Empowering roots-Some current aspects of root bioenergetics.

Roots of higher plants provide the shoot with nutrients and water. In exchange, they receive photosynthates, which serve both as energy source and building blocks for maintenance and growth. While studies in plant bioenergetics used to focus on photosynthesis, several more recent findings also aroused or renewed interest in energy conversion and allocation in roots. Root building costs were identified as a long-undervalued trait, which turned out to be highly relevant for stress tolerance and nutrient use efficiency. Reduced building costs per root length (e.g., by aerenchyma formation or by increasing the cell size) are beneficial for exploring the soil for nutrient-rich patches, especially in low-input agrosystems. Also, an apparent mismatch was frequently found between the root energy budget in the form of the ATP pool on the one side and the apparent costs on the other side, particularly the costs of membrane transport under stress conditions, e.g., the Na+ detoxification costs resulting from Na+ sequestration at the plasma membrane. Ion transport across the plasma membrane (and also endomembranes) is coupled to the proton motive force usually believed to be exclusively generated by H+ ATPases. Recently, an alternative mechanism, the biochemical pH clamp, was identified which relies on H+ formation and binding in the apoplast and the cytosol, respectively, driven by metabolism (so-called active buffering). On this background, several aspects of root bioenergetics are discussed. These are (1) root respiration in soil, with a critical view on calorimetric vs. gas exchange measurements; (2) processes of energy conversion in mitochondria with a special focus on the role of the alternative oxidases, which allow adjusting carbon flow through metabolic pathways to membrane transport processes; and (3) energy allocation, in particular to transport across the plasma membrane forming the interface to soil solution. A concluding remark is dedicated to modeling root bioenergetics for optimizing further breeding strategies. Apparent "energy spoilers" may bestow the plant with a yet unidentified advantage only unfolding their beneficial effect under certain environmental conditions.

Strong Emergence in Biological Systems: Is It Open to Mathematical Reasoning?

Complex, multigenic biological traits are shaped by the emergent interaction of proteins being the main functional units at the molecular scale. Based on a phenomenological approach, algorithms for quantifying two different aspects of emergence were introduced (Wegner and Hao in Progr Biophys Mol Biol 161:54-61, 2021) describing: (i) pairwise reciprocal interactions of proteins mutually modifying their contribution to a complex trait (denoted as weak emergence), and (ii) formation of a new, complex trait by a set of n 'constitutive' proteins at concentrations exceeding individual threshold values (strong emergence). The latter algorithm is modified here to take account of protein redundancy with respect to a complex trait ('full redundancy'). Irreducibility is considered a necessary and sufficient criterion for strong biological emergence; if one constitutive protein is missing, or its concentration drops below the threshold the trait is lost. A definition based on 'unpredictability' is dismissed, because this criterion is irrelevant for the evolution of a complex trait, and apparent unpredictability may rather reflect our basic deficits in understanding unless we can provide an unequivocal proof for it. The phenomenological approach advocated here allows to identify hidden rules according to which strongly emergent traits may be organized. This is of high value for understanding the evolution of complex traits which seems to require the saltational advent of all constitutive proteins 'in one turn' to arrive at a functional trait providing for an improved fitness of the organism. Rather than being a purely random process, it may be guided by fundamental structural principles.

Biochemical and biophysical pH clamp controlling Net H+ efflux across the plasma membrane of plant cells.

P-type H+ ATPases mediate active H+ efflux from plant cells. They generate a proton motive force across the plasma membrane, providing the free energy to drive the transport of other solutes, partly by coupling to H+ influx. Wegner & Shabala (2020) recently suggested that passive H+ influx can exceed pump-driven efflux due to 'active buffering', that is, cytosolic H+ scavenging and apoplastic H+ generation by metabolism ('biochemical pH clamp'). Charge balance is provided by K+ efflux or anion influx. Here, this hypothesis is extended to net H+ efflux: even though H+ pumping is faster than backflow via symporters and antiporters, a progressive increase in the transmembrane pH gradient is avoided. Cytosolic H+ release is associated with bicarbonate formation from CO2 . Bicarbonate serves as substrate for the PEPCase, catalyzing the reaction from phosphoenolpyruvate to oxaloacetate, which is subsequently reduced to malate. Organic anions such as malate and citrate are released across the plasma membrane and are (partly) protonated in the apoplast, thus limiting pump-induced acidification. Moreover, a 'biophysical pH clamp' is introduced, that is, adjustment of apoplastic/cytosolic pH involving net H+ fluxes across the plasma membrane, while the gradient between compartments is maintained. The clamps are not mutually exclusive but are likely to coexist.

A quantitative approach relating emergent features of complex traits to protein expression.

Linking complex, multigenic traits to protein activity is an important challenge in current biology, including applications in the medical sciences, agriculture, or forestry. Two simple algorithms are presented here to establish that link. The first one describes synergistic interactions of n proteins in shaping a complex trait ('weak emergence') as opposed to a simply additive 'modular' contribution of these proteins. A coefficient κ is defined that allows to quantify the degree of emergent interaction. For cases of strong emergence a separate formalism is introduced, implying that a number of n proteins at concentrations exceeding individual threshold values are required to spontaneously form a new, complex trait. Threshold concentrations are allowed to vary, depending on the concentrations of the other constitutive proteins. The experimental effort is estimated to provide a corresponding database for applying both formalisms, including high-throughput phenomics, and manipulation of protein concentrations using the molecular toolbox. Future efforts will be directed to overcome current limitations of the models that ignore the dynamics of protein-trait relationships with time, and the importance of the spatial arrangement of proteins for emergent interaction.

Energy costs of salt tolerance in crop plants.

Agriculture is expanding into regions that are affected by salinity. This review considers the energetic costs of salinity tolerance in crop plants and provides a framework for a quantitative assessment of costs. Different sources of energy, and modifications of root system architecture that would maximize water vs ion uptake are addressed. Energy requirements for transport of salt (NaCl) to leaf vacuoles for osmotic adjustment could be small if there are no substantial leaks back across plasma membrane and tonoplast in root and leaf. The coupling ratio of the H+ -ATPase also is a critical component. One proposed leak, that of Na+ influx across the plasma membrane through certain aquaporin channels, might be coupled to water flow, thus conserving energy. For the tonoplast, control of two types of cation channels is required for energy efficiency. Transporters controlling the Na+ and Cl- concentrations in mitochondria and chloroplasts are largely unknown and could be a major energy cost. The complexity of the system will require a sophisticated modelling approach to identify critical transporters, apoplastic barriers and root structures. This modelling approach will inform experimentation and allow a quantitative assessment of the energy costs of NaCl tolerance to guide breeding and engineering of molecular components.

Biochemical pH clamp: the forgotten resource in membrane bioenergetics.

Solute uptake and release by plant cells are frequently energized by coupling to H+ influx supported by the proton motive force (pmf). The pmf results from a stable pH difference between the apoplast and the cytosol, with bulk values ranging from 4.9 to 5.8 and from 7.1 to 7.5, respectively, in combination with a negative electrical membrane potential. The P-type H+ ATPases pumping H+ from the cytosol into the apoplast at the expense of ATP hydrolysis are generally viewed as the only pmf source, exclusively linking membrane transport to energy metabolism. However, recent evidence suggests that pump activity may be insufficient to energize transport, particularly under stress conditions. Indeed, cytosolic H+ scavenging and apoplastic H+ generation by metabolism (denoted as 'active' buffering in contrast to the readily exhausted 'passive' matrix buffering) also stabilize the pH gradient. In the cytosol, H+ scavenging is mainly associated with malate decarboxylation catalyzed by malic enzyme, and via the GABA shunt of the tricarboxylic acid (TCA) cycle involving glutamate decarboxylation. In the apoplast, formation of bicarbonate from CO2 , the end-product of respiration, generates H+ at pH ≥ 6. Membrane potential is stabilized by K+ release and/or by anion uptake via ion channels. Finally, thermodynamic aspects of active buffering are discussed.

A pump/leak model of growth: the biophysics of cell elongation in higher plants revisited.

Current concepts of growth hydraulics in higher plants are critically revisited, and it is concluded that they partly fail to interpret the experimental data adequately, particularly in the case of hydroponics-grown roots. Theoretical considerations indicate that the growth rate in roots is controlled by the extensibility of the cell wall, excluding water availability (i.e. hydraulic conductance) as a major constraint. This is supported by the findings that the growth rate does not scale with turgor, and that no radial nor axial water potential gradients have been observed in the root elongation zone. Nevertheless, a water potential deficit ranging from -0.2 to -0.6MPa has repeatedly been reported for growing cells that by far exceeds the shallow trans-membrane water potential difference required for the uptake of growth water. Unexpectedly, growth was also shown to depend on the hydraulic conductance (LP) of the plasma membrane of root cells, even though LP should generally be too large to have an impact on growth. For leaves, similar observations have been reported, but the interpretation of the data is less straightforward. Inconsistencies associated with the current model of growth hydraulics prompt the author to suggest a revised model that comprises, in addition to a passive mechanism of water transport across the plasma membrane of growing cells mediated by aquaporins ('leak') a secondary active water transport ('pump'), in analogy to a mechanism previously demonstrated for mammalian epithelia and postulated for xylem parenchyma cells in roots. Water is hypothesised to be secreted against a trans-membrane water potential difference by cotransport with solutes (salts, sugars, and/or amino acids), taking advantage of the free energy released by this transport step. The solute concentration gradient is supposed to be maintained by a subsequent retrieval of the solutes from the apoplast and back-transport at the expense of metabolic energy. Water secretion tends to reduce the turgor pressure and retards growth, but turgor and, in turn, growth can be upregulated very rapidly independent from any adjustment in the osmolyte deposition rate by increasing LP and/or reducing secondary active water transport, e.g. when the root is exposed to mild osmotic stress, as confirmed by experimental studies.

Electroporation of DC-3F cells is a dual process.

Treatment of biological material by pulsed electric fields is a versatile technique in biotechnology and biomedicine used, for example, in delivering DNA into cells (transfection), ablation of tumors, and food processing. Field exposure is associated with a membrane permeability increase usually ascribed to electroporation, i.e., formation of aqueous membrane pores. Knowledge of the underlying processes at the membrane level is predominantly built on theoretical considerations and molecular dynamics (MD) simulations. However, experimental data needed to monitor these processes with sufficient temporal resolution are scarce. The whole-cell patch-clamp technique was employed to investigate the effect of millisecond pulsed electric fields on DC-3F cells. Cellular membrane permeabilization was monitored by a conductance increase. For the first time, to our knowledge, it could be established experimentally that electroporation consists of two clearly separate processes: a rapid membrane poration (transient electroporation) that occurs while the membrane is depolarized or hyperpolarized to voltages beyond so-called threshold potentials (here, +201 mV and -231 mV, respectively) and is reversible within ∼100 ms after the pulse, and a long-term, or persistent, permeabilization covering the whole voltage range. The latter prevailed after the pulse for at least 40 min, the postpulse time span tested experimentally. With mildly depolarizing or hyperpolarizing pulses just above threshold potentials, the two processes could be separated, since persistent (but not transient) permeabilization required repetitive pulse exposure. Conductance increased stepwise and gradually with depolarizing and hyperpolarizing pulses, respectively. Persistent permeabilization could also be elicited by single depolarizing/hyperpolarizing pulses of very high field strength. Experimental measurements of propidium iodide uptake provided evidence of a real membrane phenomenon, rather than a mere patch-clamp artifact. In short, the response of DC-3F cells to strong pulsed electric fields was separated into a transient electroporation and a persistent permeabilization. The latter dominates postpulse membrane properties but to date has not been addressed by electroporation theory or MD simulations.

A thermodynamic analysis of the feasibility of water secretion into xylem vessels against a water potential gradient.

A series of recent publications has launched a debate on trans-membrane water secretion into root xylem vessels against a water potential gradient, energised by a cotransport with salts (e.g. KCl) that follow their chemical potential gradient. Cation-chloride-cotransporter -type transporters that function in this way in mammalian epithelia were detected in root stelar cells bordering on xylem vessels. Using literature data on barley (Hordeum vulgare L.) seedlings, one study confirmed that K+ and Cl- gradients across stelar cell membranes favour salt efflux. Moreover, the energetic costs of putative water secretion into the xylem (required for maintaining ionic gradients) would amount to just 0.12% of the energy captured by photosynthetic C assimilation if transpirational water flow relied exclusively on this mechanism. Here, a detailed thermodynamic analysis of water secretion into xylem vessels is undertaken, including an approach that exploits its analogy to a desalinisation process. Water backflow due to the passive hydraulic conductivity of stelar cell membranes is also considered. By comparing free energy consumption by putative water secretion with (i) the free energy pool provided by root respiration and (ii) stelar ATPase activity, the feasibility of this mechanism is confirmed but is shown to depend critically on the plant's energy status.

The conductance of cellular membranes at supra-physiological voltages.

Membrane permeabilization by pulsed electric fields (electroporation), that is supposed to be caused by the formation of aqueous pores, is widely used in biomedicine and biotechnology. It is detected most precisely by measuring membrane conductance. When whole-cell patch-clamp experiments are used to screen a wide voltage range, poration becomes manifest by large currents elicited at extreme hyper-/depolarization. The slope conductance, G(slope), can be obtained from non-linear current-voltage relations by differentiation of the current-voltage curve. Alternatively, the chord conductance, G(chord), is defined as the slope of straight lines connecting each point on the current-voltage curve with the zero-current (reversal) potential on the voltage axis. Here, Boltzmann functions were fitted to plots of G(chord) versus voltage recorded on protoplasts from bright-yellow-2 tobacco cells. These plots are supposed to reflect transition from a non-porated to a porated membrane state. Consistently, G(chord) saturated at extremely negative and positive voltages at values well below those expected for a complete demolition of the membrane (half-maximum voltages: ~-332 mV and +294 mV, respectively). The slope factor allowed inferring the change in dipole moment associated with water intrusion into the bilayer. It was -6.19 10(-4) and 3.35 10(-4)C ∗ m ∗ mol(-1), respectively. Outside-out patches rendered similar results, but half-maximum voltages were shifted to more extreme voltages with respect to whole-cell experiments.

Root pressure and beyond: energetically uphill water transport into xylem vessels?

The thermodynamics of root pressure remains an enigma up to the present day. Water is transported radially into xylem vessels, under some conditions even when the xylem sap is more dilute than the ambient medium (soil solution). It is suggested here that water secretion across the plasma membrane of xylem parenchyma cells is driven by a co-transport of water and solutes as previously shown for mammalian epithelia (Zeuthen T. 2010. Water-transporting proteins. Journal of Membrane Biology 234, 57-73.). This process could drive volume flow 'energetically uphill', against the free energy gradient of water. According to the model, solutes released by xylem parenchyma cells are subsequently retrieved from the sap at the expense of metabolic energy to maintain the concentration gradient that drives the water secretion. Transporters of the CCC type known to mediate water secretion in mammalian cells have also been found in Arabidopsis and in rice. The mechanism proposed here for root pressure could also explain refilling of embolized vessels. Moreover, it could contribute to long-distance water transport in trees when the cohesion-tension mechanism of water ascent fails. This is discussed with respect to the old and the more recent literature on these subjects.

A critical evaluation of whole cell patch clamp studies on electroporation using the voltage sensitive dye ANNINE-6.

The patch clamp technique in the whole cell configuration is potentially a powerful tool to investigate electroporation (electric-field-induced membrane permeabilization). Membrane polarization beyond certain threshold voltages leads to a steep conductance increase either indicating field-induced pore formation or being due to patch clamp artifacts (seal resistance breakdown). Protoplasts derived from tobacco culture cell lines (Bright Yellow-2, BY-2; Virginia bright Italian-0, VBI-0) were stained with the voltage-sensitive dye ANNINE-6. After establishing the whole cell patch clamp configuration 50-ms command voltage (Ucomm) steps ranging from -500 mV to +500 mV were applied while simultaneously exposing protoplasts to light at 475 nm wavelength. Pulse-induced currents and fluorescence intensity (known to be linearly related to the trans-membrane voltage, Um) were recorded. Plotting fluorescence intensity against Ucomm revealed saturation of the curve at values<-300 mV and >+300 mV and close correlation with theoretical Um values calculated on the basis of membrane pore formation. For BY-2 and VBI-0 protoplasts ANNINE-6 voltage sensitivity was calculated to be -0.0014 mV(-1) and -0.0012 mV(-1), respectively. Voltage ramp experiments revealed cation-selectivity of field-induced pores. Anions are conducted poorly independent of their size. In conclusion, the patch clamp technique is validated as a useful tool in electroporation research.

Cation selectivity of the plasma membrane of tobacco protoplasts in the electroporated state.

Cation selectivity of the cellular membrane of tobacco culture cells (cell line 'bright yellow-2') exposed to pulsed electric fields in the millisecond range was investigated. The whole cell configuration of the patch clamp technique was established on protoplasts prepared from these cells. Ion selectivity of the electroporated membrane was investigated by measuring the reversal potential of currents passing through field-induced pores. To this end the membrane was hyper- or depolarized for 10ms (prepulse); subsequently the voltage was driven to opposite polarity at a constant rate (+40 or -40mV/ms, respectively). The experiment was started by polarizing the membrane to moderately negative or positive voltages (prepulse potential ±150mV) that would not induce pore formation. Subsequently, an extended voltage range was scanned in the porated state of the membrane (prepulse potential ±600mV). IV curves in the porated and the non-porated state (obtained at the same prepulse polarity) were superimposed to determine the voltage at which both curves intersected ('Intersection potential'). Using a modified version of the Goldmann-Hodgkin-Katz equation relative permeabilities to Ca(2+) and various monovalent alkali and organic cations were calculated. Pores were found to be fairly cation selective, with a selectivity sequence determined to be Ca(2+)>Li(+)>Rb(+)≈K(+)≈Na(+)>TEA(+)≈TBA(+)>Cl(-). Relative permeability to monovalent cations was inversely related to the ionic diameter. By fitting a formalism suggested by Dwyer at al. (J. Gen. Physiol. 75 (1980), 469-492) the effective average diameter of field induced pores was estimated to be about 1.8nm. Implications of these results for biotechnology and electroporation theory are discussed.

Using the multifunctional xylem probe for in situ studies of plant water and ion relations under saline conditions.

By insertion into an individual xylem vessel at the root base, the multifunctional xylem probe allows the monitoring of the xylem pressure, the radial electrical gradients in the root (the so-called trans-root potential, TRP), as well as the activity of a particular ion such as K(+) in the xylem sap of intact, transpiring plants. The biophysical and physiological significance of these parameters with respect to salt stress is briefly explained, and the assembly of the probe, the setup used for these measurements, and the experimental procedure are outlined in detail.

A patch clamp study on the electro-permeabilization of higher plant cells: Supra-physiological voltages induce a high-conductance, K+ selective state of the plasma membrane.

Permeabilization of biological membranes by pulsed electric fields ("electroporation") is frequently used as a tool in biotechnology. However, the electrical properties of cellular membranes at supra-physiological voltages are still a topic of intensive research efforts. Here, the patch clamp technique in the whole cell and the outside out configuration was employed to monitor current-voltage relations of protoplasts derived from the tobacco culture cell line "Bright yellow-2". Cells were exposed to a sequence of voltage pulses including supra-physiological voltages. A transition from a low-conductance (~0.1 nS/pF) to a high-conductance state (~5 nS/pF) was observed when the membrane was either hyperpolarized or depolarized beyond threshold values of around -250 to -300 mV and +200 to +250 mV, respectively. Current-voltage curves obtained with ramp protocols revealed that the electro-permeabilized membrane was 5-10 times more permeable to K+ than to gluconate. The K+ channel blocker tetraethylammonium (25 mM) did not affect currents elicited by 10 ms-pulses, suggesting that the electro-permeabilization was not caused by a non-physiological activation of K+ channels. Supra-physiological voltage pulses even reduced "regular" K+ channel activity, probably due to an increase of cytosolic Ca2+ that is known to inhibit outward-rectifying K+ channels in Bright yellow-2 cells. Our data are consistent with a reversible formation of aqueous membrane pores at supra-physiological voltages.

Sequential depolarization of root cortical and stelar cells induced by an acute salt shock - implications for Na(+) and K(+) transport into xylem vessels.

Early events in NaCl-induced root ion and water transport were investigated in maize (Zea mays L) roots using a range of microelectrode and imaging techniques. Addition of 100 mm NaCl to the bath resulted in an exponential drop in root xylem pressure, rapid depolarization of trans-root potential and a transient drop in xylem K(+) activity (A(K+) ) within ∼1 min after stress onset. At this time, no detectable amounts of Na(+) were released into the xylem vessels. The observed drop in A(K+) was unexpected, given the fact that application of the physiologically relevant concentrations of Na(+) to isolated stele has caused rapid plasma membrane depolarization and a subsequent K(+) efflux from the stelar tissues. This controversy was explained by the difference in kinetics of NaCl-induced depolarization between cortical and stelar cells. As root cortical cells are first to be depolarized and lose K(+) to the environment, this is associated with some K(+) shift from the stelar symplast to the cortex, resulting in K(+) being transiently removed from the xylem. Once Na(+) is loaded into the xylem (between 1 and 5 min of root exposure to NaCl), stelar cells become more depolarized, and a gradual recovery in A(K+) occurs.

Xylem ionic relations and salinity tolerance in barley.

Control of ion loading into the xylem has been repeatedly named as a crucial factor determining plant salt tolerance. In this study we further investigate this issue by applying a range of biophysical [the microelectrode ion flux measurement (MIFE) technique for non-invasive ion flux measurements, the patch clamp technique, membrane potential measurements] and physiological (xylem sap and tissue nutrient analysis, photosynthetic characteristics, stomatal conductance) techniques to barley varieties contrasting in their salt tolerance. We report that restricting Na(+) loading into the xylem is not essential for conferring salinity tolerance in barley, with tolerant varieties showing xylem Na(+) concentrations at least as high as those of sensitive ones. At the same time, tolerant genotypes are capable of maintaining higher xylem K(+)/Na(+) ratios and efficiently sequester the accumulated Na(+) in leaves. The former is achieved by more efficient loading of K(+) into the xylem. We argue that the observed increases in xylem K(+) and Na(+) concentrations in tolerant genotypes are required for efficient osmotic adjustment, needed to support leaf expansion growth. We also provide evidence that K(+)-permeable voltage-sensitive channels are involved in xylem loading and operate in a feedback manner to maintain a constant K(+)/Na(+) ratio in the xylem sap.

Nanosecond electric pulses trigger actin responses in plant cells.

We have analyzed the cellular effects of nanosecond pulsed electrical fields on plant cells using fluorescently tagged marker lines in the tobacco cell line BY-2 and confocal laser scanning microscopy. We observe a disintegration of the cytoskeleton in the cell cortex, followed by contraction of actin filaments towards the nucleus, and disintegration of the nuclear envelope. These responses are accompanied by irreversible permeabilization of the plasma membrane manifest as uptake of Trypan Blue. By pretreatment with the actin-stabilizing drug phalloidin, the detachment of transvacuolar actin from the cell periphery can be suppressed, and this treatment can also suppress the irreversible perforation of the plasma membrane. We discuss these findings in terms of a model, where nanosecond pulsed electric fields trigger actin responses that are key events in the plant-specific form of programmed cell death.