Contribution of intrusive and symplastic growths in wood fibre tip development

At initial stages of fibre development, radial enlargement of growing fibre tip is achieved, on average, in 37.8% intrusively and in 62.2% symplastically, whereas tip tangential enlargement is purely intrusive. In this study, we have investigated the mode of growth of black locust wood fibre tips at initial stages of their development using detailed measurements. Growth of fibre tips may be considered in three directions: axial, tangential, and radial. An axial elongation of a fibre tip was described as intrusive and related to the separation of walls of neighbouring cells. However, determination of the contribution of intrusive vs. symplastic component of growth in tangential and radial directions was missing. Semi-thin transverse sections of the vascular cambium and adjacent tissues were obtained by ultramicrotome and stained with PAS and toluidine blue. An anatomical analysis of contribution of intrusive and symplastic growths in fibre tip radial and tangential enlargement was performed. Our study showed that during its development an average wood fibre tip grows only intrusively in tangential direction and shows intrusive-symplastic growth in radial direction. On average, at initial stages of its development, a fibre tip radial enlargement is achieved in 37.8% by intrusive growth and in 62.2% by coordinated (symplastic) growth.


Introduction
In the secondary xylem of angiosperm trees, in addition to parenchyma cells, vessel elements, and tracheids, there also occur wood fibres with relatively thick and rigid secondary cell walls. They are mainly responsible for mechanical strengthening of the tissue, and play an important role in determining the quality of deposited wood. As wood is one of the main raw materials, studies of development of wood fibres are of particular interest. Wood fibres, similarly to cambial initial cells and vessel elements, exhibit intrusive growth (Fujita et al. 1984;Gizińska et al. 2021;Majda et al. 2021;Miodek et al. 2021a,b). As stated by Beck (2010) intrusive growth of a cell concerns its intrusion between other cells which are separated from each other (along the middle lamella) (Fig. 1). Thus, intrusive growth results in change in contacts between an intrusively growing cell and cells in its surroundings (Hejnowicz 2012;Gizińska et al. 2021). Petrova et al. (2022) have recently shown that a flax mutant characterised by impaired intrusive growth of xylem and phloem fibres has not only shorter fibres, but also other alterations, including mechanical aberrations at the macro-and nanolevel. The second type of growth occurring in both cambial cells and cambial derivatives, e.g. wood fibres, is symplastic. Cells growing symplastically do so in unison (in a coordinated way), thus maintaining contacts between them ( Fig. 1; Wilczek-Ponce et al. 2021). Cells of the vascular cambium and their differentiating derivatives show anisotropic symplastic growth. The main direction of this growth is radial, and to a much lesser extent tangential (Wilczek et al. 2018). Mathematical analysis of cambial growth revealed that a single cambial cell grows ca. 8000 times faster in radial than in tangential direction (calculated Communicated by H. Gärtner. for vascular cambium of 1 m circumference) (Miodek et al. 2021b).
In transverse section mature wood fibres commonly have small cell lumen. While considering anatomical structure of a wood fibre one can distinguish: (I) the middle part-named fibre body, with tangential dimension usually corresponding to tangential dimension of fusiform cambial initial (from which it originates); and (II) elongated peripheral (distal) parts-also called fibre tips, which grow intrusively in axial direction (Fujita et al. 1986;Jura-Morawiec et al. 2008). Different types of wood fibres may be distinguished, i.e. libriform fibres, gelatinous fibres of tension wood, and fibretracheids (Buvat 1989;Fahn 1990;Evert 2006;Beck 2010;Crang et al. 2018). Libriform fibres constitute the main and most advanced type of fibres in broadleaved tree species. They have the thickest cell walls-usually with scarce simple or slightly bordered pits (Evert 2006).
Every cambial initial, as a consequence of cell divisions parallel to the tangential plane of an organ, produces numerous derivative cells (Srivastava 1973;Crang et al. 2018). This type of cell division is termed periclinal (additive). Cells found in the closest vicinity to the cambial initial cells on xylem side are xylem mother cells. They include vessel element mother cells (VEMCs) and fibre mother cells (FMCs). These cells sequentially enter the differentiation zone, where an intensive growth in radial direction occurs (cell divisions cease or occur occasionally), and maturation zone, where the secondary cell wall is deposited and cessation of cell growth occurs (Wilson et al. 1966).
When describing growth of plant fibres, it is usually stated that they undergo an intrusive elongation in axial direction (Mellerowicz 2006;Siedlecka et al. 2008;Gorshkova et al. 2012). However, in their latest study Majda et al. (2021) showed that elongation of fibres combines diffuse as well as tip growth. It seems that to further elucidate the mechanism of fibre tip enlargement, it is necessary to uncover how they grow in radial and tangential directions. In other words, we should find answers to the following questions. How transverse tip enlargement of secondary wood fibres is achieved? Is it through intrusive growth between tangential (periclinal) or radial (anticlinal) cell walls? What is the contribution of intrusive vs. symplastic component of growth in radial and tangential directions? There is little information on the precise mode of growth of secondary wood fibres in the context of radial growth of woody plants. One of the very scarce studies on this subject was published by Wilczek et al. (2018). The authors concluded that in initial stages of wood fibre elongation, i.e., in the zone of radially expanding cells, intrusive growth of fibre tips occurs between tangential walls of neighbouring cells. In Honjo et al. (2006) one may find a short comment on intrusive growth of wood fibres that it occurs in tangential as well  (b) show intrusive growth of the cell marked with '*' located in lower tier (a-cells before growth, b-cells after growth). As the cell grows between separated walls of cells of upper tier new contacts are established. Dislocation/deformation of cells of upper tier related to intrusive growth is not included. (c) and (d) show symplastic growth of all visible cells (including cell marked with '*') within a tissue fragment (c-cells before growth; d-cells after growth). In case of symplastic growth contacts between cells remain unchanged. Note that in the vascular cambium and its differentiating derivatives intrusive growth is accompanied by symplastic growth of cells which predominates in radial direction. Thus, in cambial and derivative cells distinction of these two types of growth should be carried out with caution as radial directions. Moreover, Rao et al. (2011) mentioned that a growing fibre tip intrudes between radial cell walls. The authors do not elaborate further on this matter. They did not specify whether they were referring to entirely intrusive growth of a distal part of wood fibre between radial cell walls of derivative cells, or maybe only to the initial separation of radial cell walls of these cells and ensuing symplastic growth of the whole cell aggregate in radial direction. To sum up, some of descriptions of wood fibre growth are rather vague and imprecise. As a result of mental shortcuts, it is possible to disregard the fact that growing tips of secondary wood fibres increase their tangential and radial dimensions simultaneously with their axial elongation-thus growing also in these two directions, not only in the axial one. This translates to the three-dimensional (axial, tangential, radial) growth, instead of one-dimensional (axial).
Up until now there was no detailed anatomical study, which would precisely elucidate the contribution of intrusive vs. symplastic component of growth of a wood fibre tip in radial and tangential directions. Therefore, the aim of this study was to perform precise measurements enabling investigation of the contribution of intrusive vs. symplastic types of growth in initial stages of wood fibre tips formation with regard to the spatial location of these two types of growth. To achieve this goal, it was vital to carefully select an appropriate measurement method, which is described below in detail.

Plant material
The study was performed on black locust (Robinia pseudoacacia L.)-a deciduous, ring-porous species (Miodek et al. 2020). Examined tree with a circumference of ca. 66 cm at breast height was selected from a tree stand located in Silesian Botanical Garden in the temperate climate zone, southern Poland (50°17'N, 18°82'E, 330 m above sea level). Black locust was chosen for this study because of the storied structure of its vascular cambium, which is also reflected in deposited layers of the secondary xylem (Miodek et al. 2022). This means that fibre bodies are located at the same level (Wilczek et al. 2018). The storied structure allowed us to conduct the precise mathematical analysis for cells found at the selected transverse plane.

Sample collection and preparation
Tree-trunk tissues were collected at breast height in early August 2014. After removal of the periderm with chisel and hammer, samples containing the vascular cambium, secondary xylem, and secondary phloem were acquired. Obtained blocks had an axial dimension of 15 mm, a rectangular tangential surface, and a trapezoidal radial surface. These blocks were then cut with a razor blade to cubes with edges 3 mm in length and fixed in glutaraldehyde (4% solution of glutaraldehyde buffered with 0.2 M phosphate buffer [pH = 7.3; 4 °C]). Tissues were rinsed three times in phosphate buffer (4 °C) and dehydrated (5,10,15,20,25,30,40,50,60,70,80, and 90% ethanol solution, pure ethanol, ethanol and propylene oxide solution [1:1], pure propylene oxide). Next, material was embedded in epon resin, which was polymerised in 35 °C, 45 °C and 60 °C (for 24 h at each temperature), cut with Tesla ultramicrotome (semi-thin transverse sections were obtained), stained with PAS (Periodic Acid, Schiff) and toluidine blue, and mounted in Euparal (Karczewska et al. 2009;Miczajka et al. 2014;Miodek et al. 2022). Sections were examined under Olympus BX41 microscope (bright field).

Anatomical analysis
Analysis of the contribution of symplastic and intrusive growths in the enlargement of libriform wood fibre tips was conducted on a transverse section comprising vascular cambium and differentiating xylem cells. The examined fragment was located between two rays and consisted of five radial files of cells of the axial system (Fig. 2). The fragment was divided into six zones (1-6), which included: (1) cambial initial cells along with their immediate derivatives. This zone has been distinguished on the basis of radial dimension of observed cells, thickness of cell walls, and frequency of periclinal, and anticlinal divisions -both within the analysed fragment of axial system and adjacent areas; (2), and (3) cambial derivative cells growing symplastically in radial direction, where no adjacent, enlarging fibre tips were present; (4), (5), and (6) cambial derivative cells having direct contact with enlarging fibre tips. The last (6th) zone was distinguished as the most distanced layers from the initial surface, where fibre bodies (cells nos. 56-60) still retained contacts with each other, despite the presence of enlarging fibre tips. Distinguishing the 6th zone was a starting point for indicating other zones. Each zone consisted of two single-cell layers. Since the fragment analysed consisted of five radial files of cells grouped in two-layered zones, each of distinguished zones consisted of 10 cells of axial system. Cells of different zones were marked with distinct colours (Fig. 2). It should be noted that the most recent periclinal divisions were not taken into consideration. This exclusion concerned cells nos. 40, 41, and 52 of the 4th, 5th, and 6th zone, respectively.

Assessment of fibre tip growth
Following the methodology introduced by Gizińska et al. (2021) we assessed intrusive growth-i.e., growth leading to change in cell contacts (Fahn 1990;Evert 2006;Jura et al. 2006;Beck 2010;Wilczek et al. 2014)-based on length reduction of walls of cells surrounding growing tip of a wood fibre. In order to do so, we analysed and compared changes in fibre tip transverse dimensions, and length of tangential/radial walls of adjacent cells in subsequent zones. Part of fibre tip dimension (tangential/radial) unrelated to the reduction of wall length of surrounding cells was considered to stem from symplastic (coordinated) growth, as it was not associated with any changes in cell contacts. Symplastic growth of cells neighbouring with fibre tips was recognised on the basis of changes in tangential/radial dimensions of these cells.

Measurements
In examined transverse section the following dimensions were measured: radial cell dimension (measured in the central part; regarded as a distance between two tangential walls); tangential cell dimension (measured in the central part; regarded as a distance between two radial walls); length of tangential cell walls (understood as length of tangential walls not separated by fibre tips); length of radial walls (understood as length of radial walls not separated by fibre tips); tangential dimension of growing fibre tip; radial dimension of growing fibre tip (Fig. 3a). The curvature of tangential and radial cell walls was taken into account. Figure 4 shows a plane in which measurements were performed in relation to location of analysed cells within the stem as well as directions of cell growth (tangential/radial/axial).
In each of six considered zones the mean values were calculated for all measured categories. In case of length of tangential walls, the mean value (in every distinguished zone) was calculated for twenty of them (all ten cells in a given zone had a total of twenty tangential walls-two per each cell). In case of length of radial cell walls the mean value (in every distinguished zone) was calculated for sixteen measured values instead. The reason for this is the main purpose of our study-estimation of contribution of intrusive and symplastic growths in fibre tip enlargement in radial and tangential directions. Since the precise contribution of a given type of growth could be figured out by analysing changes in length of corresponding cell walls in subsequent zones, it was necessary to consider only radial walls spanning across six zones in which growing fibre tips occurred. As one can see, in case of radial walls directly adjacent to rays no growth of fibre tips occurred, and thus they were excluded from the analysis ( Supplementary Information Fig.  S1). These walls (directly neighbouring with rays) do not convey any information regarding the subject of this study and are hereinafter referred to as marginal radial walls. As shown in Fig. 2 length of marginal radial walls gradually increases towards the xylem. Note that in zone 6 these walls are approx. twice as long as in zone 1 (e.g. compare the length of marginal radial walls of cell nos. 6 and 56) as opposed to the rest of the radial walls, which are localised in the inner part of the analysed fragment (e.g. compare the length of radial walls of cell nos. 7 and 57).
In case of mean values calculated for tangential and radial dimensions of growing fibre tips, the measurements were transformed to make them proportional to all other mean values obtained. Each obtained measurement value has been divided by two (20 tangential walls/10 cells) in case of tangential dimension of fibre tip, and by 1.6 (16 radial walls/10 cells) in case of radial dimension of a fibre tip. Additionally, perimeters as well as transverse surface areas of cells were measured in each of the six considered zones.

Fig. 2
Transverse section of the vascular cambium and derivative cells of black locust. Cambial initial cells and their derivatives deposited on xylem side (numbered 1-60) were divided into six zones (numbers 1-6 in circles). Enlarging fibre tips were assigned to corresponding zones, according to the adapted methodology (see Fig. 3). Cross-sectional areas of fibre tips were divided by demarcation lines (dotted lines)-these lines are an extension of tangential and radial walls of cells between which fibres tips have grown. Cells of the 1st zone most probably correspond to close vicinity of the initial surface. In zones 2 and 3 intensification of radial growth of derivative cells occurs. In zones 4-6 intrusive growth of the fibre tips occurs. Cells with recent periclinal division (marked by asterisks) are considered as single cells for the purpose of conducted analysis. A-E radial files of cells of axial system. R ray Proper assignment of tangential and radial dimensions of growing fibre tips to relevant zones required their adequate division (Fig. 3). This step was of key importance as presence of some fibre tips was related to simultaneous reduction in length of neighbouring walls belonging to cells of two adjacent zones (Fig. 3c,d,e). To accomplish this goal, we have reconstructed positions of cell walls in a way which would reflect cell arrangement prior to the commencement of axial intrusion of fibre tips, i.e. as if considered fragment of tissue grew only in a coordinated manner (symplastically). This involved linking tangential walls of cells surrounding an intruding fibre tip with demarcation lines. The same procedure was applied to the radial walls. In example shown in Fig. 3d dimensions of the wood fibre tip which were assigned to zone 5 included tangential dimensions 2F 1 + F 2 and radial dimensions 2E 1 + E 2 and to zone 6 tangential dimension F 2 and radial dimension E 2 . Growing fibre tip reduced the length of radial walls and tangential walls in cells α, β, γ, δ. In Fig. 3e dimensions assigned to zone 5 were F 2 and E 1 and to zone 6 F 2 and E 2 . In this case a fibre tip reduced the length of walls only in cells γ and δ. In Fig. 3f there are two fibre tips adjacent to one another. They were considered together as a single object (a compound fibre tip). Since such compound fibre tip is localised in zone 6, it includes following dimensions: tangential 2F 1 + 2F 2a + 2F 2b and radial 2E 1 + 2E 2 .
Measurement data collected for cells of the distinguished zones as well as fibre tips are listed in Supplementary  d, and e) show fibre tips growing between cells belonging to two different zones (for example 5th and 6th zone). Cells surrounding intrusively growing tip/tips of wood fibres are marked as: α, β, γ, δ. E 1 , E 2 are parts of radial dimension of fibre tip (E) separated by demarcation lines, and F 1 , F 2 are parts of tangential dimension of fibre tip (F) separated by demarcation lines, which were assigned to proper zones. F 2a , F 2b are parts of F 2 in case of a compound fibre tip shown in (f) Information Tables S1 and S2. Supplementary Information Table S3 contains average length of tangential and radial walls of all cells. In case of cells with marginal radial wall the length of non-marginal radial wall was included instead. Dimensions of growing fibre tips, transformed accordingly in order to make them proportional to mean values obtained for tangential walls (20 measurements) and radial walls (16 measurements), are listed in Supplementary Information Table S4. Measured cell perimeters and transverse surface areas are listed in Supplementary Information Table S5. In addition to mean values, basic statistical parameters were calculated for all measured parameters (minimal value, maximal value, and standard deviation) including the assignment of cells and wood fibre tips to proper zones (Table 1).
Anatomical results (Supplementary Information  Table S1, Table S2 and Table S6) were subjected to statistical analysis using Statistica software (ver. 13.3; TIBCO Software Inc., Tulsa, USA). Shapiro-Wilk test was used to check for normality (Supplementary Information Table S7). Mann-Whitney U Test (independent model) was performed to figure out whether there were significant differences (at the 95% confidence level) between I) a sum of average length of tangential cell wall and fibre tip tangential dimension, and II) cell tangential dimension (Supplementary Information  Table S8). Mann-Whitney U Test was also performed to  Table 1 Measured dimensions of cambial initials, derivative cells, and enlarging fibre tips For each zone measurement results are shown as mean value ± standard deviation, as well as minimal and maximal values (brackets). In case of tangential and radial cell walls average values were calculated for 20 and 16 measurements, respectively (in each zone). Other parameters were calculated based on 10 measurements per zone. In case of fibre tips average values were calculated accordingly to the number of tangential walls (for fibre tip tangential dimension) and radial walls (for fibre tip radial dimension) considered in the study. If there were no fibre tips in a given zone, it was designated as 0. Values are expressed in μm Zone determine whether there were significant differences (at the 95% confidence level) between I) a sum of average length of radial cell wall and fibre tip radial dimension, and II) cell radial dimension. The analysed data included zones 4, 5, and 6, where growing wood fibre tips occurred.

Results and discussion
Growth of fibre tips begins not far from the cambial initial surface (Wilczek et al. 2018), i.e. near the transition from the vascular cambium to differentiation zone (Wenham and Cusick 1975;Fujita et al. 1984). An intensification of radial symplastic growth of derivative cells occurs already in sixth/ seventh cell layer deposited on secondary xylem side by the cambial initials. During examination of transverse sections of the vascular cambium and differentiating cells, we have noticed that growth of fibre tips was often preceded by the formation of microspaces (Fig. 5). Microspaces are regarded as spots of separation of walls of neighbouring cells (Kojs 2012(Kojs , 2013Miodek et al. 2021aMiodek et al. , 2022, most probably accompanied by loosening of middle lamellae.

Changes occurring in tangential direction
We observed that an average tangential dimension of cells in examined zones comprising the vascular cambium and differentiating xylem is near constant-minor change from 16.79 μm in zone 1 to 16.02 μm in zone 6 occurred (Table 1). In contrast to relatively constant mean value of cell tangential dimension in subsequent zones, the average tangential wall length decreases while moving away from the initial surface-from 16.67 μm in zone 1 to 9.52 μm in zone 6. Decrease in average tangential wall length between zone 1 and 6 was 7.15 μm (16.67-9.52 μm). At the same time average tangential dimension of a fibre tip increases from 0 μm in zone 1 to 6.34 μm in zone 6 (Table 1; Fig. 6). A minor change in average cell tangential dimension between zone 1 and 6 occurred (0.77 μm). It was deduced that most probably it stemmed from specific course of rays surrounding the examined tissue fragment. This may be confirmed by the observation that the average tangential dimension of wood fibre tip in 6th zone (6.34 μm) corresponds to the change in average length of tangential cell wall between zone 1 and 6 reduced by the change in average cell tangential dimension resulting from-as already mentioned-specific course of rays (7.15 μm-0.77 μm = 6.38 μm). Analysis of changes in tangential dimensions of cells shows that an increase in average tangential dimension of growing fibre tip corresponds to average reduction in length of tangential cell walls (Table 1, Fig. 6). Moreover, when we consider that tangential dimension of a cell remains relatively constant throughout the examined zones, it indisputably proves that the growth of wood fibres in tangential direction is purely intrusive and occurs between tangential walls of surrounding cells. Statistical analysis showed that in zones 4, 5, and 6 a sum of average lengths of tangential cell walls and fibre tip tangential dimensions did not differ significantly (α = 0.05) from cell tangential dimensions (Supplementary Information  Table S8), which lends further support to the statements above. This is consistent with results obtained by Wilczek et al. (2018), and Wenham and Cusick (1975), who localised intrusive growth of wood fibres between tangential cell walls. Similar observations were conducted for the vascular cambium (Jura et al. 2006;Miodek et al. 2021b), where intrusive growth of cambial initial did not result in change in tangential dimension of analysed fragment of tissue, but instead was related to decrease in length of tangential walls of adjoining cells. As known, the onset of intrusive growth of cambial initials, VEMCs and FMCs begins close to each other-cambial initials grow intrusively in initial layer (Włoch et al. , 2013Miodek et al. 2021b), VEMCs and FMCs begin their intrusive growth at the border of vascular cambium and zone of differentiating cells (Wenham and Cusick 1975;Fujita et al. 1984). It has been said that in Fig. 5 Transverse section of cambial initials and derivative cells of black locust. Arrowheads indicate microspaces, which are formed prior to the appearance of fibre tips. Growing tips of wood fibres are shaded and indicated by asterisks. Approximated location of initial surface of the vascular cambium is marked by white, dashed line tangential direction intrusive growth of vessel elements also occurs intrusively between tangential walls of axial system cells (Wilczek et al. 2011;Hejnowicz 2012;Gizińska et al. 2021). Location of intrusive growth of initial cells between tangential walls of initial cells and their closest derivatives was shown qualitatively (Włoch et al. 2001(Włoch et al. , 2002(Włoch et al. , 2013Kojs et al. 2004a,b;Jura et al. 2006;Karczewska et al. 2009;Miodek et al. 2021b;Wilczek-Ponce et al. 2021), and in the recent time also quantitatively (Miodek et al. 2022). Thus, intrusive growth between tangential cell walls appears as a common element of cambial initials, VEMCs, and FMCs functioning.

Changes occurring in radial direction
We observed that average cell radial dimension is approx. doubled-from 4.71 μm in zone 1 to 10.37 μm in zone 6 ( Table 1). While considering the change in cell radial dimension occurring in subsequent zones, one may expect a constant increase in measured values due to progressive symplastic growth of the tissue ). After taking a closer look at mean values of cell radial dimensions for zones 1-6 it is important to notice, that indeed, mean value grows from zone 1 (4.71 μm) to 2 (5.37 μm), from zone 2 (5.37 μm) to 3 (5.95 μm), from zone 4 (5.65 μm) to 5 (6.66 μm), and from zone 5 (6.66 μm) to 6 (10.37 μm), but not from zone 3 (5.95 μm) to 4 (5.65 μm). Such an exception seems counterintuitive in the context of presumed gradual increase in mean cell radial dimension due to symplastic growth of the tissue in radial direction. This would not be so puzzling if it was limited to slowing the rate of growth or stopping it. Limitation of cell divisions/cell growth may result from unfavourable conditions for plant growth, e.g., water stress (Moehring et al. 1975;Fritts 1976). However, the observed anomaly involves a pronounced decrease in average cell radial dimension form 5.95 μm (zone 3) to 5.65 μm (zone 4). The suspicion arises that it might be an artefact encountered during anatomical investigation. Nonetheless, there seems to exist a coherent explanation of the observed anomaly. Namely, while considering cell enlargement associated with symplastic growth in radial direction,  Table 1. a Comparison of changes in cell and fibre tip tangential dimensions as well as tangential cell wall length. Microspaces were taken into account. b Comparison of changes in cell and fibre tip radial dimensions as well as radial cell wall length. Microspaces were considered or cell enlargement in general, we should keep in mind that the cell strain might be of either elastic or plastic nature (Alméras et al. 2006;Kojs 2012Kojs , 2013Kojs and Rusin 2011;Kojs et al. 2012;Cosgrove 2018). Thus, from zone 1 to 3 we observed progressive increase in average cell radial dimension, which may be explained by undisturbed symplastic growth of cells. In zone 4 first tips of growing wood fibres occur (Fig. 2). Emergence of these tips is associated with the separation of cell walls between which they grow (Wenham and Cusick 1975;Wilczek et al. 2018). It may be speculated that separation of cell walls, preceded by the presence of shear mechanical stress and loosening of middle lamellae, leads to a partial relaxation of tensile stress operating in radial direction (Gizińska et al. 2021;Miodek et al. 2021a). This in turn would result in a transient retraction of elastic cell strain. Further evidence may be found while analysing individual zones in terms of transverse surface areas of considered cells (Table 2). Changes in average cell surface areas in successive zones clearly correspond to the pattern observed in case of changes in average cell radial dimension (Fig. 7). In both cases there is a pronounced decrease in measured values form zone 3-4. This points to a nonrandom character of the change.
Average length of radial wall was reduced from 4.81 μm in zone 1 to 3.24 μm in zone 6. In zones 4-6, where growing fibre tips occur, cell radial dimension increases markedly deviating from the length of radial walls (Fig. 6). In zones 4, 5, and 6 a sum of average lengths of radial cell walls and fibre tip radial dimensions did not differ significantly (α = 0.05) from radial cell dimensions (Supplementary Information Table S8).
Conducted analysis revealed that growth of fibre tips in tangential direction is purely intrusive. The issue that still needs to be resolved is whether intrusive growth of wood fibre tips occurs between the radial cell walls as well. Based on the space-time analysis presented so far, it may be deduced that if an average length of a radial wall is reduced in subsequent zones-as it does-at least some part Table 2 Mean values of transverse surface area (TSA) of analysed cells and cell perimeter in the examined fragment of black locust tissues with consideration of six analysed zones Each value was also presented as % in relation to mean value of TSA and cell perimeter in zone 1  of growth of a wood fibre tip occurring in radial direction should be intrusive (Table 1). Reduction in an average length of radial walls accompanied by simultaneous symplastic growth of examined tissue in radial direction must, therefore, be associated with the separation of radial cell walls of adjacent cells and intrusive growth of fibre tips between these cells-into previously created spaces (initially microspaces). The above reasoning is supported by calculation performed on the mean values. First, the sum of average length of radial wall in zone 6 (3.24 μm) and average radial dimension of wood fibre tip in zone 6 (7.09 μm) corresponds almost perfectly to the average cell radial dimension in zone 6 (10.37 μm) (3.24 μm + 7.09 μm = 10.33 μm) (Fig. 6).
The difference between these values is merely 0.04 μm (10.37-10.33 μm) and may be neglected while operating on mean values. In order to figure out what was the average amount of intrusive growth of a fibre tip between radial cell walls, one should subtract average length of not separated radial walls in zone 6 (3.24 μm) from average length of not separated radial walls in zone 3 (5.92 μm), i.e. the last zone (starting from the initial layer of cambial cells) where enlarging fibre tips were not present (which means that the whole increase in average length of radial walls was symplastic until that moment). The difference is 2.68 μm (5.92 μm− 3.24 μm). Knowing how much of an average radial dimension of fibre tip in zone 6 (7.09 μm) had grown intrusively (2.68 μm), allows to calculate the contribution of symplastic component of growth. The resulting number is 4.41 μm (7.09 μm− 2.68 μm). If the above reasoning as well as calculations are true, then the quantity of symplastic growth (4.41 μm) of fibre tips should match symplastic growth of the tissue deduced from average change in cell radial dimension between zones 3 and 6. The change in question is equal to 4.42 μm (10.37 μm− 5.95 μm). It should be noted that comparison of these numbers (4.41 μm vs. 4.42 μm) shows that they are almost identical (0.01 μm difference). Such high degree of similarity of these numbers shows the accuracy of implemented measurement method. Average contribution of symplastic vs. intrusive growths in both radial and tangential directions during development of fibre tips of the secondary xylem in black locust is summarised in Fig. 8, and Table 3. Fibre tip radial enlargement is achieved in 37.8% by intrusive growth, and in 62.2% by coordinated (symplastic) growth. Fibre tip tangential enlargement is purely intrusive (100%). Our results are consistent with the conclusions drawn by Majda et al. (2021) and may be representative for most hardwood trees with libriform wood fibres. However, as the methodology used was time-consuming, this study was conducted on a limited number of wood fibre cells. Therefore, further investigation involving more tissue fragments, and performed on other angiosperm species is needed. As can be seen, intrusive growth of wood fibre tips occurs to some extent in radial direction. Such location of intrusive growth was also indicated by Rao et al. (2011) as well as Fig. 8 Diagram illustrating calculated contribution (%) of intrusive (black arrows) and symplastic (white arrows) growth in tangential and radial directions during enlargement of a wood fibre tip (based on mean values). Contribution of each type of growth is visualised geo-metrically (intrusive and symplastic-darker and lighter area respectively) within a rhombus representing a hypothetical wood fibre tip in early stage of its enlargement. Values from Table 3 were rounded to 62 and 38% respectively  Honjo et al. (2006). It may be expected that the farther away from cambial initial layer, the greater the contribution of intrusive growth in radial direction, i.e. between radial walls of neighbouring cells. It stands in accordance to the observation that mature fibre bodies change their shape to a more roundish one in a cross-section. At the same time, some fibre bodies of adjacent radial files may lose their mutual contacts entirely, as they are separated by enlarging tips of other fibres (Wilczek et al. 2018).
The above considerations as well as obtained results show that in early stages of development wood fibres grow intrusively primarily between tangential cell walls (Fig. 8). Intrusive growth also takes place between radial cell walls, but in general it does not contribute to an increase in tangential dimension of the differentiating xylem (Fig. 2). Tips of wood fibres grow symplastically in radial direction with the tissue (Wilczek et al. 2018) -the main direction of symplastic growth for most cambial derivatives (Karczewska et al. 2009;Wilczek et al. 2018;Miodek et al. 2021b;Wilczek-Ponce et al. 2021). The question arises: how is it possible that a fibre tip can grow intrusively between radial walls without enlarging the circumferential dimension of differentiating secondary xylem? It should be emphasized that the fragment analysed in our study is one of the two main encountered types of tissue arrangement. In the analysed case radial walls of rays limiting from both sides the examined fragment of the axial system run approximately parallel (as seen in cross-section)-thus, they maintain a constant distance from each other, which made it possible to carry out the analysis. In the second case distance between two rays increases to a certain extent with a distance from the initial layer (Hejnowicz 2012). We propose that intrusive growth of fibre tips between radial walls may be reconciled with lack of increase in tangential dimension of the tissue by elastic and then plastic deformation of adjacent cells in radial direction, instead of their tangential spacing. The second explanation takes into account a local spacing of cells between which intrusive growth takes place and taking over the impact of this change by means of elastic deformation of a buffering system constituted by rays integrating phloem, cambium, and xylem tissues. The narrowing of rays and simultaneous expansion of the sectors of axial system cells (located between the rays) progress with the distance from the initial layer (Hejnowicz 2012). This is accompanied by an increasing axial growth of wood fibres (Fujita et al. 1986;Wilczek et al. 2018). As tangential dimension of the fragment containing axial system cells-located between two rays-increases and the tangential dimension of rays is complementarily reduced, tangential dimension of a sector between rays' centres remains unchanged.

Conclusions
In initial stages of their enlargement wood fibre tips show: (1) entirely intrusive growth in tangential direction, i.e., between tangential cell walls; (2) symplastic and intrusive growth in radial direction, i.e., between radial cell walls. In the studied case, when rays surrounding analysed fragment of axial system maintain almost constant distance from each other, intrusive growth of wood fibres does not contribute to an increase in tangential dimension of considered tissue. This stays in agreement with circular-symmetric model of radial growth of the vascular cambium (Karczewska et al. 2009;Miodek et al. 2021b), as well as studies showing that intrusive growth of cambial initial cells and vessel elements occur between tangential cell walls of neighbouring cells (Gizińska et al. 2021;Miodek et al. 2021aMiodek et al. ,b, 2022. It is worth investigating whether cambial initial cells, vessel elements and wood fibres have a common mechanism of radial growth. Such universal mechanism may rely on a morphogenetic field of mechanical stresses, which could regulate developmental processes and appear to be placed high in the signalling hierarchy in plant organisms (Miodek et al. 2021a). This possibility still remains largely uncharted territory and seems like a tempting path towards profound progress of our knowledge on plant development in the future.
Author contribution statement Study design: AM. Tissue collection/preparation: AM. Data analysis/interpretation: AM, AG, PK. Statistical data analysis: AM. Manuscript drafting: AM, AG. Manuscript editing: AM, AG, PK. All authors read and approved the final manuscript.

Funding
The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.
Data availability All data generated or analysed during this study are included in this published article and its Supplementary Information.

Conflict of interest
The authors declare that they have no conflict of interest.
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