Non-linear feedback modeling and bifurcation of the acetylcholine neurocycle and its relation to Alzheimer's and Parkinson's diseases

A novel two-enzyme-two-compartment model is proposed in order to explore the bifurcation, dynamics, and chaotic characteristics of the acetylcholine neurocycle. The model takes into consideration the physiological events of the choline uptake into the presynaptic neuron and choline release in the postsynaptic neuron. The effects of hydrogen ion feed concentrations, acetylcholinesterase (AChE) activity, and acetylcholine (ACh) feed concentrations, as bifurcation parameters, on the system performance are studied. It is found that hydrogen ions play an important role, where they create potential differences through the plasma membranes. The concentrations of ACh, choline and acetate were affected to be affected by the activity of acetylcholinesterase (AChE) through a certain range of their concentrations, where the activity of AChE was inhibited completely after reaching certain values. A detailed bifurcation analysis over a wide range of parameters is carried out in order to uncover some important features of the system, such as hysteresis, multiplicity, Hopf bifurcation, period doubling, chaotic characteristics, and other complex dynamics. These findings are related to the real phenomena occurring in the neurons, like periodic stimulation of neural cells and non-regular functioning of acetylcholine receptors. The results of this model are compared to the results of physiological experiments and other published models. As there is strong evidence that cholinergic brain diseases like Alzheimer's disease and Parkinson's disease are related to the concentration of acetylcholine (ACh), the present findings are useful for uncovering some of the characteristics of these diseases and encouraging more physiological research.     

Effect of choline and acetate substrates on bifurcation and chaotic behavior of acetylcholine neurocycle and Alzheimer's and Parkinson's diseases

In this work a novel two-enzyme-two-compartment model is developed in order to explore the dynamics, bifurcation, and chaotic characteristics of the acetylcholine neurocycle. The model takes into consideration the physiological events of the choline uptake into the presynaptic neuron and choline release in the postsynaptic neuron. The effects of feed choline concentrations, feed acetate concentrations as bifurcation parameters are studied. It was found that feed choline concentrations play an important role and have a direct effect on the acetylcholine neurocycle through a certain important range of parameters. The feed acetate concentrations have less effect. A detailed bifurcation analysis over a wide range of parameters is carried out in order to uncover some important features of the system, such as static bifurcation, dynamic bifurcation and chaotic behavior. These findings are related to the real phenomena occurring in the neurons, like periodic stimulation of neural cells and non-regular functioning of acetylcholine receptors. The results are compared to the results of physiological experiments and other published models. As there is strong evidence that cholinergic brain diseases like Alzheimer's disease and Parkinson's disease are related to the concentration of acetylcholine, the present findings are useful for uncovering some of the characteristics of these diseases and encouraging more well-directed physiological research coupled to useful mathematical modeling. It is concluded from the results in this paper that feed choline is more important factor than feed acetate in ACh processes.     

Improvement of Cognitive Function in Ovariectomized Rats by Human Neural Stem Cells Overexpressing Choline Acetyltransferase via Secretion of NGF and BDNF

Menopause is associated with memory deficits attributed to reduced serum estrogen levels. We evaluated whether an increase in brain-derived neurotrophic factor (BDNF) and nerve-growth factor (NGF) levels, through transplantation of choline acetyltransferase (ChAT)-overexpressing neural stem cells (F3.ChAT), improved learning and memory in ovariectomized rats. PD13 mouse neuronal primary culture cells were treated with estradiol or co-cultured with F3.ChAT cells; choline transporter1 (CHT1), ChAT, and vesicular acetylcholine transporter (VAChT) expression was evaluated using real-time PCR. The relationship between estrogen receptors (ERs) and neurotrophin family members was analyzed using immunohistochemistry. After the transplantation of F3.ChAT cells into OVx rats, we evaluated the memory, ACh level, and the expression of ER, neurotrophin family proteins, and cholinergic system. Estradiol upregulated CHT1, ChAT, and VAChT expression in ER; they were co-localized with BDNF, NGF, and TrkB. Co-culture with F3.ChAT upregulated CHT1, ChAT, and VAChT by activating the neurotrophin signalling pathway. Transplantation of F3.ChAT cells in OVX animals increased the ACh level in the CSF and improved memory deficit. In addition, it increased the expression of ERs, neurotrophin signaling, and the cholinergic system in the brains of OVX animals. Therefore, the estradiol deficiency induced memory loss by the down-regulation of the neurotrophin family and F3.ChAT could ameliorate the cognitive impairment owing to the loss or reduction of estradiol.     

Bifurcation analysis of two continuous membrane fermentor configurations for producing ethanol

A detailed bifurcation/chaotic investigation of a single continuous fermentor using an experimentally verified model was published earlier by the authors (Chem. Eng. Sci. 58 (2003) 1479); the present paper is an extension of the earlier one. It uses the same biokinetic model to investigate the effects of continuous ethanol removal using permselective membranes, cell recycle with varying cell separation efficiencies and recycle of unused sugars for two configurations of fermentors. The rich static/dynamic bifurcation and chaotic behavior of two different configurations are investigated. The aim is to gain deeper understanding of the complex static/dynamic characteristics of this system as a prelude to a detailed experimental investigation. The emphasis is on achieving higher sugar conversion, ethanol yield and productivity through the exploitation of these characteristics and optimal manipulation of operating and design parameters within the bifurcation/chaotic regions.     

Bifurcation analysis of two continuous bioreactors operated in series with recycle

In this paper, bifurcation analysis has been carried out for two continuous bioreactors operated in series with recycle from the second reactor. The existence of multiplicity of steady states is analyzed by considering Contois growth kinetics in the process model. It was observed that there exist two possible steady states of which one is trivial (wash out condition). Stability analysis is carried out to determine the stability of these steady states and it was observed that both these steady states are unstable in nature. Bifurcation analysis has been carried out for substrate and biomass concentration with dilution rate as the bifurcation parameter. Effect of recycle ratio, substrate separation factor and biomass separation factor is studied and analyzed. It was observed that Hopf bifurcation occurs at a dilution rate of 1.0208 with purely imaginary Eigen values which showed that sustained oscillatory behavior exists in the substrate concentration of the second reactor. The significance of different bifurcation points and the operating conditions by considering biomass and substrate concentrations in each reactor is studied and it was observed that the bioreactors need to be operated at intermediate dilution rates to obtain improved conversion and yield.     

Complex nonlinear behaviour of a fixed bed reactor with reactant recycle

The fixed bed reactor with reactant recycle investigated in this paper can exhibit periodic solutions. These solutions bifurcate from the steady state in a Hopf bifurcation. The Hopf bifurcation encountered at the lowest value of the inlet concentration turns the steady state unstable and marks the emergence of a stable periodic solution. This periodic solution in turn undergoes a period doubling leaving it unstable and giving rise to a stable period 2 solution. It is know that if the system possesses one period doubling it often also has the possibility of posessing a chaotic attractor. It is shown, that the dynamic behaviour of a fixed bed reactor with reactant recycle is much more complex than previously reported.     

Exploration and exploitation of bifurcation/chaotic behavior of a continuous fermentor for the production of ethanol

A four-dimensional model for the anaerobic fermentation process, developed and used earlier to simulate the oscillatory behavior of an experimental continuous stirred tank fermentor is utilized in the present investigation to explore the static/dynamic bifurcation and chaotic behavior of this fermentor, which is shown to be quite rich. The present investigation is a prelude to the experimental exploration of bifurcation and chaos in a membrane fermentor.Dynamic bifurcation (periodic attractors) as well as period doubling sequences leading to different types of periodic and chaotic attractors have been uncovered. It is fundamentally and practically important to discover the fact that in some cases, periodic and chaotic attractors have higher ethanol yield and production rate than the corresponding steady states.     

Bifurcation and chaotic behaviour of a coupled acetylcholinesterase/choline acetyltransferase diffusion-reaction enzymes system

A novel model is developed for the investigation of the dynamic and static characteristics of the cholinergic neurocycle. In its simplest form it involves a two-enzymes/two-compartments diffusion-reaction system. The bifurcation, instability and chaotic behaviour of this system are investigated with special emphasis on the neural transmission in human brain. Complex dynamic bifurcations, hysteresis, multiplicity, period doubling and period halving, as well as period adding and period subtracting dominate the dynamics of the system. The behaviour of the system using the acetylcholinestrase enzyme activity as the bifurcation parameter is strongly dominated by hysteresis and multiplicity phenomena, in which the neurotransmitter concentration in the postsynaptic cell changes dramatically for different parameter values. A detailed analysis of this behaviour may give an explanation for the phenomenology associated to Alzheimer disease. This type of work may help to stimulate new research directions on cholinergic brain diseases, such as Alzheimer and Parkinson.     

The bifurcation behavior of continuous free-radical solution loop polymerization reactors

The bifurcation behavior of continuous free-radical solution loop polymerization reactors is analyzed in this work. A mathematical model is developed in order to describe the impact of the recycling pump and other external reactor parts upon the process dynamics and stability. Stability analysis is performed using bifurcation theory and continuation methods. It is shown that under certain operational conditions as many as seven steady states are predicted for the loop polymerization reactor. Oscillatory behavior is observed for a wide range of process parameters and onset of oscillations is observed during the transition from operation without material recycling to operation with partial recirculation of the polymer solution. Besides, at certain constrained range of operation conditions, complex dynamics can be observed, including the onset of chaotic behavior. It is also shown that the thermal parameters of the reactor and recycling pump exert a profound effect upon the process stability. For this reason it is shown that oscillatory behavior is very unlikely to occur in actual industrial reactors.     

Acrylamide Neurotoxicity as a Possible Factor Responsible for Inflammation in the Cholinergic Nervous System

Acrylamide (ACR) is a chemical compound that exhibits neurotoxic and genotoxic effects. It causes neurological symptoms such as tremors, general weakness, numbness, tingling in the limbs or ataxia. Numerous scientific studies show the effect of ACR on nerve endings and its close connection with the cholinergic system. The cholinergic system is part of the autonomic nervous system that regulates higher cortical functions related to memory, learning, concentration and attention. Within the cholinergic system, there are cholinergic neurons, anatomical cholinergic structures, the neurotransmitter acetylcholine (ACh) and cholinergic receptors. Some scientific reports suggest a negative effect of ACR on the cholinergic system and inflammatory reactions within the body. The aim of the study was to review the current state of knowledge on the influence of acrylamide on the cholinergic system and to evaluate its possible effect on inflammatory processes. The cholinergic anti-inflammatory pathway (CAP) is a neuroimmunomodulatory pathway that is located in the blood and mucous membranes. The role of CAP is to stop the inflammatory response in the appropriate moment. It prevents the synthesis and the release of pro-inflammatory cytokines and ultimately regulates the local and systemic immune response. The cellular molecular mechanism for inhibiting cytokine synthesis is attributed to acetylcholine (ACh), the major vagal neurotransmitter, and the α7 nicotinic receptor (α7nAChR) subunit is a key receptor for the cholinergic anti-inflammatory pathway. The combination of ACh with α7nAChR results in inhibition of the synthesis and release of pro-inflammatory cytokines. The blood AChE is able to terminate the stimulation of the cholinergic anti-inflammatory pathway due to splitting ACh. Accordingly, cytokine production is essential for pathogen protection and tissue repair, but over-release of cytokines can lead to systemic inflammation, organ failure, and death. Inflammatory responses are precisely regulated to effectively protect against harmful stimuli. The central nervous system dynamically interacts with the immune system, modulating inflammation through the humoral and nervous pathways. The stress-induced rise in acetylcholine (ACh) level acts to ease the inflammatory response and restore homeostasis. This signaling process ends when ACh is hydrolyzed by acetylcholinesterase (AChE). There are many scientific reports indicating the harmful effects of ACR on AChE. Most of them indicate that ACR reduces the concentration and activity of AChE. Due to the neurotoxic effect of acrylamide, which is related to the disturbance of the secretion of neurotransmitters, and its influence on the disturbance of acetylcholinesterase activity, it can be concluded that it disturbs the normal inflammatory response.     

Design of tubular reactors in recycle systems

The article presents an approach to design tubular reactors in recycle systems, based on non-linear analysis. A pseudo-homogeneous plug-flow reactor model is used. It is assumed that the separation unit delivers product and recycle streams with fixed composition. The stand-alone reactor has a unique stable steady state. The coupled reactor–separation–recycle system shows four types of conversion versus plant Damköhler number bifurcation diagrams. A feasible steady state exists only if the reactor volume exceeds a critical value. For isothermal reactor, the steady state is unique and stable. For non-isothermal reactor, one or two steady states are possible. In the second situation the low-conversion state is unstable. In some parameter regions, the unique state is unstable. The design should ensure state unicity and stability, which are favoured by large heat-transfer capacity, low coolant temperature and high reactor-inlet temperature. A case study demonstrates that these phenomena can be easily found in real plants.     

Blocking Muscarinic Receptor 3 Attenuates Tumor Growth and Decreases Immunosuppressive and Cholinergic Markers in an Orthotopic Mouse Model of Colorectal Cancer

Tumor cells have evolved to express immunosuppressive molecules allowing their evasion from the host’s immune system. These molecules include programmed death ligands 1 and 2 (PD-L1 and PD-L2). Cancer cells can also produce acetylcholine (ACh), which plays a role in tumor development. Moreover, tumor innervation can stimulate vascularization leading to tumor growth and metastasis. The effects of atropine and muscarinic receptor 3 (M3R) blocker, 1,1-dimethyl-4-diphenylacetoxypiperidinium iodide (4-DAMP), on cancer growth and spread were evaluated in vitro using murine colon cancer cell line, CT-26, and in vivo in an orthotopic mouse model of colorectal cancer. In the in vitro model, atropine and 4-DAMP significantly inhibited CT-26 cell proliferation in a dose dependent manner and induced apoptosis. Atropine attenuated immunosuppressive markers and M3R via inhibition of EGFR/AKT/ERK signaling pathways. However, 4-DAMP showed no effect on the expression of PD-L1, PD-L2, and choline acetyltransferase (ChAT) on CT-26 cells but attenuated M3R by suppressing the phosphorylation of AKT and ERK. Blocking of M3R in vivo decreased tumor growth and expression of immunosuppressive, cholinergic, and angiogenic markers through inhibition of AKT and ERK, leading to an improved immune response against cancer. The expression of immunosuppressive and cholinergic markers may hold potential in determining prognosis and treatment regimens for colorectal cancer patients. This study’s results demonstrate that blocking M3R has pronounced antitumor effects via several mechanisms, including inhibition of immunosuppressive molecules, enhancement of antitumor immune response, and suppression of tumor angiogenesis via suppression of the AKT/ERK signaling pathway. These findings suggest a crosstalk between the cholinergic and immune systems during cancer development. In addition, the cholinergic system influences cancer evasion from the host’s immunity.     

Theoretical analysis of inhibition effect on steady states of enzymatic membrane reactor with substrate and product retention for reaction producing weak acid

The aim of this study is to formulate a model of enzymatic membrane reactor (EMR), i.e., a continuous, stirred tank bioreactor with full enzyme recycle, for a reaction producing a weak acid, and to explore the effect of substrate and product inhibition of different mechanisms coupled with transport properties of the membrane on the static behaviour of the system. The inhibition of an enzyme by a substrate leads to the non-monotonicity of reaction rate expression with respect to the substrate concentration. If a product of enzymatic reaction, taking place in the EMR, influences the pH of a reaction mixture this is also the factor causing the non-monotonicity of the substrate and product dependent reaction rate. The character of these dependencies affects substantially the structure of the steady states of the reactor. The bifurcation diagrams, shown in the work, are of different characters depending on the bifurcation parameter. It has been found, that bifurcation diagrams for competitive and uncompetitive inhibition by a substrate differ in the number and position of bifurcation points. Steady states of multiplicity five have been localised in case of uncompetitive inhibition by the substrate at high affinity of the enzyme to this substrate. Retention of reagents, related to transport properties of a membrane, influences significantly the effectiveness of a process. A specially written software in Delphi™ has been used for the calculations.     

BIFURCATIONS AND CHAOS APPEARING IN A PERIODICALLY CONTROLLED CSTR

Bifurcations of periodic states in a CSTR subject to a periodic control which are caused by changes in the parameter values contained in the control input are investigated on the basis of the bifurcation theory. Principles which give a classification of basic possible bifurcations are briefly surveyed. Then a numerical example in which the period and switching ratio of a bang-bang periodic control are changed is worked. Most of the basic possible bifurcations appear. The chaotic phenomena are also observed and the structure of the strange attractor corresponding to a chaotic state is analysed in some detail,     

Dynamic Behavior of Industrial Gas Phase Fluidized Bed Polyethylene Reactors under PI Control

A mathematical model describing the UNIPOL process for the production of polyethylene in the gas phase using a Ziegler‐Natta catalyst in a bubbling fluidized bed is used to analyze the major processes determining the behavior and performance of these industrially important units. The investigation shows that both static bifurcation (multiplicity of the steady states) as well as dynamic bifurcation (stable/unstable periodic attractors) behavior cover wide regions of the design and operating parameter domain. A conventional proportional‐integral (PI) control policy is suggested to stabilize the behavior of the system. The control philosophy covers both aspects of stabilizing unstable steady states as well as compensating for external disturbances. It is shown that for some controller configurations and set points the controlled process can go through a period doubling sequence leading to chaotic strange attractors. The industrial implications of the phenomena discovered for both the open loop (uncontrolled) as well the closed‐loop (controlled) systems are analyzed.     

An experimental study of steady-state multiplicity features of two parallel catalytic reactions

A study of the multiplicity features of a single catalytic pellet on which either ethane, carbon monoxide or both reactants were oxidized revealed several new features such as: four different stable states during the co-oxidation of both reactants and three states during the oxidation of carbon monoxide. Very intricate bifurcation diagrams, which describe the dependence of a state variable on an operating condition, were found.It was shown that the experimental finding of a cross-section of the bifurcation set is the rational approach of studying the multiplicity features of systems characterized by a large number of parameters and for which no exact mathematical model is available. Recent theoretical results provide useful guidance in selecting the operating conditions so that all the possible multiplicity features are found. These theoretical results may be used to place constraints on the functional form of any proposed reaction rate expression.     

一氧化碳偶联反应器分岔行为

The bifurcation behavior of the CO coupling reactor was examined based on the one-dimensional pseudohomogeneous axial dispersion dynamic model. The method of finite difference was used for solving the boundary value problem; the continuation technique and the direct method were applied to determine the bifurcation diagram.The effects of dimensionless adiabatic temperature rise, Damkoehler number, activation energy, heat transfer coefficient and feed ratio on the bifurcation behavior were investigated. It was shown that there existed static bifurcation and the oscillations did not occur in the reactor. The result also revealed that the reactor exhibited at most 1-3-1 multiplilicity patterns within the range of practical possible parameters and the measures, such as weakening the axial dispersion of reactor, enhancing heat transfer, decreasing the concentration of ethyl nitrite, were efficient for avoiding the possible risk of multiple steady states.     

Stability and dynamics of isothermal CMSMPR crystallizers

Detailed analysis of stability and bifurcation properties and of the dynamic behaviour of isothermal continuous mixed suspension, mixed product removal (CMSMPR) crystallizers is presented using the moment equation model. It is shown that isothermal CMSMPR crystallizers may exhibit not only limit cycle oscillations but, in the case of magma-dependent nucleation, also saddle point instabilities. Applying the Mikhailov stability criterion, two equivalent sets of necessary and sufficient conditions are derived for checking the stability of steady states.Stability maps are presented in the planes of different pairs of system parameters. It is shown that saddle node and boundary bifurcation, as well as bifurcation at infinity may arise in the case of magma-dependent secondary nucleation. Oscillations of the population density and distribution functions are also presented and analysed, approximating the size distribution by gamma distribution. In dynamic states, the crystal size distribution may differ significantly from the exponential one, while the mean values of oscillations of supersaturation are lower than the corresponding steady state values. A causal loop diagram between the variables reveals that instabilities are created by the interactions of the autoinhibition generated negative feedback and a positive feedback between the four leading moments of crystal size.