Mariusz Pietruszka

Effect of Selenium on Magnesium, Iron, Manganese, Copper, and Zinc Accumulation in Corn Treated by Indole‐3‐acetic Acid

In this work, the relationship among accumulation of selenium, auxin, and some nutrient elements [magnesium (Mg2+), iron (Fe3+), manganese (Mn2+), copper (Cu2+), zinc (Zn2+)] in tissues of roots, mesocotyls, and leaves of Zea mays L. plants was studied. Seeds of maize were cultivated for 4 days in the darkness at 27 °C on moist filter paper, then the individual seedlings were transferred into an aerated solution containing the macro‐ and microelements and were cultivated in a greenhouse for 12 h in the light and 12 h (12‐h photoperiod) in the dark at 25 °C. The seedlings were exposed to the solution containing sodium hydrogen selenite (NaHSeO3), indole‐3 acetic acid (IAA), or IAA+NaHSeO3 for approximately 96 h before chemical analysis. The concentration of IAA in the external medium was 10−4 mol dm−3, concentration of selenite (NaHSeO3) was 10−6 mol dm−3, and the pH of the medium was 6.5. The accumulation of the probed elements in seedlings of maize was measured by inductively coupled plasma optical emission spectroscopy (ICP‐OES). It was determined that the selenite and IAA, present in the external medium of growing plants, changed the uptake and accumulation of some cations in tissues of leaves, mesocotyls, and roots. The change of transport conditions of these nutrient elements is probably one of the first observed symptoms of selenium effects on plants.

Pressure–Induced Cell Wall Instability and Growth Oscillations in Pollen Tubes

In the seed plants, the pollen tube is a cellular extension that serves as a conduit through which male gametes are transported to complete fertilization of the egg cell. It consists of a single elongated cell which exhibits characteristic oscillations in growth rate until it finally bursts, completing its function. The mechanism behind the periodic character of the growth has not been fully understood. In this paper we show that the mechanism of pressure – induced symmetry frustration occurring in the wall at the transition-perimeter between the cylindrical and approximately hemispherical parts of the growing pollen tube, together with the addition of cell wall material, is sufficient to release and sustain mechanical self-oscillations and cell extension. At the transition zone, where symmetry frustration occurs and one cannot distinguish either of the involved symmetries, a kind of ‘superposition state’ appears where either single or both symmetry(ies) can be realized by the system. We anticipate that testifiable predictions made by the model () may deliver, after calibration, a new tool to estimate turgor pressure from oscillation frequency of the periodically growing cell. Since the mechanical principles apply to all turgor regulated walled cells including those of plant, fungal and bacterial origin, the relevance of this work is not limited to the case of the pollen tube.

Solutions for a local equation of anisotropic plant cell growth: an analytical study of expansin activity

This paper presents a generalization of the Lockhart equation for plant cell/organ expansion in the anisotropic case. The intent is to take into account the temporal and spatial variation in the cell wall mechanical properties by considering the wall ‘extensibility’ (Φ), a time- and space-dependent parameter. A dynamic linear differential equation of a second-order tensor is introduced by describing the anisotropic growth process with some key biochemical aspects included. The distortion and expansion of plant cell walls initiated by expansins, a class of proteins known to enhance cell wall ‘extensibility’, is also described. In this approach, expansin proteins are treated as active agents participating in isotropic/anisotropic growth. Two-parameter models and an equation for describing α- and β-expansin proteins are proposed by delineating the extension of isolated wall samples, allowing turgor-driven polymer creep, where expansins weaken the non-covalent binding between wall polysaccharides. We observe that the calculated halftime (t1/2 = εΦ0 log 2) of stress relaxation due to expansin action can be described in mechanical terms.

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.

Exact analytic solutions for a global equation of plant cell growth.

A generalization of the Lockhart equation for plant cell expansion in isotropic case is presented. The goal is to account for the temporal variation in the wall mechanical properties--in this case by making the wall extensibility a time dependent parameter. We introduce a time-differential equation describing the plant growth process with some key biophysical aspects considered. The aim of this work was to improve prior modeling efforts by taking into account the dynamic character of the plant cell wall with characteristics reminiscent of damped (aperiodic) motion. The equations selected to encapsulate the time evolution of the wall extensibility offer a new insight into the control of cell wall expansion. We find that the solutions to the time dependent second order differential equation reproduce much of the known experimental data for long- and short-time scales. Additionally, in order to support the biomechanical approach, a new growth equation based on the action of expansin proteins is proposed. Remarkably, both methods independently converge to the same kind, sigmoid-shaped, growth description functional V(t) proportional, exp(-exp(-t)), properly describing the volumetric growth and, consequently, growth rate as its time derivative.

General proof of the validity of a new tensor equation of plant growth

Plant cell/organ growth may be partly described by a local tensor equation. We provide a mathematical proof that the Lockhart (global) equation is the diagonal component of this tensor equation.

Temperature and the Growth of Plant Cells

In cell elongation, the juvenile cell vacuolates, takes up water, and expands by irreversible extension of the growth-limiting primary walls. This process was elaborated analytically by Lockhart in the mid-1960s. His growth equation does not, however, include the influence of the environmental temperature at which cell growth takes place. In this article we consider a phenomenological model including temperature in the equation of growth. Also, by introducing the possible influence of growth regulators treated here as external perturbations, linear and nonlinear solutions are found. A comparison of experimental and theoretical results permits qualitative and quantitative conclusions concerning change in the magnitude of the cell wall yielding coefficient Φ as a function of both time and temperature (with or without external perturbations), which has acquired reasonable values throughout.

Critical behaviour of the chemical potential at phase transitions

Abstract Investigating the thermodynamic properties of the generalized s–f model with intersite pairing in the context of magnetic, superconducting and reentrant-type phase transitions, as well as, structural phase transitions, we claim that all critical temperatures can easily be identified from the critical behaviour of the chemical potential and from the average occupation numbers (critical electron redistribution) of the electronic system. These quantities exhibit small but well-defined kinks at all critical temperatures as the evidence for phase transitions. The system undergoes a phase transition at such a critical temperature for which the chemical potential acquires its critical value. This new observation suggests a practical experimental application of the effect of how to find all critical temperatures when applied to real solids. The agreement between the calculated temperature dependence of the chemical potential, presented in our paper, and experimental measurement for high-temperature superconductor YBa 2 Cu 3 O 7−δ entirely supports this point of view.

Pressure-induced wall thickness variations in multi-layered wall of a pollen tube and Fourier decomposition of growth oscillations.

The augmented growth equation introduced by Ortega is solved for the apical portion of the pollen tube as an oscillating volume, which we approach in the framework of a two-fluid model in which the two fluids represent the constant pressure and the fluctuating features of the system. Based on routine Fourier analysis, we calculate the energy spectrum of the oscillating pollen tube, and discuss the resonant frequency problem of growth rate oscillations. We also outline a descriptive model for cell wall thickness fluctuations associated with small, yet regular variations (~ 0.01 MPa) observed in turgor pressure. We propose that pressure changes must lead to the sliding of wall layers, indirectly resulting in a wave of polarization of interlayer bonds. We conclude that pollen tube wall thickness may oscillate due to local variations in cell wall properties and relaxation processes. These oscillations become evident because of low amplitude/high frequency pressure fluctuations δP being superimposed on turgor pressure P. We also show that experimentally determined turgor pressure oscillates in a strict periodical manner. A solitary frequency f0 ≈ 0.066 Hz of these (~ 0.01 MPa in magnitude) oscillations for lily pollen tubes was established by the discrete Fourier transform and Lorentz fit.

Special Solutions to the Ortega Equation

The previously established augmented growth equation (Cosgrove, Plant Physiol 78:347–356, 1985; Ortega, Plant Physiol 79:318–320, 1985), suitable for description of pressure relationships in the growing plant cell, is revised with respect to the inclusion of changing cell wall properties hitherto represented by two constants, Φ and ε, connected with viscoelastic behavior. This phenomenological equation in the modified form is capable of appropriate description of volumetric extensibility, growth rate, and pressure changes in growing plant cells. This concerns deposition of new material in the polymer cell wall intercalation process, but it can also be used successfully for induced cell wall loosening, for example, by expansin EXPA (EXPB) proteins. In this context, a specific shape of the proposed equations, armed with a small number of physiologically explained parameters, opens up an experimental perspective for determining vital numbers connected with interactions at the nanoscale (polymer bonds “dilution” of an extending cell wall), or even at the molecular level in the cell wall (calculating numbers proportional to the expansin molecule’s active surface area). A systematic survey of ready-to-use deterministic solutions originating from the Ortega equation, reporting on both reversible (elastic) and irreversible (plastic) features of a growing plant cell, is presented. These findings also provide a quantitative cytomechanical model able to account for the important role of mechanical properties of the cell wall in cellular growth processes. An important feature of the analytical approach is that all model equations, after calibrating on existing data, allow new results to be inferred without further experimental work.