Nonlinear Epigene-c Variance: empirical data and neural network development

Transcription

1 Nonlinear Epigene-c Variance: empirical data and neural network development Maartje Raijmakers 1 Kees- Jan Kan 1,2 University of Amsterdam Free University, Amsterdam

2 Twin Simula-on Study What individual differences are created in a popula-on of non- linear dynamical systems due to nonlinear characteris-cs like bifurca-ons? Behavioral gene-c analysis of a popula-on of simulated developing neural networks

3 Unexplained Variance Cloned Swines Varia-on in the number of teats Hair growth papern varia-on Varia-on in body height and weight (Archer et al. 2003a)

4 Unexplained Variance Behavioral Traits Archer et al. (2003b) compared the variance in several behavioral traits of cloned swines with control (outbred) swines that were held under similar condi-ons The variance within the cloned group was as great as or even greater than the variance in the control group

5 UnU Gene-cally Iden-cal marbled crayfish raised in highly controlled environments. (Vogt et al., 2008)

6 Unexplained Variance Isogenic animal studies Several animal studies (mice, caple, swines, crayfish) have shown that the total variance in gene-cally iden-cal animals under iden-cal condi-ons, is comparable to variance in control groups. (Gärtner, 1990; Archer et al. 2003; Smith, 2011) The prenatal environment was also not a major source of phenotypic varia-on

7 Unexplained Variance Teeth Development (Townsend et al., 2005) MZ Twin Hypodon-a (missing teeth) at mirror sites Missing third molar (wisdom teeth)

8 Unexplained Variance Brain Structure (Hulshoff Pol et al., 2006) Heritability: Low for minor gyri and sulci. Low for asymmetry (Eckert, 2005) Higher for gray and white maper volume

9 Unexplained Variance Fluctua-ng asymmetry: Small morphological asymmetries in various bilateral traits In humans, e.g., bodily and facial features (Fink et al., 2004; Kowner, 2001) Minor physical anomalies: Several studies have demonstrated the existence of atypical asymmetries e.g., in humans, significant dissimilari-es in gyral and sulcal features between monozygo-c twins (Eckert et al., 2002) The direc-on of these dissimilari-es is not under gene-c control Overviews of empirical literature by Gärtner (1990), Archer et al. 2003, Smith (2011), Kan et al. (2009, 2011)

10 Tradi-onal Behavior Gene-c Model Decomposition of phenotypic variance into latent factors 1) A genetic factor Decomposed into Additive genetic (A) Dominance and Epistasis (D) 2) An environmental factor Decomposed into Shared environment (C) Nonshared environment (E) (includes Error variance)

11 Tradi-onal Behavior Gene-c Model e.g., the ACE model A C E Ph Assump-on: genotypic and environmental factors reflect the underlying mechanisms causing phenotypic individual differences

12 Smith, G. D. (2011). Epidemiology, epigene-cs and the Gloomy Prospect : embracing randomness in popula-on health research and prac-ce. Interna4onal journal of epidemiology, 40(3),

13 A causal interpreta-on requires cau-on Research is based on the premise that the phenotypic variance is ul-mately traceable to iden-fiable variables To date apempts to iden-fy such variables have met with only limited success Why is it so difficult to iden-fy these variables?

14 Hypotheses about Unexplained Variance Interac-on between genotype and non- shared environment Stochas-c influences in developmental process Stochas-c events in life Stochas-c processes at the molecular level Circumstances in prenatal development Epigenesis: Nonlinear growth processes

15 Epigenesis: Third Source of Variance Nonlinear growth processes result in addi-onal variance that cannot be explained by Gene-c and Environmental factors (Molenaar et al., 1993)

16 Overview Epigenesis: the kind of processes Eduard d Alton ( ) First days of chicken development Epigene-c growth in a standard behavior gene-c design Simula-on Study

17 Epigenesis Tradi-onal Epigene-cs (Waddington, 1957) The context- dependent unfolding of gene-c control of development As in the epigene-c landscape Modern Epigene-cs Refers to the study of heritable traits that do not involve changes to the underlying DNA sequence As in epigene-c inheritance

18 Epigene-c Landscape (Waddington, 1957) The system has a limited number of developmental paths, which results in stability At cri-cal points (bifurca-on points) small differences may have large consequences for development (trajectory A versus B) Recurrent Interac-on Genes and Environment: Gene products may alter the landscape, whereas altera-ons in the landscape may result in altera-ons in gene expression

19 Epigenesis: Recurrent Interac-ons between Brain and Environment Adapta-on of the brain in abnormal development Verbal memory func-ons in visual cortex of people with congenital blindness (Amedi et al., 2003)

20 Neuroconstruc-vism A. Karmiloff- Smith (1998) Developmental Psychopathology: Performance can be intact by underlying atypical cogni-ve processes (Williams syndrome: Karmiloff- Smit et al., 2004) Minor devia-ons from normal values in early development can give rise to large effects on behavior level, later in development (Simula-on studies: Thomas & Karmiloff- Smith, 2002, BBS)

21 Dynamical Systems & Nonlinearity Small causes, e.g., effec-ng ini-al condi-ons, may have large effects. If the system is sensi-ve to ini-al condi-ons, the outcome of the system may be hard to predict The outcome will appear stochas-c Two different sources of unpredictability 1. Seemingly random behavior (chaos) 2. Qualita-ve change in behavior (bifurca-on)

22 Single Chaos: pendulums Discrete linear systems Logis-c Equa-on Sensi-vity to Ini-al Condi-ons I

23 Twin Simula-on: Chao-c system Molenaar & Raijmakers (1999) MZ pair DZ Pair Heritability parameters = 1.0 Ini-al condi-ons =

24 Twin Simula-on: Chao-c system Eaves et al. (1999) and Molenaar & Raijmakers (1999) The discrete logis-c equa-on as a simple model of chao-c processes in development Over -me, DZ within- pair correla-ons decreased at higher rates to low levels (close to zero) than did MZ within- pair correla-ons Observed heritability of zero Thus, the role of chao-c epigene-c processes in development may be quite limited (Eaves et al., 1999)

25 Varia-on related to Bifurca-ons It is important to consider how nonlinear effects may accumulate and combine In chao-c systems nonlinear effects amplify each other In epigene-c systems they can average out to produce a kind of sta-s-cal macro- level behavior (papern forma-on or self- organisa-on)

26 PaPern Forma-on (Miyazama et al., 2010)

27 Epigenesis: non- linear characteris-cs Different parameter values give qualita-ve different outcomes Bifurca-ons separate different dynamical regimes small smooth change made to the parameter values (the bifurca-on parameters) of a system causes a sudden 'qualita-ve' or topological change in its behavior. In the proximity of bifurca-ons, sensi-vity to fluctua-ons Mul-- stability: same parameters, different ini-al condi-ons may result in different outcomes.

28 Twin Simula-on: Epigenesis Kan, Ploeger, Raijmakers, Dolan & van der Maas (2009) Neural network growth model of van Oss and van Ooyen (1997) as a simple model of epigene-c development This model shows nonlinear epigene-c processes with bifurca-ng, but non- chao-c, behavior Biologically mo-vated model of epigene-c development

29 Ac-vity- Dependent Neurite Outgrowth Van Ooyen et al. (1995) Excitatory Ac-vity Inhibitory Ac-vity Connec-on Strength W ij

30 Ac-vity- Dependent Neurite Outgrowth Van Ooyen et al. (1995) Cri-cal periods for pruning connec-ons Ini-al Overshoot Van Pelt et al. (1996)

31 Synap-c Density: HuPenlocher (1997) rep(1, 10) Auditory cortex Visual cortex Prefrontal cortex Auditory cortex Visual cortex Prefrontal cortex :10

32 Simula-on Study: The Two- Cell Model ε: membrane potential at which neurite outgrowth is 0 p: the relative inhibitory connection strength. Individual differences in ε and p

33 Two Cell model: Bifurca-on Diagram Mul-- stable One equilibrium

34 Simula-on Study: The Two- Cell Model In the absence of bifurca-ons, p =.435, p =.420, p =.402 In the proximity of bifurca-ons, p =.315, p =.300, p =.282

35 Simula-on Study: The Two- Cell Model Time series for 200 MZ and 200 DZ twin pairs Parameters p and ε in a simple ACE design: h 2 =.50 c 2 =.49 e 2 =.01 Star-ng values of x, y and w were set at 0 Es-ma-on of the contribu-ons of the gene-c and environmental factors (latent variable modeling + linear regression) And interac-ons effects (in regression models)

36 Simula-on Study: The Two- Cell Model Good fit (Χ 2 (3)=.00, p=.99) Unexplained variance: MZ =.05%, DZ =.06% In the absence of bifurca-ons Es-mated h 2 =.47 c 2 =.52 e 2 =.01 GxE interac-on does contribute very liple Unexplained variance: MZ =.01%, DZ =.01%

37 Simula-on Study: The Two- Cell Model ACE- model: Good fit (Χ 2 (3)=.50, p=.91) Regression model: Unexplained variance: MZ = 58.1%, DZ = 63.3% Es-mated h 2 =.63 c 2 =.00 e 2 =.37 GxE interac-on does contribute very liple Unexplained variance: MZ = 53.1%, DZ = 62.5% In the proximity of bifurca-ons

38 Consistency with empirical studies Results are consistent with the well established findings in behavior gene-c studies in psychology! A substan-al amount of variance can be apributed to gene-c differences Over -me In intelligence, heritability increases Shared variance ozen decreases (to 0) Non- shared variance ozen increases Monozygo-c twins are more than twice as similar as dizygo-c twin (e.g., Turkheimer, 2000; McGue et al., 1998; Haworth et al., 2010)

39 Conclusions 1. Nonlinear epigene-c variance is subsumed under the nonshared environmental factor 2. Nonlinear epigene-c variance cannot be modeled by GxE interac-on 3. Nonlinear epigene-c variance is an independent source of individual differences 4. Nonlinear epigene-c variance may be one source of the unexplained variance in experimental studies 5. The presence of nonlinear epigene-c variance complicates iden-fica-on and quan-fica-on of ul-mate gene-c and environmental causes of individual differences

40 Thank You Molenaar, P.C.M., Boomsma, D.I., & Dolan, C.V. (1993). A third source of developmental differences. Behaviour Gene-cs, 23, Molenaar, P. C., & Raijmakers, M. E. (1999). Addi-onal aspects of third source varia-on for the gene-c analysis of human development and behaviour: a commentary on Eaves et al. Twin research : the official journal of the Interna4onal Society for Twin Studies, 2(1), Kan, K.- J., Ploeger, A., Raijmakers, M. E. J., Dolan, C. V., & van der Maas, H. L. J. (2010). Nonlinear epigene-c variance: review and simula-ons. Developmental science, 13(1), Kan, K- J, Boomsma, D.I., Dolan, C.V. & van der Maas, H.L.J. (Accepted). The presence of bifurca-ons as a third component of individual differences : Implica-ons for quan-ta-ve (behavior) gene-cs. Interna4onal journal of Epidemology. Contributors Kees- Jan Kan (Free University) Han van der Maas (University of Amsterdam) Peter Molenaar (Penn State University) Conor Dolan (University of Amsterdam) Dorret Boomsma (Free University) Annemie Ploeger (University of Amsterdam)