Bridging the gap between in silico and cell-based analysis of the nuclear factor-kappaB signaling pathway by in vitro studies of IKK2

Previously, we have shown by sensitivity analysis, that the oscillatory behavior of nuclear factor (NF-kappaB) is coupled to free IkappaB kinase-2 (IKK2) and IkappaBalpha(IkappaBalpha), and that the phosphorylation of IkappaBalpha by IKK influences the amplitude of NF-kappaB oscillations. We have performed further analyses of the behavior of NF-kappaB and its signal transduction network to understand the dynamics of this system. A time lapse study of NF-kappaB translocation in 10,000 cells showed discernible oscillations in levels of nuclear NF-kappaB amongst cells when stimulated with interleukin (IL-1alpha), which suggests a small degree of synchronization amongst the cell population. When the kinetics for the phosphorylation of IkappaBalpha by IKK were measured, we found that the values for the affinity and catalytic efficiency of IKK2 for IkappaBalpha were dependent on assay conditions. The application of these kinetic parameters in our computational model of the NF-kappaB pathway resulted in significant differences in the oscillatory patterns of NF-kappaB depending on the rate constant value used. Hence, interpretation of in silico models should be made in the context of this uncertainty.     

Sources of Variability in a Synthetic Gene Oscillator

Synthetic gene oscillators are small, engineered genetic circuits that produce periodic variations in target protein expression. Like other gene circuits, synthetic gene oscillators are noisy and exhibit fluctuations in amplitude and period. Understanding the origins of such variability is key to building predictive models that can guide the rational design of synthetic circuits. Here, we developed a method for determining the impact of different sources of noise in genetic oscillators by measuring the variability in oscillation amplitude and correlations between sister cells. We first used a combination of microfluidic devices and time-lapse fluorescence microscopy to track oscillations in cell lineages across many generations. We found that oscillation amplitude exhibited high cell-to-cell variability, while sister cells remained strongly correlated for many minutes after cell division. To understand how such variability arises, we constructed a computational model that identified the impact of various noise sources across the lineage of an initial cell. When each source of noise was appropriately tuned the model reproduced the experimentally observed amplitude variability and correlations, and accurately predicted outcomes under novel experimental conditions. Our combination of computational modeling and time-lapse data analysis provides a general way to examine the sources of variability in dynamic gene circuits.     

Vacuolar pH oscillations in mesophyll cells accompany oscillations of photosynthesis in leaves: Interdependence of cellular compartments,and regulation of electron flow in photosynthesis

Oscillations of photosynthesis induced in leaves of Vicia faba L. were accompanied by oscillations not only in the pH of the chloroplast stroma, but also by pH oscillations in the cytosol and in the vacuole of leaf mesophyll cells. Cytosolic pH oscillations were in phase with stromal oscillations, but antiparallel to vacuolar pH oscillations. During maxima of photosynthesis, the cytosolic pH exhibited maxima and the vacuolar pH minima. Vacuolar acidification is interpreted to be the result of energized proton transport from the cytosol into the vacuole. Since the ratio of dihydroxyacetone phosphate to phosphoglycerate is maximal during the peaks of photosynthesis (Stitt et al., 1988, J. Plant Physiol. 133, 133–143; Laisk et al., 1991, Planta 185, 554–562), while the activity of NADP-malic dehydrogenase is highest during minima of photosynthesis (Scheibe and Stitt, 1988, Plant Physiol. Biochem. 26, 473–481), the present data indicate in agreement with earlier observations (Yin et al., 1991, Planta 184, 30–34) that light-dependent cytosolic energization is brought about by the oxidation of dihydroxyacetone phosphate rather than of malate. They also indicate that the over-reduction of the electrontransport chain observed during minima of photosynthesis is relieved not predominantly by oxaloacetate reduction and export of the resulting malate from the chloroplasts but by another reaction, presumably oxygen reduction.Abbreviations CDCF 5-(and 6-)carboxy-2,7-dichlorofluorescein     

Steady States and Oscillations in the p53/Mdm2 Network

p53 is activated in response to events compromising the genetic integrity of a cell. Recent data show that p53 activity does not increase steadily with genetic damage but rather fluctuates in an oscillatory fashion (Lahav et al., Nature Genetics, 36, 147-150, 2004). Theoretical studies suggest that oscillations can arise from a combination of positive and negative feedbacks or from a long negative feedback loop alone. Both negative and positive feedbacks are present in the p53/Mdm2 network, but it is not known what roles they play in the oscillatory response to DNA damage. We developed a mathematical model of p53 oscillations based on positive and negative feedbacks in the p53/Mdm2 network. According to the model, the system reacts to DNA damage by moving from a stable steady state into a region of stable limit cycles. Oscillations in the model are born with large amplitude, which guarantees an all-or-none response to damage. As p53 oscillates, damage is repaired and the system moves back to a stable steady state with low p53 activity. The model reproduces experimental data in quantitative detail. We suggest new experiments for dissecting the contributions of negative and positive feedbacks to the generation of oscillations.     

Oscillatory dynamics of cell cycle proteins in single yeast cells analyzed by imaging cytometry

Progression through the cell division cycle is orchestrated by a complex network of interacting genes and proteins. Some of these proteins are known to fluctuate periodically during the cell cycle, but a systematic study of the fluctuations of a broad sample of cell-cycle proteins has not been made until now. Using time-lapse fluorescence microscopy, we profiled 16 strains of budding yeast, each containing GFP fused to a single gene involved in cell cycle regulation. The dynamics of protein abundance and localization were characterized by extracting the amplitude, period, and other indicators from a series of images. Oscillations of protein abundance could clearly be identified for Cdc15, Clb2, Cln1, Cln2, Mcm1, Net1, Sic1, and Whi5. The period of oscillation of the fluorescently tagged proteins is generally in good agreement with the inter-bud time. The very strong oscillations of Net1 and Mcm1 expression are remarkable since little is known about the temporal expression of these genes. By collecting data from large samples of single cells, we quantified some aspects of cell-to-cell variability due presumably to intrinsic and extrinsic noise affecting the cell cycle.     

A two variable delay model for the circadian rhythm of Neurospora crassa

A two variable model with delay in both the variables, is proposed for the circadian oscillations of protein concentrations in the fungal species Neurospora crassa. The dynamical variables chosen are the concentrations of FRQ and WC-1 proteins. Our model is a two variable simplification of the detailed model of Smolen et al. (J. Neurosci. 21 (2001) 6644) modeling circadian oscillations with interlocking positive and negative feedback loops, containing 23 variables. In our model, as in the case of Smolen's model, a sustained limit cycle oscillation takes place in both FRQ and WC-1 protein in continuous darkness, and WC-1 is anti-phase to FRQ protein, as observed in experiments. The model accounts for various characteristic features of circadian rhythms such as entrainment to light dark cycles, phase response curves and robustness to parameter variation and molecular fluctuations. Simulations are carried out to study the effect of periodic forcing of circadian oscillations by light-dark cycles. The periodic forcing resulted in a rich bifurcation diagram that includes quasiperiodicity and chaotic oscillations, depending on the magnitude of the periodic changes in the light controlled parameter. When positive feedback is eliminated, our model reduces to the generic one dimensional delay model of Lema et al. (J. Theor. Biol. 204 (2000) 565), delay model of the circadian pace maker with FRQ protein as the dynamical variable which represses its own production. This one-dimensional model also exhibits all characteristic features of circadian oscillations and gives rise to circadian oscillations which are reasonably robust to parameter variations and molecular noise.     

A Model of a Segmental Oscillator in the Leech Heartbeat Neuronal Network

We modeled a segmental oscillator of the timing network that paces the heartbeat of the leech. This model represents a network of six heart interneurons that comprise the basic rhythm-generating network within a single ganglion. This model builds on a previous two cell model (Nadim et al., 1995) by incorporating modifications of intrinsic and synaptic currents based on the results of a realistic waveform voltage-clamp study (Olsen and Calabrese, 1996). Due to these modifications, the new model behaves more similarly to the biological system than the previous model. For example, the slow-wave oscillation of membrane potential that underlies bursting is similar in form and amplitude to that of the biological system. Furthermore, the new model with its expanded architecture demonstrates how coordinating interneurons contribute to the oscillations within a single ganglion, in addition to their role of intersegmental coordination.     

Photosynthetic oscillation in individual cells of the marine diatom <Emphasis Type="Italic">Coscinodiscus wailesii</Emphasis> (Bacillariophyceae) revealed by microsensor measurements

Oscillations with a period of 1–2 min in the rate of photosynthesis have been found in leaves of C₃ and C₄ land plants under invariant, saturating, light and carbon dioxide. This article reports the occurrence of similar oscillations with a period of 2–2.5 min in individual cells of the marine diatom Coscinodiscus wailesii. These oscillations were determined by measurements of both oxygen (oxygen microelectrode) and carbon dioxide (pH microelectrode) just outside the plasmalemma. These oscillations were found in less than 1% of the cells examined. The occurrence of oscillations in unicelluar diatoms rules out for these organisms hypotheses as to the origin of oscillations in land plant leaves that are based on cell–cell interactions.     

Change of contractile behavior in plasmodia ofPhysarum polycephalum during mitosis

Summary Oscillations of ectoplasmic contraction in plasmodia of the myxomycetePhysarum polycephalum growing on agar containing semidefined medium were studied to determine if the contractile force is altered during the synchronous mitosis. In interphase the regular oscillations of contraction in the plasmodial sheet had an average period of 0.93 minutes in plasmodia growing at 24 °C. During mitosis the amplitude of these oscillations gradually decreased, ceasing for an average time of 2.7 minutes in 74% of the 23 plasmodia studied. Cessation of oscillating contractions in mitosis was accompanied by a decrease in the width of the channels embedded in the plasmodial sheet, and a decrease in the velocity of endoplasmic shuttle streaming usually to a complete standstill. Of 13 plasmodia in which the mitotic stage was very accurately determined, the stop in oscillating contractions occurred during metaphase in 10 plasmodia, and in prometaphase, anaphase, telophase in the 3 others. The cessation of contractile oscillations or of streaming did not occur absolutely simultaneously during mitosis in widely separated locations within one plasmodium, indicating mitotic asynchrony over a period of a few minutes within each plasmodium. We suggest that the halt of plasmodial migration during mitosis reported by others is caused by a decrease or cessation at slightly different times in the amplitude of ectoplasmic contractile oscillations in different areas of a plasmodium in mitosis resulting in an overall lack of coordination of endoplasmic flow throughout the plasmodium, thus temporarily halting migration. Possible physiological mechanisms linking a decrease in actomyosin contraction with the metaphase stage of mitosis are discussed.     

Stochastic aspects of oscillatory Ca2+ dynamics in hepatocytes

Signal-induced Ca²⁺ oscillations have been observed in many cell types and play a primary role in cell physiology. Although it is the regular character of these oscillations that first catches the attention, a closer look at time series of Ca²⁺ increases reveals that the fluctuations on the period during individual spike trains are far from negligible. Here, we perform a statistical analysis of the regularity of Ca²⁺ oscillations in norepinephrine-stimulated hepatocytes and find that the coefficient of variation lies between 10% and 15%. Stochastic simulations based on Gillespie's algorithm and considering realistic numbers of Ca²⁺ ions and inositol trisphosphate (InsP₃) receptors account for this variability if the receptors are assumed to be grouped in clusters of a few tens of channels. Given the relatively small number of clusters (∼200), the model predicts the existence of repetitive spikes induced by fluctuations (stochastic resonance). Oscillations of this type are found in hepatocytes at subthreshold concentrations of norepinephrine. We next predict with the model that the isoforms of the InsP₃ receptor can affect the variability of the oscillations. In contrast, possible accompanying InsP₃ oscillations have no impact on the robustness of signal-induced repetitive Ca²⁺ spikes.     

FW2.2 and cell cycle control in developing tomato fruit: a possible example of gene co-option in the evolution of a novel organ

fw2.2 is one of the few QTLs thus far isolated from plants and the first one known to control fruit size. While it has been established that FW2.2 is a regulator (either directly or indirectly) of cell division, FW2.2 does not share sequence homology to any protein of known function (Frary et al. Science 289:85–88, 2000; Cong et al. Proc Natl Acad Sci USA 99:13606–13611, 2002; Liu et al. Plant Physiol 132:292–299, 2003). Thus, the mechanism by which FW2.2 mediates cell division in developing fruit is currently unknown. In an effort to remedy this situation, a combination of yeast two-hybrid screens, in vitro binding assays and cell bombardment studies were performed. The results provide strong evidence that FW2.2 physically interacts at or near the plasma membrane with the regulatory (beta) subunit of a CKII kinase. CKII kinases are well-studied in both yeast and animals where they form part of cell cycle related signaling pathway. Thus while FW2.2 is a plant-specific protein and regulates cell division in a specialized plant organ (fruit), it appears to participate in a cell-cycle control signal transduction pathway that predates the divergence of single- and multi-cellular organisms. These results thus provide a glimpse into how ancient and conserved regulatory processes can be co-opted in the evolution of novel organs such as fruit.     

Endogenous oscillator controls surface density of mating receptors in Chlamydomonas eugametos

Summary We describe a circadian rhythm in the surface density of receptors that play a dominant role in the mating process of the unicellular green alga Chlamydomonas eugametos.These receptors — called agglutinins — are large glycoproteins extrinsically bound to the membrane of gamete flagella. We found circadian fluctuations in their density. Since inhibition of protein synthesis affected the agglutinin density without a lag period at any time,we conclude that the density was dependent on de novo synthesis and that the fluctuations in density are caused by circadian oscillations in the rate of agglutinin synthesis. This phenomenon evidently underlies the pronounced endogenous rhythm in mating competence that we described previously (Demets et al. 1987). Finally, we speculate on the nature of the time keeping mechanism that is generating these rhythmic events.     

Harmonic Oscillations in Homeostatic Controllers: Dynamics of the p53 Regulatory System

Homeostatic mechanisms are essential for the protection and adaptation of organisms in a changing and challenging environment. Previously, we have described molecular mechanisms that lead to robust homeostasis/adaptation under inflow or outflow perturbations. Here we report that harmonic oscillations occur in models of such homeostatic controllers and that a close relationship exists between the control of the p53/Mdm2 system and that of a homeostatic inflow controller. This homeostatic control model of the p53 system provides an explanation why large fluctuations in the amplitude of p53/Mdm2 oscillations may arise as part of the homeostatic regulation of p53 by Mdm2 under DNA-damaging conditions. In the presence of DNA damage p53 is upregulated, but is subject to a tight control by Mdm2 and other factors to avoid a premature apoptotic response of the cell at low DNA damage levels. One of the regulatory steps is the Mdm2-mediated degradation of p53 by the proteasome. Oscillations in the p53/Mdm2 system are considered to be part of a mechanism by which a cell decides between cell cycle arrest/DNA repair and apoptosis. In the homeostatic inflow control model, harmonic oscillations in p53/Mdm2 levels arise when the binding strength of p53 to degradation complexes increases. Due to the harmonic character of the oscillations rapid fluctuating noise can lead, as experimentally observed, to large variations in the amplitude of the oscillation but not in their period, a behavior which has been difficult to simulate by deterministic limit-cycle models. In conclusion, the oscillatory response of homeostatic controllers may provide new insights into the origin and role of oscillations observed in homeostatically controlled molecular networks.