little b short course

1
little b short course

• harvard medical school
• sept 2006

2
outline

• The modelers burden
• Writing Math (in Matlab) Biology (in little b)
• Biological concepts
• Break
• The core language
• Example multisite phosphorylation
• Lisp (if time)

3
Some of the following slides contain animations.
You should view this in slideshow mode (F5 in
Powerpoint).
4
little b

• computer language which automates model
  construction
• reads text files which describe biochemistry
• produces matlab code (and hopefully Octave, SBML,
  MathML soon)
• full-featured programming language based in Lisp
• programmers toolkit useful for building modeling
  tools

5
models combine reactions and species in
compartments
E
species and reactions

,
,
P
X
models
1
2
6
translating from math to matlab code more
changes, more bookkeeping
dE/dt - EPkEP dP/dt - EPkEP dX/dt
EP kEP
dE/dt - EXkEP dS/dt - ESkES dP/dt
ESkES -EPkEP dX/dt EPkEP
dE/dt 0 dS/dt - ESkES dP/d ESkES
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assumptions affect mathematical structure
1. mechanism (e.g., steps)
dE/dt 0 dS/dt - ESkES dP/dt
ESkES
dE/dt ESkES - ESkES dS/dt -
ESkES dP/dt ESkES dES/dt
ESkES - ESkES
6 changes
3 total of 9 changes
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assumptions affect mathematical structure (2)
2. kinetics
m1R1 m2R2 mnRn ?
mass-action
dE/dt ESkES - E(S/(KS))hes dS/dt -
E(S/(KS))hes dP/dt ESkES dES/dt
E(S/(KS))hes - ESkES
dE/dt ESkES - ESkES dS/dt -
ESkES dP/dt ESkES dES/dt
ESkES - ESkES
9
bookkeeping requirements

• result from
• model combination
• kinetic assumptions
• code generation
• molecular, location, multicellular and geometric
  complexity

10
molecular complexity
14-3-3
MEK
P
KSR
C-TAK1
KSR
11
location complexity
distinct mathematical variables account for
species in different locations
12
reasoning about biochemistry
13
multicellular complexity
hh
wg
CID
CN
ptc
en
EN
cid
14
geometric complexity
in the real world, lattice structure is irregular
15
computer-assisted model construction

• PRO
• ? entry errors
• ? models ? systematic model exploration
• reuse formal knowledge
• enables computer-assisted verification

• CON
• bugs ? computer-generated errors
• loss of control understanding
• requires verification

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summary

• bookkeeping requirements arise from
• model combination
• kinetic assumptions
• code generation
• biological complexity
• complexity arises from molecular, compartmental
  and multicellular structure
• computer-assisted model construction requires
  math and reasoning capabilities

17
the little b environment

• input editor, command-line or file
• like Matlab, Mathematica, Perl and others
• read/eval/print loop
• a form is read (symbol, number, or matched
  parenthesis (),,)
• the form is evaluated
• the result is printed
• next form is read
• based in Lisp

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a simple model

• reversible isomerization of glucose-6-phosphate

G6P
F6P
G6PI
G6PI


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a simple model two steps

• reversible isomerization via an ES complex

G6P
G6PI
G6PI-RXN-ES
F6P
G6PI


20
dealing with location complexity
generic molecular locations are classes
specific situations described as connected
instances of those classes
cytoplasm
compartment
nucleus
channel.(in nuclear-membrane)
ion.(in cytoplasm)
ion.(in nucleus)
ion
channel
species-type
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ion transport
reaction-type
reaction
22
connected locations
classes
instances
biological situation
compartment
cyto1-m1
cyto1-m2
cyto1-m6
cyto1-m3
cyto1-m5
cyto1-m4
in apposition-c1-c2
in apposition-c1-c2
23
dealing with location complexity
dish
cell-membrane
ion
nucleus
ion
reaction-type ion.(required c1)
ion-channel
ion.(required c2) ion-channel
membrane
reaction-type refers to generic situations gt
independent of specific locations
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the symbolic math subsystem is a an extensible
toolkit for theoreticians to express mathematical
concepts

• units, dimensions
• quantities, gaussian distributions
• polynomial, rational-polynomial and radical
  expressions

• system is extensible
• possible additions
• matricies
• poisson distributions
• others?

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END
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libraries

• little b libraries
• contain pre-existing modules (files) which can be
  included
• B-USER library contains 2 standard environments
• 3d-ode-biochemistry
• (include b-user/3d-ode-biochemistry)
• non-dimensional-biochemistry
• (include b-user/non-dimensional-ode-biochemistry)
• F3 File browser
• B core library

27
toy egf receptor model - reactions
egf
egfregf
egfr
mapkkk
mapkkk
mapkk
mapkk
mapk
mapk
28
toy egf receptor model modular mechanism
K
provide mechanism
K

K

mapk__
mapk__
mapk__
mapk__
29
toy egf receptor model - mathematics
the mass action rate-method, calculates T, the
rate of the reaction
T kA2 dA/dt - 2 T . dB/dt T
e.g.,
2
A
B
A
C
T kAB dA/dt - T dB/dt - T
Zmembrane / Zcompartment dC/dt T

B
Zcompartment
Zmembrane

• given a reaction with n LHS speciess, Ri with
  stoichiometries si
• s1R1 siRi snRn
• where the reaction occurs in a location of size Z
  (which may be a volume, area or length).
• reaction rate, T (moles / size-units / seconds)
• k x R1s1 x Risi x Rnsn
• reaction rate in moles/seconds T x Z
• dRi/dt T x Z / Ci
• where Ci is the size of the compartment
  containing Ri

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modular kinetics
31
now imagine.

• libraries of such components have been previously
  defined by experts, and are available
• over the web
• in a database in your lab
• in your own personal collection
• b enables these parts to be combined

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lets describe a situation composed of predefined
parts
cell-a
dish
33
b builds symbolic mathematical expressions
cell-a
dish
object-oriented syntax meets symbolic math
enables programmers and theorists to write
debug functions which translate between the world
of objects and the world of mathematical
expressions.