Feedback control of a competitive mixed-culture system

Three feedback strategies for the on-line control of cell densities in a mixed-culture system have been examined. A competitive mixed-culture system of Candida utilis and Corynebacterium glutamicum grown on glucose as the limiting carbon source was modeled using Monod growth kinetics. First-order time constants were added to simulate transient growth effects. Multivariable feedback control of cell densities by manipulation of substrate feed and dilution rate was investigated. Feedback strategies directed to minimizing control interactions were found to be superior to classical feedback. Transients in the growth-rate response produced oscillations in cell density and required retuning of control constants. The relative time constants of the two species were important, with the largest oscillations resulting when the faster growing organism had the faster time constant.     

Oscillating growth patterns of multicellular tumour spheroids

The growth kinetics of 9L (rat glioblastoma cell line) and U118 (human glioblastoma cell line) multicellular tumour spheroids (MTS) have been investigated by non-linear least square fitting of individual growth curves with the Gompertz growth equation and power spectrum analysis of residuals. Residuals were not randomly distributed around calculated growth trajectories. At least one main frequency was found for all analysed MTS growth curves, demonstrating the existence of time-dependent periodic fluctuations of MTS volume dimensions. Similar periodic oscillations of MTS volume dimensions were also observed for MTS generated using cloned 9L cells. However, we found significant differences in the growth kinetics of MTS obtained with cloned cells if compared to the growth kinetics of MTS obtained with polyclonal cells. Our findings demonstrate that the growth patterns of three-dimensional tumour cell cultures are more complex than has been previously predicted using traditional continuous growth models.     

Whole-cell modeling framework in which biochemical dynamics impact aspects of cellular geometry

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.     

Persistent Symmetry Frustration in Pollen Tubes

Pollen tubes are extremely rapidly growing plant cells whose morphogenesis is determined by spatial gradients in the biochemical composition of the cell wall. We investigate the hypothesis (MP) that the distribution of the local mechanical properties of the wall, corresponding to the change of the radial symmetry along the axial direction, may lead to growth oscillations in pollen tubes. We claim that the experimentally observed oscillations originate from the symmetry change at the transition zone, where both intervening symmetries (cylindrical and spherical) meet. The characteristic oscillations between resonating symmetries at a given (constant) turgor pressure and a gradient of wall material constants may be identified with the observed growth-cycles in pollen tubes.     

Temperature dependence and temperature compensation of kinetics of chemical oscillations; Belousov-Zhabotinskii reaction, glycolysis and circadian rhythms

Based on the distribution of activation energies around the experimental mean and averaging of rate constants we propose a theoretical scheme to examine the temperature dependence and temperature compensation of time periods of chemical oscillations. The critical finite width of the distribution is characteristic of endogeneous oscillations for compensating kinetics as observed in circadian oscillations, while the vanishing width corresponds to Arrhenius temperature dependent kinetics of non-endogeneous chemical oscillation in Belousov-Zhabotinskii reaction in a CSTR or glycolysis in cell-free yeast extracts. Our theoretical analysis is corroborated with experimental data.     

Periodic cell aggregation in suspensions of Dictyostelium discoideum

Abstract. Periodic activities of Dictyostelium discoideum can be observed in cell suspension as two types of oscillations in the light-scattering properties, spike-shaped and sinusoidal. Responses of suspended cells to applied chemoattractants are also reflected by transient changes in light scattering. Alterations in the light-scattering properties are due to structural changes such as changes in cell shape and/or changes in the size of cell aggregates. Therefore, changes in the aggregation state during autonomous oscillations and during attractant-induced responses were investigated. In order to be able to withdraw multiple samples and larger sample volumes from optically monitored cell suspensions, a photometer comprising glass fiber optics immersable in a cell suspension was constructed. Samples were fixed with formaldehyde and photographed. The aggregation state of the samples was quantified by counting the number of particles (cells and cell aggregates) per volume. Folic acid elicited in suspensions of undifferentiated cells a transient decrease in the number of particles per volume as did cAMP in suspensions of preaggregation cells. Periodic changes in the number of particles per volume occurred synchronously with spike-shaped and sinusoidal oscillations. The relative amplitude of the oscillations in particle number was larger during sinusoids than during spikes. Photographs showed periodic changes in the aggregate size during sinusoidal oscillations. In each cycle, the cell-aggregation phase was followed by a phase of partial disaggregation. The recurring loosening of cell-cell contacts may be relevant for sorting out the different cell types. The potential role of contact site as synchronizer and as constituent of an oscillator is discussed.     

Growth of yeast Candida utilis in crotonaldehyde containing media

Summary The inhibitory influence of the higher concentration of 20butenal, crotonaldehyde was followed during the batch and long-term continuous fermentation of Candida utilis growing on synthetic ethanol. Most crotonaldehyde is removed from the medium by biotransformation. Crotonaldehyde inhibits the growth, lengthens the lag phase and decreases the biomass yield and the content of crude proteins in the biomass. The yeast C. utilis is capable of growing on media containing very high concentrations of inhibitor in the in-flow during continuous cultivation. Uncharacteristic transport oscillations of the content of crotonaldehyde were observed for which acidic groups on the cell membrane are probably responsible. A sensitive method which is suitable for measuring very low concentration of crotonaldehyde in aqueous solutions is described. Crotonaldehyde acts as an uncompetitive inhibitor with slight mixed type of inhibition. An equation describing the kinetics of inhibition was derived.     

Hyper-osmotic stress induces volume change and calcium transients in chondrocytes by transmembrane, phospholipid, and G-protein pathways

Mechanical compression of cartilage is associated with a rise in the interstitial osmotic pressure, which can alter cell volume and activate volume recovery pathways. One of the early events implicated in regulatory volume changes and mechanotransduction is an increase of intracellular calcium ion ([Ca²⁺]_i). In this study, we tested the hypothesis that osmotic stress initiates intracellular Ca²⁺ signaling in chondrocytes. Using laser scanning microscopy and digital image processing, [Ca²⁺]_i and cell volume were monitored in chondrocytes exposed to hyper-osmotic solutions. Control experiments showed that exposure to hyper-osmotic solution caused significant decreases in cell volume as well as transient increases in [Ca²⁺]_i. The initial peak in [Ca²⁺]_i was generally followed by decaying oscillations. Pretreatment with gadolinium, a non-specific blocker of mechanosensitive ion channels, inhibited this [Ca²⁺]_i increase. Calcium-free media eliminated [Ca²⁺]_i increases in all cases. Pretreatment with U73122, thapsigargin, or heparin (blockers of the inositol phosphate pathway), or pertussis toxin (a blocker of G-proteins) significantly decreased the percentage of cells responding to osmotic stress and nearly abolished all oscillations. Cell volume decreased with hyper-osmotic stress and recovered towards baseline levels throughout the duration of the control experiments. The peak volume change with 550 mOsm osmotic stress, as well as the percent recovery of cell volume, was dependent on [Ca²⁺]_i. These findings indicate that osmotic stress causes significant volume change in chondrocytes and may activate an intracellular second messenger signal by inducing transient increases in [Ca²⁺]_i.     

A model for 8-10 Hz spindling in interconnected thalamic relay and reticularis neurons.

We investigated a simplified model of a thalamocortical cell and a reticular thalamic cell interconnected with excitatory and inhibitory synapses, based on Hodgkin-Huxley type kinetics. The intrinsic oscillatory properties of the model cells were similar to those observed from single cells in vitro. When synaptic interactions were included, spindle oscillations were observed consisting of sequences of rhythmic oscillations at 8-10 Hz separated by silent periods of 8-40 s. The model suggests that Ca2+ regulation of lh channels may be responsible for the waxing and waning of spindles and that the reticular cell shapes the 10-Hz rhythmicity. The model also predicts that the kinetics of gamma-aminobutyric acid inhibitory postsynaptic potentials as well as the intrinsic properties of reticular cells are critical in determining the frequency of spindle rhythmicity.     

A framework for whole-cell mathematical modeling

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.     

Signal processing times in neutrophil activation: dependence on ligand concentration and the relative phase of metabolic oscillations

Intracellular NAD(P)H oscillations exhibited by polarized neutrophils display congruent with 20 s periods, which are halved to congruent with 10 s upon stimulation with chemotactic peptides such as FNLPNTL (N-formyl-nle-leu-phe-nle-tyr-lys). By monitoring this frequency change, we have measured accurately the time interval between stimulus and metabolic frequency changes. A microscope flow chamber was designed to allow rapid delivery of FNLPNTL to adherent cells. Using fluorescein as a marker, we found delivery to be complete and stable throughout the chamber within approximately 400 ms. Peptides were injected into the chamber at concentrations ranging from 10(-6) to 10(-9) M. Injections also varied with respect to the relative phase of a cell's NAD(P)H oscillations. The time interval between injection of 10(-6) M FNLPNTL and the acquisition of congruent with 10 s period metabolic oscillations was found to be 12.2+/-3.3 s when injections occurred at the NAD(P)H oscillation peak whereas the lag time was 22.5+/-4.8 s when coinciding with a trough. At 10(-8) M FNLPNTL, lag times were found to be 26.1+/-5.2 and 30.5+/-7.3 s for injections at NAD(P)H peaks and troughs, respectively. FNLPNTL at 10(-9) M had no effect on metabolic oscillations, consistent with previous studies. Our experiments show that the kinetics of transmembrane signal processing, in contrast to a simple transmembrane chemical reaction, can depend upon both ligand dose and its temporal relationship with intracellular metabolic oscillations.     

Oscillations in free cytosolic calcium during IgE-mediated stimulation distinguish human basophils from human mast cells

Free cytosolic calcium ([Ca2+]i) levels increase after the stimulation of either human basophils or mast cells with anti-IgE antibody. Previous studies found that the mast cell [Ca2+]i response was graded in magnitude, according to stimulus strength, and that the activated level was free of oscillations. The current studies demonstrate several new features of the mast cell and basophil response. First, in mast cells, the transition to activated [Ca2+]i levels was abrupt (width = 6.5 +/- 2 s), after a period of quiescence whose duration (5 to 300 s) was a function of the strength of the stimulus. At optimal concentrations of anti-IgE, 97% of mast cells showed only abrupt transitions and oscillation-free activated calcium levels. In contrast, basophils showed marked oscillations whose magnitudes were partially dependent on the strength of stimulus. Like the mast cell, there was a quiescent period before the first transition and this period was also dependent on the strength of the stimulus. Oscillations were generally superimposed on an elevated [Ca2+]i level at a frequency of 0.5 to 3/min, had half-widths of 5 to 20 s, and were markedly chaotic in the frequency domain. In general, oscillations were more apparent at suboptimal concentrations of anti-IgE. Despite the apparent contrast in basophil and mast cell responses, oscillations (1 or 2 in a 10-min period) could be observed in a small percentage of mast cells and some basophils showed characteristics of mast cells. We tentatively conclude that mast cells and basophils utilize a similar mechanism of calcium mobilization but that the nonlinear characteristics of the calcium response may account for the mast cell/basophil differences. These studies indicated that the calcium kinetics, as measured by population averages, did not reflect the kinetics observed at the single cell level. Both mast cells and basophils had characteristics which could be described as graded and characteristics resembling all-or-nothing processes; the magnitude of a response was graded according the strength of stimulus while the kinetics profile appeared as an all-or-nothing event.     

Oscillatory enzyme reactions and Michaelis–Menten kinetics

Oscillations occur in a number of enzymatic systems as a result of feedback regulation. How Michaelis–Menten kinetics influences oscillatory behavior in enzyme systems is investigated in models for oscillations in the activity of phosphofructokinase (PFK) in glycolysis and of cyclin-dependent kinases in the cell cycle. The model for the PFK reaction is based on a product-activated allosteric enzyme reaction coupled to enzymatic degradation of the reaction product. The Michaelian nature of the product decay term markedly influences the period, amplitude and waveform of the oscillations. Likewise, a model for oscillations of Cdc2 kinase in embryonic cell cycles based on Michaelis–Menten phosphorylation–dephosphorylation kinetics shows that the occurrence and amplitude of the oscillations strongly depend on the ultrasensitivity of the enzymatic cascade that controls the activity of the cyclin-dependent kinase.     

Respiratory oscillations and heat evolution in synchronous cultures of Candida utilis

Synchronous cultures of the budding yeast Candida utilis prepared by continuous-flow size selection showed respiratory oscillations when the energy source was either glucose, acetate or glycerol. The period of the oscillations was about one-third of the cell cycle time (i.e. about 0.5 h). No fluctuations in heat evolution could be detected. In organisms growing with acetate or glycerol, the effects of cyanide, N,N'-dicyclohexylcarbodi-imide and carbonyl cyanide m-chlorophenylhydrazone (maximum inhibition of respiration at respiratory maxima, maximum uncoupling of energy conservation at respiratory minima) suggest that the control mechanism responsible for the oscillations is mitochondrial respiratory control in vivo. The effects of cyanide and N,N'-dicyclohexylcarbodi-imide on the respiration of cultures growing synchronously with glucose were different from those for cultures growing with the non-fermentable substrates; this suggests that the mitochondrial respiratory system interacts with the early reactions of glucose utilization.     

Hydrodynamics and cell volume oscillations in the pollen tube apical region are integral components of the biomechanics of Nicotiana tabacum pollen tube growth

Pollen tube growth is localized at the apex and displays oscillatory dynamics. It is thought that a balance between intracellular turgor pressure (hydrostatic pressure, reflected by the cell volume) and cell wall loosening is a critical factor driving pollen tube growth. We previously demonstrated that water flows freely into and out of the pollen tube apical region dependent on the extracellular osmotic potential, that cell volume changes reflect changes in the intracellular pressure, and that cell volume changes differentially induce, increases or decreases in specific phospholipid signals. This article shows that manipulation of the extracellular osmotic potential rapidly induces modulations in pollen tube growth rate frequencies, demonstrating that changes in the intracellular pressure are sufficient to reset the pollen tube growth oscillator. This indicates a direct link between intracellular hydrostatic pressure and pollen tube growth. Altering hydrodynamic flow through the pollen tube by replacing extracellular H₂O with ²H₂O adversely affects both cell volume and growth rate oscillations and induces aberrant morphologies. Normal growth and cell morphology are rescued by replacing ²H₂O with H₂O. Further studies revealed that the cell volume oscillates in the pollen tube apical region. These cell volume oscillations were not from changes in cell shape at the tip and were detectable up to 30 μm distal to the tip (the longest length measured). Cell volume in the apical region oscillates with the same frequency as growth rate oscillations but surprisingly the cycles are phase-shifted by 180°. Raman microscopy yields evidence that hydrodynamic flow out of the apex may be part of the biomechanics that drive cellular expansion. The combined results suggest that hydrodynamic loading/unloading in the apical region induces cell volume oscillations and has a role in driving cell elongation and pollen tube growth.     

Optical recording of the odor-evoked responses in olfactory structures of the brain of the terrestrial mollusk Helix

Regular oscillations were recorded in olfactory part of the brain (procerebrum) of gastropod mollusk Helix both electrographically and optically. In general, oscillations resembled those in slugs reported earlier. Odor application caused a transient change in the procerebral oscillations followed by appearance of a special pattern. For the first time the evoked potential was recorded in procerebrum and mapped in reference to the area of oscillations. The area of spreading of evoked potential roughly corresponded to the neuropil projection, while the oscillations were recorded in the projection of the cell body layer of procerebrum. The wave of the evoked potential emerged near the place of the olfactory nerve entrance into the procerebrum and propagated via the procerebrum neuropil towards the cell body layer. The evoked potential did not produce a phase-independent wave in rhythmical oscillations.     

Simulation of chemical oscillations in membranes

A computer simulation model has been developed to follow chemical oscillations in a membrane for immobilized enzyme systems. It is a discrete particle type model which follows the spatial and temporal fluctuations of the concentrations in a reaction involving two substrates. The parameters can be readily varied to allow dissipative structures to result from the sustained nonlinear reaction kinetics and to determine which parameters cause damping of the oscillations. The nature of the diffusion mechanism allows extension to more than one dimension.     

Hypoosmotic cell swelling as a novel mechanism for modulation of cloned HCN2 channels

This work demonstrates cell swelling as a new regulatory mechanism for the cloned hyperpolarization-activated, cyclic nucleotide-gated channel 2 (HCN2). HCN2 channels were coexpressed with aquaporin1 in Xenopus laevis oocytes and currents were monitored using a two-electrode voltage-clamp. HCN2 channels were activated by hyperpolarization to -100 mV and the currents were measured before and during hypoosmotic cell swelling. Cell swelling increased HCN2 currents by 30% without changing the kinetics of the currents. Injection of 50 nl intracellular solution resulted in a current increase of 20%, indicating that an increase in cell volume also under isoosmotic conditions may lead to activation of HCN2. In the absence of aquaporin1 only negligible changes in oocyte cell volume occur during exposure to hypoosmotic media and no significant change in HCN2 channel activity was observed during perfusion with hypoosmotic media. This indicates that cell swelling and not a change in ionic strength of the media, caused the observed swelling-induced increase in current. The increase in HCN2 current induced by cell swelling could be abolished by cytochalasin D treatment, indicating that an intact F-actin cytoskeleton is a prerequisite for the swelling-induced current.