A mathematical framework for modelling cambial surface evolution using a level set method

Background and Aims

During their lifetime, tree stems take a series of successive nested shapes. Individual tree growth models traditionally focus on apical growth and architecture. However, cambial growth, which is distributed over a surface layer wrapping the whole organism, equally contributes to plant form and function. This study aims at providing a framework to simulate how organism shape evolves as a result of a secondary growth process that occurs at the cellular scale.

Methods

The development of the vascular cambium is modelled as an expanding surface using the level set method. The surface consists of multiple compartments following distinct expansion rules. Growth behaviour can be formulated as a mathematical function of surface state variables and independent variables to describe biological processes.

Key Results

The model was coupled to an architectural model and to a forest stand model to simulate cambium dynamics and wood formation at the scale of the organism. The model is able to simulate competition between cambia, surface irregularities and local features. Predicting the shapes associated with arbitrarily complex growth functions does not add complexity to the numerical method itself.

Conclusions

Despite their slenderness, it is sometimes useful to conceive of trees as expanding surfaces. The proposed mathematical framework provides a way to integrate through time and space the biological and physical mechanisms underlying cambium activity. It can be used either to test growth hypotheses or to generate detailed maps of wood internal structure.     

Levels of endogenous indole-3-acetic acid in the vascular cambium region of Abies balsamea trees during the activity - rest - quiescence transition

Indole-3-acetic acid (IAA) levels in the cambial region were measured by radioimmunoassay during the annual cambial activity - rest - quiescence transition at the crown top (current-year shoots) and at the middle and base of the stem of two 21-year-old Abies balsamea (L.) Mill. trees about 7.5 m in height. The IAA level declined throughout the experimental period (July 24 - December 3) at all positions in both trees. The earlywood - latewood transition, which occurred throughout each tree about the end of July, was associated in time with the largest decrease in the absolute amount of IAA. Tracheid production ceased towards the end of September, the cessation occurring earlier at the top of the tree than at the base. The cessation of tracheid production was only poorly correlated in time and space with the decline in IAA level, and it was not prevented by exogenous IAA. The results suggest that IAA level is involved in the control of tracheid radial enlargement, but not in the regulation of the cessation of tracheid production.     

泡桐维管形成层及木质部区的转录组分析

采用Illumina HiSeqTM2500高通量测序技术,获得泡桐维管形成层及木质部区组织转录组的109021918条clean reads(16.35 Gb)。将clean reads从头组装得到104432个单基因簇(Unigene),平均长度662 nt。将组装得到的Unigenes与公共数据库进行序列比对,分别有40789(Nr:39.05%)、31675(NT:30.33%)、15539(COG:14.87%)、29168(GO:27.93%)、16316(KEGG:15.62%)、30499(SwissProt:29.20%)以及28828(Pfam:27.6%)个Unigenes获得功能注释。通过与GO数据库的比对分析,注释的29168个Unigenes归于生物过程、细胞组分及分子功能三大类的55个功能组;15539条Unigenes注释到COG数据库,被分为25个类别中;基于KEGG数据库可将16316个Unigenes归于130个代谢途径。此外,在泡桐的维管形成层及木质部区转录组中共检测出16118个简单序列重复(SSR)位点。为进一步挖掘泡桐重要功能基因提供了大量数据。     

Xylem pathways in liana stems with variant secondary growth

FISHER, J. B. & EWERS, F. W., 1992. Xylem pathways in liana stems with variant secondary growth. The three-dimensional construction of stem xylem in tropical lianas (woody vines) was studied using several approaches: 1. observations of the xylem surface in stems with bark removed after NaOH treatment or natural retting; 2. reconstructions from serial transverse sections; 3. movement of dye solutions up isolated xylem sectors in intact plants, and 4. flow of dye solutions down branches and xylem sectors in isolated stem segments. Long distance (up to several metres) xylem pathways in unbranched stems and connections between lateral branches and main stems are described for !5 species in eight families which represented seven differnt patterns of secondary growth. The xylem in even the most complex stems is integrated by three-dimensional interconnections of xylem regions which may appear isolated in transverse section. Interconnections are most common at leaf and branch nodes. Some old stems have peripheral xylem that remains isolated over long distances in unbranched stems, but even these had structural and physiological interconnections between xylem regions at branch nodes.