Speaker:

1
Modelling and analysis of spatially distributed
systems regulation in apical meristem of
Arabidopsis thaliana

• Speaker
• Dr. N. A. Kolchanov,1,2
• Coauthors
• I. R. Akberdin1, E. A. Ozonov2, V.V. Mironova1,
  D.N. Gorpinchenko1,
• N. A. Omelyanchuk1, V. A. Likhoshvai1,2, S.I.
  Fadeev3, Eric Mjolsness4
• 1-Institute of Cytology and Genetics SB RAS,
  Novosibirsk, Russia
• 2-Novosibirsk State University
• 3-Institute of Mathematics, Novosibirsk, Russia
• 4-Institute for Genomics and Bioinformatics,
• University of California, Irvine, USA
• e-mail kol_at_bionet.nsc.ru
• Corresponding author
• http//www.bionet.nsc.ru/labs/modelgroup/

2
Integration of the experimental fragments
3
Subject of the research Arabidopsis thaliana L.
Arabidopsis was the first completely sequenced
plant genome. There is special international
research program targeted to identification of
functions of all the genes by 2010. Number of
papers about expression of the known genes goes
up each year

• The Basic phytohormones
• Auxin is the basic family of plant hormones
  regulating cells division. Among them is the
  differentiation factor Indole-3-acetic acid (IAA
  or heteroauxin).
• Cytokinin - plant hormone originating from
  6-aminopurine The basic natural cytokinin is
  zeatin (his synthetic analog is kinetin ???????)
  Cytokinin in charges of totipotency
  maintenance.
• 6-phurphurilaminopurine

MCCMB,2007
4
Final goal of this study

• Reconstruction of the mathematical models that
  describe development of different parts of plant
  organism under the auxin control. in this report,
  we will consider two mathematical models 1d
  model of root development in ordinary
  differentiation equations and 2d model describing
  meristem development in cellular automaton terms.

5
Outline

• 1D-model of auxin distribution in plant roots
• Auxin metabolism gene network
• 2D-model of primary shoot apical meristem (SAM)
  morphogenesis of Arabidopsis thaliana

6
Auxin function on root development

• Auxin regulates cell division and elongation in
  root
• Auxin regulates functioning of primary RAM
• Auxin induces development of lateral RAM
• Auxin regulates the gravity response

MCCMB,2007
From Tanaka H. et al., 2006
7
Pattern of auxin distribution in root
Wang et al., 2005
Sabatini et al., 1999
The maximum of auxin distribution in root
coincide with location of stem cell niche in RAM
tipically
MCCMB,2007
8
There are two types of auxin transport in the
root acropetal and basipetal

• Influx of auxin is mediated by the influx carrier
  AUX1.
• Efflux of auxin is mediated by several efflux
  carriers.
• PIN proteins exhibit synergistic interactions.
• The loss of a specific PIN protein is compensated
  for by auxin dependent ectopic expression of its
  homologues.

From Vieten. et al., 2005
MCCMB,2007
9
Polar auxin transport is regulated by auxin

• Positive feedback
• Auxin promotes degradation of the AUX/IAA
  repressors, thus releasing auxin response factor
  (ARF) transcriptional regulators from inhibition.
  In this manner the expression of different sets
  of genes is activated including PIN genes (Sauer
  et al., 2006).
• Auxin promotes its own efflux from cells by
  inhibiting endocytosis and by this way increasing
  levels of PINs at the plasma membrane (Paciorek
  et al., 2005).

• - Negative feedback
• High concentrations of auxin decreases its own
  efflux by auxin-dependent post-transcriptional
  downregulation of PIN proteins (Vieten et al.,
  2005) by proteasome-dependent turnover (Sieberer
  et al., 2000).

PIN1 expression
-
Dependence of PIN1 expression from auxin
concentration Vieten et al., 2005
MCCMB,2007
10
1D-model of auxin distribution in plant roots.
The array of cells located on the longitudinal
axis
1
2
3
i
i1
N
Auxin influx from shoot to root
- influx stream
Auxin dissipation
- constant of dissipation rate
Constant Auxin bidirectional passive efflux stream
- constant of passive efflux stream
active Auxin unidirectional stream regulated by
auxin Ko - constant of active efflux stream
Problem definitionIs it enough for auxin
distribution such set of rules in transport
regulation?
11
Regulation function of auxin active transport
q111,q12100,p12
q23,p110
a
a
a the auxin concentration in cell
q11 the activation threshold
q12 the saturation threshold of the activation
q2 the inhibition threshold
p1, p2 Hill coefficients
12
1D-model of auxin distribution in plant
roots.The equations
(1)
nonlinear dependence on unidirectional efflux
from auxin linear dependence on bidirectional
efflux and dissipation The positive feedback on
the auxin transport when auxin concentration
below the ingibition threshold The negative
feedback on the auxin transport when auxin
concentration upper the ingibition threshold
(2)
MCCMB,2007
13
Correspondence of the simulation to the real
auxin gradient in roots
Wang et al., 2005 Simulation
Values of parameters of 1D-? model at which
simulation is adequate to real auxin gradient
- parameter values are in arbitrary units cu
for concentrations, tu for time
MCCMB,2007
14
The model analysis
1. The model has the great number of stationary
solution.
The characteristic property of all of them is the
maximum at the end of root. There is available to
form maximum at the different part of the root
depending on auxin influx and model parameters
We was distinguish the 4 type of stationary
solution
MCCMB,2007
15
Biological interpretation of the model. Cyclic
change of root development phases in depending
on auxin stream intensity from shoot to root.
lateral root
auxin stream from shoot to root
maximum at the end of root
root thickening
16
Shoot apical meristem
MCCMB,2007
17
Cellular automaton model. The Basic principles
Cell parameters in the model
Cell types in the model

• The cells in the model may receive and, depending
  on the cell type, produce signals that should be
  accepted by other cells in the model. Three
  biologically meaningful signals, which
  unambiguously stimulate the morphodynamics of
  cell tissues at the generally accepted level of
  abstraction, were selected
• SS is Stem Signal (most likely it is cytokinin)
• SD is Differentiation Signal (most likely it is
  auxin)
• BS is Basal Signal (most likely it is analogy of
  the auxin)
• All the embryo cells in the model can be
  classified according to the type of the signal
  they produce
• Cell types and duration of the cell cycle depend
  on the local signal concentration
• Direction of the cell division depends on
  gradients of the signal distribution.

Type Cell type BS0 (Basal Signal value), SS0
(Stem Signal value), SD0 (Differentiation Signal
value) the values of the signals produced by
the cell BS, SS, SD - the values of the above
mentioned signals accepted by the cell Kij the
characteristic of cell state at position (i, j)
calculated as the ratio of SS to SD. At the
current point of time, the cell state is
characterized by the parameter T(Kij)ij the
period of cell division, which depends on the
current value of the characteristic Kij Tpij
the number of iterations after the last division
of the cell at position (i, j).
Cellular automation is the multi-object computer
simulation tool that consists of the large
number of simple identical components with local
interactions layered over a lattice or grid. In a
cellular automaton model the embryo is described
as a two-dimensional array of cells, the rates
of which divisions depend on the cellular
environment.
Directions of the models hypothetical signal
distributions in heart-stage embryo tissues
Ilya R. Akberdin, Evgeniy A. Ozonov, Victoria V.
Mironova, Nadezda A. Omelyanchuk, Vitaly A.
Likhoshvai, Dmytry N. Gorpinchenko, Nikolai A.
Kolchanov (2007). A CELLULAR AUTOMATON TO MODEL
THE DEVELOPMENT OF PRIMARY SHOOT MERISTEMS OF
ARABIDOPSIS THALIANA. Journal of Bioinformatics
and Computational Biology, Vol. 5, 02B, pp.
641-650
Berleth T. and Chatfield S. Embryogenesis
Pattern Formation from a Single Cell. The
Arabidopsis Book, Published Online September
30, 2002. http//www.bioone.org/perlserv/?request
get-abstractdoi10.11992Ftab.0051
MCCMB,2007
18
According to experimental data, the period of
cell division in the stem meristem cell niche
depends on the ratio of auxin to cytokinin

• According to the model adaptation
• the threshold value of the parameter K providing
  transition from Promeristem to L2. L3 Meristem
  is equal to 15
• the threshold value of the parameter K arresting
  the cell division is equal to 1.

MCCMB,2007
19
Interactions between model cells
The system of ordinary differential equations is
calculated for each cell

• Local interaction

• Global interaction

MCCMB,2007
20
Visualization of the cellular automaton model
Stem signal
Basal signal
Differentiation signal
MCCMB,2007
21
Results of model. Normal development of SAM
torpedo stage
globular stage
heart stage
16 cell embryo
Quantitative coincidence structure of meristem,
and cell types localization Qualitative
coincidence cell number of the different type
cells at the current stage
MCCMB,2007
22
Results of model. Mutant development of SAM
Experiment. According to the experimental data
(Sharma V.K. and Fletcher J.C., 2003) , wus-1
mutant lead to meristem differentiation and
meristem zone decreases in the size. Model.
According to simulations, the abovementioned
phenotype could be obtained under the following
assumptions the threshold value of parameter K
in Promeristem cell is lower in mutants than in
the wild type.
Experiment. According to the experimental data
(Aida M., Ishida T., Tasaka M.,1999) , cuc1 cuc2
mutants lead to meristem differentiation and
arrest of the plant development. Model.
According to simulations, the abovementioned
phenotype could be obtained under the following
assumptions sensitivity of Promeristem cell to
Signal of Differentiation is higher in the mutant
than in the wild type The sensitivity of L2,
L3meristem cells to Stem Signal is lower in the
mutant than in the wild type.
MCCMB,2007
23
Analyze sensitivity model to SD (differentiation
signal) penetrance and synthesis
Isoline characterizes number cell at the k (nltk)
development stage under parameter variations
Isoline characterizes number cell at the n
development stage under parameter variations
wus-1 mutant lead to meristem differentiation
and meristem zone decreases in the size.
Normal development
cuc1 cuc2 mutants lead to meristem
differentiation and arrest of the plant
development.
coefficient of SD synthesis
coefficient of SD diffusion
MCCMB,2007
24
Next problem

• Described before model allows to obtain
  quantitatively interesting results that enable to
  interpret some features of the meristem growth
  and development. In order to turn to molecular
  genetic mechanisms consideration of meristem
  growth and development regulations, its
  necessary, first of all, to reconstruct gene
  networks regulating that processes. One of the
  key gene network is auxin metabolism gene network
  in the cell.
• This task was solved by using of GeneNet
  computer technology that allows to describe
  complex biological processes in terms of
  molecular genetic and biochemical objects and
  processes.

25
Auxin biosynthesis gene networkis reconstructed
by GeneNet
peroxisome
nucleus
ER lumen
cytoplasm
chloroplast
mitochondria
cell membrane
- Ananko E.A., Podkolodny N.L., Stepanenko
I.L., Podkolodnaya O.A., Rasskazov D.A., Miginsky
D.S., Likhoshvai V.A., Ratushny A.V.,
Podkolodnaya N.N., Kolchanov N.A. (2005) GeneNet
in 2005. Nucleic Acids Res., 33, D425-D427
MCCMB,2007
26
Auxin biosynthesis gene network
MCCMB,2007
27
Conclusions
Future prospects

• consider in the model more
• complex geometry of cell interactions,
• molecular processes regulating active transport
  of morphogenes and
• genetic processes regulating their biosynthesis
  and conjugation-degradation!!!

• The GeneNet technology was used to reconstruct
  the auxin biosynthesis gene network

We constructed a mathematical model of the SAM
development in embryogenesis of Arabodopsis
thaliana
The model adequately describes two processes
cell differentiation and maintenance of stem cell
population
In this cellular automaton we modeled abnormal
SAM development in two mutants cuc1 cuc2, wus-1
Early development step of the SAM was adequately
simulated without considering active transport
of Basic signal. Embryo anisotropy is formed
mainly by Basal signal. Processes of the signal
distribution can be described in diffusion
framework
SAM development is more affected by parameters
responsible for morphogene transport than by
parameters related to morphogene biosynthesis.
MCCMB,2007
28
Acknowledgements

• INNOVATION PROJECT IT-CP.5/001 Development of
  software for computer modeling and design in post
  genomic system biology (system biology in
  silico)
• US National Science Foundation (FIBR EF-0330786
  Development Modeling and Bioinformatics)
• Russian Foundation for Basic Research No
  05-07-98012-p 06b B,05-07-9801204-01-00458,
  05-07-98011
• projects of the SB RAS Presidium No
  10104-34/?-18/155-270/1105-06-001/28/2006-1
• the Russian Federal Agency for Science and
  Innovations (State contract No 02.467.11.1005)
• interdisciplinary integration projects of
  fundamental study of the SB RAS No 34, No 115.

MCCMB,2007
29
Eric Mjolsness
Fadeev S.I.

• Thank you for
• your attention!!!

Gorpinchenko D.
Likhoshvai V.A.
Omelyanchuk N.A.
Ilya Akberdin
Mironova V.V.
Ozonov E.
30
MGSmodeller computer system for reconstruction,
calculation and analyze models of the
molecular-genetic systems
?????, 2007
31
Objective

• Aim of the study
• Analysis of mechanisms that regulate maintenance
  of pluripotency and cell differentiation during
  shoot apical meristem development in A. thaliana
• Tasks
• Reconstruction of gene network of auxin
  biosynthesis
• Development of mathematical model that describes
  auxin metabolism with account of genetic
  regulation
• Development of spatial distributed model that
  describes development of the SAM in embryogenesis
  with account of genetic regulation.