Semantics as Dynamics

Djinnisys Corporation

Semantics as Dynamics

Walter Fontana (Harvard Systems Biology, Djinnisys Corporation),

Jim Karkanias (Executive Director Clinical Analytical Systems, Merck),

L.G. MeredithL.G. Meredith (Djinnisys Corporation, Harvard Systems Biology) and

Matthias Radestock (LShift)

Systems Biology, Process Algebras and the Semantic Web

Djinnisys Corporation 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. It’s like NYC, ‘if you can make there, you can make it anywhere’


The importance of approximating from below…Stupid! Just stupid enough http: had no notion of session; consumed a connection for every request; …

http was simple enough to be easily understood, and implemented and focus attention on the real value proposition of the web

xml: a data representation format before an agreed schema language?

xml simple enough for ‘me’ to understand and capture ‘my’ data

rdf: how will triples represent dynamics?context?The evolution of semantics?

???


An analogy from digital media

Rock, Pop, Jazz, Classical, Hip-Hop, New Age, …

A static and externally imposed ontology:

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’?


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


Specification of system dynamics

Traditionally, ODE’s have been used to represent dynamical systems like signal pathways. Should we write up an XSD for ODE’s and call it a day?

An ODE representation suffers several drawbacks:

• it is not compositional (you can’t 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


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


Pi-calculusP ::= 0

a.P(new x)PP | P(rec K(x).P)p

a ::= x[x]x(x)

P|0 P, P|Q Q|P, P|(Q|R) (P|Q)|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)(P|Q)

(x FN(Q))…

<xs:complex-type name=“process”/><xs:complex-type name=“zero”> <xs:complex-content> <xs:extension base=“process”/> </xs:complex-content></xs:complex-type><xs:complex-type name=“guardedprocess”> … <xs:sequence> <xs:element name=“prefix” type=“action”/> <xs:element name=“continuation” type=…/> </xs:sequence></xs:complex-type><xs:complex-type name=“summation”> … <xs:sequence maxOccurs=“unbounded”> <xs:element name=“summand” type=“guardedprocess”/> </xs:sequence></xs:complex-type>…

Compare with CDLProcess

Computation is interaction

Process


Pi-calculusBut, in addition to structure, the pi-calculus also has a dynamics…

… + x(y).P | x[z].Q + … P{z/y}|QP P' P|Q 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 ::= (x[x],r) | (x(x),r)

… + (x(y),r).P | (x[z],r).Q + … x,rb*1*1 P{z/y}|Q

… + (x(y),r).P + (x[z],r).Q | (x[z],r).Q + (x(y),r).P … x,1/2*rb*2*(2-1) P{z/y}|Q

P x,rb*r0*r1 P' P|Q x,rb*r0’*r1’ P'|Q, with r0' =r0+Inx(Q), r1' =r1+Outx(Q)

P x,rb*r0*r1 P' (new x)P x,rb*r0*r1 (new x)P’

P P', P' x,rb*r0*r1 Q', Q' Q P x,rb*r0*r1 Q


Catalysis: an exampleE + 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)))


Catalysis: an exampleFrom 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?


Bell ModelPi-calculus simulation of extra-vasation in multiple sclerosis highlighted a new behavior of leukocytes proved in lab experiments a posteriori


This model is publishable and searchable

Priami, et al…


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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<SYSTEM name = “MS0”/>

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…

•Search for models with spatial and behavioral similarities may be expressed in terms of standard logics

• these also have a simple expression in terms of XSD schema


ConclusionThe 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-Choreography’s 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

Semantics as Dynamics

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