Semantics as Dynamics

1
Semantics as Dynamics
Systems Biology, Process Algebras and the
Semantic Web

• Walter Fontana (Harvard Systems Biology,
  Djinnisys Corporation),
• Jim Karkanias (Executive Director Clinical
  Analytical Systems, Merck),
• L.G. Meredith (Djinnisys Corporation, Harvard
  Systems Biology) and
• Matthias Radestock (LShift)

2
Acknowledging the importance of semantic web

• The problems identified by the semantic web
  initiative are of critical importance at this
  juncture
• not despite the fact that we have been
  struggling with these issues throughout the
  history of science
• but because this struggle is brought to a
  heightened pitch by our increased connectivity
• Considering these issues in the context of the
  life sciences is -- no pun intended -- is of
  vital importance
• For the life sciences to capitalize on the
  connectivity of offered by the web, ontology is a
  really pressing issue
• Going the other way, the life sciences offers a
  real proving ground for semantic technologies.
  Its like NYC, if you can make there, you can
  make it anywhere

3
The importance of approximating from below
4
An analogy from digital media
A static and externally imposed ontology
Rock, Pop, Jazz, Classical, Hip-Hop, New Age,
Clashes with a dynamic ontology arising from
interaction in context
The Kronos Quartet playing Purple Haze
What meaning can we extract from recorded music?
how it composes with other music - is it in A
minor?, is it 180 BPM?, does it have a subtype of
string or bass?
5
From digital media to systems biology

• These observations are also relevant to trends we
  note regarding biological data in the midst of
  the systems biology revolution
• Biological data will be increasingly about
  dynamics behavior and behavior in context, and
  there will be great volumes of it
• Observing that it is difficult, error-prone and
  ultimately questionable to annotate such data at
  such volumes with an externally imposed ontology,
  why not let the data speak for itself?
• Recognize that dynamics is what gives rise to
  semantics, and find a way to extract the latter
  from the former
• In short, we propose that frameworks for
  specifying dynamical systems and probing them for
  properties lie at the heart of useful semantic
  web technology for the life sciences

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Specification of system dynamics

• Traditionally, ODEs have been used to represent
  dynamical systems like signal pathways. Should we
  write up an XSD for ODEs and call it a day?
• An ODE representation suffers several drawbacks
• it is not compositional (you cant make DJ-like
  mixes of models)
• two modelers may build the exact same model, but
  use different names, and it is still impossible
  to compare them
• complexity issues, such as non-linearity put up
  significant barriers to analysis of these systems
  of equations, except by simulation
• We may levy the same critiques against
  traditional agent-based modeling, as well
• A framework like SBML that sits at some level of
  abstraction above these two is also in danger of
  suffering this fate if it does not have an
  independent semantics

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Specification of system dynamics

• Stated positively, these requirements amount to
  seeking a specification language that allows us
  to
• mix models in silico much like we mix chemicals
  in vitro and
• analyze models (even mixed ones) statically for
  properties, in addition to running simulations
• What would such a language look like? The mobile
  process algebras give us a pretty good proxy
• They already have a track record of modeling
  chemical, biochemical and biological processes
• They are demonstrably the only model of
  computation that allows one to mix models in
  silico (like we mix chemicals) and
• Statically check for properties in addition to
  running simulations

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Pi-calculus

• P 0
• ? a.P
• (new x)P
• P P
• (rec K(x).P)p
• a xx
• x(x)
• P0 ? P, PQ ? QP,
• P(QR) ? (PQ)R,
• (new x)(new x)P ? (new x)P,
• (new x)(new y)P
• ? (new y)(new x)P
• ((new x)P)Q ? (new x)(PQ)
• (x ? FN(Q))

ltxscomplex-type nameprocess/gt ltxscomplex-type
namezerogt ltxscomplex-contentgt
ltxsextension baseprocess/gt
lt/xscomplex-contentgt lt/xscomplex-typegt ltxscompl
ex-type nameguardedprocessgt
ltxssequencegt ltxselement
nameprefix typeaction/gt
ltxselement namecontinuation type/gt
lt/xssequencegt lt/xscomplex-typegt ltxscomplex-type
namesummationgt ltxssequence
maxOccursunboundedgt ltxselement
namesummand
typeguardedprocess/gt lt/xssequencegt lt/xsc
omplex-typegt
Compare with CDL
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Pi-calculus
But, in addition to structure, the pi-calculus
also has a dynamics x(y).P xz.Q ?
Pz/yQ P ? P' ? PQ ? P'Q P ? P' ? (new x)P ?
(new x)P' P ? P', P' ? Q', Q' ? Q ? P ? Q To
model biological systems we adopt a stochastic
variant of the calculus a (xx,r)
(x(x),r) (x(y),r).P (xz,r).Q ?
x,rb11 Pz/yQ (x(y),r).P (xz,r).Q
(xz,r).Q (x(y),r).P ? x,1/2rb2(2-1)
Pz/yQ P ? x,rbr0r1 P' ? PQ ? x,rbr0r1
P'Q, with r0' r0Inx(Q), r1' r1Outx(Q) P ?
x,rbr0r1 P' ? (new x)P ? x,rbr0r1 (new
x)P P ? P', P' ? x,rbr0r1 Q', Q' ? Q ? P ?
x,rbr0r1 Q
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Catalysis an example

• E S ? ES ? E P
• Interpret molecules (cells, individuals, ) as
  processes
• Mixture as autonomous execution (running in
  parallel)
• Molecular interaction as communication
• E S ? ES ? E P?(s,c)
• E S?(s,c) ? ES?(s,c) ? E S?(s,c)
• E S?(s,c) E?(s,c) (new t)S?(c,t)
• E P?(s,c) E?(s,c) P?(s,c)
• Molecular complexes as processes sharing an
  internal connection
• ES?(s,c) (new l r)(l! r! (l?. E
  S?(s,c) r?. E P?(s,c)))

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Catalysis an example
From these external descriptions and constraints
we derive an internal specification of the agents
representing enzyme and substrate E?(s,c)
(new l r m) s?(). E?s(s,c)
c!(l,r,m).m?(y,n).(l!.(y!.(r!.n!
E?(s,c))) r!.(y!.(l!.n!
E?(s,c)))) S?(s,c) (new y n)
s?(l,r,m).m!(y,n).(l?.(y?.S?(s,c)n?)
r?.(y?.P?(s,c)n?) c!().
S?c(s,c) Is there anything that corresponds to
an external description in this framework?
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Bell Model
Pi-calculus simulation of extra-vasation in
multiple sclerosis highlighted a new behavior of
leukocytes proved in lab experiments a posteriori
13
This model is publishable and searchable
Priami, et al
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Model-checking and search

• true 0 ? ? ??? 'x(? N? ?x.?
  lx.? ??
• Questions one might ask of this and other such
  systems
• Does it reach a state where it makes no progress?
  
• SYSTEM \ ?A Ntrue
• Is there a state where input on site ? is not
  possible?
• SYSTEM \ N? '?(true
• Does it reach a state where the process is
  spatially divided into two distinct agents joined
  by a site?
• SYSTEM \ Nlx.(? 0 ? 0)

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Conclusion

• The mobile process algebras give us a pretty good
  proxy
• They already have a track record of modeling
  chemical, biochemical and biological processes
• They are demonstrably the only model of
  computation that allows one to mix models in
  silico (like we mix chemicals) and
• Statically check for properties in addition to
  running simulations
• They are also the first scale-invariant model of
  computation. They are equally at home modeling
  high-level human organizational processes, as
  they are modeling business processes.
• In this very venue, the W3C, the pi-calculus is
  being used as the basis of WS-Choreographys CDL
• We sit at a historic moment when we could see
  the convergence of standards for the description
  of business processes aligning with a standards
  for the description of biological processes