli into cellular responses. While there are several suggestions for how this encoding is achieved, we still lack a comprehensive theory. To achieve this goal it is necessary to reliably predict the temporal evolution of calcium spike sequences for a given stimulus. Here, we propose a modelling framework that allows us to quantitatively describe the timing of calcium spikes. Using a Bayesian approach, we show that Gaussian processes model calcium spike rates with high fidelity and perform better than standard tools such as peri-stimulus time histograms and kernel smoothing. We employ our modelling concept to analyse calcium spike sequences from dynamically-stimulated HEK293T cells. Under these conditions, different cells often experience diverse stimulus time courses, which is a situation likely to occur in vivo. This single cell variability and the concomitant small number of calcium spikes per cell pose a significant modelling challenge, but we demonstrate that Gaussian processes can successfully describe calcium spike rates in these circumstances. Our results therefore pave the way towards a statistical description of heterogeneous calcium oscillations in a dynamic environment.

Upon stimulation a large number of cell types respond with transient increases of the intracellular calcium concentration, which often take the form of repetitive spikes. It is therefore believed that calcium spikes play a central role in cellular signal transduction. A critical feature of these calcium spikes is that they occur randomly, which raises the question of how we can predict the timing of calcium spikes. We here show that by using Bayesian ideas and concepts from stochastic processes, we can quantitatively compute the calcium spike rate for a given stimulus. Our analysis also demonstrates that traditional methods for spike rate estimation perform less favourably compared to a Bayesian approach when small numbers of cells are investigated. To test our methodology under conditions that closely mimic those experienced in vivo we challenged cells with agonist concentrations that vary both in space and time. We find that cells that experience similar stimulus profiles are described by similar calcium spike rates. This suggests that calcium spike rates may constitute a quantitative description of whole-cell calcium spiking that reflects both the randomness and the spatiotemporal organisation of the calcium signalling machinery.

Capturing intracellular Ca2+ dynamics in computational models of neurodegenerative diseases

Many signaling pathways crucial for homeostatic regulation, synaptic plasticity, apoptosis and immune response depend on Ca²⁺. Ca²⁺ dysregulation disrupts normal function of neurons and neuronal networks. This causes severe motor and cognitive disabilities. Understanding how Ca²⁺ dysregulation triggers disease onset and progression, and affects downstream processes, can help identify targets for treatments. Because of intermingling of molecular pathways, dissecting the role of individual mechanisms and establishing causality is very challenging. Computational models provide a way to decipher these processes. I review some computational models with Ca²⁺ dynamics to illustrate their predictive power, and note where extending those models to capture multiscale interaction of Ca²⁺ dependent molecular pathways can be useful for therapeutic and drug discovery purposes.

Ca2+ dysregulation in the endoplasmic reticulum related to Alzheimer's disease: A review on experimental progress and computational modeling

Alzheimer's disease (AD) is a devastating, incurable neurodegenerative disease affecting millions of people worldwide. Dysregulation of intracellular Ca(2+) signaling has been observed as an early event prior to the presence of clinical symptoms of AD and is believed to be a crucial factor contributing to its pathogenesis. The progressive and sustaining increase in the resting level of cytosolic Ca(2+) will affect downstream activities and neural functions. This review focuses on the issues relating to the increasing Ca(2+) release from the endoplasmic reticulum (ER) observed in AD neurons. Numerous research papers have suggested that the dysregulation of ER Ca(2+) homeostasis is associated with mutations in the presenilin genes and amyloid-β oligomers. These disturbances could happen at many different points in the signaling process, directly affecting ER Ca(2+) channels or interfering with related pathways, which makes it harder to reveal the underlying mechanisms. This review paper also shows that computational modeling is a powerful tool in Ca(2+) signaling studies and discusses the progress in modeling related to Ca(2+) dysregulation in AD research.