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 (f ∝ √P) may deliver, after calibration, a new tool to estimate turgor pressure P from oscillation frequency f 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

Simple method to estimate cell wall extensibility coefficient by using only two cardinal numbers

In this short communication we consider the extensibility properties of the cell wall. This is accomplished by a heuristically motivated equation for the expanding volume of the cell. The experimentally determined characteristic time t0 and temperature T0 are the only numbers required for evaluating the effective yielding coefficient F(t, T) in the respective time and temperature domains

Chemical Potential‑Induced Wall State Transitions in Plant Cell Growth

The pH/T duality of acidic pH and temperature (T) action for the growth of grass shoots was examined in order to derive the phenomenological equation of wall properties for living plants. By considering non-meristematic growth as a dynamic series of state transitions (STs) in the extending primary wall, the critical exponents were identified, which exhibit a singular behaviour at a critical temperature, critical pH and critical chemical potential (μ) in the form of four power laws: f ( ) ∝ −1 , f ( ) ∝ 1− , g ( ) ∝ −2− +2 and g ( ) ∝ 2− . The indices α and β are constants, while π and τ represent a reduced pH and reduced temperature, respectively. The convexity relation α + β ≥ 2 for practical pH-based analysis and β ≡ 2 “meanfield” value in microscopic (μ) representation were derived. In this scenario, the magnitude that is decisive is the chemical potential of the H+ ions, which force subsequent STs and growth. Furthermore, observation that the growth rate is generally proportional to the product of the Euler beta functions of T and pH, allowed to determine the hidden content of the Lockhart constant Ф. It turned out that the pH-dependent time evolution equation explains either the monotonic growth or periodic extension that is usually observed—like the one detected in pollen tubes—in a unified account

Extracellular ionic fluxes suggest the basis for cellular life at the 1/f ridge of extended criticality

The criticality hypothesis states that a system may be poised in a critical state at the boundary between different types of dynamics. Previous studies have suggested that criticality has been evolutionarily selected, and examples have been found in cortical cell cultures and in the human nervous system. However, no one has yet reported a single- or multi-cell ensemble that was investigated ex vivo and found to be in the critical state. Here, the precise 1/f noise was found for pollen tube cells of optimum growth and for the physiological (“healthy”) state of blood cells. We show that the multi-scale processes that arise from the so-called critical phenomena can be a fundamental property of a living cell. Our results reveal that cell life is conducted at the border between order and disorder, and that the dynamics themselves drive a system towards a critical state. Moreover, a temperature-driven re-entrant state transition, manifest in the form of a Lorentz resonance, was found in the fluctuation amplitude of the extracellular ionic fluxes for the ensemble of elongating pollen tubes of Nicotiana tabacum L. or Hyacintus orientalis L. Since this system is fine-tuned for rapid expansion to reach the ovule at a critical temperature which results in fertilisation, the core nature of criticality (long-range coherence) offers an explanation for its potential in cell growth. We suggest that the autonomous organisation of expansive growth is accomplished by self-organised criticality, which is an orchestrated instability that occurs in an evolving cell

Chemical potential evidence for phase transitions in magnetic and superconducting compounds and alloys

We announce that all phase transitions (induced by temperature or concentration) including structural ones and transitions between metastable or "exotic" states can be detected by the chemical potential critical behaviour, as well as, from the average occupation numbers of the electronic system (critical electron redistribution)

Modified Bohm's theory for abstruse measurements: application to layer depth profiling by Auger spectroscopy

Modified Bohm formalism is applied to solve a problem of abstruse layer depth profiles measured by the Auger electron spectroscopy technique in real physical systems, i.e., the desorbed carbon/passive layer on NiTi substrate and the adsorbed oxygen/surface of NiTi alloy. It is shown that abstruse layer profiles may be converted to real layer structures using the modified Bohm theory, where the quantum potential is due to an Auger electron effect. It is also pointed out that the stationary probability density predicts multilayer structures of abstruse depth profiles caused by carbon desorption and oxygen adsorption processes. The criterion for a kind of break between the physical and unphysical multilayer systems was found. We have concluded that the physics is also characterized by the abstruse measurement and the modified Bohm formalismComment: 6 pages, 4 figure

Derivation of the formula for the filtration coefficient by application of Poiseuille's law in membrane transport

On the basis of Kedem-Katchalsky equations a mathematical analysis of volume flow (Jv) of a binary solution through a membrane (M) is presented. Two cases of transport generators have been considered: hydrostatic (Dp) as well as osmotic (DP) pressure difference. Based on the Poiseuille's law we derive the formula for the membrane filtration coefficient (Lp) which takes into account the membrane properties, kinetic viscosity and density of a solution flowing across the membrane. With use of this formula we have made model calculations of the filtration coefficient Lp and volume flow Jv for a polymer membrane in the case when the solutions on both sides of the membrane are mixed

Chemical potential derivative as hallmark for phase transitions

We study antiferromagnetic properties of the two-band extended s— f model with fluctuating valence in the context of two mutually bound new effects of chemical potential critical behaviour, as well as of critical electron redistribution. In order to exemplify both phenomena we build phase diagrams of the system displaying the dependence of the critical Neel temperatures (TN) of the system versus 4f (5f) level positions. The phase diagram consists of two different areas corresponding to antiferromagnetic and paramagnetic phases. We plot the magnetizations and the correlation functions of the system as functions of temperature. Next, we investigate the temperature dependence of the relative average occupation numbers Δn f( d) and the chemical potential ΔA for a given 4f (5f)" level position Ef. Plotting this quantities along the Ef cross-section lines we observe small (of the order of 10 -4 -10 -3 ) but well localized kinks exactly at the Neel temperature TN. Last but not least, we plot the first derivative of the chemical potential ,wdT mhiacμyh t uars/n iN tod suht otTwo sb eclearly visible jumps at very accurate and sensitive (auxiliary) tool to find critical temperatures of the considered system. Moreover, we plot the difference μAF — μPARA where we subtract a chemical potential value of a reference paramagnetic sample from the actual value of the antiferromagnetic system. Also in this case we report the observation of discontinuous change in slope at TN. Our observations can be extended to point out to a new practical possibility of how to find experimentally the critical temperatures of the antiferromagnetic systems exclusively from the chemical potential measurements. We expect that the same type of measurement, according to our recent and present results, would also apply to all types of critical phenomena in real solids