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1.
Continuous bioreactors are critical unit operations in many biological systems, but the unique modeling is very complicated
due to the underlying biochemical reactions and the distributed properties of cell population. The scope of this paper considers
a popular modeling method for microbial cell cultures by population balance equation models, and the control objective aims
to attenuate undesired oscillations appeared in the nonlinear distributed parameter system. In view of pursuing the popular/practical
control configuration and the lack of on-line sensors, an approximate technique by exploiting the “pseudo-steady-state” approach
constructs a simple nonlinear control model. Through an off-line estimation mechanism for the system having self-oscillating
behavior, two kinds of nonlinear PI configurations are developed. Closed-loop simulation results have confirmed that the regulatory
and tracking performances of the control system proposed are good. 相似文献
2.
N. MacDonald 《Journal of theoretical biology》1977,65(4):727-734
Some results are presented relating to the question whether self-sustained oscillations are possible in a sequence of biochemical reactions with end- point inhibition. The model used has a single nonlinear ordinary differential equation coupled to a set of linear equations, with all coefficients in the linear terms equal. The explicit algebraic form of the Hopf-Friedrich bifurcation theory is used to show that when the number of coupled equations is large enough this model has a stable periodic solution when the equilibrium point of the equations has just become unstable. 相似文献
3.
John Z. Hearon 《Bulletin of mathematical biology》1965,27(2):265-269
When an experimenter determines the “internal concentration” of a substance in a cell (or cell suspension) it is in general
the average concentration (quantity of substance divided by cell volume or volume of cell water) which is measured. When this
concentration is less than that in the ambient medium but there is either no flow into the cell or flow from the cell into
the medium, then (under the usually tacit assumption of spatial uniformity in the cell) the possibility of active transport
is considered. The possibility that lack of spatial uniformity could lead to apparent active transport was early proposed
by A. Bierman and later examined quantitatively by N. Rashevsky for a special case. In this paper spherical cells are treated
but under quite general conditions regarding the metabolic aspects of the problem. It is shown that apparent active transport
can result for a metabolite which is a reactant in one set of reactions and a product in another provided the sites of these
sets of reactions are spatially separated in the cell. 相似文献
4.
Pernarowski M 《Bulletin of mathematical biology》2000,62(1):101-120
A continuum model for a heterogeneous collection of excitable cells electrically coupled through gap junctions is introduced
and analysed using spatial averaging, asymptotic and numerical techniques. Heterogeneity is modelled by imposing a spatial
dependence on parameters which define the single cell model and a diffusion term is used to model the gap junction coupling.
For different parameter values, single cell models can exhibit bursting, beating and a myriad of other complex oscillations.
A procedure for finding asymptotic estimates of the thresholds between these (synchronous) behaviors in the cellular aggregates
is described for the heterogeneous case where the coupling strength is strong. This procedure is tested on a model of a strongly
coupled heterogeneous collection of bursting and beating cells. Since isolated pancreatic β-cells have been observed to both burst and beat, this test of the spatial averaging techniques provides a possible explanation
to measured discrepancies between the electrical activities of isolated β-cells and coupled collections (islets) of β-cells.
This work was supported by the National Science Foundation Grant DMS-97-04-966. 相似文献
5.
A framework for whole-cell mathematical modeling 总被引:4,自引:0,他引:4
The default framework for modeling biochemical processes is that of a constant-volume reactor operating under steady-state conditions. This is satisfactory for many applications, but not for modeling growth and division of cells. In this study, a whole-cell modeling framework is developed that assumes expanding volumes and a cell-division cycle. A spherical newborn cell is designed to grow in volume during the growth phase of the cycle. After 80% of the cycle period, the cell begins to divide by constricting about its equator, ultimately affording two spherical cells with total volume equal to twice that of the original. The cell is partitioned into two regions or volumes, namely the cytoplasm (Vcyt) and membrane (Vmem), with molecular components present in each. Both volumes change during the cell cycle; Vcyt changes in response to osmotic pressure changes as nutrients enter the cell from the environment, while Vmem changes in response to this osmotic pressure effect such that membrane thickness remains invariant. The two volumes change at different rates; in most cases, this imposes periodic or oscillatory behavior on all components within the cell. Since the framework itself rather than a particular set of reactions and components is responsible for this behavior, it should be possible to model various biochemical processes within it, affording stable periodic solutions without requiring that the biochemical process itself generates oscillations as an inherent feature. Given that these processes naturally occur in growing and dividing cells, it is reasonable to conclude that the dynamics of component concentrations will be more realistic than when modeled within constant-volume and/or steady-state frameworks. This approach is illustrated using a symbolic whole cell model. 相似文献
6.
A simple, general, and efficient method for calculating the response of a set of coupled first-order (or pseudo-first-order) chemical reactions to an arbitrarily large periodic field is described. The method is applied to a four-state membrane transport enzyme that is electroconformationally coupled to an ac field, i.e., the enzyme has electric charges that move concomitantly with a conformational transition. The calculation is done both for enzymes in a planar membrane and for enzymes in the spherical membrane of a cell or vesicle in suspension. 相似文献
7.
Just as complex electronic circuits are built from simple Boolean gates, diverse biological functions, including signal transduction, differentiation, and stress response, frequently use biochemical switches as a functional module. A relatively small number of such switches have been described in the literature, and these exhibit considerable diversity in chemical topology. We asked if biochemical switches are indeed rare and if there are common chemical motifs and family relationships among such switches. We performed a systematic exploration of chemical reaction space by generating all possible stoichiometrically valid chemical configurations up to 3 molecules and 6 reactions and up to 4 molecules and 3 reactions. We used Monte Carlo sampling of parameter space for each such configuration to generate specific models and checked each model for switching properties. We found nearly 4,500 reaction topologies, or about 10% of our tested configurations, that demonstrate switching behavior. Commonly accepted topological features such as feedback were poor predictors of bistability, and we identified new reaction motifs that were likely to be found in switches. Furthermore, the discovered switches were related in that most of the larger configurations were derived from smaller ones by addition of one or more reactions. To explore even larger configurations, we developed two tools: the “bistabilizer,” which converts almost-bistable systems into bistable ones, and frequent motif mining, which helps rank untested configurations. Both of these tools increased the coverage of our library of bistable systems. Thus, our systematic exploration of chemical reaction space has produced a valuable resource for investigating the key signaling motif of bistability. 相似文献
8.
Most previous models of the spinal central pattern generator (CPG) underlying locomotion in the lamprey have relied on reciprocal
inhibition between the left and right side for oscillations to be produced. Here, we have explored the consequences of using
self-oscillatory hemisegments. Within a single hemisegment, the oscillations are produced by a network of recurrently coupled
excitatory neurons (E neurons) that by themselves are not oscillatory but when coupled together through N-methyl-d-aspartate (NMDA) and α-amino-3-hydroxy-5-methyl-4-isoxazolepropionicacid (AMPA)/kainate transmission can produce oscillations.
The bursting mechanism relies on intracellular accumulation of calcium that activates Ca2+-dependent K+. The intracellular calcium is modeled by two different intracellular calcium pools, one of which represents the calcium entry
following the action potential, CaAP pool, and the other represents the calcium inflow through the NMDA channels, CaNMDA pool. The Ca2+-dependent K+ activated by these two calcium pools are referred to as KCaAP and KCaNMDA, respectively, and their relative conductances are modulated and increase with the background activation of the network.
When changing the background stimulation, the bursting activity in this network can be made to cover a frequency range of
0.5–5.5 Hz with reasonable burst proportions if the adaptation is modulated with the activity. When a chain of such hemisegments
are coupled together, a phase lag along the chain can be produced. The local oscillations as well as the phase lag is dependent
on the axonal conduction delay as well as the types of excitatory coupling that are assumed, i.e. AMPA/kainate and/or NMDA.
When the caudal excitatory projections are extended further than the rostral ones, and assumed to be of approximately equal
strength, this kind of network is capable of reproducing several experimental observations such as those occurring during
strychnine blockade of the left-right reciprocal inhibition. Addition of reciprocally coupled inhibitory neurons in such a
network gives rise to antiphasic activity between the left and right side, but not necessarily to any change of the frequency
if the burst proportion of the hemisegmental bursts is well below 50%. Prolongation of the C neuron projection in the rostrocaudal
direction restricts the phase lag produced by only the excitatory hemisegmental network by locking together the interburst
intervals at different levels of the spinal cord.
Received: 29 September 1998 Accepted in Revised Form: 26 March 1999 相似文献
9.
10.
The probable existence of oscillating chemical reactions has been attracting some interest in recent years for their possible
role in explaining certain biological phenomena. Perhaps the simplest model of oscillating reactions is that of Lotka (1910),
which consists of a chain of autocatalytic reactions. Two “reactor systems” in which such a chain of reactions could take
place are considered in this work and are called homogeneous and compartmental models, respectively. The differential equations
governing the temporal behavior of the reacting species are solved on an analog computer, and the conditions under which sustained
oscillations occur are obtained and discussed. Comparisons of the solution obtained in the two models are discussed. 相似文献
11.
From hormonal secretion to gene expression, multicellular dynamics are rich in oscillatory regulation. When organized in space and time, periodic cell-cell signaling can give rise to long-range coordination of gene expression and cell movement in tissues. Lack of synchrony of the oscillations on the other hand can serve as a source of initial divergence of cell fate in stem cells. How properties of individual cells can account for collective rhythmic behaviors at the tissue level remains elusive in most cases. Recently, studies in chemical reactions, synthetic gene circuits, yeast and social amoeba Dictyostelium have greatly enhanced our view of collective oscillations in cell populations. From these relatively simple systems, a unified view of how excitable and oscillatory regulations could be tuned and coupled to give rise to tissue-level oscillations is emerging. The review focuses on recent progress in cyclic adenosine monophosphate oscillations in Dictyostelium and highlights similarities and differences with other systems. We will see that the autonomy of single-cell level oscillations and different ways in which cells are coupled influence how group-level information can be encoded in collective oscillations. 相似文献
12.
We introduce a 3D model for a motile rod-shaped bacterial cell with a single polar flagellum which is based on the configuration
of a monotrichous type of bacteria such as Pseudomonas aeruginosa. The structure of the model bacterial cell consists of a cylindrical body together with the flagellar forces produced by
the rotation of a helical flagellum. The rod-shaped cell body is composed of a set of immersed boundary points and elastic
links. The helical flagellum is assumed to be rigid and modeled as a set of discrete points along the helical flagellum and
flagellar hook. A set of flagellar forces are applied along this helical curve as the flagellum rotates. An additional set
of torque balance forces are applied on the cell body to induce counter-rotation of the body and provide torque balance. The
three-dimensional Navier–Stokes equations for incompressible fluid are used to describe the fluid dynamics of the coupled
fluid–microorganism system using Peskin’s immersed boundary method. A study of numerical convergence is presented along with
simulations of a single swimming cell, the hydrodynamic interaction of two cells, and the interaction of a small cluster of
cells. 相似文献
13.
Galina N. Borisyuk Roman M. Borisyuk Alexander I. Khibnik Dirk Roose 《Bulletin of mathematical biology》1995,57(6):809-840
In this paper we present an oscillatory neural network composed of two coupled neural oscillators of the Wilson-Cowan type.
Each of the oscillators describes the dynamics of average activities of excitatory and inhibitory populations of neurons.
The network serves as a model for several possible network architectures. We study how the type and the strength of the connections
between the oscillators affect the dynamics of the neural network. We investigate, separately from each other, four possible
connection types (excitatory→excitatory, excitatory→inhibitory, inhibitory→excitatory, and inhibitory→inhibitory) and compute
the corresponding bifurcation diagrams. In case of weak connections (small strength), the connection of populations of different
types lead to periodicin-phase oscillations, while the connection of populations of the same type lead to periodicanti-phase oscillations. For intermediate connection strengths, the networks can enter quasiperiodic or chaotic regimes, and can also
exhibit multistability. More generally, our analysis highlights the great diversity of the response of neural networks to
a change of the connection strength, for different connection architectures. In the discussion, we address in particular the
problem of information coding in the brain using quasiperiodic and chaotic oscillations. In modeling low levels of information
processing, we propose that feature binding should be sought as a temporally coherent phase-locking of neural activity. This
phase-locking is provided by one or more interacting convergent zones and does not require a central “top level” subcortical
circuit (e.g. the septo-hippocampal system). We build a two layer model to show that although the application of a complex
stimulus usually leads to different convergent zones with high frequency oscillations, it is nevertheless possible to synchronize
these oscillations at a lower frequency level using envelope oscillations. This is interpreted as a feature binding of a complex
stimulus. 相似文献
14.
N. Rashevsky 《Bulletin of mathematical biology》1969,31(3):591-603
A previous study (Bull. Math. Biophysics,30, 735–749) is generalized to the case of active transport, which acts together in general with ordinary diffusion. The basic
results obtained are the same except for an additional important conclusion. In principle it is possible to obtain sustained
oscillations even when the secretions of the different glands do not affect the rates of formation or decay of each other
at all, but affect the “molecular pumps,” which are responsible for the active transports in various parts of the system.
Thus no biochemical interactions need necessarily take place between then-metabolites to make sustained oscillations possible in principle. This is an addition to a previous finding (Bull. Math. Biophysics,30, 751–760) that due to effects of the secreted hormones on target organs, non-linearity of biochemical interactions is not
needed for production of sustained oscillations. 相似文献
15.
A. Peskoff 《Bulletin of mathematical biology》1979,41(2):163-181
The problem of calculating the potential induced in an electrical syncytium by a point source of current is studied. The interiors
of the many interconnected cells are treated as one continuum with resistivity ρ
i
. The interdigitated extracellular space is treated as a second continuum of resistivity ρ
e
, occupying the same overall volume, coupled to the first via the resistanceR
m and capacitanceC
m of the cell membranes. The intra- and extracellular potentials are then solutions to a pair of coupled partial differential
equations. The equations are uncoupled, yielding a cable equation for the transmembrane potential and a Poisson equation for
a second auxiliary potential. For an unbounded syncytium the potential for a step function source is obtained in terms of
error functions. For a spherical syncytium of radiusa, bounded by a membrane with surface resistanceR
a, and capacitanceC
a, expansions are obtained in spherical harmonics and spherical Bessel functions. For ɛ=ρ
ia/R
a and β=ρ
i
/ρ
e
small, an asymptotic expansion of the potential is developed. The results are compared to earlier results for a spherical
cell as well as to microelectrode measurements of the lens of the eye. 相似文献
16.
The excitation of inphase (0-type) and antiphase (π-type) electromagnetic oscillations by a relativistic electron beam in
a system of identical coupled cavities is considered. It is shown that, in the case of excitation of antiphase oscillations,
instability develops in a shorter system of cavities than it does when inphase oscillations are excited. In the nonlinear
stage of the excitation of antiphase oscillations in a system of coupled cavities, a virtual cathode forms that breaks the
initially uniform relativistic electron beam into a periodic sequence of spatially separated short bunches. 相似文献
17.
Mayer Landau Paco Lorente Jacques Henry Stephane Canu 《Journal of mathematical biology》1987,25(5):491-509
We were interested in investigating the behaviour of a cardiac electrophysiological model including coupled pacemaker (PM) and nonpacemaker (NPM) cells. To this aim, a modified version of the model of Van Capelle and Durrer was used. First, few discrete values were assigned to coupling resistance (CR) and respective cell sizes and numerical simulations versus time showed three possible kinds of response pattern: sustained rhythmic activity, subthreshold oscillations, and complete inhibition. Then, after setting a fixed value to PM cell size, we undertake a thorough study of the system by using bifurcation-continuation techniques and CR was chosen as the continuation parameter. On the maximum action potential — CR plane representation, we could describe five behavioural zones: complete inhibition, coexistence of complete inhibition and NPM large oscillations, NPM large oscillations, coexistence of NPM large oscillations and subthreshold oscillations, subthreshold oscillations. Within the zones of qualitatively different coexisting solutions, a detailed exploration clearly demonstrated the presence of hysteresis cycles. Indeed, the status of the system depended on its immediate previous story within narrow ranges of CR values. Such a coexistence of stable solutions for identical values of CR may suggest an explanation of the intermittant activity elicited from abnormal ectopic foci observed in certain ventricular rhythm disturbances. In addition, a Hopf bifurcation point, from which emerged stationary and periodic solutions, was followed on the PM cell size — CR plane and from this representation we could deduce that the smaller the PM cell, the higher the CR must be for the PM cell to escape from the NPM cell inhibition. 相似文献
18.
Cell proliferation is considered a periodic process governed by a relaxation timer. The collective behavior of a system composed
of three identical relaxation oscillators in numerically studied under the condition that diffusion of the slow mode dominates.
We demonstrate: (1) the existence of three periodic regimes with different periods and phase relations and an unsymmetrical,
stable steady-state (USSS); (2) the coexistence of in-phase oscillations and USSS; (3) the coexistence of periodic attractors;
and (4) the emergence of a two-loop limit cycle coexisting with both in-phase oscillations and a stable steady-state. The
qualitative reasons for such a diversitiy and its possible role in the generation of cell cycle variability are discussed.
Received: 18 March 1992/Accepted in revised form: 16 April 1994 相似文献
19.
A mathematical framework for modeling biological cells from a physicochemical perspective is described. Cells modeled within this framework consist of at least two regions, including a cytosolic volume encapsulated by a membrane surface. The cytosol is viewed as a well-stirred chemical reactor capable of changing volume while the membrane is assumed to be an oriented 2-D surface capable of changing surface area. Two physical properties of the cell, namely volume and surface area, are determined by (and determine) the reaction dynamics generated from a set of chemical reactions designed to be occurring in the cell. This framework allows the modeling of complex cellular behaviors, including self-replication. This capability is illustrated by constructing two self-replicating prototypical whole-cell models. One protocell was designed to be of minimal complexity; the other to incorporate a previously reported well-known mechanism of the eukaryotic cell cycle. In both cases, self-replicative behavior was achieved by seeking stable physically possible oscillations in concentrations and surface-to-volume ratio, and by synchronizing the period of such oscillations to the doubling of cytosolic volume and membrane surface area. Rather than being enforced externally or artificially, growth and division occur naturally as a consequence of the assumed chemical mechanism operating within the framework. 相似文献
20.
Gap-junctional coupling is an important way of communication between neurons and other excitable cells. Strong electrical
coupling synchronizes activity across cell ensembles. Surprisingly, in the presence of noise synchronous oscillations generated
by an electrically coupled network may differ qualitatively from the oscillations produced by uncoupled individual cells forming
the network. A prominent example of such behavior is the synchronized bursting in islets of Langerhans formed by pancreatic
β-cells, which in isolation are known to exhibit irregular spiking (Sherman and Rinzel, Biophys J 54:411–425, 1988; Sherman and Rinzel, Biophys J 59:547–559, 1991). At the heart of this intriguing phenomenon lies denoising, a remarkable ability of electrical coupling to diminish the
effects of noise acting on individual cells. In this paper, building on an earlier analysis of denoising in networks of integrate-and-fire
neurons (Medvedev, Neural Comput 21 (11):3057–3078, 2009) and our recent study of spontaneous activity in a closely related model of the Locus Coeruleus network (Medvedev and Zhuravytska,
The geometry of spontaneous spiking in neuronal networks, submitted, 2012), we derive quantitative estimates characterizing denoising in electrically coupled networks of conductance-based models
of square wave bursting cells. Our analysis reveals the interplay of the intrinsic properties of the individual cells and
network topology and their respective contributions to this important effect. In particular, we show that networks on graphs
with large algebraic connectivity (Fiedler, Czech Math J 23(98):298–305, 1973) or small total effective resistance (Bollobas, Modern graph theory, Graduate Texts in Mathematics, vol. 184, Springer, New
York, 1998) are better equipped for implementing denoising. As a by-product of the analysis of denoising, we analytically estimate the
rate with which trajectories converge to the synchronization subspace and the stability of the latter to random perturbations.
These estimates reveal the role of the network topology in synchronization. The analysis is complemented by numerical simulations
of electrically coupled conductance-based networks. Taken together, these results explain the mechanisms underlying synchronization
and denoising in an important class of biological models. 相似文献