N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

Stem cells are promising for the treatment of myocardial infarction (MI) and large animal models should be used to better understand the full spectrum of stem cell actions and preclinical evidences. In this study, bone marrow mesenchymal stem cells (BM-MSCs) were transplanted into swine heart ischemia model. To detect glucose metabolism in global left ventricular myocardium and regional myocardium, combined with assessment of cardiac function, positron emission tomography-computer tomography (PET-CT) and magnetic resonance imaging (MRI) were performed. To study the changes of glucose transporters and glucose metabolism-related enzymes and the signal transduction pathway, RT-PCR, Western-blot, and immunohistochemistry were carried out. Myocardium metabolic evaluation by PET-CT showed that mean signal intensity (MSI) increased in these segments at week 4 compared with that at week 1 after BM-MSCs transplantation. Moreover, MRI demonstrated significant function enhancement in BM-MSCs group. The gene expressions of glucose transporters (GLUT1, GLUT4), glucose metabolism-related enzymes phosphofructokinase (PFK), and glyceraldehyde-3-phosphate dehydrogenase (GAPDH)) and 70-kDa ribosomal protein S6 kinase (p70s6k) in BM-MSCs injected areas were up-regulated at week 4 after BM-MSCs transplantation and this was confirmed by Western-blot and immunohistochemistry. In conclusions, BM-MSCs transplantation could improve cardiac function in swine MI model by activation of mTOR signal transduction pathway.

Erratum: Bone Marrow Mesenchymal Stem Cells (BM-MSCs) Improve Heart Function in Swine Myocardial Infarction Model through Paracrine Effects

A psychoengineering paradigm for the neurocognitive mechanisms of biofeedback and neurofeedback.

Cerebral ischemic diseases including ischemic stroke and cerebral ischemia reperfusion injury can result in serious dysfunction of the brain, which leads to extremely high mortality and disability. There are no effective therapeutics for cerebral ischemic diseases to date. Circular RNAs are a kind of newly investigated noncoding RNAs. It is reported that circular RNAs are enriched in multiple organs, especially abundant in the brain, which indicates that circular RNAs may be involved in cerebral physiological and pathological processes. In this chapter, we will firstly review the pathophysiology, underlying mechanisms, and current treatments of cerebral ischemic diseases including ischemic stroke and cerebral ischemia/reperfusion injury. Secondly, the characteristics and function of circular RNAs will be outlined, and then we are going to introduce the roles circular RNAs play in human diseases. Finally, we will summarize the function of circular RNAs in cerebral ischemic diseases.

The Role of Circular RNAs in Cerebral Ischemic Diseases: Ischemic Stroke and Cerebral Ischemia/Reperfusion Injury

The computational neuroscience field has heavily concentrated on the modeling of neuronal functions, largely ignoring other brain cells, including one type of glial cell, the astrocytes. Despite the short history of modeling astrocytic functions, we were delighted about the hundreds of models developed so far to study the role of astrocytes, most often in calcium dynamics, synchronization, information transfer, and plasticity in vitro, but also in vascular events, hyperexcitability, and homeostasis. Our goal here is to present the state-of-the-art in computational modeling of astrocytes in order to facilitate better understanding of the functions and dynamics of astrocytes in the brain. Due to the large number of models, we concentrated on a hundred models that include biophysical descriptions for calcium signaling and dynamics in astrocytes. We categorized the models into four groups: single astrocyte models, astrocyte network models, neuron-astrocyte synapse models, and neuron-astrocyte network models to ease their use in future modeling projects. We characterized the models based on which earlier models were used for building the models and which type of biological entities were described in the astrocyte models. Features of the models were compared and contrasted so that similarities and differences were more readily apparent. We discovered that most of the models were basically generated from a small set of previously published models with small variations. However, neither citations to all the previous models with similar core structure nor explanations of what was built on top of the previous models were provided, which made it possible, in some cases, to have the same models published several times without an explicit intention to make new predictions about the roles of astrocytes in brain functions. Furthermore, only a few of the models are available online which makes it difficult to reproduce the simulation results and further develop the models. Thus, we would like to emphasize that only via reproducible research are we able to build better computational models for astrocytes, which truly advance science. Our study is the first to characterize in detail the biophysical and biochemical mechanisms that have been modeled for astrocytes.

/pdf/computational-models-for-calcium-mediated-astrocyte-10ia6wgig2.pdf

Computational Models for Calcium-Mediated Astrocyte Functions.

Generalised multivariable supertwisting algorithm

Positive feedback loops are common regulatory elements in metabolic and protein signalling pathways The length of such feedback loops determines stability and sensitivity to network perturbations Here we provide a mathematical analysis of arbitrary length positive feedback loops with protein production and degradation These loops serve as an abstraction of typical regulation patterns in protein signalling pathways We first perform a steady state analysis and, independently of the chain length, identify exactly two steady states that represent either biological activity or inactivity We thereby provide two formulas for the steady state protein concentrations as a function of feedback length, strength of feedback, as well as protein production and degradation rates Using a control theory approach, analysing the frequency response of the linearisation of the system and exploiting the Small Gain Theorem, we provide conditions for local stability for both steady states Our results demonstrate that, under some parameter relationships, once a biological meaningful on steady state arises, it is stable, while the off steady state, where all proteins are inactive, becomes unstable We apply our results to a three-tier feedback of caspase activation in apoptosis and demonstrate how an intermediary protein in such a loop may be used as a signal amplifier within the cascade Our results provide a rigorous mathematical analysis of positive feedback chains of arbitrary length, thereby relating pathway structure and stability

/pdf/equilibria-and-stability-of-a-class-of-positive-feedback-224nxfjwo3.pdf

Equilibria and stability of a class of positive feedback loops

Calcium ions act as messengers in a broad range of processes such as learning, apoptosis, and muscular movement. The transient profile and the temporal accumulation of calcium signals have been suggested as the two main characteristics in which calcium cues encode messages to be forwarded to downstream pathways. We address the analytical quantification of calcium temporal-accumulation in a long, thin section of a nonexcitable cell by solving a boundary value problem. In these expressions we note that the cytosolic Ca $^{2+}$ accumulation is independent of every intracellular calcium flux and depends on the Ca $^{2+}$ exchange across the membrane, cytosolic calcium diffusion, geometry of the cell, extracellular calcium perturbation, and initial concentrations. In particular, we analyse the time-integrated response of cytosolic calcium due to i) a localised initial concentration of cytosolic calcium and ii) transient extracellular perturbation of calcium. In these scenarios, we conclude that i) the range of calcium progression is confined to the vicinity of the initial concentration, thereby creating calcium microdomains; and ii) we observe a low-pass filtering effect in the response driven by extracellular Ca $^{2+}$ perturbations. Additionally, we note that our methodology can be used to analyse a broader range of stimuli and scenarios.

/pdf/spatial-quantification-of-cytosolic-ca-2-accumulation-in-ce6sh1ne2e.pdf

Spatial Quantification of Cytosolic Ca $^{2+}$ Accumulation in Nonexcitable Cells:An Analytical Study

We consider a Markov process in continuous time with a finite number of discrete states. The time-dependent probabilities of being in any state of the Markov chain are governed by a set of ordinary differential equations, whose dimension might be large even for trivial systems. Here, we derive a reduced ODE set that accurately approximates the probabilities of subspaces of interest with a known error bound. Our methodology is based on model reduction by balanced truncation and can be considerably more computationally efficient than solving the chemical master equation directly. We show the applicability of our method by analysing stochastic chemical reactions. First, we obtain a reduced order model for the infinitesimal generator of a Markov chain that models a reversible, monomolecular reaction. Later, we obtain a reduced order model for a catalytic conversion of substrate to a product (a so-called Michaelis-Menten mechanism), and compare its dynamics with a rapid equilibrium approximation method. For this example, we highlight the savings on the computational load obtained by means of the reduced-order model. Furthermore, we revisit the substrate catalytic conversion by obtaining a lower-order model that approximates the probability of having predefined ranges of product molecules. In such an example, we obtain an approximation of the output of a model with 5151 states by a reduced model with 16 states. Finally, we obtain a reduced-order model of the Brusselator.

/pdf/order-reduction-of-the-chemical-master-equation-via-balanced-2914cxbe36.pdf

Order reduction of the chemical master equation via balanced realisation.

In this paper we compare two families of multivariable super-twisting algorithms. The first family is an implementation of independent generalised super-twisting algorithms, whereas the second one presents nonlinearities that couple all the states. For the latter, the Lyapuov stability proof boils down to the positive-definitiveness test of a 2 × 2 matrix, in spite of the number of states. This second family is a generalisation of the multivariable super-twisting algorithm available in the literature. Furthermore, we highlight differences between these families regarding i) the discontinuity of the state space; ii) the number of design parameters; and iii) their convergence properties. We show their applicability and differences by designing an observer for a continuous-time, linear, time-invariant system. To conclude, we present a motivating example that suggests the robust stability of the feedback interconnection of generalised super-twisting algorithms.

Fernando López-Caamal

Papers

Generalised multivariable supertwisting algorithm

Equilibria and stability of a class of positive feedback loops

Spatial Quantification of Cytosolic Ca $^{2+}$ Accumulation in Nonexcitable Cells:An Analytical Study

Order reduction of the chemical master equation via balanced realisation.

Qualitative differences of two classes of multivariable super-twisting algorithms