Identification of possible two-reactant sources of oscillations in the Calvin photosynthesis cycle and ancillary pathways

A mathematical model to simulate the dynamics of photosynthetic light reactions under harmonically oscillating light

Alternating electric current and alternating electromagnetic fields revolutionized physics and engineering and led to many technologies that shape modern life. Despite these undisputable achievements that have been reached using stimulation by harmonic oscillations over centuries, applications in biology remain rare. Photosynthesis research is uniquely suited to unleash this potential because light can be modulated as a harmonic function, here sinus. Understanding the response of photosynthetic organisms to sinusoidal light is hindered by the complexity of dynamics that such light elicits, and by the mathematical apparatus required for understanding the signals in the frequency domain which, although well-established and simple, is outside typical curricula in biology. Here, we approach these challenges by presenting a mathematical model that was designed specifically to simulate the response of photosynthetic light reactions to light which oscillates with periods that often occur in nature. The independent variables of the model are the plastoquinone pool, the photosystem I donors, lumen pH, ATP, and the chlorophyll fluorescence (ChlF) quencher that is responsible for the qE non-photochemical quenching. Dynamics of ChlF emission, rate of oxygen evolution, and non-photochemical quenching are approximated by dependent model variables. The model is used to explain the essentials of the frequency-domain approaches up to the level of presenting Bode plots of frequency-dependence of ChlF. The model simulations were found satisfactory when compared with the Bode plots of ChlF response of the green alga Chlamydomonas reinhardtii to light that was oscillating with a small amplitude and frequencies between 7.8 mHz and 64 Hz.

Modeling chlorophyll a fluorescence transient: relation to photosynthesis

To honor Academician Alexander Abramovitch Krasnovsky, we present here an educational review on the relation of chlorophyll a fluorescence transient to various processes in photosynthesis. The initial event in oxygenic photosynthesis is light absorption by chlorophylls (Chls), carotenoids, and, in some cases, phycobilins; these pigments form the antenna. Most of the energy is transferred to reaction centers where it is used for charge separation. The small part of energy that is not used in photochemistry is dissipated as heat or re-emitted as fluorescence. When a photosynthetic sample is transferred from dark to light, Chl a fluorescence (ChlF) intensity shows characteristic changes in time called fluorescence transient, the OJIPSMT transient, where O (the origin) is for the first measured minimum fluorescence level; J and I for intermediate inflections; P for peak; S for semi-steady state level; M for maximum; and T for terminal steady state level. This transient is a real signature of photosynthesis, since diverse events can be related to it, such as: changes in redox states of components of the linear electron transport flow, involvement of alternative electron routes, the build-up of a transmembrane pH gradient and membrane potential, activation of different nonphotochemical quenching processes, activation of the Calvin-Benson cycle, and other processes. In this review, we present our views on how different segments of the OJIPSMT transient are influenced by various photosynthetic processes, and discuss a number of studies involving mathematical modeling and simulation of the ChlF transient. A special emphasis is given to the slower PSMT phase, for which many studies have been recently published, but they are less known than on the faster OJIP phase.

Entropy production in oscillatory processes during photosynthesis

The flow of matter and heat and the rate of enzymatic reactions are examined using two models of photosynthesis that exhibit sustained and damped oscillatory dynamics, with the objective of calculating the rate of entropy generation and studying the effects of temperature and kinetic constants on the thermodynamic efficiency of photosynthesis. The global coefficient of heat transfer and the direct and inverse constants of the formation reaction of the RuBisCO-CO2 complex were used as control parameters. Results show that when the system moves from isothermal to non-isothermal conditions, the transition from a steady state to oscillations facilitates an increase in the energy efficiency of the process. The simulations were carried out for two photosynthetic models in a system on a chloroplast reactor scale.

Oscillations of the internal CO(2) concentration in tobacco leaves transferred to low CO(2)

Measurement of the internal CO(2) concentration (Ci) in tobacco leaves using a fast-response CO(2) exchange system showed that in the light, switching from 350 microLL(-1) to a low CO(2) concentration of 36.5 microLL(-1) (promoting high photorespiration) resulted in the Ci oscillating near the value of CO(2) compensation point (Gamma*). The oscillations are highly irregular, the range of Ci varying by 2-4 microLL(-1) in substomatal cavities with a period of a few seconds. The statistical properties of the time series became stationary after a transient of approximately 100s following transfer to low CO(2). Attractor reconstruction shows that the observed oscillations are not chaotic but exhibit stochastic behavior. The period of oscillations is consistent with the duration of photorespiratory post-illumination burst (PIB). We suggest that the observed oscillations may be due to a similar mechanism to that which leads to PIB, and may play a role in switching mitochondrial operation between oxidation of the photorespiratory glycine and of the tricarboxylic acid cycle substrates.

Computational approaches to the topology, stability and dynamics of metabolic networks

Cellular metabolism is characterized by an intricate network of interactions between biochemical fluxes, metabolic compounds and regulatory interactions. To investigate and eventually understand the emergent global behavior arising from such networks of interaction is not possible by intuitive reasoning alone. This contribution seeks to describe recent computational approaches that aim to asses the topological and functional properties of metabolic networks. In particular, based on a recently proposed method, it is shown that it is possible to acquire a quantitative picture of the possible dynamics of metabolic systems, without assuming detailed knowledge of the underlying enzyme-kinetic rate equations and parameters. Rather, the method builds upon a statistical exploration of the comprehensive parameter space to evaluate the dynamic capabilities of a metabolic system, thus providing a first step towards the transition from topology to function of metabolic pathways. Utilizing this approach, the role of feedback mechanisms in the maintenance of stability is discussed using minimal models of cellular pathways.

Structural kinetic modeling of metabolic networks

To develop and investigate detailed mathematical models of metabolic processes is one of the primary challenges in systems biology. However, despite considerable advance in the topological analysis of metabolic networks, kinetic modeling is still often severely hampered by inadequate knowledge of the enzyme-kinetic rate laws and their associated parameter values. Here we propose a method that aims to give a quantitative account of the dynamical capabilities of a metabolic system, without requiring any explicit information about the functional form of the rate equations. Our approach is based on constructing a local linear model at each point in parameter space, such that each element of the model is either directly experimentally accessible or amenable to a straightforward biochemical interpretation. This ensemble of local linear models, encompassing all possible explicit kinetic models, then allows for a statistical exploration of the comprehensive parameter space. The method is exemplified on two paradigmatic metabolic systems: the glycolytic pathway of yeast and a realistic-scale representation of the photosynthetic Calvin cycle.

Function of mitochondria during the transition of barley protoplasts from low light to high light

Mitochondrial contribution to photosynthetic metabolism during the transition from low light (25-100 micromol quanta m(-2) s(-1), limiting photosynthesis) to high light (500 micromol quanta m(-2) s(-1), saturating photosynthesis) was investigated in protoplasts from barley (Hordeum vulgare) leaves. After the light shift, photosynthetic oxygen evolution rate increased rapidly during the first 30-40 s and then declined up to 60-70 s after which the rate increased to a new steady-state after 80-110 s. Rapid fractionation of protoplasts was used to follow changes in sub-cellular distribution of key metabolites during the light shift and the activation state of chloroplastic NADP-dependent malate dehydrogenase (EC 1.1.1.82) was measured. Although oligomycin (an inhibitor of the mitochondrial ATP synthase) affected the metabolite content of protoplasts following the light shift, the first oxygen burst was not affected. However, the transition to the new steady-state was delayed. Rotenone (an inhibitor of mitochondrial complex I) had similar, but less pronounced effect as oligomycin. From the analysis of metabolite content and sub-cellular distribution we suggest that the decrease in oxygen evolution following the first oxygen burst is due to phosphate limitation in the chloroplast stroma. For the recovery the control protoplasts can utilize ATP supplied by mitochondrial oxidative phosphorylation to quickly overcome the limitation in stromal phosphate and to increase the content of Calvin cycle metabolites. The oligomycin-treated protoplasts were deficient in cytosolic ATP and thereby unable to support Calvin cycle operation. This resulted in a delayed capacity to adjust to a sudden increase in light intensity.

New insights into photosynthetic oscillations revealed by two-dimensional microscopic measurements of chlorophyll fluorescence kinetics in intact leaves and isolated protoplasts

Chlorophyll fluorescence kinetic microscopy was used to analyze photosynthetic oscillations in individual cells of leaves and in isolated leaf cell protoplasts. Four Brassicaceae species were used: Arabidopsis halleri (L.) O'Kane & Al-Shehbaz, Thlaspi fendleri (Nels.) Hitchc, Thlaspi caerulescens J.&C. Presl and Thlaspi ochroleucum Boiss et Helder. With the latter two, the measurements were extended also to isolated protoplasts. The oscillations were induced under the microscope by exposing dark-adapted samples to actinic irradiance. Detailed analysis of the induced transients revealed that they consist of several processes oscillating with different frequencies and not only one component as reported earlier. Furthermore, it was found that most of these processes are controlled inside each individual cell. This was shown by differences in oscillations in neighboring cells and protoplasts that share a uniform intercellular environment. The frequency of the dominant oscillation frequency depended neither on irradiance nor on CO2 concentration and is, therefore, not controlled by the photosynthetic rate. Characteristic differences in the frequency spectrum and damping of oscillations have been found among the plant species examined.

A new class of biochemical oscillator models based on competitive binding

It has been noted that single-enzyme systems can undergo strongly damped transient oscillations. In this paper, we present a nonlinear dynamics analysis of oscillations in undriven chemical systems. This analysis allows us to classify transient oscillations into two groups. In the first group, oscillations arise from rapid oscillatory relaxation to a slower transient relaxation mode. These oscillations are always strongly damped. In the second group, it is the slowest relaxation mode which is implicated in the oscillations so these can be very lightly damped. This second class of oscillations has not previously been studied in enzymology. We show that a remarkably simple single-enzyme system, namely competitive inhibition with substrate flow, generates transient oscillations which belong to the second class. In an attempt to design an experimentally realizable version of this model, we then discovered a system which is capable of sustained oscillations. In this experimentally realizable model, two substrates compete to bind to a macromolecule. The flow of one substrate is controlled by a simple feedback device. Sustained oscillations are observed over a very wide range of parameters. In both models, oscillations are favored by a wide disparity in rates of binding and dissociation of the two substrates to the macromolecule.

Imaging of chlorophyll-a-fluorescence in leaves: Topography of photosynthetic oscillations in leaves of Glechoma hederacea

Images of chlorophyll-a-fluorescence oscillations were recorded using a camera-based fluorescence imaging system. Oscillations with frequencies around 1 per min were initiated by a transient decrease in light intensity during assimilation at an elevated CO2-concentration. The oscillation was inhomogenously distributed over the leaf. In cells adjacent to minor veins, frequency and damping rate was high, if there was any oscillation. In contrast, the amplitude was highest in cells most distant from phloem elements (maximal distance about 300 μm). The appearance of minor veins in oscillation images is explained by a gradient in the metabolic control in the mesophyll between minor veins and by transport of sugar from distant cells to phloem elements. The potential of fluorescence imaging to visualize 'microscopic' source-sink interactions and metabolic domains in the mesophyll is discussed.

Caffeine-induced calcium oscillations in heavy-sarcoplasmic-reticulum vesicles from rabbit skeletal muscle

Heavy-sarcoplasmic-reticulum vesicles from rabbit skeletal muscle show not only caffeine-induced calcium release in a medium allowing active calcium loading, but also oscillations in calcium concentration under appropriate conditions. The xanthine derivatives 7-isobutyl-1-methylxanthine and theophylline also induce oscillations under the same conditions. Calcium-releasing substances with other chemical structures such as adenosine nucleotides or calmodulin antagonists do not induce this effect. With the help of specific inhibitors such as ruthenium red, neomycin or magnesium it was demonstrated that the oscillation mechanism involves the ryanodine receptor/calcium channel. When ATP was substituted by GTP or ITP no oscillations occurred after caffeine application. The subsequent application of ATP, but not of adenosine 5'-[gamma-thio]triphosphate or adenosine 5'-[beta,gamma-methylene]triphosphate activated the oscillating mechanism, showing ATP to be an essential component of the oscillating system. We investigated the influence of the experimental conditions by altering the caffeine and ATP concentrations, calcium load, pH and ionic strength amongst other parameters. Potassium and anion channels are not involved in calcium oscillations of heavy sarcoplasmic reticulum, nor are the oscillations dependent on membrane potential.

Modelling and analysis of metabolic pathways

Modelling and analysis of metabolic pathways has received an increasing amount of attention over the past few years. Progress has been made in many aspects such as the identification of rate-controlling steps, applications of optimization principles, and stoichiometric analyses. In addition, the scope of modelling has also expanded. These efforts have led to an improved understanding of metabolic pathways and have facilitated their manipulation.