Holocrine Secretion and Kino Flow in Angiosperms: Their Role and Physiological Advantages in Plant Defence Mechanisms

Kinos are plant exudates, rich in polyphenols, produced by several angiosperms in reaction to damage. They flow out of kino veins, schizolysigenous ducts composing an anatomically distinct continuous system of tangentially anastomosing lacunae produced by the vascular cambium, which encircle the plant. Kino is secreted holocrinously into the vein lumen by a cambiform epithelium lined by suberized cells that separate kino veins from the surrounding axial parenchyma. A model describing kino flow in eucalypts is presented to investigate how vein distribution and structure, as well as kino holocrine loading, crystallization, and viscosity affect flow. Considering viscosity, vein anatomy, and a time-dependent holocrine loading of kino, the unsteady Stokes equation was applied. Qualitatively, kino flow is similar to resin flow. There is an increase in flow towards the vein open end, and both pressure and flow depend on vein dimensions, kino properties and holocrine loading. However, kino veins present a much smaller specific resistance to flow compared to resin ducts. Also, unlike resin loading in conifers, holocrine kino loading is not pressure-driven. The pressure and pressure gradient required to drive an equally fast flow are smaller than what is observed on the resin ducts of conifers. These results agree with previous observations on some angiosperms and suggest that holocrinous gum flow may have lower metabolic energy costs; thus presenting physiological advantages and possibly constituting an evolutionary step of angiosperms in using internal secretory systems in plant defence mechanisms compared to resin flow in conifers. Understanding of how these physiological and morphological parameters affect kino flow might be useful for selecting species and developing more sustainable and economically viable methods of tapping gum and gum resin in angiosperms.


Introduction
Based on the model first proposed by Münch (Büsgen and Münch, 1929) and the current knowledge of resin synthesis (Beck, 2010), a pressure-driven resin loading mechanism was suggested by applying the unsteady Stokes equation to describe flow in resin ducts, using conifers as model plants (Cabrita, 2018). Accordingly, resin is granulocrinously loaded into the duct lumen, along its wall lined by epithelial cells, depending on the pressure difference between the duct and the epithelium. However, as it is known, resin flow varies considerably among plant species, being higher in conifers, namely Pinaceae, and lower in angiosperms. In addition, albeit the great similarity in structure among most species, resin ducts can be differently surrounded by epithelial and adjacent subsidiary cells. Not only can their number and distribution be different, but also their size, living state, and wall structure vary (Wiedenhoeft and Miler, 2002;Wu and Hu, 1997). Therefore, these anatomical and structural differences together with the very well-known differences in resin chemical composition between species may suggest different loading mechanisms, which in turn might be related with several defence strategies used by plants. Gum and gum resin ducts of many angiosperms share many anatomical and physiological similarities with resin ducts (Evert, 2006;Nair, 1995). That is, in many cases and similarly to resin, many components of gum or gum resin are secreted into the duct granulocrinously, involving the fusion of Golgi or endoplasmic reticulum vesicles with the plasma membrane and releasing their contents through the cell wall, or eccrinously, which involves the passage of small molecules directly through the plasma membrane and cell wall (Beck, 2010;Evert, 2006). The model proposed by Cabrita (2018) suggests that a pressure-driven granulocrine loading of resin into ducts gives some physiological advantages regarding its role in plant defence mechanisms. Therefore, considering the similar role that gum plays in plant defence mechanisms and the anatomical similarities shared 4 by gum producing angiosperms with resin producing species, the unsteady Stokes equation can be equally applied to describe flow inside gum and gum resin ducts (Cabrita, 2018).

Gum ducts development and holocrine secretion
Contrary to schizogenous ducts (i.e. intercellular spaces developed by separation of cells) into which granulocrine or eccrine secretion occurs, there are lysigenous gum and gum resin ducts that develop by the lysis of epithelial cell protoplasts and their initials with subsequent partial or complete dissolution of the cell wall. Initially, there is a set of meristematic cells called rosette (Prado and Demarco, 2018). Typically, due to the programmed cell death and lysis of one or more central parenchyma duct initials of the rosette, an intercellular space is formed, around which the cells surrounding it differentiate into epithelial cells, usually with a dense cytoplasm and a thicker and swollen wall facing the duct (Fahn, 1988b;Subrahmanyan and Shah, 1988;Setia 1984b). The intercellular space thus formed may widen by further lysis of the lining epithelial cells. An irregular lysis of epithelial cells results in ducts with uneven shape, called cavities. Consequently, the contents of these ducts are derived directly from the autolysed cells in what is called holocrine secretion, which is considered of limited occurrence in plants (Nair et al., 1983. There are also cases in which the initiation of the duct is schizogenous but its widening is made through lysis of the surrounding epithelial cells. These ducts are considered to be formed schizolysigenously. The autolysis of the epithelial cells that occurs after a secretory phase is in many cases non-uniform and may happen occasionally through time, which leads to difficulties in defining schizolysigenous duct development rigorously. For this reason, some authors regard this type of duct development still as schizogenous (Evert, 2006). The gum and gum resin ducts that present lysigeny in their development are mostly associated with plant responses to trauma, e.g. Ailanthus excelsa Roxb. Rajput and Kothari, 2005), Anogeissus latifolia (Roxb. ex DC.) Wall. ex Guill. 8 species-and trauma-dependent (Eyles andMohammed, 2002, 2003;Hills, 1962Hills, , 1987Tippett, 1986). Kino veins, typically filled with kino and cell debris, form an anatomically distinct continuous system of tangentially anastomosing lacunae or canals, embedded in a sheet of traumatic parenchyma, running longitudinally and often encircling the plant stem and branches (Skene, 1965). Once ruptured, kino veins exude kino, initially a brownish viscous liquid that upon exposure to air solidifies and becomes brittle. They are initiated in the zone of traumatic parenchyma that is produced by the vascular cambium shortly after stimulus to vein formation is given. In the same way as the gum ducts observed in Citrus and Prunus during gummosis resulting from bacterial, chemical, fungal, viral or insect attack (Butler, 1911;Fahn, 1988a;Fawcett, 1923;Gedalovich and Fahn, 1985a), as well as the traumatic resin cysts and ducts in the Abietoideae (Bannan, 1936), kino veins extend for a greater distance up from the zone of stimulus than down (Skene, 1965;Tippett, 1986).
The plant hormone ethylene, either of microbial or host origin, is thought of playing a major role in giving stimulus for the formation of kino veins after injury (Eyles andMohammed, 2002, 2003;Hillis, 1975Hillis, , 1987Nelson and Hillis, 1978;Tippett, 1986), resembling what is observed in other angiosperms that produce gum or gum resin, e.g. Ailanthus excelsa Roxb., which produces gum resin holocrinously when infected or damaged Rajput and Kothari, 2005), and Citrus spp., which presents gummosis after infection from the water mould Phytophthora citrophthora (R. E. Sm. & E. H. Sm.) Leonian (Gedalovich and Fahn, 1985a, b). After stimulus, periclinal and transverse divisions in the cambium result in layers of generally isodiametrically or tangentially elongated thin-walled anomalous traumatic parenchyma cells. They have larger crosssectional area and shorter length than cambial cells, and accumulate polyphenolic compounds (one of the main components of kino) in their vacuoles noticeably (Eyles and Mohammed, 2002;Skene, 1965;Tippett, 1986). These divisions in the cambium are similar regardless of whether they initiated from xylem or phloem initials (Tippett, 1986). Although a xylem origin is frequently reported (Jacobs, 1937), Eyles andMohammed (2002, 2003) observed that in Eucalyptus nitens (H. Deane & Maiden) Maiden the traumatic parenchyma originated from differentiating preexisting phloem parenchyma as in Moringa oleifera Lam. (Subrahmanyan and Shah, 1988). A similar parenchymal phloem origin was also observed in Eucalyptus gomphocephala A. Cunn. ex DC. (Day, 1959). However, origin in both tissues has also been observed (Jacobs, 1937;Tippett, 1986???). After expanding up to four times their original size, the central traumatic parenchyma cells of the future vein, composing the rosette (Prado and Demarco, 2018), autolyse and collapse forming lacunae that are filled with the cellular contents rich in polyphenols thus released. Collapse of the rosette usually takes place tangentially, and because of this kino veins tend to show greater dimension radially; but radial collapse also occurs (Day, 1959). In recently formed veins, the walls of the autolysed central cells remain attached to the living epithelial cells around the edge of the vein lumen. Many of the cell walls are broken, so that the vein lumen originates through mechanical rupture of the cell walls. As the lacunae are formed, the traumatic parenchyma cells around the edge of the vein divide actively periclinally and anticlinally forming a peripheral cambium. In the same way as the initial rosette cells that started the vein lumen, the derivatives of the peripheral cambium originated inwards increase similarly in size, differentiate into epithelial cells accumulating polyphenols, and autolyse eventually, thus increasing the vein lumen. This process extends vertically, upwards and downwards from the point of stimulus (injury), breaking down large areas of traumatic parenchyma and forming a tangentially anastomosing network of veins intersected by rays, which are not traversed by them. The peripheral cambium also produces layers of compact cells outwards that can extend differently between veins from one up to seven cells thick. In later stages of development, the outer layer of cells derived from the peripheral cambium becomes suberized with thick walls forming a typical periderm lining the epithelium and separating the veins from the surrounding vascular parenchyma tissue (Eyles and Mohammed, 2002;Hills, 1987;Skene, 1965). By then the vein lumen is lined by a layer of two to three cells thick without any further development, which marks the final stage in the formation of kino veins (Skene, 1965;Tippett, 1986).
Given the almost ubiquitous presence of torn partly broken as well as complete walls from collapsed cells, the development of kino veins is not totally lysigenous as it does not involve the entire dissolution of cell walls. Also, as lacunae are not created by splitting entire cells apart at the middle lamella, kino veins development is not purely schizonegous in origin either. Due to the simultaneous development of the lacuna and division of the peripheral cambium, some authors suggest that rupture and collapse of the autolysed epithelial protoplasts occurred because of an unequal distribution of growth amongst the peripheral cambium derivatives; as suggested by their rapid increase in size (Eyles and Mohammed, 2002;Skene, 1965). The traumatic parenchyma surrounding kino veins eventually becomes thick-walled and lignified forming radial parenchyma bridges with, in some cases, phloem fibres, e.g. Eucalyptus obliqua L'Hér. (Eyles and Mohammed, 2002), and Eucalyptus wandoo Blakely (Tippett, 1986). The parenchyma bridges are widest closest to the vascular cambium, and may develop either into normal thick-walled and lignified xylem or phloem or both and associated parenchyma progressively. The number, size, and rate of development of kino veins and associated traumatic parenchyma seems to vary not only among species, but also individuals. Kino veins can be from small, scattered and embedded in a continuous parenchymal matrix to very large and numerous separated by small pegs of parenchyma tissue.
These differences may relate to plant age and nature of trauma (Eyles andMohammed, 2002, 2003;Skene, 1965;Tippett, 1986). The cambiform traumatic parenchyma, from which kino veins originate in eucalypts, and its consequent holocrine secretion system, including its later inactivation, are also observed in the gum and gum resin ducts of several angiosperms, e.g.
In eucalypts, kino veins can differ considerably in size of a few centimetres to 5 m or more in length, from 1 to 7 mm in diameter, and from a few isolated veins to a dense anastomosing network extending for considerable distances vertically in the stem (Dowden and Foster, 1973;Fahn, 1990;Loewus and Runeckles, 1977;Skene, 1965;Tippett, 1986). Occasionally, large and isolated kino veins of a few centimetres in width and extending up to half a meter or more, called kino pockets, thus accumulating a considerable volume of kino, may develop without parenchyma bridges and are usually found in knobs and external swellings in the stem (Hillis, 1962(Hillis, , 1987Phillips, 1931) or even burst its limiting periderm and extend through a large area of the rhytidome (Chattaway, 1953;Day, 1959). Eyles and Mohammed (2003) measured kino pockets of 4 to 7 cm in width and 15 to 177 cm in length in Eucalyptus globulus Labill. This organization of specialized traumatic parenchyma cells and lacunae makes the transition from normal wood to kino veins or pockets very abrupt, normally taking place just over one to four rows of cells; thus making them easily identifiable. The development of kino veins and subsequent release of kino can occur as fast as one to two weeks after injury and continue from a few days to several weeks or even months (Das, 2014;Eyles, 2003;Eyles and Mohammed, 2002;Skene, 1965;Tippett, 1986). About 45 l of kino were extracted from a single kino pocket of a red gum tree, Corymbia calophylla (R. Br. ex Lindl.) K. D. Hill & L. A. S.Johnson (Phillips, 1931). If the vascular cambium has been extensively and continuously stimulated, kino may be secreted for several years. Under prolonged stimulus, there is a continuous activity of the vascular cambium in producing new veins, as well as maintaining active a permanent meristematic peripheral cambium and a holocrine kino secretion system in existing veins, as described above. The secretory activity of kino veins depends on the continued meristematic activity of the peripheral cambium, as it involves the destruction of the secretory cells (epithelium). At the same time the first kino is being released to the outside in response to trauma, the anomalous parenchyma cells surrounding the lacunae divide repeatedly forming a peripheral cambium producing concentric layers of thin-walled epithelial cells that accumulate phenolic compounds in their vacuoles and breaking down eventually, adding to the volume already present in the veins (Eyles, 2003;Eyles and Mohammed, 2002;Skene, 1965). In addition, in some cases, the area of the kino secreting epithelium is further increased by the formation of hemispherical or elongate protuberances on the outer edge of the lacuna (Dowden and Foster, 1973;Eyles and Mohammed, 2002).
Despite being secreted holocrinously, i.e. when all its components are released into veins lumina by epithelial cells autolysis, many of the gummous components of kino are generally synthesized within Golgi bodies and transported by the Golgi-mediated smooth vesicles that will deposit their contents between the plasmalemma and the cell wall by exocytosis, thus contracting the cytoplasm as more secreted substances accumulate (granulocrine secretion) (Fahn, 1988b;Gedalovich and Fahn, 1985a). Additionally, while polyphenols are synthesized by the endoplasmic reticulum and then released and transported into the vacuole through the vesicle transfer system (Catesson and Moreau, 1985;Shahidi and Yeo, 2016), other gummous components, e.g. polysaccharides, are also released into the lacunae by sloughing off the outer layers of the cell wall of epithelial cells (Setia, 1984b;Venkaiah, l986), similarly to what happens in gum and gum resin ducts (Fahn and Evert, 1974;Venkaiah, 1992). However, the release of all secreted substances, which will make kino, and the autolysed protoplast into the lumina occur after the degeneration of the cell wall only (Nair, 1995;Nair et al., 1983). Initially, kino is a sticky straw-coloured exudate that upon exposure to air solidifies becoming a brittle semi-transparent solid of cherry red to brown or black colour, depending on the species and age of the plant. Upon contact with the outside air, kino solidification is thought to be the result of enzymatic activity and the simultaneous evaporation of some of its volatile components (Penfold, 1961).
Most authors agree that kino veins generally play a role in defence as a resistance mechanism by acting as a barrier zone protecting the vascular cambium, including a great amount of axial parenchyma, from which kino veins originate, lack of fibres and few conducting elements, preventing access of boring insects, bacteria and fungal invaders (Eyles and Mohammed, 2002;Hillis, 1987;Tippett and Shigo, 1981). Infected plants defend themselves and resist the spread of pathogens by compartmentalization or formation of barrier zones, i.e. forming boundaries that isolate the injured or necrotic tissues from the living cambium. This process starts with the accumulation of chemicals, e.g. polyphenols, gum, within tissues at the time of injury or infection as plant and pathogen interact. It then progresses to the formation of both chemical and anatomical boundaries after infection as the cambium responds to form a barrier zone between the infected and the new tissues Shigo, 1984). Therefore, it seems that barrier zones may be most important in restricting the transport of either fungal toxins or phytotoxic metabolites produced by host necrotic reactions towards the cambia. Some studies suggest that kino astringency is related to antimicrobial activity, as well as some of its flavonoid and simple phenolic components have shown antibacterial, antiviral, and fungicidal properties (Locher and Currie, 2010;Martius et al., 2012). However and similarly to other plant internal secretory systems, e.g. latex, resin, gum, and gum resin, the function and purpose of kino synthesis and vein formation is still not completely understood, though it is generally considered to be a type of defence mechanism.
Apart from kino veins, drought crack on Eucalyptus camaldulensis Dehnh. and discolouration of the phloem extending tangentially from kino veins on Eucalyptus gomphocephala A. Cunn. ex DC.
were observed in specimens suffering from drought stress (Day, 1959). The fact that these phenomena known to relate to water stress in conifers also occur in species presenting kino veins, led Day to suggest that water stress could be one of the stimuli for kino vein formation. However, all other studies made on the development and functioning of kino veins never confirmed Day's hypothesis, as well as he does not seem to have studied the early phases of development of kino veins in great detail. Therefore, water stress being one of the possible stimulus for the formation of kino veins seems thus unlikely. Nevertheless, according to some studies, the link between water stress and kino may in fact exist but not in the way that Day suggested. Mucilage may play an important role in water transport (Czarnes et al. 2000), specifically in trees (Zimmermann et al. 2007). Mangroves and some halophytic trees contain high amounts of mucilage in their xylem vessels (Zimmermann et al., 1994;. Due to its high water and salt-binding capacity, i.e. it modifies surface tension, the accumulation of mucilage in vessels seems to be an important strategy of halophytic trees to save water on its way to the uppermost crown. Water moves then at the interface between adhering gas bubbles and the inner walls of cavitated vessels through filamentary polymeric chains of mucilage as well as surface films to adjacent vessels and cells (Zimmermann et al., 2004(Zimmermann et al., , 2007. Xylem mucilage, although at lower concentrations than in halophytic species, has also been found in other species, e.g. Eucalyptus pilularis Sm., Nothofagus dombeyi (Mirb.) Oerst., Populus nigra L., Sequoia sempervirens (D.Don) Endl., and Sequoiadendron giganteaum (Lindl.) J. Buchholz (Zimmermann et al., 2004;. In these species, similarly to halophytes, water stress (e.g. caused by drought, sun exposure, high salinity) results in an enhanced synthesis of xylem mucilage contributing to higher balancing pressures in the upper crown that help the plant to cope better with water shortage by supplying it to its uppermost parts (Zimmermann et al., 2007).
In addition to xylem mucilage, kino was also observed filling the lumina of xylem vessels of Eucalyptus pilularis Sm. variably. Therefore, considering the high solubility of kino in water and the fact that it modifies surface tension, similarly to mucilage, the simultaneous occurrence of kino with mucilage in Eucalyptus pilularis Sm. xylem seems to enhance further the effects of mucilaginous gels on interfacial water movement (Zimmermann et al., 2007). Supporting this second physiological role of kino and complementing that in plant defence strategies is the fact that many of the polyphenols and gummous components of kino are also synthesized and accumulated in rays (Wardrop and Cronshaw, 1962) and in the phloem parenchyma (Skene, 1965) and then released to occlude xylem vessels (Chattaway, 1949). However, since they are not released into the vessels holocrinously, the composition of the kino-like xylem occlusions is different from that observed in nearby kino veins (Skene, 1965). The synthesis and physiological function of the kinolike occlusions observed in xylem vessels (Zimmermann et al. 2007) is similar to that observed in gum producing species (Chattaway, 1949;Bonsen, 1991;De Micco et al., 2016). All the families presenting kino veins (Table 1) also present vessel occlusions (De Micco et al., 2016;InsideWood, 2004).
Considering the role of gum and gum resin in plant defence strategies, this study intends to investigate the physiological and anatomical advantages of holocrine secretion on gum flow in angiosperms and compare them to the pressure-driven resin loading of conifers (Cabrita, 2018) using kino veins as model. To that end, special focus will be given to several anatomical and physiological features of kino veins, as well as kino properties, e.g. viscosity, density, and how they affect flow and contribute to plant defence strategies. In addition, the author hopes that this study contributes not only to a better understanding of the physiological processes behind kino synthesis and flow, but also to the development of better tapping methods envisaging a more sustainable and economically viable extraction of kino, gum, and gum resin from other plant secretory systems that rely on holocrine secretion.

Kino flow model
Let one adapt the model approach of Cabrita (2018) to a fully developed kino vein of radius R, surrounded by an active and stimulated epithelium that autolysis (Fig. 1), open at the end of its length L where kino, of constant viscosity  and density , flows out of it through a wound and solidifies when exposed to the outside air at normal pressure and temperature. For the sake of simplicity and mostly due to lacking of experimental data, one neglects the contribution of the balance between the autolysis and cell division of the epithelium to the enlargement of the vein lumen, as described before, by considering the kino vein of constant radius R (Fig. 1). Similarly to resin flow in conifers, all the necessary conditions are observed so that one can classify kino flow as Stokes flow, i.e. with a very small Reynolds number << 1, and apply the unsteady Stokes equation (Cabrita, 2018): where  = / is the kino kinematic viscosity and p stands for the kino vein dynamic pressure, i.e. due to dynamic effects (Kundu and Cohen, 2008), from now on simple called pressure. As an incompressible fluid, the continuity equation for kino flow implies that: Therefore, considering the nature of holocrine secretion, described before, the loading of kino into the vein occurs similarly throughout its entire length at a rate that is constant with the axial distance that defines the vein axis, z. That is: where Ne is the number of autolysing epithelial cells in the peripheral cambium releasing kino into the vein lumen after the accumulation of polyphenolic compounds in the vacuole and gummous components between the plasmalemma and the cell wall. Thus, in these conditions, the radial velocity component ur is a function of the radial distance r and time t solely, and assumed of the form: At the lacuna boundary, which is considered fixed, there is the no-slip condition: b) Centre of the kino vein: symmetry at the centre of the kino vein, r = 0, implies that: c) Origin: at z = 0 and t = 0, when the vein is ruptured, one has that: where: U0 is the average initial axial velocity; pi is the average initial pressure; and z u and p are the average axial velocity and pressure in the vein respectively. d) Wound region: at z = L and t = 0: There is outflow of kino that is subsequently solidified once in contact with the air outside: where V is the volume of the liquid fraction of the kino being exuded at the wound of which a part of it solidifies at a rate  (m 3 .s -1 ), which is assumed constant for modelling purposes, and U is the average initial kino outflow velocity at the wound where pressure equals the local atmospheric pressure, pa.
Except when noted otherwise the same symbols were used as in the model of Cabrita (2018).
Hence, using definition (4) and the continuity equation (2) one concludes that the axial velocity uz is a linear function of the axial distance z, and the scalar governing equations derived from the unsteady Stokes equation describing flow within the kino vein (1) become:

Properties of kino flow
Solving governing equations (15) and (16) considering the boundary conditions described before, (3) to (12)  where J0 and J1 are Bessel functions of zero and first orders, and  is a non-dimensional undetermined parameter characterizing kino loading into the vein, regardless of its dimensions, which might depend on the species. From result (18), one hast that the holocrine loading of kino at the lacuna boundary, r = R, (4) (Fig. 1) is given by: From which one has that veins with smaller surface to volume ratio, that is, wider and longer veins, present higher loading rates than narrower and shorter veins. This results is expected, considering that holocrine loading will be bigger in wider veins surrounded by a larger autolysing epithelium than in narrower veins surrounded by a smaller epithelium, thus a smaller number of autolysing cells.
Solutions (17) and (18)  Therefore, based on these results, the half-life, t1/2, of kino flow, i.e. the time required for it to reduce to half its initial value, is: Physiologically, one can interpret the decay constant 2 R   as describing the rate of holocrine kino secretion into a fully developed vein resulting from cell autolysigeny that occurs due to stimulus and happens throughout its length (Fig. 1). From result (20), one has that higher kino loading rates are kept through time, i.e. changing more slowly with time for smaller values of the decay constant 2 R   , in veins with smaller surface to volume ratio; that is, wider veins. Therefore, wider veins present higher values of kino flow half-life (22). For a given set of vein dimensions, the smaller value of the decay constant reflecting higher holocrine loading rates is achieved by having smaller values of parameter . In this case, higher holocrine loading rates may be expressed either by faster accumulation of polyphenolic compounds and gummous components or cell autolysis or even both.
In addition, a stronger meristematic activity of the epithelium affecting these processes will also contribute to a higher holocrine loading of kino.
From the continuity equation, i.e. mass conservation (2), or, alternatively, from equations (19) and (20) one finds that: The change in the average flow with distance is linear with the loading of kino, i.e. flow increases towards the wound as more kino is loaded into the vein lumen, due to epithelial cells autolysis.
However, the magnitude of the changes in the average flow with distance decreases with time reflecting the concomitant decrease in holocrine loading of kino (20).
Pressure in the kino vein is given by: and the average pressure is: From this result one has that the average pressure gradient is a linear function of the axial distance z: as it is expected when the average pressure (25) presents a parabolic profile with the axial distance.
Comparing it with the average velocity (19) one concludes that: The average pressure gradient is linear with the average axial velocity as it is expected for a laminar flow regime (Cabrita, 2018; Kundu and Cohen, 2008) in which the kino vein specific resistance  (Pa.s.m -2 ) is given by: Using this result, the average pressure in the kino vein (25) can be written as: and the change in the average pressure with time is given by: From result (29) one finds that the decline in the kino vein pressure with distance in the direction of flow (27) will be smaller for veins presenting smaller values of the specific resistance,  (28).
Whilst pressure in wider veins presenting smaller specific resistance and higher holocrine loading rates, i.e. smaller values of parameter , will increase more slowly with time (30) allowing flow to continue for longer, as reflected in their higher values of kino flow half-life (22). Also, this result agrees with the fact that wider veins delivering higher amounts of kino at the wound will take longer to close by the solidification of kino, meaning that pressure in them will increase at a slower rate as the wound closes. Additionally, from result (30), one has that slower change of pressure with time will be further enhanced by producing less viscous but denser kinos; that is, presenting smaller values of the kinematic viscosity, .
Considering result (28) and the range of values observed on the dimensions of fully developed and functional kino veins and pockets (Dowden and Foster, 1973;Eyles and Mohammed, 2003;Fahn, 1990;Loewus and Runeckles, 1977;Skene, 1965;Tippett, 1986), one finds that the minimum value of parameter  possible, i.e. for which the kino veins offer a resistance to flow, is 2.16×10 -8 approximately. Parameter  characterises holocrine loading of kino into veins and does not depend on their dimensions rather on the physiology (3), i.e. on the rates of accumulation of gummous components, between the plasmalemma and the cell wall, and phenolic compounds in the vacuole, which are then all released into the vein lumen upon subsequent cell autolysis in the peripheral cambium (Fig. 1). The contribution and importance of these processes may vary among species, and depend on the age of the plant and stimuli given to vein formation. Comparing the specific 28 resistance of a kino vein of radius R (28) with that of a tube of similar dimensions under Poiseuille flow regime, Poiseuille, one finds that: As Fig. 2A shows, the specific resistance of a kino vein, , is bigger than that of a tube of similar As suggested by the differences in pressure and kino loading between wider and narrower veins described above, wider kino veins with smaller values of parameter , i.e. with smaller specific resistance (28) and presenting higher kino loading rates (20) Unfortunately, experimental data on kino flow are rare compared to other plant exudates such as latex, oleoresins, and some gums economically important. This fact is most certainly related to the limited economic importance of kino as a niche product with limited applications (Locher and Currie, 2010;Martius et al., 2012). However, there are some measurements, sadly scattered in time, from which one can obtain valuable information and get a clearer picture of the physiology behind 31 kino flow in angiosperms. Kino is referred to having thick consistency similar to that of honey (Hillis, 1962). Therefore, considering the typical high content of tannins (Bolza, 1978), its viscosity  = 10 Pa.s, i.e. 10,000 times more viscous than pure water, and density  = 1,400 kg.m -3 , which falls within the range of values normally found for honey at normal ambient temperature, one finds kino kinematic viscosity = 7.1410 -3 m 2 .s -1 . In addition, from the several observations made on kino and gum flow in some species (Table 2), one has that the average kino flow is not faster than the resin flow observed in pines (Cabrita, 2018;Hodges et al., 1977Hodges et al., , 1981Schopmeyer et al., 1954), i.e. in the order of 10 -5 to 10 -4 m.s -1 . Therefore, one has from result (27)  m.s -1 ; and U0 = 110 -6 m.s -1 . For this value of parameter  considered, the specific resistance (28) of the 0.5 cm radius kino vein and the 3 cm radius kino pocket is about 1.3 times that of similar dimensions ducts under Poiseuille regime ( Fig. 2A), that is, 4.0710 6 and 1.1310 5 Pa.s.m -2 respectively. Taking the values of the kino kinematic viscosity, , and parameter  considered, the 0.5 cm radius kino vein has a decay constant (21) of 2.8610 -5 s -1 , while this parameter for the 3 cm radius kino pocket is 7.9410 -7 s -1 ; that is, about 360 times smaller. This gives a kino half-life of 6.7 h and 10.d for the 0.5 cm radius kino vein and the 3 cm radius kino pocket respectively.
Having a time-dependent loading of kino that does not change with the axial distance (20) results in having a parabolic decrease of pressure (25) within kino veins in the direction of flow (Fig. 3A), which means that the pressure gradient (26) increases linearly in magnitude with distance z towards the wound (Fig. 3B). Consequently, the average flow speed (19) increases linearly with the axial distance (Fig. 4A). Once in contact with the air outside, kino solidifies eventually sealing the wound  164 -193 Bhatt (1987); Ghritlahare (2017) completely. As more kino crystalizes, partially blocking the exit wound, pressure at the wound and consequently throughout the vein lacuna builds up, so that 48 h after rupture pressure within the 0.5 cm radius kino vein is almost uniform throughout (Fig. 3A). In this case, the average pressure gradient is practically non-existent (Fig. 3B), and flow (Fig. 4A) as well as loading of kino ( Fig.   4B) have almost ceased completely. As times passes and the loading of kino decreases in magnitude ( Fig. 4B), so does the average flow speed (Fig. 4A) and the pressure gradient becomes less prominent, i.e. less negative (Fig. 3B). Naturally and in order to maintain a Stokes flow regime, pressure within kino veins evolves by decaying exponentially with time towards equilibrium (25), after which flow no longer occurs (Fig. 3). The closing of the wound by kino crystallization just makes this scenario happening sooner in time (33) Qualitatively, the scenario here described for a 0.5 cm radius kino vein is not different from that of a 3 cm radius kino pocket. However, given its bigger surface to volume ratio, both the kino pocket specific resistance (28) and decay constant 2 R   are smaller than what is observed on the narrower  kino vein. This means that the disturbance caused by rupturing the kino pocket at its end will remain longer through time, i.e. pressure (Fig. 6A), pressure gradient (Fig. 6B), kino loading rate (Fig. 4B) and flow speed (Fig. 7) will change more slowly than in the narrower kino vein (Figs. 3, 4A). Due to the kino pocket higher loading rate (20) (Fig. 4B), the changes, i.e. the decrease, in the average axial speed with time will be smaller (23) (Fig. 7). Additionally, due to its smaller specific resistance, pressure in the kino pocket will decrease less with the axial distance z (29) (Fig. 6A).
This means that compared to narrower veins, not only smaller pressure gradients are needed to drive flow throughout larger kino pockets, but also they are kept longer through time (Fig. 6B). In this way, the holocrine secretion of kino into wider kino pockets allows them to deliver bigger volumes for longer periods of time compared to narrower veins. As Fig. 4B shows, 48 h after rupture the loading of kino into a 3 cm radius kino pocket has decreased about 13% of its initial value, whilst in a narrower 0.5 cm radius vein it has practically ceased. About 7 kino flow halflives have elapsed after 48 h for the narrower vein, whilst at that time only a 1/5 of the kino flow half-life has elapsed in the kino pocket. Consequently, at that time, while the kino pocket is still able to deliver flow at a speed that is a bit less than 90% of what it was initially, the average flow speed in the narrower vein has become essentially non-existent (Fig. 4B), i.e. basically unmeasurable. Similarly to narrower veins (Fig. 5), kino flow within kino pockets also presents a varying quasi parabolic profile that sharpens towards the wound with the axial distance, decaying in magnitude with time and reaching its maximum at the centre. Flow stops (33) after 67 h in the narrower vein and 100 d in the kino pocket approximately, giving a kino crystallization rate, , in the order of 110 -11 m 3 .s -1 .

Discussion
Despite sharing many similarities in terms of their role in plant defence strategies, the internal secretory systems that rely on holocrine secretion differ from those presenting granulocrine or eccrine secretion not only in development, distribution, and structure, but also physiologically.
However, regardless of being considered of limited occurrence in plants (Nair et al., 1983, holocrine secretion seems to present some advantages regarding the loading and flow inside ducts and cavities when compared to pressure-driven ganulocrine secretion (Cabrita, 2018).

Kino loading is not pressure-driven and its flow requires less metabolic energy
Typically, kino veins form a tangential anastomosing network in the stem and branches encircling the plant, while resin ducts, despite being present in all plant organs, distribute vertically and radially making, in some cases, a three-dimensional network extending throughout the plant body.
The much longer and wider kino veins (e.g. when they become kino pockets), contribute greatly to their specific resistance being four to five orders of magnitude smaller when compared to the specific resistance of the biggest resin ducts found in Pinaceae. Furthermore, physiologically, while the resin duct specific resistance also depends on the duct wall permeability to resin, which in turn depends on the wall composition and thickness (Cabrita, 2018), the kino vein specific resistance depends on the holocrine loading of kino through parameter  (28), which does not involve any membrane transport. Hence, there are no metabolic energy costs associated with membrane carriers or transporters. This means that the kino vein capacity to deliver a given amount of kino (32) is mostly determined by the rate of epithelium autolysis (3) that relates to the synthesis and accumulation of polyphenolic compounds and gummous components. Additionally, both these processes depend on the meristematic capacity of the peripheral cambium in substituting autolysed epithelial cells by producing new ones that will accumulate and release kino subsequently. The balance and contribution of these processes may well depended on the species, age of the plant, and the stimuli given to vein formation, i.e. trauma. Therefore, the anatomy, structure and physiology of kino veins and associated epithelium suggest that the holocrine kino loading is not driven by pressure contrary to what is observed in conifers resin ducts (Cabrita, 2018). This result agrees with the observations of Skene (1965) on Eucalyptus obliqua L'Hér., in which the secretory activity of kino veins is dependent on the continued activity of the peripheral cambium; thus quite different from what is known of the synthesis and flow of resin in conifers (Bannan, 1936;Cabrita, 2018), as well as gum and gum resin in some angiosperms, e.g. in the normal ducts of Ailanthus excelsa Roxb. .
Apart from the anatomical and physiological differences between resin producing species, with granolucrine pressure-driven loading, and gum producing species with holocrine loading, here exemplified by kino veins, perhaps, the most striking feature distinguishing them is the values of pressure and pressure gradients observed in kino veins and resin ducts. Pressure inside resin ducts falls within the range of values observed in plant cells, i.e. between 0.3 and 1 MPa (Bourdeau and Schopmeyer, 1958;Cabrita, 2018;Rissanen et al., 2015;Schopmeyer et al., 1954). The model presented in this work suggests that pressure within kino veins, in the order of 110 5 Pa, is most likely smaller than that observed in resin ducts but still higher than the pressure observed in the apoplast (Nobel, 1999). Therefore, considering the much smaller kino veins specific resistance and that kino flow (Fig. 4A) may be equally as fast as resin flow (Cabrita, 2018;Hodges et al., 1977Hodges et al., , 1981Schopmeyer et al., 1954), the pressure gradients needed to drive kino flow, eventually through considerable distances, range up to four to five orders of magnitude smaller, i.e. of 10 to 10 2 Pa.m -1 (Figs. 3B, 6B), than the pressure gradients observed in resin ducts (Cabrita, 2018), and 42 up to three orders of magnitude smaller than the pressure gradients in the xylem of trees at maximum rates of transpiration; estimated to be between 2 and 5×10 4 Pa.m -1 (Nobel, 1999;Zimmermann and Brown, 1971). In this way, eucalypts and other species that secrete kino, gum or gum resin holocrinously seemed to have found a way of defending themselves by accumulating and releasing their exudates under pressure within extensive vertical and tangential anastomosing networks, possibly with less metabolic energy costs. Unlike resin, gum, and gum resin ducts that are loaded granulocrinously, there is no energy spent on maintaining, through membrane channels or transporters, a pressure difference driving the flow between the surrounding epithelium and the kino veins lumen. The metabolic energy seems thus to be mostly spent on the meristematic activity of the epithelium and on the synthesis and accumulation of polyphenolic compounds in the vacuole and gummous compounds between the plasmalemma and the cell wall, which will be then released holocrinously into the vein lumen after programmed cell autolysis. Combined, these processes  (Table 2).With slower flow rates, the metabolic energy costs will be even lower, possibly also translated into smaller rates of synthesis and accumulation of polyphenols, gummous components, or cell autolysis, as well as meristematic activity, in order to produce smaller pressure gradients needed to drive flow holocrinously. Judging from the few experimental observations on gum and kino flow rates, this seems to be the case in some species of Azadirachta, Butea and Moringa, which are known to yield kino (Table 2).

Epithelial cells autolysis and the accumulation of polyphenols and gummous components determine kino flow without changing its dynamics
The This means that the different capacity to produce and exude kino holocrinously would ultimately reflect differences in anatomy and physiology, either through kino composition, which would be shown in its viscosity and is known to vary between species (Martius et al., 2012), or through the synthesis and accumulation of polyphenols and gummous components, epithelium autolysis and meristematic activity or, most likely, a combination of all these factors, expressed in the values of parameter K. The values of the decay constant and kino flow hal-life here obtained agree with the values estimated from observations on other species producing kino, e.g. Acacia nilotica (L.) Delile (Das, 2014). This result together with the estimates of mass flux obtained exemplifies how well the model here presented describes holocrine secretion and kino flow.

44
A 10 fold increase in the value of parameter K used in this model, i.e. up to 110 -6 , meaning a higher decay constant reflecting a smaller holocrine loading rate, either due to smaller rates of synthesis and accumulation of polyphenols and gummous components or epithelium autolysis or both, changes the kino vein specific resistance very little (Fig. 2B). Additionally, the increase in the vein specific resistance caused by decreasing the value of parameter K 10 times (Fig. 2B) does not change the order of magnitude of the pressure gradients needed to drive flow. Therefore, these results suggest that the species that secrete kino holocrinously, e.g. eucalypts, react and respond differently to trauma by changing the rates of synthesis and accumulation of polyphenols and gummous components, thus affecting kino composition and consequently its viscosity, as well as epithelium autolysis, expressed in the values of parameter K, without changing the dynamics of flow. Thus, facing the likelihood of prolonged trauma by continuous stimuli, the possibility of having large kino pockets exuding continuously seems advantageous. This agrees the variability of kino exudation observed in eucalypts (Angophora, Corymbia, and Eucalpytus), from small amounts being exuded in short periods of time to large volumes being exuded during longer periods (Hillis and Hasegawa, 1963;Phillips, 1931). In this work, this is exemplified by comparing a narrower kino vein to a six time wider kino pocket that exudes for a much longer period of time ( Fig. 4B). Due to their smaller specific resistance associated with bigger holocrine secretation rates, pressure within wider veins and pockets decreases less with distance and increases more slowly with time than in narrower veins. This allows them to deliver equally fast responses as those of narrower veins, but with bigger volumes under smaller pressure gradients. Ultimately, this results in having less energy costs needed to drive such flow through wider veins without changing its dynamics. Hence, the investment in maintaining wider ducts surrounded by larger epithelia that secrete holocrisnously seems to compensate by keeping flow at lower costs. Compared to the narrower resin ducts in conifers that rely on granulocrine secretion, internal secretory systems that rely on holocrine secretion seem thus advantageous and may possibly constitute an evolutionary step of angiosperms in using internal secretory systems in plant defence mechanisms.
The overall duration of flow, tc, up to 100 d in the kino pocket, and kino crystallization rate, in the order of 10 -11 m 3 .s -1 , fall within the range of values obtained from the data of Das (2014) on Acacia nilotica (L.) Delile. However, considering the differences in kino composition among species (Martius et al., 2012) and the changes in the flow rate observed on Eucalyptus sieberi L. A. S.
Hence, the variability observed on exuding kino complicates its tapping and perhaps it is one of the reasons for not having more successful and sustainable methods developed so far. In conifers, resin flow rate is more or less uniform between the ruptured ducts. The amount of resin exuded, thus the magnitude and duration of the plant's response, depends on the species and duct density and width (Cabrita, 2018). In this respect, it would be helpful to investigate if and how the dimensions and distribution of kino veins relate to the type of stimulus, i.e. the nature of the trauma, behind their origin, and consequently the ability of the plant to exude kino.

Kino role in plant defence mechanisms is enhanced by vein structure and organization
The chemical role played by kino on plant defence strategies, i.e. its biocidal properties against bacteria, fungi and virus (Locher and Currie, 2010;Martius et al., 2012), may be further enhanced physically by the contribution of kino vein structure and organization while acting as a barrier zone (Hillis, 1987;Tippett and Shigo, 1981). The outer layers of the peripheral cambium with highly suberized cells lining fully developed kino veins and pockets seem to behave like a periderm (Fig.   1). The main role of the periderm with its suberized cells is protective by preventing water and nutrient loss, as well as pathogen attack. In this regard, the periderm-like outer layer of cells lining fully developed kino veins seems to prevent not only water and solute loss from the surrounding axial parenchyma, but also possible incursions into it by pathogens, or substances released by them, which have successfully managed to penetrate deeper into kino veins. With highly suberized cells lining kino veins, water and solute exchange with the surrounding axial parenchyma and, subsequently, the rest of the plant is only possible through the symplast; thus becoming more limited. This gives the plant more control on the possible exchanges between the symplast and kino veins. Access to other regions of the plant body is further complicated by the sparse vascular system conducting elements present in the axial parenchyma surrounding kino veins. Considering the chemical properties of kino together with their distribution and structural organization, kino veins seem thus to form an effective barrier to harmful agents, especially against vascular diseases similarly to what is observed in species that develop parenchymal barrier zones, e.g. Acer sp., Fagus sylvatica L. (Torelli et al., 1994), Ulmus americana L., (Tippett and Shigo, 1981). In this respect, the presence of kino veins seems more advantageous compared to the apparent easier access offered by the resin ducts, lined by thin-walled epithelial cells densely connected to surrounding subsidiary cells that in turn connect to adjacent tracheids, i.e. vascular system (Ferreira and Tomazello-Filho, 2012).

Conclusions
Some angiosperms, here exemplified by eucalypts that produce kino veins as a response to trauma, seemed to have found an efficient way of using holocrine secretion as defence by combining physical and chemical strategies. Compared to conifers and other species that rely on pressuredriven loading of resin, gum or gum resin, these species present an equivalent secretory system that delivers equally fast flows at lower pressure, driven by smaller pressure gradients, and possibly with lower energy costs to plant metabolism. Hence, with different organization, structure and physiology, kino veins may present a more efficient defence strategy of some angiosperms when compared to resin ducts. It would be then worthwhile to study and compare the effects of development, distribution, structure and physiology of ducts on flow, and ultimately on plant defence, of other species that produce gum or gum resin. Understanding of how these physiological and morphological parameters affect gum flow might be useful to not only elucidate the plants abilities to resist different pathogens, but also select species or varieties, and develop more sustainable and economically viable methods of tapping gum and gum resin in angiosperms. Many of the tapping methods still in use today are not only unproductive, but also quite destructive and wasteful (Bhatt, 1987;Das, 2014;Nair, 2003). Considering that the initial average axial flows at z = 0 and z = L are known; i.e. U0 (9) and U (11) respectively, one finds that:          and 1 m length kino vein filled with kino of dynamic viscosity  = 10 Pa.s, kinematic viscosity ν = 7.1410 -3 m 2 .s -1 , ruptured at the end of its length, at t = 0 h, where kino is exposed to air at constant normal atmospheric pressure pa = 1 atm, considering:  = 1.010 -7 ; U = 1.010 -4 m.s -1 ; and U0 = 1.010 -6 m.s -1 .