Conductance-Based Refractory Density Approach for a Population of Bursting Neurons

The conductance-based refractory density (CBRD) approach is a parsimonious mathematical-computational framework for modeling interact- ing populations of regular spiking neurons, which, however, has not been yet extended for a population of bursting neurons. The canonical CBRD method allows to describe the firing activity of a statistical ensemble of uncoupled Hodgkin-Huxley-like neurons (differentiated by noise) and has demonstrated its validity against experimental data. The present manuscript generalises the CBRD for a population of bursting neurons; however, in this pilot computational study we consider the simplest setting in which each individual neuron is governed by a piecewise linear bursting dynamics. The resulting popula- tion model makes use of slow-fast analysis, which leads to a novel method- ology that combines CBRD with the theory of multiple timescale dynamics. The main prospect is that it opens novel avenues for mathematical explo- rations, as well as, the derivation of more sophisticated population activity from Hodgkin-Huxley-like bursting neurons, which will allow to capture the activity of synchronised bursting activity in hyper-excitable brain states (e.g. onset of epilepsy).Russian Science Foundation grant (project 16-15- 10201) Spanish grant MINECO-FEDER-UE MTM-2015-71509-C2-2-R Catalan Grant number 2017SGR104

Why we should use topological data analysis in ageing: Towards defining the “topological shape of ageing”

Living systems are subject to the arrow of time; from birth, they undergo complex transformations (self-organization) in a constant battle for survival, but inevitably ageing and disease trap them to death. Can ageing be understood and eventually reversed? What tools can be employed to further our understanding of ageing? The present article is an invitation for biologists and clinicians to consider key conceptual ideas and computational tools (known to mathematicians and physicists), which potentially may help dissect some of the underlying processes of ageing and disease. Specifically, we first discuss how to classify and analyse complex systems, as well as highlight critical theoretical difficulties that make complex systems hard to study. Subsequently, we introduce Topological Data Analysis - a novel Big Data tool – which may help in the study of complex systems since it extracts knowledge from data in a holistic approach via topological considerations. These conceptual ideas and tools are discussed in a relatively informal way to pave future discussions and collaborations between mathematicians and biologists studying ageing.Basque Government under the grant “Artificial Intelligence in BCAM number EXP. 2019/00432” Inria associated team "NeuroTransSF

Canards, Folded Nodes, and Mixed-Mode Oscillations in Piecewise-Linear Slow-Fast Systems

Canard-induced phenomena have been extensively studied in the last three decades, from both the mathematical and the application viewpoints. Canards in slow-fast systems with (at least) two slow variables, especially near folded-node singularities, give an essential generating mechanism for mixed-mode oscillations (MMOs) in the framework of smooth multiple timescale systems. There is a wealth of literature on such slow-fast dynamical systems and many models displaying canard-induced MMOs, particularly in neuroscience. In parallel, since the late 1990s several papers have shown that the canard phenomenon can be faithfully reproduced with piecewise-linear (PWL) systems in two dimensions, although very few results are available in the three-dimensional case. The present paper aims to bridge this gap by analyzing canonical PWL systems that display folded singularities, primary and secondary canards, with a similar control of the maximal winding number as in the smooth case. We also show that the singular phase portraits are compatible in both frameworks. Finally, we show using an example how to construct a (linear) global return and obtain robust PWL MMOs

Model for (a)synchronous/spontaneous release, applied to CCK-positive Interneuron synapses

Asynchronous and spontaneous neurotransmitter release remain elusive and constitute topics of considerable research both from the experimental and modeling perspective. This study proposes a parsimonious model that accounts for all modes of vesicle exocytosis and Short-Term Synaptic Plasticity (STSP). The modeling novelty is based on principles of slow-fast dynamical systems theory. The model's validity is shown by its good agreement with experimental data obtained from in vitro electrophysiological dual whole-cell recordings between local cholecystokinin (CKK)-positive, Schaffer collateral associated (SCA) interneurons in the CA1 region of rat hippocampus~\cite{AfiaAli2007,AfiaAli2010}. These unitary synapses display asynchronous release, governed by the retrograde release of endocannabinoid in response to post-synaptic membrane depolarisation. This work will advance our understanding of the physiology underlying differential exocytosis, and facilitate large-scale neuronal simulations

Observational evidence for matter propagation in accretion flows

We study simultaneous X-ray and optical observations of three intermediate polars EX Hya, V1223 Sgr and TV Col with the aim to understand the propagation of matter in their accretion flows. We show that in all cases the power spectra of flux variability of binary systems in X-rays and in optical band are similar to each other and the majority of X-ray and optical fluxes are correlated with time lag <1 sec. These findings support the idea that optical emission of accretion disks, in these binary systems,largely originates as reprocessing of X-ray luminosity of their white dwarfs. In the best obtained dataset of EX Hya we see that the optical lightcurve unambiguously contains some component, which leads the X-ray emission by ~7 sec. We interpret this in the framework of the model of propagating fluctuations and thus deduce the time of travel of the matter from the innermost part of the truncated accretion disk to the white dwarf surface. This value agrees very well with the time expected for matter threaded onto the magnetosphere of the white dwarf to fall to its surface. The datasets of V1223 Sgr and TV Col in general confirm these findings,but have poorer quality.Comment: 7 pages, 6 figures. Accepted for publication in MNRA

Targeting Impaired Antimicrobial Immunity in the Brain for the Treatment of Alzheimer’s Disease

Alzheimer’s disease (AD) is the most common form of dementia and aging is the most common risk factor for developing the disease. The etiology of AD is not known but AD may be considered as a clinical syndrome with multiple causal pathways contributing to it. The amyloid cascade hypothesis, claiming that excess production or reduced clearance of amyloid-beta (Aβ) and its aggregation into amyloid plaques, was accepted for a long time as the main cause of AD. However, many studies showed that Aβ is a frequent consequence of many challenges/pathologic processes occurring in the brain for decades. A key factor, sustained by experimental data, is that low-grade infection leading to production and deposition of Aβ, which has antimicrobial activity, precedes the development of clinically apparent AD. This infection is chronic, low grade, largely clinically silent for decades because of a nearly efficient antimicrobial immune response in the brain. A chronic inflammatory state is induced that results in neurodegeneration. Interventions that appear to prevent, retard or mitigate the devel- opment of AD also appear to modify the disease. In this review, we conceptualize further that the changes in the brain antimicrobial immune response during aging and especially in AD sufferers serve as a foundation that could lead to improved treatment strategies for preventing or decreasing the progression of AD in a disease-modifying treatment

Hyperactivation of monocytes and macrophages in MCI patients contributes to the progression of Alzheimer's disease

Background: Alzheimer’s disease (AD) is the most common neurodegenerative disease ultimately manifesting as clinical dementia. Despite considerable effort and ample experimental data, the role of neuroinflammation related to systemic inflammation is still unsettled. While the implication of microglia is well recognized, the exact contribution of peripheral monocytes/macrophages is still largely unknown, especially concerning their role in the various stages of AD. Objectives: AD develops over decades and its clinical manifestation is preceded by subjective memory complaints (SMC) and mild cognitive impairment (MCI); thus, the question arises how the peripheral innate immune response changes with the progression of the disease. Therefore, to further investigate the roles of monocytes/macrophages in the progression of AD we assessed their phenotypes and functions in patients at SMC, MCI and AD stages and compared them with cognitively healthy controls. We also conceptualised an idealised mathematical model to explain the functionality of monocytes/macrophages along the progression of the disease. Results: We show that there are distinct phenotypic and functional changes in monocyte and macrophage populations as the disease progresses. Higher free radical production upon stimulation could already be observed for the monocytes of SMC patients. The most striking results show that activation of peripheral monocytes (hyperactivation) is the strongest in the MCI group, at the prodromal stage of the disease. Monocytes exhibit significantly increased chemotaxis, free radical production, and cytokine production in response to TLR2 and TLR4 stimulation. Conclusion: Our data suggest that the peripheral innate immune system is activated during the progression from SMC through MCI to AD, with the highest levels of activation being in MCI subjects and the lowest in AD patients. Some of these parameters may be used as biomarkers, but more holistic immune studies are needed to find the best period of the disease for clinical intervention

Targeting Infectious Agents as a Therapeutic Strategy in Alzheimer’s Disease

Alzheimer’s disease (AD) is the most prevalent dementia in the world. Its cause(s) are presently largely unknown. The most common explanation for AD, now, is the amyloid cascade hypothesis, which states that the cause of AD is senile plaque forma- tion by the amyloid β peptide, and the formation of neurofibrillary tangles by hyperphosphorylated tau. A second, burgeoning theory by which to explain AD is based on the infection hypothesis. Much experimental and epidemiological data support the involvement of infections in the development of dementia. According to this mechanism, the infection either directly or via microbial virulence factors precedes the formation of amyloid β plaques. The amyloid β peptide, possessing antimicrobial properties, may be beneficial at an early stage of AD, but becomes detrimental with the progression of the disease, concomi- tantly with alterations to the innate immune system at both the peripheral and central levels. Infection results in neuroinflam- mation, leading to, and sustained by, systemic inflammation, causing eventual neurodegeneration, and the senescence of the immune cells. The sources of AD-involved microbes are various body microbiome communities from the gut, mouth, nose, and skin. The infection hypothesis of AD opens a vista to new therapeutic approaches, either by treating the infection itself or modulating the immune system, its senescence, or the body’s metabolism, either separately, in parallel, or in a multi-step way.Basque Government under the grant “Artificial Intelligence in BCAM number EXP. 2019/00432