Equilibrium and Out-Of-Equilibrium Investigation of Proton Exchange and CuII and ZnII Complexation on Fungal Mycelium ( Trametes hirsuta )

This work presents potentiometric investigations of [mycelium/metal ion/water] complex systems and the development of a new model investigating the ion-mycelium-fluid interactions. Since pH is a major parameter in soil ecology exhibiting large fluctuations, we proposed an improved equilibrium and also out-of-equilibrium potentiometric titration method in order to characterize the proton exchange behavior of the [mycelium/metal ion/water] system. Our model describes the dynamic relations and interactions within the soil complex subsystems consisting of fungal mycelium of Trametes hirsuta, water with or without metal ions (Cu and Zn). Equilibrium modeling based on potentiometric titrations can be well described using four mycelium related components which are active in the pH range studied. In addition, our equilibrium calculations show clear differences with respect to metal-mycelium interactions: Cu interacts with acidic and basic deprotonable sites, while Zn binds with neutral and basic deprotonable sites. Potentiometric outof-equilibrium (i.e., perturbed pH) characterization suggests that important fungal heterogeneous complexity may act as definite proton pressure entities under continuously perturbed soil conditions. Raman micro-spectroscopy was also used to characterize the [mycelium/metal ion/water] complex systems. Our results demonstrate that potentiometry is a useful tool (intermediate technology) in studying biological complex matrices, facing pH perturbations, as well as their interactions with metal ions.


Introduction
The complexity of natural systems, such as the biosphere, calls for the creation of new paths for research and knowledge development. 1,2][5][6] Here, we propose specific practice of model development relevant to biogeochemistry but also in a broader sense to transdisciplinary investigations.In order to do it, we will explore a physical-chemical model description of a specific complex soil subsystem -[mycelium/metal ion/water]-and associated ubiquitous phenomena involving the proton exchange and metal interactions.
8][9] A system can be considered alive when it is able to transform external energy in an internal process of maintenance and production of its own constituents.1][12][13] The branch-like mycelium communities crucially contribute to plant water and nutrient uptake, organic matter decay and mineral transformation, all of which participate in the soil formation processes in geological timescales.][12][13][14][15][16] The somatic macro-structure of fungi (i.e., hypha) is composed of tubular cells.The hyphal cell wall is made of structural fibrillar polymers (mainly chitin, chitosan or glucans) that provide rigidity and matrix sub-systems (mannoproteins, glucans and uronic acids) that cross-link the fibrillar components and coat the structural polymers.15,16 Some other chemical characteristics will be presented below in the discussion section.The first important remark is the extensive heterogeneity in the make-over and organization of fungal mycelium.][17] One of the remarkable characteristics of fungal activity is its relations with metal ions.Increasing literature describes the capacity of fungi to bind, transport, precipitate and transform metal ions (toxic or bio-essential, depending on the local concentrations and the type of metals) in natural and artificial environments (e.g., chemical reactors and remediation or waste water treatments).][20][21] In a recent review on biosorption and related research, Michalak et al. 22 remarked that "pH is one of the key factors that influences not only dissociation of sites, solution chemistry of metal ions, hydrolysis, complexation by organic and/or inorganic ligands, redox reactions, precipitation, but also strongly influences the speciation and the biosorption affinity of metal ions".Even though potentiometry has been classically used to study physical chemical properties of a wide range of complex living organisms, we propose here to push forward its application by combining systemic conceptions and new data interpretation methods.Indeed, we couple classical potentiometric titration with out-of-equilibrium pH responses to gain insights into the behavior of fungal system as a function of pH and, in the present work, its interactions with Zn II and Cu II .

Complex system model
The procedure began with the cultivation of the ubiquitous basidiomycete fungi species Trametes hirsuta, a dead wood degrader (Figure 1).In the laboratory, small pieces of the fungi fruiting body were placed in sterilized Petri-dishes containing agar-gel (3% in fresh water) growth media.After one week of growth, the mycelium was transferred to 250 mL erlenmeyer flasks containing 100 mL of a sterilized liquid cultivation media: potato extract (filtered solution of cooked potato, 200 g L -1 ) and brown sugar (4%, m/v).After two weeks of growth period at room temperature, aliquots of liquid growth medium were examined with a fluorescent and optical microscope to ensure for the purity of our fungal culture.Fungal mycelia were stained using wheat germ agglutinin (WGA, Aldrich) which has a high specificity for chitin. 23No bacteria were detected and a strong fluorescent signal was detected on each hypha observed (Figure 1).The mycelium was then collected; the growth media was thoroughly washed with reverse osmosis water and dried at 35 °C for 72 h.The  23 and photographs of the basidiome (fruiting body) of the sampled specimen of Trametes hirsuta.Vol. 27, No. 1, 2016   dehydrated mycelium was then gently ground in an agate mortar and stored in a sterilized Petri-dish placed in a desiccator (the mycelium biomass was shown to be viable for at least 3 months).The resulting mycelium biomass was then submitted to potentiometric titration perturbation and spectroscopic investigations as described below.

Potentiometric titrations
Before titration, the potentiometric system (using Metrohm combined glass electrode) was calibrated by titrating 40 mL of a standard 0.01016 mol L -1 HCl (ionic strength 0.1 mol L -1 KCl) solution with a standard 0.1151 mol L -1 CO 2 -free NaOH solution in a 100 mL potentiometric cell, maintained at 25 °C with a circulating water bath, flushed with water-saturated N 2 gas (N 2 was bubbled twice in a 0.05 mol L -1 NaOH solution) and stirred vigorously with a magnetic stirring bar.The results from calibration titrations were compared with theoretical values (calculated for 40 mL of 0.01016 mol L -1 HCl titrated by 0.1151 mol L -1 NaOH) using Best7 software and presented a small error (s fit < 0.03) and an accurate slope (-59.1 mV pH unit -1 ). 24,25he potentiometric titrations of the mycelium of Trametes hirsuta were performed as follows.A fraction of 108 mg of mycelium was placed in the potentiometric cell with 40.0 mL of degassed ultra-pure water (Milli-Q) containing 0.1 mol L -1 KCl.The system was left to stabilize during 1 h under constant N 2 flow at 25 °C and continuous stirring.After stabilization at pH 6.7, the system was acidified to pH 3 with 0.8 mL of 0.1019 mol L -1 HCl.The potentiometric titration began from pH 3 to pH 10 by sequential addition of 0.05 mL aliquot of 0.1151 mol L -1 CO 2 -free NaOH using a precision (0.01 mL) manual burette (Gilmont 2 mL).After each base titrant addition, the pH stabilization kinetics was monitored from the aliquot addition initial time to a maximum of 24 min.The pH stabilization kinetic measurements at each point of the titration were used to further characterize the slow-proton exchange processes discussed below.
Similar procedures were repeated in the presence of dissolved Cu II or Zn II as follows.A fraction of 108 mg of mycelium biomass was left to stabilize during 30 min in 24 mL of water containing 0.298 g of KCl (with a final concentration of 0.1 mol L -1 in a total initial volume of 40.8 mL).After the initial stabilization period, 4 mL of 1001 mg L -1 standard solution of Cu II or Zn II (Merck, in 0.5 mol L -1 HNO 3 ) was added and immediately followed by the addition of 12.8 mL of 0.1151 mol L -1 CO 2 -free NaOH (initial metal ion concentration of ca.1.5 mmol L -1 in 40.8 mL).Then the very same sequential titration and kinetic out-of-equilibrium monitoring procedure were performed.Blank titrations with Cu II or Zn II were also conducted under the same conditions and no significant out-of-equilibrium evolution was observed (pH stabilization occurs in less than 1 min for most of the studied pH ranges).
Inductively coupled plasma optical emission spectrometry (ICP-OES) was also performed using a Varian Liberty instrument in order to measure the concentration of Cu II and Zn II in solution/suspension phase.For each pH unit from 2 to 10, a 1.05 mL suspension aliquot was filtered from [metal ion/water] and [mycelium/metal ion/water] systems through a 0.2 µm cellulose acetate membrane, and diluted 20 times with 0.5 mol L -1 HNO 3 for further analysis.

Raman scattering
Raman confocal micro-spectroscopy was performed using a LabRAM HR Evolution-Horiba Scientific instrument operating a 532 nm green laser and using a long working distance objective 50X in order to collect Raman spectra of the fungi in suspensions with and without metal ions ([mycelium/metal ion/water]) collected from potentiometric titration experiments at pH 7 and further analyzed in glass slides.

Equilibrium modeling
We propose a potentiometric approach to explore the experimental behavior of the complex soil subsystem model, the fungal mycelium biomass, under perturbed conditions (in terms of pH and also in the presence of metal ions).The definition of the studied complex systems was made by simple components and interactions/relations.The fundamental distinction is made between the complex model system and water, such as for example [mycelium/water].Since the sensing tool is a combined pH glass-electrode, it is established that the present components: mycelium, metal ions and water, are observable in the potential perturbation and measurement.The first distinction to be done is the ionization of water as: and the relation: 10 -13.78 (2) That made possible the description of the differences in terms of [H + ]. 24,25 Coupled to it is the second distinction related to the complex system (S), according to: where K is the protonation equilibrium constant of S.
Components are expressed using bold letters and their related species, i.e., conjugate bases and conjugate acids are not bolded.Hence, for the complex system S, the associated species are noted "S" and "H + S".Equations 3a and 3b are at the core of the out-of-equilibrium characterization (see equations 12-15) and are extended by further distinctions.
In the case of [mycelium/water] system the conjugate bases S and conjugate acids H + S can be defined as: where S i and H + S i are, respectively, the i th component conjugate bases and conjugate acids that compose the complex system S, and x S i and x H + S i are their respective mole fractions.In the study of [mycelium/water] complex system, four components i (A, B, C and D) give us the best fits to the experimental titration curves (see Equilibrium chemical modeling sub-section in Results and Discussion).
The four components have the same property structure for instance, for component A: with: and similarly for components B, C and D, where We can then define the characteristics of the complex model in the presence of metal ions, Cu II or Zn II , or simply metal ions M. As M is an acid, it is expected to consume base titrant as: where the β values are the conditional overall stability constants for the proton exchange of M. In the same way, the acid M can also interact with the mycelium components.If we represent the four conjugate bases A, B, C and D of the four mycelium components as generic ligands "L", we can propose the following possible reactions: The set of equations 8a to 8d define that the components of the mycelium are able to form the complex ML, the protonated complex MH + L and the deprotonated complexes M(H + ) -1 L and M(H + ) -2 L. In summary, the model proposition give rise to the following 26 possible species for [mycelium/Cu II /water] or [mycelium/Zn II /water] complex systems: A, B, C, D, Using Best7 software, 25 these 26 species and their relevant associated reactions (presented by the adequate quotients in Table 2 and equations 1, 2, 6, 7 and 8) were used to fit the experimental titration curves of the simple blank systems [water], [Cu II /water] and [Zn II /water] and those of the complex systems [mycelium/water], [mycelium/Cu II /water], [mycelium/Zn II /water].Brackets emphasize the studied systems as whole complexes and the term "water" may be omitted during the text, when convenient.
The Best7 software sequentially solves the following equation: 27, No. 1, 2016   (where T i is the total concentration of the i th component in mol L -1 , [R r ] is the concentration of all reactant r that compose species j, and e ij is the stoichiometric coefficient of each reactant r in the corresponding equilibrium equation for all components i and their related species j, at each point of the titration) in order to minimize the difference between measured and calculated pH at each point of the titration. 25n the case of [mycelium/Cu II /water] system, for example, the components present are A, B, C, D, Cu II and H + and the related equilibrium are described in equations 1, 2, 6,  7, 8 and Table 2.In the discussion section, we will explore the coherence of the equilibrium modeling and show why it can be considered as a powerful investigation tool for the study of complex systems as suggested by Martell and co-workers 24 and as also suggested herein.

Out-of-equilibrium characterization
Besides the equilibrium modeling, we have also explored out-of-equilibrium processes related to pH perturbation caused by the successive titrant additions.In other words, after each base addition, we monitored the perturbed pH response over time.When the titrant is added the majority of exchangeable protons are rapidly consumed (in the present case around 90% of total exchangeable protons are consumed in the first 30 s) but kinetically measurable residual proton exchange still occurs even 1 h after the titrant addition. 14,26Similar behavior was observed for humic acids and also for biotite. 27,28For biotite, the slow proton exchange reactions can reach quantitative proportions of total exchangeable protons; and in the case of humic substances, data are scarce in the literature but indicate that significant slow processes can take place in proton exchange phenomena. 27,28These slow-proton exchange processes provide us with special information about the studied system, notably in the present case, the way the biological heterogeneous complex system qualitatively responds to the titration perturbations.In what follows, we present the derivation of out-of-equilibrium physical-chemical model parameters.
Usually, when slow-proton exchange processes are observed in potentiometric titrations, the pH stabilization curves take the shape of an exponential decay approaching a pseudo-equilibrium pH, the final pH of each titration point. 14,29After the fast proton exchange reactions (that are faster than the technical possibility of kinetic measurement using traditional potentiometric apparatus), we begin to measure the slow-proton exchange reactions.It should be noted that these slow-proton exchange processes are specific of complex systems, such as biological samples, bio-mimetical complexes, humic substances, minerals, soil samples, etc., 14,24,26,[30][31][32][33][34] while not observable in simple systems, i.e., highly soluble low molecular weight organic acids (e.g., phthalic acid).
The differences of proton concentration between the initial kinetic pH and final pH measurement (pH final ), as presented in Figure 2a, were used to derive a first order slow-proton exchange as described below.Firstly, we obtained out-of-equilibrium slow-exchangeable proton amount, [H + ex ] (t -final) , at each time t of pH response as: (10)   where: Equation 10 is the calculation step in which we use the kinetic pH measurement (the values of pH at each time t) to obtain the proton concentration at time t, [H + ] t , and derive the slow-exchangeable proton concentration [H + ex ] (t-final) , which is the difference in proton concentration between time t and the time when the last pH measurement is taken, or [H + ] final (pH final in Figure 2).
Fitting the curve [H + ex ] (t -final) versus time with the following first-order rate law, gives the initial slow-proton exchange concentration, [H + ex ] t0 (which is a calculated concentration of exchangeable protons at t = 0), and the first-order rate constant, k, specific of each slow pH response after titrant addition (see Figure 2).
Using [H + ex ] t0 , the first order rate constant k and the parameters of equilibrium calculations (described in the previous section), component concentrations and conditional overall stability constants β, we can calculate (i) the equilibrium condition K, (ii) the out-of-equilibrium condition Q (at time t0) and (iii) the entropy production dS/dt related to the irreversible slow-proton exchange that was kinetically observed at each point of the titration.The equilibrium condition (index "eq") is determined by K (equation 3) using (i) the concentration of all conjugate bases and conjugated acids present in the system (calculated using the program Aqueous Solutions) 35 (ii) their respective molar fractions (equations 4 and 5) and (iii) the proton concentration, [H + ] final , at pH final .Conversely, the out-of-equilibrium condition (index "t0") is described by Q that is defined as: where: and: Equation 14 is the solution of a second order polynomial equation (i.e., -([H + ] t0 ) 2 + ([H + ] t0 )c + β OH -= 0) that is obtained by the substitution of the difference [H + ex ] (t -final) by the difference [H + ex ] t0 in equation 10 at t = t0.Then we can define [H + ] t0 as the modeled proton concentration (10 -pH t0 ) of the perturbed state t0.
Then, the last step is the calculation of entropy production dS/dt as: Equation 15 defines that the slow-proton exchange entropy production is proportional to affinity A, RT ln (K/Q), times the reaction rate dξ/dt, -k[H + ex ] t0 as described by Kondepudi and Prigogine,29 where R is the constant of gases 8.314 J mol -1 K -1 .For volume of 1 L, dS/dt is given in J K -1 s -1 .These values were calculated for the kinetic dataset of all points of the potentiometric titrations and are presented below.

Raman microspectroscopy and emission spectrometry
Raman scattering measurements well demonstrate the complexity of the mycelium system.Tentative signal attributions (according to literature) [36][37][38][39] are listed in Table 1. Figure 3a illustrates that fungal biochemical structure is not strongly affected by the presence of high metal concentrations (c.a.1.5 mmol L -1 ) since the spectral pattern remains, in general, similar to the one observed in the absence of metals.However, a closer inspection of minor signals in Figure 3b indicates subtle shifts/changes in the scattering profile of the mycelium in the presence of Cu II and Zn II which may be related to specific interactions of metals with carboxylic, amino and phosphate groups at least, as proposed in our potentiometric investigations (see next section).We can speculate over some specific spectral changes in the presence of Cu II and/or Zn II at: (i) 900-1000 cm -1 , where we can observe a general hypsochromic shift for [mycelium/Zn II ] system in comparison to [mycelium] system, possibly related to metal-phosphate and/or metal-protein interactions; (ii) 1120 cm -1 , where a different spectral shape is observed for [mycelium/Cu II ] system, possibly related to metalprotein interactions; (iii) 1370 cm -1 , where a more intense peak is observed for [mycelium/Zn II ], possibly related to metal-nucleic acid (phosphate backbone) interactions and; (iv) 1625 cm -1 (left shoulder of major peak at 1654 cm -1 ), where significant differences are observed between [mycelium] and [mycelium/metal ion] spectra, mostly for Cu II , probably related to metal interactions with complex organization of protein-chitin-nucleic structures in the mycelium (see arrows in Figure 3b, see also Table 1).In addition, since the metal ions were obtained from a diluted nitric acid solution, it is possible to observe the presence of nitrate (N-O stretch) at 1050 cm -1 for the [mycelium/metal ion] spectra (see Figure 3b).It should be noted that the above tentative spectral observations are delicate and should be interpreted with great caution.Even so, Raman microspectroscopy can be considered as a powerful spectroscopic method for biogeochemical complex investigations, as observed in Figure 3.
Inductively coupled plasma optical emission spectrometry was also used as a complement to the main fungal/metal ion interactions potentiometric study.In Figure 4, it is observed that fungal complexing agents (proteins, oligopeptides, organic acids, phosphates, etc.) are probably, to a significant extent, free in solution.In the case of [mycelium/Cu II /water] system, we can observe that more than 50% of total Cu II is in suspension (as aqueous complexes with dissolved biomolecules or bound to < 0.2 µm fungal particles) even above pH 6 where without the presence of mycelium Cu II precipitates quantitatively.A similar effect is observed for [mycelium/Zn II /water].However, to a lesser extent and with some differences: at neutral pH, a lower concentration of soluble or suspended particle bound Zn II is observed in comparison with [Zn II /water] blank experiment.This behavior suggests that, at neutral pH, Zn II is complexed by fungal structures > 0.2 mm (ca. 10 to 20% of total Zn II at pH 7.7, Figure 4).In the following section, we propose that the quantitative formation of M(H + ) -2 insoluble precipitated systems (observed without the presence of mycelium) are replaced or substituted by M(H + ) -1 L (where L are mycelium-related ligands) complex systems, mostly at neutral pH.

Equilibrium chemical modeling
The use of the above presented theoretical system (modeling section) enables the investigation of the pH buffering capacity as an ecological relevant property.The perturbation patterns may have partial, but direct, relation with the behavior of this type of system, mycelium complex systems, in nature.From the curve of the [mycelium/water] system shown in Figure 5, we can observe that the major part of the buffering capacity (total of 1.34 mmol g -1 of mycelium, in accordance with literature for fungi) 14,19,20 is related to components D (39%, pK a 9.34) and A (28%, pK a 3.24).Components B (17%, pK a 4.61) and C (16%, pK a 7.02) represent the smaller part of the buffering capacity of the [mycelium/water] system.In recent work on dead fungi biomass of Trametes villosa the same pK a values (A, B, C and D) presented above were reported but with a smaller total buffering capacity of 0.75 mmol g -1 . 14Other  works on different fungal species present total buffering capacity values that vary from 0.81 to 3.87 mmol g -1 . 19,20or different bacteria species, Claessens et al. 40 presented total buffering capacity values varying from 0.14 to 1.77 mmol g -1 .The higher total buffering capacity values are found for humic acids which vary from 4.0 to 13.0 mmol g -1 . 28,41For the biotite mineral we found a value of 0.94 mmol g -1 . 27][33] This quantitative information may represent, in general terms, the contribution of soil subsystems to soils buffering capacity and note the importance of fungi and humic substances to soil stability.
In our present model, the components (A, B, C and D) and their respective deprotonation constants suggest the presence of a complex biological matrix composed by the usual fungal biopolymers and biomolecules such as carbohydrates, proteins, nucleic acids and (in)organic salts as observed in the Raman scattering measurements (Figure 3 and Table 1).All conditional stability constant values are listed in Table 2 and represented in Figure 6.From the curve of [Cu II /water] and [Zn II /water] we found that the major proton exchange contribution is due to the formation of the bis-deprotonated metal ion species, M(H + ) -2 presumably related to precipitates in accordance to ICP-OES measurements (Figure 4).From the titration curves of [mycelium/Cu II /water] and [mycelium/Zn II /water] (Figure 5), we observed new patterns that does not resembles the summation of separated (mycelium and metal ions alone) systems.This indicates substantial interactions between the metal ions and mycelium system.In Table 2 are listed the β ML constants of associated mycelium-metal interactions calculated using Best7 software.
Indeed, we have found that, in the case of the mycelium system in the presence of metal ions, fit is not obtained with metal complex formation constants (ML formation, equation 8a for β ML and Table 2) smaller than 10 4 which can be considered as relatively strong binding constants. 20,24n the case of [mycelium/Cu II /water] interactions, we observe an intense complexation distributed between components A, B and D with β ML formation constants around 10 6 (Table 2).For the [mycelium/Zn II /water] system, the formation constants are smaller, around 10 5 , but an important contribution is attributed to metal complexation with component C. Based on our results (calculated concentration and pK a values for species of A, B, C, D and related complex stability constants with Cu II and Zn II presented in Table 2), it is difficult to precisely identify the groups involved in the metal complexation, either at the cell wall or in the liquid phase.But one point should be remarked: the presence of carboxylic acids, phosphates and amino groups are considered important in the complexing reactions of the [mycelium/metal ion/water] systems.
Combinations between carboxylic acids (and activated organic acids) that present strong acidity are possible candidates for the general component A. 24 Ionic molecules, oligopeptides and proton releasing systems (e.g., proton ATPase) can also participate as component A and contribute to the acidic buffering capacity of fungi. 10,15Component B is consistent with reported values of carboxylic acids.Component D can represent amine groups in the mycelium complex systems.Component C can be an average representation of more complex subsystems such as enzyme sites, mixed-chemical-group binding sites and also phosphate neutral deprotonation related processes. 24,42As already stated, the four proposed components are in good accordance with the possible chemical components tentatively assigned in the Raman scattering investigation (Figure 3 and Table 1).Although there is relatively good correspondence between our stability constant values for protonation reactions and the ones for known functional groups (i.e., COOH, −NH 2 or HPO 4 2-, etc.), the representation of the [mycelium/water] system, by four components A, B, C and D, should be interpreted as heterogeneous complex distribution, most probably between soluble organic compounds excreted actively or not by the fungi and the heterogeneous cell wall surface binding sites.
Despite the presence of a large diversity of possible metals-mycelium interactions, we found a clear difference between the behavior of [mycelium/Cu II /water] and Cu II ] and [mycelium/Zn II ]) lines (calculated average error function s fit < 0.04). 25Water (standard 0.01016 mol L -1 HCl titration) curve was presented in order to provide qualitative comparison with the studied complex systems.[mycelium/Cu II /water] and (c) [mycelium/Zn II /water] complex systems calculated with Aqueous Solutions software. 35In graph (a) black lines represent the dominant component D while the other components are represented by different gray lines.In graph (b) and (c), metal complex species are represented by black lines while free metal, metal hydroxides and free ligand species by gray lines.Vol. 27, No. 1, 2016   [mycelium/Zn II /water] systems.In the presence of metal ions, the fungi components may occupy at least one metal coordination position (species ML, MH + L and M(H + ) -1 L) while the formation of bis-deprotonated complex species (M(H + ) -2 L) is not significant.In contrast, in single metal, [metal ion/water] system, titrations, bis-deprotonated species (M(H + ) -2 ) are formed quantitatively, as observed in Figure 4. Figure 6 shows the species diagram of the calculated models for the [mycelium/water] and [mycelium/ metal ion/water] studied systems.Cu II tends to interact predominantly with carboxylic acids (A, B) and amine groups (D) while Zn II interacts mostly with amine groups (D) and with other combination of deprotonable groups, mixed sites and/or phosphate groups, represented in our model by the component C (see Figure 6).
The stability constants in Table 2 indicate stronger binding of Cu II to the mycelium of Trametes hirsuta compared to Zn II as previously observed for other fungi, and bacteria. 18,20,21,39Using potentiometric titration methods, Sanna et al. 20 presented metal ion-binding constants (Cu II and Zn II ) in the range of 10 5 for living Trichoderma viride fungal biomass, and values around 10 7 for Cu II -chitin system. 20In studies of metal biosorption on Penicillium chrysogenun fungal biomass, Niu et al. 18 found bigger binding affinity for Cu II than for Zn II .In the case of the bacteria Shewanella putrefaciens, Claessens et al. 39 found Cu II and Zn II binding constants of 10 7.3 and 10 5.4 , respectively, as also observed herein (Table 2).Using several different Petri-dish microcosm experiments regarding Cu II and Zn II interactions with fungi (qualitatively investigated through syncrotron techniques), Fomina et al. 21mphasize that fungal-metal complexation processes, of both Cu II and Zn II , are dominated by the action of carboxylic and phosphate (organic and inorganic) chemical groups related to fungal structure/organization.These authors also suggest that metal complexation by amine groups in fungal systems may be important in the metal biotransformation which may be followed by other phenomena such as metal ion immobilization in cell wall or precipitation as metal phosphates, oxalates, carbonates or oxides. 21In a recent study on mosses, González and Pokrovsky 43 showed that the biosorption of Cu II (ca.90%) is more effective than the biosorption of Zn II (ca.75%) and that for both metal ions the adsorption is completed in less than 10 min, but more complex absorption processes may occur after this initial period.Hence, it is coherent to expect that all these processes may take longer time periods, as discussed in the following out-of-equilibrium section.
The results of our equilibrium investigations are also coherent with the low toxicity of Zn II towards fungi, suggesting that neutral pH deprotonable groups, related to component C, may play a significant role in key pH-dependent biological processes (such as the absorption of the bio-essential Zn II ) in the studied fungi. 11,24,42t is interesting to remark that four weeks after our potentiometric experiments, fungal growth was observed  6).The present results are unique and the details suggest that modeling can be used, at least, as qualitative reference in the literature for describing living fungi macroscopic physical-chemical properties.
Out-of-equilibrium investigation In the modeling section, we demonstrated how to derive the slow-proton exchange entropy production of the [mycelium/water] and [mycelium/metal ion/water] systems in relation to titrant perturbation during potentiometric titrations.Out-of-equilibrium states can be defined by their stability as a function of time.While (in linear out-of-equilibrium thermodynamics) stable systems maintain slow out-of-equilibrium processes, unstable systems, upon perturbations, evolve quickly to a new pseudo-equilibrium state.Since change is driven by difference (negentropy or energy input), we use entropy production as a fundamental parameter to investigate the stability of the complex [biological/metal ion] studied systems.As pointed by Prigogine and co-workers, 2,29 out-of-equilibrium properties, such as entropy production of complex systems (relevant, in a transdisciplinary point of view, for agroecology) 1,7,8 are special characteristics related to evolution and stability of the same complex systems under perturbed conditions.It is important to note that here we are dealing with linear out-of-equilibrium thermodynamics and that several complex conditions in nature are often observed as non-linear phenomena. 1,2,11,16,29ven though, we can expect that linear out-of-equilibrium thermodynamic information (which are also important in ecological/nature processes and homeostasis) may be useful in order to obtain some abstract representation of the evolution properties of the fungal/metal ion systems.
During the out-of-equilibrium measurements, from acidic to basic pH the slow rate constants k decreases while the slow-proton exchange concentration [H + ex ] t0 increases (Figures 7 and 8).This observed patterns in the perturbed states of the [mycelium/water] and [mycelium/metal ion/ water] complex systems (Figures 7 and 8) suggest that subsystems of higher heterogeneity (e.g.mostly proteins and chitin complexes) exerts an increasing slow proton pressure/buffering capacity as pH becomes more basic.Under acidic pH conditions, slow-proton exchange reactions are faster than at basic pH (Figures 7a).With the presence of metal ions, the slow-proton exchange becomes measurable at lower pH (i.e., starting at pH 4) while, in the absence of metal ions, it is only measurable above pH 4.6 (see inset Figure 7b), as a result of general Lewis acid properties of metal ions.Figure 8 suggests that amine groups (i.e., component D), or basic pH deprotonable groups, in different organized structures (mainly protein and chitin complexes) are important slow-proton exchangers at basic pH.Under acidic pH conditions, there is also some significant slow proton exchange, however to a much lesser extent.At neutral pH, the slow proton exchange is not as high (in moles) as in the basic pH region but we remark that, since pH is a logarithmic value, the observed slow processes in the neutral pH region (which are not negligible, see Figure 2) may indicate important complex interactions that regulate biological processes (it is to say that slow stabilization curves are also significant at neutral pH as observed in Figure 2).In the presence of metal ions, the shape of the slowproton entropy production curve (Figure 8) is generally the same (i.e., increasing entropy production as pH becomes basic).However, we can observe that Cu II , in the [mycelium/Cu II /water] system, promotes an intense enhancement of slow-proton exchange processes at a lower pH (above pH 7, Figure 8), which is much more significant in comparison to the [mycelium/Zn II /water] system and even further in comparison to [mycelium/water] system.We believe that this pattern reflect the stronger affinity of Cu II (compared to Zn II ) for important complex heterogeneous basic pH deprotonable sites (dominated by amine groups in proteins and also chitin, Figures 7b and 8), at least in the time scale studied here.
It is interesting to note that in the case of the [mycelium/ Zn II /water] system at neutral pH, the measurable slow pH stabilization curves evolve in the acidic-to-basic sense (see small-magnitude negative values of [H + ex ] t0 in the inset of Figure 7b between pH 6 and 8 for the [mycelium/Zn II / water] system), which is in opposition to basic-to-acid out-of-equilibrium slow evolution of the majority of the pH considered here (as shown in Figure 2).This acidicto-basic evolution of the [mycelium/Zn II /water] system at neutral pH is also accompanied by much larger k values (Figure 7a).This suggests that a larger contribution of fast (usually non-monitorable) proton exchange may become observable as slow-proton exchange processes.This unusual inversion pattern was also observed for out-ofequilibrium response at discrete basic pH conditions for humic acids and biotite. 27,28ith the present study we can state that when mycelium is perturbed with base, it counter-reacts through active and/ or passive proton releasing reactions (acids of different strength and structure at different levels of organization, in membrane proteins, oligopeptides, etc.).The hyphal cell-wall and associated biomolecules (plus the released dissolved organic acids) form a complex three dimensional structure/organization that can present different level of accessibility to the perturbed water environment.Due to possible difference in diffusion coefficient, as shown by Kazakov et al.,26 the protons bound to dissolved organic acids, phosphates, oligopeptides, siderophores, etc. may be consumed first whereas the protons bound to protein cavities or inner cell organelles are expected to be consumed last, if consumed.We remark, as also pointed by Fomina et al. 21, that experimental studies (even being extremely informative) of all complex systems should be interpreted as partial models which may present differences both between the model experiments in parallel and in relation to natural conditions, i.e., in terms of metal ion sources (minerals or soluble, concentration etc.), fungal species, experimental/investigation time periods and temperature conditions, etc.
In terms of natural implication, we can hypothesize that the slow proton exchanges from mycelium may be dominant over fast proton exchange in natural soils due to a much more limited amount of free water compared to our potentiometric water-suspension experiments.These slow processes may also be more significant under colder conditions.Hence, we suggest that some similarity to the interaction patterns presented in Figures 6, 7 and 8 can be partially expected to occur in natural soils, provided significant fungal biomasses are present.
Finally, our results indicate that fungal systems can counter-balance (to a certain extent) soil basification.In contrast, other studies demonstrate that biotite, a phyllosilicate mineral, tends to prevent acidification while humic substances favor neutral pH stable conditions. 14,27,28,30,34In this regard, further investigations will provide the different characteristics (in relation to proton exchange and other important parameters such as redox properties) of the miscellaneous components and sub-components of complex ecological and soil systems under out-of-equilibrium conditions.We propose that the method presented herein can be considered as an interesting tool for the characterization of soils and their stability upon physical-chemical perturbations.

Conclusions
The potentiometric method presented in this study can serve as a useful tool for the investigation of different samples from natural complex systems, such as soils and soil subsystems.Using [mycelium/metal ion/water] complex model systems, selective interactions between fungi and metal ions are found to be coherent with the general [biological/inorganic ions] interaction properties.In summary the mycelium of Trametes hirsuta may interact with Cu II mainly through acids, weak-acids and weak bases while neutral pH deprotonable species remain rather unaffected.In the case of Zn II , mycelium neutral pH and weak-basic deprotonable species appear to be important metal complexing agents.
Furthermore, out-of-equilibrium slow-proton exchange investigation is proposed to reveal interaction patterns that may be related to the heterogeneous protein and chitin complexes characteristic of fungal mycelium.Complementary Raman spectroscopy and inductively coupled plasma optical emission spectrometry data presented good agreements with modeling and interpretation of potentiometric studies.7]9  will be respectively corrected by (9)   (15)

Figure 1 .
Figure 1.Confocal fluorescence microscopy of cultivated mycelium (coloration method is described in Bonfante-Fasolo et al.) 23 and photographs of the basidiome (fruiting body) of the sampled specimen of Trametes hirsuta.

Figure 2 .
Figure 2. Example of (a) out-of-equilibrium pH stabilization measurement from pH final of the previous titration point to pH final of actual titration point (passing through (i) fast and (ii) slow proton exchange) and (b) first order kinetic plot for the [mycelium/Cu II /water] system at pH final 7.27 (plot construction and derivation of [H + ex ] t0 and k are detailed in out-ofequilibrum modeling section).

Figure 5 .
Figure 5. Potentiometric titration curves for [mycelium/metal ion/water] combination systems.Experimental data are presented in light grey lines (Cu II , Zn II , water, [mycelium/Cu II ] and [mycelium/Zn II ]) while calculated values are presented in gray (Cu II , Zn II and water) and black ([mycelium/Cu II ] and [mycelium/Zn II ]) lines (calculated average error function s fit < 0.04).25 Water (standard 0.01016 mol L -1 HCl titration) curve was presented in order to provide qualitative comparison with the studied complex systems.

Figure 6 .
Figure 6.Species distribution diagrams for (a) [mycelium/water], (b)[mycelium/Cu II /water] and (c) [mycelium/Zn II /water] complex systems calculated with Aqueous Solutions software.35In graph (a) black lines represent the dominant component D while the other components are represented by different gray lines.In graph (b) and (c), metal complex species are represented by black lines while free metal, metal hydroxides and free ligand species by gray lines.

Figure 7 .
Figure 7. (a) Slow-proton exchange first order rate constant k and (b) slow-proton exchange concentration [H + ex ] t0 for the studied [mycelium/ metal ion/water] complex systems.The [mycelium], [mycelium/Zn II ] and [mycelium/Cu II ] complex systems are represented by black, gray and light gray lines.Positive [H + ex ] t0 values indicate irreversible proton flux from the [mycelium/meta ion] subsystem to the aqueous phase.Negative [H + ex ] t0 values indicate the opposite, water-to-[mycelium/meta ion], proton flux and/or the slow consumption of protons by the added strong base titrant, as observed for [mycelium/Zn II ] at pH 6.3-7.5 (see inset in b).

Figure 8 .
Figure 8. Slow-proton exchange entropy production (dS/dt) for out-of-equilibrium processes during titration for the [mycelium/metal ion/ water] complex systems.[mycelium], [mycelium/Zn II ] and [mycelium/ Cu II ] complex systems are represented by black, gray and light gray lines respectively.Entropy production values are normalized with respect to pH variation between sequential titration points (DpH -1 ) and mycelium mass (g -1 ).
meaning strongest acidity for conjugate acid H + A and weakest for H + D species.