Brook et al. 2013.1 3 The development of the mammalian dentition as a complex adap- tive system Alan H. Brook 1,2 , Toby E. Hughes 1 , Grant C. Townsend 1 , Richard N. Smith 3 and Matthew D. Brook O’Donnell 4 1School of Dentistry, University of Adelaide, 2School of Dentistry, Queen Mary University of London 3Dental School, University of Liverpool, 4Annenberg School for Communication Studies, University of Pennsylva- nia Complex Systems are widespread in biological systems and communities. Interacting adaptive entities produce dynamic patterns and structure. In a biological complex adaptive system the inter- action of lower level components leads to the emergence of high level phenomena and struc- tures. Such systems have the general characteris- tics of self-adaptation, self-organisation, emer- gence, multitasking, robustness, critical phases, diversity and compatibility, with such statistical properties as Thresholds and Scale Free Networks (Barabasi, 2003; Camzine et al., 2003; Mitchell, 2009). The aim of this study was to investigate whether development of the dentition exhibits the general and statistical characteristics of a Complex Adaptive System by examining data on normal and abnormal dental development. DENTAL DEVELOPMENT Key characteristics of dental development are that it is multi-levelled, has multiple interactions, is multi-factorial, is multidimensional and is pro- gressive over time (Brook, 2009). The core compo- nents of this process are summarised in Table 1 and are illustrated in Figure 1. THE DENTITION AS A COMPLEX SYSTEM The next step is to examine the components of dental development against the key characteristics of complex systems. Self-organisation and emergence are evident as tooth germs emerge from molecular level inter- actions (Lesot and Brook, 2009)and then progres- sively develop and grow in size and shape until they commence calcification and form mature teeth. The initiation of tooth germs occurs at spe- cific sites within a field and they progress to form different shapes and sizes, so that the calcified macroscopic teeth which emerge are discrete but organised into groups that have different shapes and functions around the dental arch. ABSTRACT General characteristics of Complex Adaptive Systems include self-adaptation and or- ganisation, emergence, multitasking, robustness, critical phases, diversity and compatibility with such statistical models as Thresholds and Scale Free Networks. The aim was to investigate wheth- er dental development exhibits the general and statistical characteristics of a Complex Adaptive System, by examining data on normal and abnor- mal dental development. The findings were that self-adaptation and organisation occur while inter- actions between genes, epigenetic and environ- mental factors lead to the emergence of cells, tooth germs and mineralised teeth. Multitasking occurs as signalling pathways act simultaneously and reiteratively during initiation and morphogenesis. Tooth germs that do not attain a critical threshold during development may undergo apoptosis. Di- versity is evident in tooth number, size, shape and mineralisation. Statistical investigation shows that males have significantly larger teeth and higher prevalences of megadontia and supernumerary teeth (p<0.05), supporting Brook’s Threshold Model which is further developed here to include shape. Image Analysis of tooth dimensions showed they followed a Power Law distribution, with the first 8 of 34 factors in upper lateral inci- sors accounting for 94.4% of the total variation. In conclusion, the development of the dentition shows the general and statistical characteristics of a Complex Adaptive System. Correspondence to: Alan Brook, School of Dentistry, University of Adelaide, Adelaide, South Australia, 5005 Email: alan.brook@adelaide.edu.au Telephone: +61 (0)8 8313 2910 Keywords: Complex Systems, Networks, Dental Development 4 Fig. 1. The multilayered developmental process of tooth formation illustrating the molecular changes within the cells and tissues and the macroscopic outcomes (part of figure from http://bite-it.helsinki.fi/). TABLE 1. The key characteristics and components of dental development Characteristic Components Multilevel Mature tooth Cells, tissues, tooth germs Molecular Multiple interactions Tooth germ – Tooth germ Cell – Matrix Cell – Cell Gene – Epigenetic – Environment Gene – Gene Multifactorial Environmental – local / systemic Epigenetic – narrow / broad Over 300 genes Multidimensional Spacial – x, y, z dimensions Time Progressive over time Each dentition Tooth type / morphogenetic field Each tooth 5 The outcome is an integrated, balanced, complex system. It is a major characteristic of a complex system that the mature units bear no resemblance to the precursor entities. Self-Adaptation is demonstrated by the within -species and between-species diversity that is found. In humans, variations in the number, size, shape and mineralisation of teeth occur frequently (Brook et al., 2009; Townsend et al., 2009). Between species variation in these parameters is also exten- sive (Hillson, 1986).One of the factors to consider is the adaptive interaction that can occur between developing tooth germs, with the timing of devel- opment of each being important. Timing is also significant in the critical phases of dental develop- ment. For progression from the initial phase to morphogenesis (Fig. 1), transcription factors in the Msx, Dlx and Lhx families are required. The tooth germ may undergo apoptosis if this progress does not occur at this critical time. Similarly, if the ma- trix proteins are not removed during enamel calci- fication, defects in mineralisation result. Robustness in the development of the denti- tion comes from the satisfactory functioning of the system even in the presence of variations and moderate developmental defects. Mature teeth have some ability to self-repair and continue to develop in response to environmental challenges, a property akin to self-awareness. This robustness is also associated with excess capacity: genes are switched on and off and function reiteratively in multiple tissues; genes can also be up-regulated, down-regulated and, if their function is defective, other genes sometimes function to produce the necessary product; genes in function can be alter- natively spliced and the products varied in amount and nature. Multitasking adds to this robustness as signal- ling pathways act simultaneously and reiterative- ly. Similarly, the ameloblasts control the secretion and later removal of the enamel matrix proteins, as well as the deposition of the minerals. STATISTICAL MODELS Based on epidemiological and clinical data, Brook (1984) developed a model to explain the relationship between the prevalence of dental anomalies of number and size. This model is based on a normal distribution on which thresholds are superimposed beyond which microdontia, hypo- dontia, megadontia and supernumerary teeth oc- cur. Here the model is further developed to in- clude shape (Fig. 2). As tooth size moves closer to the thresholds that determine variation in tooth number, teeth tend to display abnormal shape as well as size. An example is the diminutive perma- Fig. 2. This development of the Threshold Model of Brook (1984) now incorporates the shape changes seen at the extremes of tooth size. 6 nent upper lateral incisor which is often ‘peg- shaped’ as well as being very small. The develop- mental process underlying these clinical findings and modelling has been elucidated in molecular genetics and histological studies (Brook, 2009; Lesot and Brook, 2009). The Scale Free Network model reflects findings that when the frequencies of each of the compo- nents in some systems are plotted, the result is a Power Law Distribution (Fig. 3). This distribution occurs when a few compo- nents occur with a high frequency and the large majority occur with lower frequency. In a Princi- pal Component Analysis of 34 dimensions in up- per incisor teeth, 94 per cent of the total variance was accounted for by 7 dimensions (Khalaf et al., 2009), thereby displaying the properties of a Scale Free Network. CONCLUSIONS The dentition exhibits the characteristics of a Complex Adaptive System, both in development and in its mature form. During evolution it has become adapted to different environments. It serves as a valuable model for investigating how genetic, epigenetic and environmental factors in- teract during somatic development. ACKNOWLEDGMENTS This project was part of the studies funded by Wellcome Programme Grant 3256. LITERATURE CITED Barabasi AL. 2003. Linked. Plume Books. Penguin Group New York. Brook AH. 1984. A unifying aetiological explana- tion for anomalies of tooth number and size in humans. Arch Oral Biol 29:373-378. Brook AH. 2009. Multilevel complex interactions between genetic, epigenetic and environmental factors in the aetiology of anomalies of dental development. Arch Oral Biol 54:S3-S17. Brook AH, Griffin RC, Smith R, Townsend GC, Kaur G, Davis GR, Fearne G. 2009. Tooth size patterns in patients with hypodontia and super numerary teeth. Arch Oral Biol 54:S63-S70. Camazine S, Deneubourg J-L, Franks NR, Sneyd J, Theraula G, Bonabeau E. 2003 Self-Organization in Biological Systems. Princetown, NJ: Princeton University Press. Hillson S. 1986. Teeth. Cambridge University Press. Khalaf K, Smith RN, Elcock C, Brook AH. 2009. Multiple crown variables of the upper inci- sors in patients with supernumerary teeth com- pared with controls. Arch Oral Biol 54:S71- S78. Lesot H, Brook AH. 2009. Epithelial histo- genesis during tooth development. Arch of Oral Biol 54:S25-S33. Mitchell M. 2009. Complexity. A guided tour. Ox- ford University Press. Townsend G, Harris EF, Lesot H, Clauss F, Brook AH. 2009. Morphogenetic fields within t h e h u man dentition: A new, clinically relevant synthesis of an old concept. Arch Oral Biol 54: S34-S44. Fig. 3. A typical power law distribution where a few factors occur frequently in a system