Compartmental Systems Research Articles

A Fast Averaging Synchronization Algorithm for Clock Oscillators in Nonlinear Dynamical Network with Arbitrary Time-delays

This paper investigates the synchronization problem of clock oscillators in nonlinear dynamical network with arbitrary time-delays. First, a dynamic synchronization algorithm based on consensus control strategy, named fast averaging synchronization algorithm (FASA), is presented to find a solution to the synchronization problem. This algorithm can compensate the clock skew and offset differences between clock nodes, achieving the synchronization of clock nodes in a shorter time as compared to previous synchronization methods. Second, because of the dynamical performance of FASA, it is characterized from the perspective of compartmental dynamical system with arbitrary time-delays. In this case, the algorithm guarantees the states of all clock nodes in dynamical network converge to Lyapunov stable equilibria. Finally, numerical simulations and experimental results demonstrate the correctness and efficiency of the FASA, which means that the clock nodes can reach global consensus, and the synchronization error can reach nanosecond order of magnitude.

Compartmental culture of embryonic stem cell-derived neurons in microfluidic devices for use in axonal biology

Axonal pathology has been clearly implicated in neurodegenerative diseases making the compartmental culture of neurons a useful research tool. Primary neurons have already been cultured in compartmental microfluidic devices but their derivation from an animal is a time-consuming and difficult work and has a limit in their sources. Embryonic stem cell (ESC)-derived neurons (ESC_Ns) overcome this limit, since ESCs can be renewed without limit and can be differentiated into ESC_Ns by robust and reproducible protocols. In this research, ESC_Ns were derived from mouse ESCs in compartmental microfluidic devices, and their axons were isolated from the somal cell bodies. Once embryoid bodies (EBs) were localized in the microfluidic culture chamber, ESC_Ns spread out from the EBs and occupied the cell culture chamber. Their axons traversed the microchannels and finally were isolated from the somata, providing an arrangement comparable to dissociated primary neurons. This ESC_N compartmental microfluidic culture system not only offers a substitute for the primary neuron counterpart system but also makes it possible to make comparisons between the two systems.

Limit cycle stability analysis and adaptive control of a multi-compartment model for a pressure-limited respirator and lung mechanics system

Acute respiratory failure due to infection, trauma or major surgery is one of the most common problems encountered in intensive care units, and mechanical ventilation is the mainstay of supportive therapy for such patients. In this article, we develop a general mathematical model for the dynamic behaviour of a multi-compartment respiratory system in response to an arbitrary applied inspiratory pressure. Specifically, we use compartmental dynamical system theory and Poincaré maps to model and analyse the dynamics of a pressure-limited respirator and lung mechanics system, and show that the periodic orbit generated by this system is globally asymptotically stable. Furthermore, we show that the individual compartmental volumes, and hence the total lung volume, converge to steady-state end-inspiratory and end-expiratory values. Finally, we develop a model reference direct adaptive controller framework for the multi-compartmental model of a pressure-limited respirator and lung mechanics system where the plant and reference model involve switching and time-varying dynamics. We then apply the proposed adaptive feedback controller framework to stabilise a given limit cycle corresponding to a clinically plausible respiratory pattern.

DNA-mediated self-assembly of artificial vesicles.

BackgroundAlthough multicompartment systems made of single unilamellar vesicles offer the potential to outperform single compartment systems widely used in analytic, synthetic, and medical applications, their use has remained marginal to date. On the one hand, this can be attributed to the binary character of the majority of the current tethering protocols that impedes the implementation of real multicomponent or multifunctional systems. On the other hand, the few tethering protocols theoretically providing multicompartment systems composed of several distinct vesicle populations suffer from the readjustment of the vesicle formation procedure as well as from the loss of specificity of the linking mechanism over time.Methodology/Principal FindingsIn previous studies, we presented implementations of multicompartment systems and resolved the readjustment of the vesicle formation procedure as well as the loss of specificity by using linkers consisting of biotinylated DNA single strands that were anchored to phospholipid-grafted biotinylated PEG tethers via streptavidin as a connector. The systematic analysis presented herein provides evidences for the incorporation of phospholipid-grafted biotinylated PEG tethers to the vesicle membrane during vesicle formation, providing specific anchoring sites for the streptavidin loading of the vesicle membrane. Furthermore, DNA-mediated vesicle-vesicle self-assembly was found to be sequence-dependent and to depend on the presence of monovalent salts.Conclusions/SignificanceThis study provides a solid basis for the implementation of multi-vesicle assemblies that may affect at least three distinct domains. (i) Analysis. Starting with a minimal system, the complexity of a bottom-up system is increased gradually facilitating the understanding of the components and their interaction. (ii) Synthesis. Consecutive reactions may be implemented in networks of vesicles that outperform current single compartment bioreactors in versatility and productivity. (iii) Personalized medicine. Transport and targeting of long-lived, pharmacologically inert prodrugs and their conversion to short-lived, active drug molecules directly at the site of action may be accomplished if multi-vesicle assemblies of predefined architecture are used.

Bioenergetics and life's origins.

Bioenergetics is central to our understanding of living systems, yet has attracted relatively little attention in origins of life research. This article focuses on energy resources available to drive primitive metabolism and the synthesis of polymers that could be incorporated into molecular systems having properties associated with the living state. The compartmented systems are referred to as protocells, each different from all the rest and representing a kind of natural experiment. The origin of life was marked when a rare few protocells happened to have the ability to capture energy from the environment to initiate catalyzed heterotrophic growth directed by heritable genetic information in the polymers. This article examines potential sources of energy available to protocells, and mechanisms by which the energy could be used to drive polymer synthesis.

Mobile and modular sensitive compartmented information facility system

A modular SCIF includes a frame made from a plurality of prefabricated channels, and a plurality of prefabricated wall and ceiling panels that are attached to the frame. The frame, channels and panels are meet a set of standard dimensions. The SCIF fits within most offices and dwellings. The modular SCIF includes a prefabricated door and doorframe that are attached to the modular SCIF. The SCIF is attached directly to a concrete floor, the floor of a vehicle or to a track system. The panels include several layers, including a core layer of expanded metal and two layers of acoustic board. Additional layers include two layers of ABS plastic sheet, two layers of mass loaded vinyl sheet, two layers of galvanized steel sheet, and two layers of aluminum sheet. The additional layers may be used singly or collectively.

An elementary approach to modeling drug resistance in cancer

Resistance to drugs has been an ongoing obstacle to a successful treatment of many diseases. In this work we consider the problem of drug resistance in cancer, focusing on random genetic point mutations. Most previous works on mathematical models of such drug resistance have been based on stochastic methods. In contrast, our approach is based on an elementary, compartmental system of ordinary differential equations. We use our very simple approach to derive results on drug resistance that are comparable to those that were previously obtained using much more complex mathematical techniques. The simplicity of our model allows us to obtain analytic results for resistance to any number of drugs. In particular, we show that the amount of resistance generated before the start of the treatment, and present at some given time afterward, always depends on the turnover rate, no matter how many drugs are simultaneously used in the treatment.

Modelling rhizosphere transport in the presence of goethite, including competitive uptake of phosphate and arsenate

A modelling approach was used to extend the knowledge about the processes that affect the availability of the nutrient P and the toxic agent AsV in the rhizosphere in the presence of a strong sorbent. Based on compartment system experiments in which Zea mays was grown the following hypothesis were assumed: a) measured P concentration gradients can be explained by the mobilisation of P by the root exudate citrate, and b) measured AsV concentration gradients can be explained by the simultaneous effect of the competitive sorption of AsV and P and the competitive uptake of AsV and P. First, the feasibility of the applied description of soil chemical processes was justified. Then competitive uptake was implemented in the computer code using two different mathematical approaches. Our model calculation provided support for hypothesis a) and suggested that hypothesis b) has to be extended. The results show that the competitive uptake of AsV and P has an influence on AsV concentrations in the rhizosphere, but including competitive uptake was not sufficient to predict observed AsV concentration profiles. Recent results on plant As-metabolism like AsIII efflux and Si AsIII interaction probably have to be included in addition for simulation of measured AsV concentration profiles.

Abstract A253: Acquired Bcr-Abl kinase domain mutations are not responsible for persistence of dasatinib-refractory disease in murine Ph+ ALL

Abstract Despite the dramatic efficacies of imatinib and second-generation BCR-ABL kinase inhibitors (dasatinib and nilotinib) in chronic myelogenous leukemia (CML), these drugs fail to provide durable therapeutic benefit in patients with Philadelphia-chromosome positive (Ph+) BCR-ABL-induced acute lymphoblastic leukemias (ALLs). In contrast to chronic-phase CML, deletion of the CDKN2A (INK4A-ARF) tumor suppressor locus occurs in 65% of Ph+ ALL cases. Accordingly, introduction of cultured Arf−/− p185BCR-ABL-expressing (p185+) pre-B cells, but not their Arf+/+ counterparts, into healthy syngeneic recipient mice induces fulminant B cell leukemia; virtually every p185+, Arf−/− cell is a leukemia-initiating cell (LIC). We have now monitored disease progression and dasatinib-responsiveness in vivo by following the fate of p185+ Arf−/− luciferase-expressing LICs. In animals bearing high leukemic burdens (simulating the human clinical condition at diagnosis), two weeks of dasatinib therapy induced dramatic reductions in luminescent signals, but all animals harbored persistent, measurable deposits of drug-refractory cells. The vast majority of BCR-ABL alleles from these residual cells were free of kinase domain (KD) mutations, but rare leukemic clones harboring the T315I KD mutation, known to confer near-complete drug resistance to imatinib, dasatinib and nilotinib, were detectable in a subset of recipients. Following several weeks of continued dasatinib therapy, all mice developed clinical relapse preceded by dramatic increases in luminescent signals, both in the hematopoietic compartment and central nervous system. Many of these drug-resistant leukemic cells now harbored the T315I KD mutation. Animals that had been maintained in remission with 4 weeks of continuous dasatinib therapy quickly relapsed upon therapy discontinuation, almost always without evidence of KD mutations. In this clinically-relevant Ph+ ALL model, several factors including Arf loss-of-function, disease burden, intensity of therapy, and length of drug exposure interact to determine therapeutic outcome and to trigger confluent mechanisms of drug resistance. Critically, while continuous dasatinib therapy efficiently selects for and maintains cells harboring drug-resistant KD mutations that mediate eventual clinical relapse, most drug-refractory leukemic cells survive in hematopoietic tissues in the absence of KD mutations during maintenance therapy, implying that mutation-independent factors sustain LIC survival. We propose that Arf inactivation in Ph+ ALL (but not in CML) enhances the biological ‘fitness’ of leukemic cells and diminishes the efficiency with which targeted therapy can successfully eradicate drug-refractory disease. This facilitates the subsequent emergence of cell-intrinsic drug resistance, most frequently manifested as BCR-ABL KD mutations. Citation Information: Mol Cancer Ther 2009;8(12 Suppl):A253.

The construction of next-generation matrices for compartmental epidemic models

The basic reproduction number (0) is arguably the most important quantity in infectious disease epidemiology. The next-generation matrix (NGM) is the natural basis for the definition and calculation of (0) where finitely many different categories of individuals are recognized. We clear up confusion that has been around in the literature concerning the construction of this matrix, specifically for the most frequently used so-called compartmental models. We present a detailed easy recipe for the construction of the NGM from basic ingredients derived directly from the specifications of the model. We show that two related matrices exist which we define to be the NGM with large domain and the NGM with small domain. The three matrices together reflect the range of possibilities encountered in the literature for the characterization of (0). We show how they are connected and how their construction follows from the basic model ingredients, and establish that they have the same non-zero eigenvalues, the largest of which is the basic reproduction number (0). Although we present formal recipes based on linear algebra, we encourage the construction of the NGM by way of direct epidemiological reasoning, using the clear interpretation of the elements of the NGM and of the model ingredients. We present a selection of examples as a practical guide to our methods. In the appendix we present an elementary but complete proof that (0) defined as the dominant eigenvalue of the NGM for compartmental systems and the Malthusian parameter r, the real-time exponential growth rate in the early phase of an outbreak, are connected by the properties that (0) > 1 if and only if r > 0, and (0) = 1 if and only if r = 0.

Boundedness analysis for open Chemical Reaction Networks with mass-action kinetics

This paper describes the working principles of an algorithm for boundedness analysis of open Chemical Reaction Networks endowed with mass-action kinetics. Such models can be thought of both as a special class of compartmental systems or a particular type of continuous Petri Nets, in which the firing rates of transitions are not constant or preassigned, but expressed as a function of the continuous marking of the network (function which in chemistry is referred to as the "kinetics"). The algorithm can be applied to a broad class of such open networks, and returns, as an outcome, a classification of the possible dynamical behaviors that are compatible with the network structure, by classifying each variable either as bounded, converging to 0 or diverging to ?. This can be viewed as a qualitative study of Input---Output Stability for chemical networks, or more precisely, as a classification of its possible I---O instability patterns. Our goal is to analyze the system irrespectively of values of kinetic parameters. More precisely, we attempt to analyze it simultaneously for all possible values. Remarkably, tests on non-trivial examples (one of which is discussed in this paper) showed that, as the kinetic constants of the network are varied, all the compatible behaviors could be observed in simulations. Finally, we discuss and illustrate how the results relate to previous works on the qualitative dynamics of closed reaction networks.

The Endomembrane System: A Representation of the Extracellular Medium?

Both prokaryotic and eukaryotic cells share the basic mechanisms of secretory protein synthesis. However, unlike prokaryotes, eukaryotic cells posses a system of compartments, the so-called endomembrane system, which are involved in the synthesis process. A comparison of the prokaryotic and eukaryotic protein synthesis processes and particularly the observation of the functional and structural similarity between the prokaryotic cell membrane (the interface to the cell exterior) and the membrane of the eukaryotic endoplasmic reticulum (one of the compartments within the endomembrane system) inspire a description that refers to either the eukaryotic endoplasmic reticulum or its membrane or the endomembrane system altogether as a representation of the extracellular medium. However, unless the terms in such a statement are carefully analysed and refined the description would be just a colloquial usage of the concept of “representation” rather than a biosemiotic statement. Another problem associated with employing the concept of “representation” in a biosemiotic context is due to the fact that it may evoke the impression of a conscious mind as the “owner” of the representation. In this paper theories about the emergence of the eukaryotic endomembrane system, as well as its functionality within secretory protein synthesis will be analysed in order to specify in what sense the concept of “representation” can be employed in this context without implying consciousness. Such a study is expected not only to provide an insight into the conditions and assumptions under which this concept can be used for lower level biological processes but also to shed some light on how representations emerge in general.

Dynamic environ analysis of compartmental systems: A computational approach

Ecosystems are often modeled as stocks of matter or energy connected by flows. Network environ analysis (NEA) is a set of mathematical methods for using powers of matrices to trace energy and material flows through such models. NEA has revealed several interesting properties of flow–storage networks, including dominance of indirect effects and the tendency for networks to create mutually positive interactions between species. However, the applicability of NEA is greatly limited by the fact that it can only be applied to models at constant steady states. In this paper, we present a new, computationally oriented approach to environ analysis called dynamic environ approximation (DEA). As a test of DEA, we use it to compute compartment throughflow in two implementations of a model of energy flow through an oyster reef ecosystem. We use a newly derived equation to compute model throughflow and compare its output to that of DEA. We find that DEA approximates the exact results given by this equation quite closely – in this particular case, with a mean Euclidean error ranging between 0.0008 and 0.21 – which gives a sense of how closely it reproduces other NEA-related quantities that cannot be exactly computed and discuss how to reduce this error. An application to calculating indirect flows in ecosystems is also discussed and dominance of indirect effects in a nonlinear model is demonstrated.

ATP-dependent but proton gradient-independent polyphosphate-synthesizing activity in extraradical hyphae of an arbuscular mycorrhizal fungus.

Arbuscular mycorrhizal (AM) fungi benefit their host plants by supplying phosphate obtained from the soil. Polyphosphate is thought to act as the key intermediate in this process, but little is currently understood about how polyphosphate is synthesized or translocated within arbuscular mycorrhizas. Glomus sp. strain HR1 was grown with marigold in a mesh bag compartment system, and extraradical hyphae were harvested and fractionated by density gradient centrifugation. Using this approach, three distinct layers were obtained: layers 1 and 2 were composed of amorphous and membranous materials, together with mitochondria, lipid bodies, and electron-opaque bodies, and layer 3 was composed mainly of partially broken hyphae and fragmented cell walls. The polyphosphate kinase/luciferase system, a highly sensitive polyphosphate detection method, enabled the detection of polyphosphate-synthesizing activity in layer 2 in the presence of ATP. This activity was inhibited by vanadate but not by bafilomycin A(1) or a protonophore, suggesting that ATP may not energize the reaction through H(+)-ATPase but may act as a direct substrate in the reaction. This report represents the first demonstration that AM fungi possess polyphosphate-synthesizing activity that is localized in the organelle fraction and not in the cytosol or at the plasma membrane.

Linear Programming Based Routing Design for a Class of Positive Systems with Integral and Capacity Constraints

We present techniques to design routing parameters for positive compartmental conservative systems. Such systems capture the dynamics of some material flowing through a network of interconnected reservoirs and have become popular, in particular, as models of air traffic flows. These techniques use Linear Programs (LP) to design static routing parameters for single destination networks with the following objectives: (a) minimize delay, (b) minimize delay and satisfy additional delay constraints which are formulated as integral constraints on the states of the network, and (c) satisfy capacity constraints. For each of these problems, we prove that the resulting closed loop systems are stable, positive, conservative and exhibit a user defined interconnection of sections. Additionally, problems (a) and (b) are shown to minimize delay over all choices of routing parameters such that the closed loop system exhibits these characteristics.

Modeling and analysis of mass-action kinetics

Mass-action kinetics are used in chemistry and chemical engineering to describe the dynamics of systems of chemical reactions, that is, reaction networks. These models are a special form of compartmental systems, which involve mass- and energy-balance relations. Aside from their role in chemical engineering applications, mass-action kinetics have numerous analytical properties that are of inherent interest from a dynamical systems perspective. Because of physical considerations, however, mass- action kinetics have special properties, such as nonnegative solutions, that are useful for analyzing their behavior. With this motivation in mind, this article has several objectives. First, a general construction of the kinetic equations based on the reaction laws is provided in a state-space form. Next, the nonnegativity of solutions to the kinetic equations is considered. The realizability problem, which is concerned with the inverse problem of constructing a reaction network having specified essentially nonnegative dynamics, is also considered. In particular, an explicit construction of a reaction network for essentially nonnegative polynomial dynamics involving a scalar state is provided. Next, the reducibility of the kinetic equations is considered as well as the stability of the equilibria of the kinetic equations. Lyapunov methods are applied to the kinetic equations, and semistability is guaranteed through the convergence to a Lyapunov- stable equilibrium that depends on the initial concentrations. Semistability is the appropriate notion of stability for compartmental systems in general, and reaction networks in particular, where the limiting concentration maybe nonzero and may depend on the initial concentrations. Finally, the zero deficiency result for mass-action kinetics in standard matrix terminology is presented and semistability is proven.

Stability of the linearization method in compartmental analysis

PurposeThe purpose of this paper is to prove that under sufficient conditions the linearization method used for identifying a nonlinear bicompartmental system is stable.Design/methodology/approachThe problem of identifying a nonlinear compartmental system appears as badly stated a priori. In fact the problem is not to identify the general behavior law of exchange between compartments, but to assume these laws known such as in Michaelis‐Menten systems or in polynomial compartmental systems with coefficients that need to be identified. It has been proved previously that with a linearization method an approximation can be obtained to the identification of these nonlinear systems. To validate this method, a stability study is necessary.FindingsSufficient conditions are established for the evolution law of a nonlinear bicompartmental system under which the linearization method is stable, and an upper bound is given on the approximation error – with an application, in the last section to the case of an open Michaelis‐Menten system.Originality/valueThe paper is of value in establishing sufficient conditions about the evolution law of a nonlinear system in order to show that this method is stable and to give an upper bound on the approximation error.

Oxidative Stress and Compartment of Gene Expression Determine Proatherosclerotic Effects of Inducible Nitric Oxide Synthase

Genetic and pharmacological inhibition of inducible nitric oxide synthase (iNOS) decreases atherosclerosis development. Potential proatherogenic effects of iNOS include iNOS mediated oxidative stress and iNOS expression in different cellular compartments. Lesional iNOS can potentially produce nitric oxide radicals (NO), superoxide radicals (O2(-)), or both; these radicals may then react to form peroxynitrite. Alternatively, O2(-) radicals from oxidases co-expressed with iNOS could react with NO to produce peroxynitrite. Therefore, the expression profiles of the genes that modulate the redox system in different iNOS-expressing cell compartments may determine the role of iNOS in atherosclerosis. We used apoE (apoE(-/-)) and apoE/iNOS double knockout (apoE(-/-)/ iNOS(-/-)) mice to assess vascular NO, O2(-), and peroxynitrite formation by electron spin resonance spectroscopy, high performance liquid chromatography, and 3-nitrotyrosine staining. The relevance of the iNOS expressing cell compartment was tested by bone marrow transplantation. We show that iNOS significantly contributes to vascular NO production and itself produces O2(-), leading to peroxynitrite formation in atherosclerotic lesions. Our bone marrow transplantation experiments show that bone marrow derived cells exclusively mediate the proatherosclerotic effects of iNOS in males, while both parenchymal and bone marrow derived iNOS equally contribute to atherosclerosis in females. Moreover, iNOS expression affects vascular remodeling. These findings establish for the first time that the proatherosclerotic effects of iNOS vary with sex in addition to the compartment of its expression.

Impact of antifungals producing rhizobacteria on the performance of Vigna radiata in the presence of arbuscular mycorrhizal fungi

Plant growth-promoting rhizobacteria (PGPR) that produce antifungal metabolites are potential threats for the arbuscular mycorrhizal (AM) fungi known for their beneficial symbiosis with plants that is crucially important for low-input sustainable agriculture. To address this issue, we used a compartmented container system where test plants, Vigna radiata, could only reach a separate nutrient-rich compartment indirectly via the hyphae of AM fungi associated with their roots. In this system, where plants depended on nutrient uptake via AM symbiosis, we explored the impact of various PGPR. Plants were inoculated with or without a consortium of four species of AM fungi (Glomus coronatum, Glomus etunicatum, Glomus constrictum, and Glomus intraradices), and one or more of the following PGPR strains: phenazine producing (P(+)) and phenazine-less mutant (P(-)), diacetylphloroglucinol (DAPG) producing (G(+)) and DAPG-less mutant (G(-)) strains of Pseudomonas fluorescens, and an unknown antifungal metabolite-producing Alcaligenes faecalis strain, SLHRE425 (D). PGPR exerted only a small if any effect on the performance of AM symbiosis. G(+) enhanced AM root colonization and had positive effects on shoot growth and nitrogen content when added alone, but not in combination with P(+). D negatively influenced AM root colonization, but did not affect nutrient acquisition. Principal component analysis of all treatments indicated correlation between root weight, shoot weight, and nutrient uptake by AM fungus. The results indicate that antifungal metabolites producing PGPR do not necessarily interfere with AM symbiosis and may even promote it thus carefully chosen combinations of such bioinoculants could lead to better plant growth.

Comparison of the Pseudorabies Virus Us9 Protein with Homologs from Other Veterinary and Human Alphaherpesviruses

Pseudorabies virus (PRV) Us9 is a small, tail-anchored (TA) membrane protein that is essential for axonal sorting of viral structural proteins and is highly conserved among other members of the alphaherpesvirus subfamily. We cloned the Us9 homologs from two human pathogens, varicella-zoster virus (VZV) and herpes simplex virus type 1 (HSV-1), as well as two veterinary pathogens, equine herpesvirus type 1 (EHV-1) and bovine herpesvirus type 1 (BHV-1), and fused them to enhanced green fluorescent protein to examine their subcellular localization and membrane topology. Akin to PRV Us9, all of the Us9 homologs localized to the trans-Golgi network and had a type II membrane topology (typical of TA proteins). Furthermore, we examined whether any of the Us9 homologs could compensate for the loss of PRV Us9 in anterograde, neuron-to-cell spread of infection in a compartmented chamber system. EHV-1 and BHV-1 Us9 were able to fully compensate for the loss of PRV Us9, whereas VZV and HSV-1 Us9 proteins were unable to functionally replace PRV Us9 when they were expressed in a PRV background.