There are key facts in calcification that derive straightforward from the laws of thermodynamics, and therefore must always be obeyed. The most basic concept is the second law of thermodynamics, stating that the entropy of an isolated system can never decrease (see Box 1). This law sets forth the condition for spontaneous chemical processes governed by the Gibbs expression (Gibbs, 1874–1878): DG < 0, where DG is the variation of the Gibbs free energy, which it is related to the entropy change. In this review we use often the term precipitation concerning the process of calcium phosphate solid formation from its free ions in a solution state. With this term we refer to its classic definition: “a relatively rapid formation of a sparingly soluble crystalline—or sometimes amorphous—solid phase from a liquid solution phase” (Karpiński and Jerzy Bałdyga, 2019). Thus, translating the Gibbs condition to the precipitation of ions from solutions or biological matrices, it turns out that the activity product of free ions in solution must by higher than the corresponding activity in the solid. This relationship, expressed in terms of supersaturation (S), characterizes the thermodynamic conditions for all spontaneous calcifications as S > 1 (Myerson et al., 2019), with no exceptions. Thus, this expression means that the precipitate will be formed only if the product of the activities of free ions in the fluid state is higher than the product of the activities of ions in the solid state given by the solubility product, K_sp; when S < 1, the solid will dissolve. Thus, the key point for determining whether MVC is likely to occur is to determine the activity of the free ions in the tissues that compose the medial layer. However, this is not a trivial task, given that there are many factors that affect the activities of free ions in a fluid, such as ionic strength, phosphate proton dissociation equilibria, the sequestration of free ions by ligands, the precipitation of different calcium phosphate solids, and the viscosity of the medium. Due to such high level of biological complexity, the available values of K_sp and other related thermodynamic constants needed for these calculations that have been derived from in-vitro conditions may be only approximates. In addition, it is important to realize that the thermodynamic condition for solid growth is related to ionic activities and not the ionic concentration. While the latter can be determined by chemical analysis, the former are far more difficult to determine due to the biological and the structural complexity of the medial layer. Concentrations and activities are related by the activity coefficient, γ(a = γ⋅ conc), which, in turn, is related to the ionic strength, I (see Box 2 and Table 1).

For a given ion concentration, ion activity decreases with the ionic strength. For example, for I = 0.15, the activity of the Ca²⁺ ion is reduced threefold with respect to the Ca²⁺ concentration, and the activity of the PO₄^3– ion decreases 10-fold. Such reductions ultimately prevent spontaneous crystallization in blood and, thus also, for example, invalidate the hypothesis that CKD- or ESRD-related hyperphosphatemia per se causes precipitations seen in MVC.

Calcium ions in aqueous solution are not totally free rather they are solvated with water (Zavitsas, 2005). In other words, they form a coordination sphere of water molecules. This coordination sphere is composed of an inner shell of six water molecules with strong binding energy and an outer shell of 0–6 water molecules with weaker binding energy. The strong hydration of calcium is an important factor in the crystallization of calcium salts from water. Actually, the detachment of water molecules from calcium ions occurring on a crystal surface before they are incorporated into the crystal lattice is often the rate-limiting factor in crystal growth kinetics (van der Voort and Hartman, 1991). This is the case, for example, in calcium oxalate crystallization, for which trihydrate and dihydrate salts are kinetically favored and precipitate earlier than the monohydrate polymorph that has lower solubility and higher thermodynamic stability (Grases et al., 1990).

There are three different phosphate ions derived from the dissociation of phosphoric acid (H₃PO₄): H₂PO₄^–, HPO₄^2–, and PO₄^3–. In aqueous solution produces several species of phosphate ions according to the following equilibria (Vega et al., 1994):

Their relative presence in a medium depends on the pH (Figure 1A). At the physiological pH = 7.4, the concentrations of H₂PO₄^–, HPO₄^2–, and PO₄^3– are 0.049, 0.95, and 1.08 × 10^–5, respectively. In solutions with a pH of 6.8, the concentrations change to 0.17, 0.83, and 0.27 × 10^–5, respectively. In solutions with pH of 7.6, the concentrations become 0.031, 0.97, and 1.71 × 10^–5. Thus, in this pH – range of 6.8–7.6, the variations of HPO₄^2– are minimal, but the concentration of H₂PO₄^– is reduced more than fivefold and that of PO₄^3– is increased in a similar proportion (see Box 3).

The different phosphate ions can combine with calcium ions into 12 different compounds, although only six can be produced directly from solution. The empirical formulas and solubility products of these six compounds are given in Table 2.

The important question is which of those species may be relevant in MVC? An analysis of in vitro and in vivo calcifications shows that from the six different calcium phosphate solid compounds (Bohner, 2010), only amorphous calcium phosphate (ACP) and hydroxyapatite (HAP) are generally present in MVC (Chernov, 1984; Mullin, 2001; Klaus-Werner, 2019).

ACP is usually the first phase to precipitate under physiological conditions (Manas et al., 2012; Hortells et al., 2017; Lotsari et al., 2018), and therefore it is the relevant early phase in pathophysiology of ectopic calcifications. Importantly, the ACP and HAP are mainly composed of PO₄^3– ions as confirmed by IR analysis (Vecstaudza et al., 2019). Therefore, although the concentrations of H₂PO₄^– and HPO₄^2– ions are substantially higher than that of PO₄^3– ions at physiological systemic pH values, it appears that in MVC the concentration of PO₄^3– ions will be the most critical one.

Given that ACP is the first compound to be observed in the MVC process (Hortells et al., 2017), the supersaturation of this compound (S_ACP) within the media will likely predict and trigger the appearance of MVC. To calculate S_ACP, reliable values of K_sp(ACP) in biological tissues would be needed. However, the only value of Ksp available at present K_sp(37°C) = aC⁢a2+×aH+0.22×aP⁢O43-0.74 = 3.35 × 10^–12 was determined in vitro, while allowing for a wide variation of pH values (Christoffersen et al., 1990). Such pH variation is unlikely occur in the living tissues closely controlling the pH homeostasis. Therefore, the Ksp(ACP) would need to be determined to reflect the conditions within the media. Meanwhile, we have used the in vitro K_sp (ACP) value in our calculations of ACP supersaturation keeping in mind that the results can be only approximates. The results are provided and compared with those of dicalcium phosphate dihydrate (DCPD), octacalcium phosphate (OCP), and HAP in normal subjects in Table 3. These calculations show that within the biological range of minimum and maximum calcium and phosphate concentrations in humans, the supersaturation should vary from S = 0.65 to S = 0.83. During the hyperphosphatemic conditions in patients with CKD, S equals 0.92, which is still below the precipitation level (S ≥ 1). However, the local changes in pH within the media or imbalance between the promoters and inhibitors could favor precipitation, as shown below. The changes in local pH within the media could explain the fact that MVC appears in CKD before hyperphosphatemia is observed (Hortells et al., 2017), may be as a consequence of VSMC transdifferentiation, and possibly also the occurrence of MVC observed in non-CKD conditions, such as diabetes or aging.

The knowledge of the molecular mechanisms of the physiological bone and teeth mineralization may be helpful to understand ectopic calcifications, as they may share common mechanisms (Allen and Moe, 2020). In summary, physiological calcification is a complex phenomenon carried out by specialized cells, and it involves a variety of actors, mainly proteins that in the bone constitute the osteoid: (a) collagenous proteins and elastin that, in the vascular wall, create close compartments to facilitate confined crystallization and crystal growth (Veis, 2005); (b) amphiphilic proteins self-assembled to form scaffolds to provide potential nucleation sites before mineralization begins (Beniash et al., 2000); and (c) non-collagenous proteins that promote nucleation and control crystal growth morphology through interactions with certain crystal faces (Veis, 2005). In the first stage of biomineralization, an amorphous inorganic compound is produced in an environment occupied by a majority of organic compounds (60% of the total volume; 82). In the second stage, the inorganic compound crystallizes, and the crystals are organized into highly hierarchical superstructures. This complex biological machinery exercises complete control over the crystallization process, including crystal size, crystalline purity, growth orientation, shape molding, and hierarchical superstructuring.

Recent analyses of the early stages of CaP precipitation using high-resolution molecular techniques and ab initio molecular dynamics simulations (Lin and Chiu, 2018; Zhao et al., 2018) provide better insights into the molecular processes involved in CaP precipitation (Habraken et al., 2016). During the initial step, calcium and phosphate ions associate to form dinuclear and trinuclear complexes and subsequently polynuclear Posner clusters (Beniash et al., 2000) composed of nine Ca²⁺ ions and six phosphate PO₄^3– anions, surrounded by 30 water molecules, as depicted in Figures 2A, 3. After that, Posner clusters agglomerate to form hydrated precipitates with a low density and a Ca/P ratio of 1:1 (Zhang et al., 2015; Jiao et al., 2016; Niu et al., 2017). In the third step, the precipitate becomes denser by losing water and increasing the Ca-O-P connectivity to form ACP, with a Ca/P ratio of 1:1.35. Finally, through slow transformation in the solid state, crystalline HAP nanoparticles are formed within the precipitate (Figure 3). This mechanism does not follow classical nucleation theory that is based on the one by one incorporation of add-atoms to the growing nuclei. This also applies to the process of CaCO₃ nucleation (Smeetsa et al., 2017). One of the consequences features of this non-classical behavior is the lowering of the nucleation energy barrier (see below) (Yang et al., 2019).

Amorphous calcium phosphate precipitates gradually transform into HAP (Hortells et al., 2015). The amorphous ACP solid evolves by slow reorganization of the loosely packed clusters into crystalline, rod-like domains of nanometer size, with a HAP structure (Figure 2). The appearance of HAP implies a dramatic change of the calcification regime. Because HAP is virtually insoluble, the crystallization process turns largely irreversible. It should be noted that the blood and fluids contained in biological tissues are highly supersaturated in HAP. The fact that HAP does not precipitate spontaneously in tissues appears to be due to a high nucleation barrier of this calcium phosphate phase keeping the medium in a metastable state. Once HAP has been formed, there is no energy barrier to stop growth, provided S > 1, unless inhibitors are present on site. Thus, in this sense at pH of 7.40 and at the lowest level of blood Ca concentration (1.02 mM), calcifications composed of HAP would be allowed to grow even when the concentration of Pi would be 1,000 times less than the lowest value in blood (see Figures 1C,D).

Transmission Electron Microscopy analyses of CaP calcifications in cell cultures are consistent with the precipitation mechanism described above (Hortells et al., 2015). Fresh precipitates appear as low-density sheets having a Ca/P ratio of one and showing some areas of higher electron density. After some aging time, precipitates show spherulite formations, which do not exhibit any crystalline order in electron diffraction and have a Ca/P ratio of 1.35, like ACP. After longer aging periods, precipitates show rod-like nanoparticles that yield electron diffraction rings, and they show crystal planes at high resolution. Based on observations of in a rat model using scanning electron microscopy (SEM), the arterial calcifications are localized and not uniformly distributed, suggesting a heterogeneous nucleation induced by a promoter, or a local increase in supersaturation, or both mechanisms as the origin of the calcification (Hortells et al., 2017). A chemical analysis of the deposits yielded mostly a Ca/P ratio of 1.35, close to that of ACP, although occasionally higher values were found, approaching that of HAP (1.67). Rat arteries that did not show any sign of calcification in optical microscope, at closer observation by SEM revealed small areas with a strong presence of Ca, but no detectable phosphate (Hortells et al., 2017). Although this preliminary observation should be studied in greater detail, it appears possible that these Ca aggregates may actually trigger CaP deposition in similar fashion as observed in physiological calcification in bones and/or teeth with calcium-rich proteins serving as promoters of mineralization.

It is important to note that solubility products are calculated based on the activities of ions in solution that are in direct contact with the solid phase. However, in the absence of the solid phase, precipitation does not occur immediately after the ionic product exceeds the solubility product. In other words, S > 1 is a necessary but not sufficient condition for precipitation because there is an energy barrier for nucleation, similar to the majority of chemical reactions (Vallence, 2017) that has to be overcome before precipitation takes place. The onset of nucleation occurs when the size of the nuclei reaches a certain critical value, due to the large surface energy of small nuclei (Chernov, 1984; Mullin, 2001; Klaus-Werner, 2019). Below that critical size, the process of ion association is transient and reversible. Below that critical size, the process of ion association is transient and reversible. This is due to the fact that ions on the particle surface have greater energy than those in the bulk, given that the number of nearest neighbors of ions on the surface is obviously lower than that of ions in the bulk. The total Gibbs free energy of a particle growing from its component free ions is the sum of that of bulk ions and surface ions, and for small sizes, the number of surface ions is relatively large, so they tend to re-dissolve until the supersaturation in solution reaches the critical value. The process of formation of stable nuclei requires a definite induction time defined by the period between the time the critical supersaturation has been established and the first nuclei were detected (Chernov, 1984; Mullin, 2001; Klaus-Werner, 2019). As the size of the nuclei increases, they can grow with decreasing levels of supersaturation. Finally, large crystals will continue to grow even at very low levels of supersaturation, as shown in Figure 2. Thus, while induction of nucleation requires high levels of supersaturation, once larger particles have been formed, the growth will proceed with ever decreasing levels of supersaturation.

Consequently, a supersaturated solution can remain in a metastable state until the activation barrier has been overcome, i.e., the critical supersaturation value, S_c, has been reached, therefore enabling the formation of stable nuclei (Christoffersen et al., 1990; Figure 1B). Thus, S (ACP) > 1 is the necessary condition for growth, and S (ACP) > Sc is the necessary condition to trigger precipitation. Using data from spontaneous nucleation experiments in water (Strates et al., 1957; Fleish and Neuman, 1961), we have estimated the S_c values of 1.03 (Fleish and Neuman, 1961) and 1.05 (Strates et al., 1957) for ACP. These values represent early estimates and require validation using well-controlled experimental models emulating in vivo conditions. Nevertheless, these early Sc (ACP) estimates indicate that the critical supersaturation for MVC should be rather low, underscoring the non-classical character of ACP nucleation (Smeetsa et al., 2017; Yang et al., 2019). Thus indeed, the molecular mechanism of ACP nucleation appears to proceed through the gradual formation of soluble CaP complexes of increasing size, eventually forming multinuclear clusters with the formula, Ca₉(PO₄)₆⋅nH₂O (Mancardi et al., 2016). These clusters having the same structure as HAP are the likely precursors of ACP. initially forming the low-density amorphous precipitates with a Ca/P ratio of approximately 1 (ACP1) and eventually evolving into denser particles (ACP2) with a Ca/P ratio of 1.35, typically found in MVC, in bones, and other physiological and ectopic calcifications.

The process of CaP precipitation described above can be altered by the presence of promoters and/or inhibitors in the system. Promoters are agents that favor the precipitation of compounds in solutions that otherwise would remain metastable. Conversely, nucleation inhibitors restrain the formation of precipitates from solutions that otherwise would experience spontaneous homogeneous nucleation. In thermodynamic terms, promoters decrease S_c and induce heterogeneous nucleation located at the promoter site, whereas inhibitors increase S_c and retard the calcification process (Figure 1B). Thus, promoters and inhibitors may control the spontaneous crystallization processes and appear to dominate MVC.

Calcification promoters typically harbor abundant Ca²⁺-ligand groups in their chemical structure, responsible for the local accumulation of these ions. In this calcium-rich environment created by the promoter, nucleation might occur with minor increases in phosphate ion activities; calcification mechanism responsible for the formation of bones and teeth (Addadi and Weiner, 1992; Beniash et al., 2000; Veis, 2005). However, the disordered texture of the deposits observed in MVC suggests that the mechanism of mineralization and the agents involved in the process are likely different. Yet the two processes, bone formation and MVC, may have in common that the nucleation promoters can induce the onset of precipitation, because in both cases, the occurrence of deposits is discrete and localized, both being typical features of heterogeneous nucleations. Disseminated foci of calcifications within the medial layers are the outstanding hallmark of the MVC. However, the nature of promoters in MVC has not yet been studied in detail and requires further clarification.

CaP nucleation promoters are molecules or macromolecules with a high affinity for calcium and/or phosphate ions. To interact with phosphate ions, promoters must have positive charges, which in biomolecules are mostly provided by ammonium ions or quaternary amines. In any case, however, the interactions are weak. Figure 4A shows the typical Ca²⁺-ligand groups in biomolecules. In descending order according to their binding strength, these groups include phosphonate, phosphate > carboxylate > sulfonate = sulfate > alkoxide ≈ water (Zhao et al., 2018). Several kinds of biomolecules may contain large numbers of these groups, as it is the case of phosphate in multiphosphorylated proteins (Figure 4Aa), such as phosvitin (Greengard et al., 1964), involved in physiological calcifications (Sarem et al., 2017). Phosvitin consists of approximately 50% serine residues, which carry a phosphate group (Greengard et al., 1964) that gives this protein an extraordinary capacity to accumulate Ca²⁺ ions. Sarem et al. (2017) were able to show that the precipitation of CaP proceeded by the incorporation of Ca²⁺ ions into phosvitin, followed by the precipitation of ACP, and subsequent recrystallization into HAP by aging. The experimental conditions included HEPES buffer (pH = 8), 1.25 mM Ca(NO₃)₂, and 1.5 mM (NH₄)₃PO₄. Under these conditions, the supersaturations of ACP and HAP correspond to 1.21 and 8, respectively. Furthermore, recently, it has been shown that the disordered secondary structure of phosvitin orchestrates the nucleation and growth of biomimetic bone such as apatite (Sarem et al., 2017).

Phospholipids (Figure 4Ad), the main component of cell membranes, matrix vesicles and exosomes, have also been proposed as promoters of pathogenic calcifications (Felix and Fleisch, 1976; Boskey, 1978; Schoen et al., 1988; Anderson, 2007; Wuthier and Lipscomb, 2011). Phospholipids are arranged in layers with a high density of phosphate-charged groups endowed with the capacity to concentrate Ca²⁺ ions. Indirect evidence of their role as promoters has been found in analyses of medial sclerosis of large arteries, aortic valves, and atherosclerotic plaques (Felix and Fleisch, 1976; Boskey, 1978; Schoen et al., 1988; Anderson, 2007; Wuthier and Lipscomb, 2011). Phospholipids may be released following degradation of cells or matrix vesicles (Felix and Fleisch, 1976). In addition, their phosphate groups may be also released as PO₄^3– ions by alkaline phosphatase, potentially also facilitating calcium precipitation (Towler, 2005).

Promoter biomolecules containing sulfate include glycosaminoglycans (GAGs) (Figure 4Ab) or mucopolysaccharides (Kepa et al., 2015), such as chondroitin sulfate, dermatan sulfate, keratan sulfate, hyaluronic acid, and heparin. In combination with proteins, form mucoproteins are formed. Mucopolysaccharides and mucoproteins have been the object of intense research based on their role as a matrix for the nucleation and structuring of calcium oxalate renal calculi. Among the mucopolysaccharides, dermatan appears the most interesting one, because its presence in the skin, blood vessels, and heart valves.

Biomolecules with a large number of carboxylic residues include glutamic- and carboxy-glutamic-rich proteins (Figure 4Ac). Collagen and elastin neutral proteins have also been proposed as promoters of VC (Urry, 1971). This hypothesis is based on the observation that Ca²⁺ ions may interact strongly with protein carbonyl groups from glycine amino acids arranged in a helix conformation. However, it should be noted that the carbonyl groups can barely compete in Ca²⁺ binding with charged groups, such as phosphate, carboxylate, and sulfate ions, because these groups interact through strong electrostatic forces, in a bidentate (also named chelate and it means bonded by to atoms to the central atom) manner. Instead, most likely, carbonyl groups appear to bind to Ca²⁺ ions by means of hydrogen bonds with hydration water (see section “Key Concepts”). Therefore, glycoproteins such as bone acidic glycoprotein-75, or bone phosphoproteins such as osteopontin or bone sialoprotein (Chen et al., 1992), appear to be more suitable promoters than collagen and elastin. These proteins not only have a higher capacity to bind Ca²⁺, but they interact with collagen itself in the presence of Ca²⁺ in a concentration-dependent manner. This Ca²⁺-mediated interaction with collagen has also been observed in matrix vesicles (Kirsch and von der Mark, 1991). Furthermore, studies on Ca²⁺-collagen interactions have shown that they take place through electrostatic interactions with the carboxylate groups (Glu and Asp) present in collagen (Pang et al., 2017).

All of these biomolecules have demonstrated the capacity to promote CaP nucleation in metastable solutions in vitro and appear to be suitable potential candidates for triggering and sustaining the calcification process in MVC, whether they are present in exosomes, apoptotic bodies, long-life proteins or transdifferentiated cells. A scheme of CaP deposition induced by promoters is shown in Figure 4C. In the first step the promoter expedites an accumulation of Ca²⁺ ions that are trapped by the high density of calcium ligand groups in the promoter structure. In the presence of phosphate, Ca²⁺ ions will form soluble CaP clusters, eventually ending up as precipitates, as described above.

In addition to the promoters the onset and propagation of VC is also determined by the presence of agents that retard or restrain CaP precipitation. These agents comprise the class of inhibitors. Based on the mechanisms of action, four main groups of agents may be distinguished. The first group consists of agents precluding or retarding the formation of stable nuclei by increasing the activation barrier (nucleation inhibitors) (Giocondi et al., 2010). The second consists of agents that are in small amounts capable of restraining the crystals’ growth by attaching to the crystals’ surfaces (crystal growth inhibitors) (Dobberschuütz et al., 2018). The third constitute agents slowing the maturation from ACP to HAP and the fourth compounds that, without being truly inhibitors, can reduce supersaturation by sequestering calcium ions in the form of soluble complexes (Reznikov et al., 2016) or, in the case of renal disease, reduce hyperphosphatemia with the use of phosphate binders (Floege, 2016) or renal Pi reabsorption (Tsuboi et al., 2020), thus reducing the risk of calcification.

In some cases, nucleation promoters may possibly also act as crystal growth inhibitors based on their capacity to bind and accumulate Ca²⁺ and to adsorb on CaP crystal surfaces. This is the case of GAGs with respect to calcium phosphate brushite (Zhai et al., 2019). Occasionally, the inhibition of crystal growth by typical nucleation promoters [i.e., chondroitin sulfate (CS) and mucoproteins] has been claimed in batch precipitation reports (Hunter and Goldberg, 1993). But this apparent inhibition effect may just be the result of Ca²⁺ absorption and the consequent decrease of the supersaturation. In constant composition studies, which more accurately reflect the conditions in blood vessels, CS has promoted precipitation. Phosvitin is a special case, which behaves like a nucleation inhibitor in dissolution but promotes nucleation when it is immobilized on a collagen surface (Onuma, 2005). Protein immobilization is also decisive in the promoter-inhibitor behavior of osteocalcin, mucoproteins, phosvitin, and phosphophoryn.

Of the three phosphate ion species, only PO₄^3– participates in all stages of precipitation, as evidenced by: (i) PO₄^3– is the main component of soluble precursor clusters; (ii) PO₄^3– is the main phosphate ion in the first precipitating phase, ACP; and (iii) PO₄^3– is also the phosphate component of HAP. As outlined above, the concentration of PO₄^3– in solution is very low at pH = 6.9, (Figure 1A), but it increases rapidly with increasing pH. Consequently, the supersaturation of ACP, and the risk of CaP precipitation, is highly dependent on the pH (Figure 1C): the pH has a much greater impact than a variation in the phosphate concentration. Actually, an increase in local pH to 7.90 would be enough to reach the critical supersaturation value (S = 1.03) estimated for the average blood Ca and P_i concentration in healthy subjects. In physiological Ca²⁺ and pH conditions, for example, it would be necessary to increase the local concentration of Pi to 3.0 mM to reach that S value, which is far above the usual level in hyperphosphatemic patients. In vitro experiments assessing the effect of cell activity onto the calcification process have also shown a notable importance of pH, mainly as a consequence of the used of highly bicarbonate media and low CO₂ concentration in the atmosphere (Hortells et al., 2015). Significant changes in local pH in vivo in contrast to the serum’s strictly regulated pH homeostasis, could arise, as explained below, through a modification of the activities of Na⁺/H⁺- and bicarbonate exchangers and of proton pumps, carbonic anhydrases, and other factors related to VSMC’ metabolism (Leibrock et al., 2016; Yuan et al., 2019). Although local alkalinity has not been demonstrated to play a role in the pathogenesis of MVC, it could be hypothesized by combination of mechanisms, such as increased presence of promoters, depletion of inhibitors possibly orchestrated by a perfect metabolic storm signifying the transdifferentation of VSMC.

With respect to calcium carbonate, it is present in considerable amounts in pathological calcifications (Bazin et al., 2012) and in in vitro calcifications (our own experiments). The concentration of CO₃^2– ions also increases rapidly above a pH of 7 (Figure 1A), and the supersaturation of CaCO₃ in blood can be higher than that of ACP under physiological conditions (Table 4) supporting the hypothesis that VC may be, at least in part, related to pH rather than phosphate concentration’s changes. In culture media, MEM or DMEM (media commonly used in the in vitro calcification procedures) maintained at 5% CO₂ atmosphere at given concentrations of bicarbonate and the pH (Hortells et al., 2015), the supersaturation of calcium carbonate (CaCO₃) exceeds that of CaP in both media. This finding may not only explain the co-precipitations of CaCO3 with CaP but may also suggest its role in seeding calcium phosphate nucleation sites.

To date, studies in the real in vivo or ex vivo medial layer environment are not available. Thus, the hypothesis charting the pathogenesis of CaP precipitation thermodynamics in the medial layer must be based only on the currently available incomplete evidence derived largely from in vitro observations.

Medial layer consists of ECM comprising matrisome with a number of different glycoproteins and proteoglycans with embedded networks of collagen and elastic fibers (Hynes and Naba, 2012) and VSMC. Due to the extensive extra- and intracellular compartmentalization and due to the higher viscosity of both ECM and VSMC cytoplasm compared with the water solutions and other solvents’ the mobility of the ions will be less predictable and more restricted. However, based on the available data, the viscosity of cytoplasm is approximately 1.2–1.5 times higher compared to water (Fushimi and Verkman, 1991; Bicknese et al., 1993; Kao et al., 1993; Luby-Phelps et al., 1993; Chang H. C. et al., 2008). To our knowledge, no data on viscosity of the ECM are available. Thus, as a matter of approximation, we assume that the environment of the media corresponds to viscous solution rather than solid gel. Based on these scanty reports we tentatively conclude that an increase in viscosity as suggested in the medial layer will mainly affect the ion transport, leading to a diffusion-controlled CaP crystal growth, possibly the single most important difference to the crystal growth in vitro solutions.

However, it is important to understand that in any biological system regardless of the composition and physical-chemical properties such as viscosity, the laws of thermodynamics and the links between supersaturation and CaP crystals’ growth retain their validity.

It is well known that electrochemical gradient between the micromolar concentration of Ca²⁺ in the VSMC cytoplasm and the millimolar extracellular Ca²⁺ concentration can be only maintained at high energy cost. This extremely low [Ca²⁺ _i] in cytosol along with the presence of PPi prevent spontaneous CaP precipitation inside the cell under physiological conditions [the cytosol also contains 3–5 mM free Pi (Peacock, 2021)] and normal metabolic states. Disruption of energy supply by the mitochondria, oxidative stress, electrophilic insults, etc., will cause uncontrolled influx of [Ca²⁺_i] from the extracellular space or endoplasmic reticulum followed by breakdown of intracellular homeostasis and cell death (Orrenius et al., 2013). Apoptotic bodies or cell debris could become nucleation sites and thus contribute to calcification.

The hypothesis of the medial CaP crystallization’s stepwise process outlined in the section “Molecular Processes in CaP Precipitation” has received support by experimental data from Transmission Electron Microscopy analysis of CaP deposits from cell cultures and rat arteries demonstrating that early CaP deposits consist of ACP undergoing progressive densification process and resulting in the crystallization of HAP nanoparticles (Villa-Bellosta et al., 2011; Hortells et al., 2015, 2017). The fact that the two methods of VC research, in vitro and in vivo, show similar early deposits but both calcification processes are unrelated (in vitro being alkali-mediated homogeneous precipitation, whereas in vivo is heterogeneous precipitation caused by promoter nucleation) clearly shows that deposit formation and crystal maturation thermodynamics are constant and similar, independently of the environmental setup (Hortells et al., 2015).

Given the impact of pH on the supersaturation of ACP and therefore potentially initiation of calcifications, changes in pH should be considered as a potential important factor in MVC, in both intra- and extracellular milieu. The pH in both milieus is determined by a number of factors including the metabolic production of the acid moieties, the transmembrane protons’ transport, the activity of bicarbonate transporters and exchangers, and the enzymatic synthesis of bicarbonate. While the intravasal homeostasis of pH is strictly controlled within narrow boundaries, the local tissue pH appears less stable depending on the type of the tissue and specific metabolic activities (Martin and Jain, 1994). Osteoblasts, for example, thrive in vitro at alkaline pH (Galow et al., 2017), in agreement with the effect of metabolic alkalosis increasing osteoblastic collagen synthesis and reducing bone resorption related to a decrease in osteoclastic beta-glucuronidase release (Bushinsky, 1996). Albeit it has never been demonstrated as yet, it is tempting to conclude that local changes in tissue pH possibly caused by contractile or partially transdifferentiated VSMC could be involved in triggering MVC, particularly if combined with nucleation promotion and VC inhibitor depletion.

Local interstitial-intracellular pH changes are interdependent and determined by both local and systemic factors. In VSMC, several transporters participate in the movement of protons and bicarbonate to quickly control intracellular pH (pH_i) and local extracellular pH (pH_o). Sodium-proton exchanger 1 (NHE1, Slc9a1) eliminates protons from the cell, whereas the bicarbonate transporter, NBCn1 (Slc4a7), inwardly co-transports sodium and bicarbonate anions. With an intracellular excess of bicarbonate, this is eliminated by anion exchanger 2 (AE2, Slc4a2) (Boedtkjer et al., 2012). More recently, additional bicarbonate transporter transcripts—Slc4a3, Slc26a2, Slc26a6, Slc26a8, and Slc26a11—have been identified in rat aortic SMC in vitro, further increasing the complexity of intracellular pH control in VSMC (Hortells et al., 2020). In addition, carbonic anhydrases also present in VSMC can increase the concentration of bicarbonate and also alter the intracellular acid-base equilibrium. Interestingly, the inhibition of these enzymes with acetazolamide prevents the soft tissue calcification of klotho-hypomorphic mice (Leibrock et al., 2016) and in apolipoprotein E (ApoE^–/–) mice (Yuan et al., 2019).

Furthermore, changes in pH in VSMC have been implicated in several physiological and pathological states. For example, alkaline pH_i is necessary for VSMC proliferation (Beniash et al., 2000; Boedtkjer et al., 2012), as well as for ECM remodeling and the activation of matrix metalloproteinases (Harrison et al., 1992; Stock et al., 2005). NHE1 inhibits apoptosis by increasing pH_i, cell volume, and sodium content and by reducing the activity of enzymes required for apoptosis (Pedersen, 2006). Conversely, the inhibition of NHE1 or of NBCn1 should cause intracellular acidification and the reciprocal local extracellular alkalinity, consequently promoting MVC by promoting apoptosis associated with calcium nucleation (Shroff et al., 2008). This local alkalinity could also create an optimal TNAP environment for hydrolyzing PPi and organic phosphates such as phospholipids. In turn, the increased expression of TNAP seems to be one of the first steps of MVC in CKD (Hortells et al., 2017). In addition, the local alkalinity will also supersaturate the medium with respect to ACP and calcium carbonate. These examples illustrate the potential importance of pH regulation of activities in VSMC, potentially applicable to MVC pathogenesis.

Changes in local pH, TNAP overexpression and other factors, could accompany transdifferentiation of VSMC into osteo/chondroblastic-like cells. Following the detection of the bone forming gene expression in atherosclerotic lesions (Boström et al., 1993), the active role of VSMC in VC process has been extensively studied (e.g., 153–155). Osteo/chondrogenic transdifferentiation of VSMC has been mainly studied in CKD-related MVC. In these patients, the observed uremic and hyperphosphatemic conditions have tempted to the use of a simple research model accounting for a design of a fairly complete pathogenetic proposal based on direct effects of Pi as follows. The highly abundant phosphate would either permeate directly into the VSMC or it would be sensed through the sodium-phosphate cotransporters (PiT1/2), activating a signal transduction pathway resulting in a phenotypic transformation into osteochondroblast-like cells. This transformation could be mediated by the expression of Pi-induced transcription factors such as Msx2 (msh homeobox 2), Runx2 (Runt-related transcription factor 2), osterix, etc., that, in turn, would increase the expression of bone-forming proteins, such as Bmp2 (bone morphogenetic protein-2), TNAP, osteocalcin, collagen type I, etc., causing PPi depletion, increased number of nucleating sites, formation of calciprotein particles, etc., therefore facilitating, initiating, and stimulating calcification (Voelkl et al., 2019; Lee et al., 2020; Tyson et al., 2020).

Whereas VSMC transdifferentiation and the thermodynamics of CaP precipitation belong to different scientific fields, they complement each other in exploring MVC pathogenesis. While the former provides hypothesis, the later accounts for hypothesis testing. Consequently, the above outlined pathogenetical scenario has still to be considered with caution, for several reasons. Firstly, in the model or 5/6-nephrectomized rats, hyperphosphatemia is observed only after the first deposits have been formed and not before (Hortells et al., 2017), therefore, hyperphosphatemia should not be considered a necessary cause of calcification, but as an accelerator and complicating agent. Secondly, MVC may require interplay of different systemic and local factors absent in a cellular culture such as VSMC. Thirdly, thermodynamic principles suggest that calcium phosphates are not supersaturated in the normal or even CKD patients and therefore homogenous precipitation is an excluded possibility. Fourthly, in VSMC cultures, nanoparticles of calcium phosphate (or possibly calcium carbonate) rather than soluble Pi are responsible for osteo-/chondrogenic transdifferentiation. This can be easily observed by incubating VSMC cultures with high Pi concentrations in the presence of nucleating inhibitors, such as PPi, phosphonoformic acid or bisphosphonates: such nanoprecipitates are not formed and, consequently, no bone-related genes are expressed in VSMC despite the high Pi concentration (Villa-Bellosta et al., 2011; Lee et al., 2020). Fifthly, the nanoparticles do not appear to be caused by the native or transdifferentiated VSMC that would nucleate calcium heterogeneously, but rather by an alkaline pH-mediated supersaturation that causes homogeneous precipitation in media when using highly bicarbonated media in the presence of low CO₂, along with the extremely high concentrations of Pi (Hortells et al., 2015). It is important to note that homogeneous precipitation does not occur in vivo. If pH is set at pH 7.4 in culture medium, no precipitates are formed, and no transdifferentiation of VSMC occurs. In fact, calcification also occurs using non-transdifferentiated, dead cells (Villa-Bellosta and Sorribas, 2009). Thus, the above in vitro experimental model represents an extreme case of biomedical research reductionism, misrepresenting the multifactorial complexity of the MVC. For example, because fluoride prevents the growth of calcium deposits in vitro it could be considered calcification inhibitor, yet, in contrast, fluoride promotes MVC in in vivo experimental rat model (5/6-nephrectomy) likely due to multitude of effects, mainly nephrotoxicity (Martín-Pardillos et al., 2014).

It has been established that osteo/chondrogenic transformation of VSMC does occur in the medial layer in MVC in vivo, as shown by the expression of several bone forming genes. Nevertheless, if CaP homogeneous precipitation in blood and direct Pi effect on bone forming gene expression rather effected by the calcium nanoprecipitate depositions can be excluded, s are then osteo/chondrogenic transformation could be considered a consequence of preceding calcium depositions caused for example by factors such as the local ACP supersaturation, AP overexpression and/or abundance of nucleation promoter (Hortells et al., 2017; Hruska et al., 2017), depending of the processes associated with CKD, DM, aging, or other. Therefore, we suggest, that any hypothesis of pathogenesis of MVC needs to comply with the thermodynamic principles and pass successfully the filter of energetic plausibility.