brooklyn poly

1st bio-geometry workshop

6.12.2004

¦ ¦

¦ ¦

¦ ¦

¦ ¦

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Robert Hooke (1635-1703)

Robert

Hooke

• Robert Hooke (1635-1703) was an experimental scientist, mathematician, architect, and astronomer. Secretary of the Royal Society from 1677 to 1682, …

• Hooke was considered the “England’s Da Vinci” because of his wide range of interests.

• His work Micrographia of 1665 contained his microscopical investigations, which included the first identification of biological cells.

• In his drafts of Book II, Newton had referred to him as the most illustrious Hooke—”Cl[arissimus] Hookius.”

• Hooke became involved in a dispute with Isaac Newton over the priority of the discovery of the inverse square law of gravitation.

Hooke

to H

alle

y

• “[Huygen’s Preface] is concerning those properties of gravity which I myself first discovered and showed to this Society and years since, which of late Mr. Newton has done me the favour to print and publish as his own inventions.“

New

ton t

o H

alle

y

• “Now is this not very fine? Mathematicians that find out, settle & do all the business must content themselves with being nothing but dry calculators & drudges & another that does nothing but pretend & grasp at all things must carry away all the inventions…

• “I beleive you would think him a man of a strange unsociable temper.”

New

ton t

o H

ooke

• “If I have seen further than other men, it is because I have stood on the shoulders of giants and you my dear Hooke, have not." --Newton to Hooke

Image & Logic

• The great distance between – a glimpsed truth

and – a demonstrated

truth• Christopher

Wren/Alexis Claude Clairaut

Cell Talk

Bud Mishra

Courant Inst. ² Cold Spring Harbor Lab. ² Tata Inst of Fund. Res. ² Mt. Sinai School

of Medicine

MicrographiaMicrographiaPrincipiaPrincipia

Mic

rogra

phia

“The B

rain

& t

he F

ancy

”

• “The truth is, the science of Nature has already been too long made only a work of the brain and the fancy. It is now high time that it should return to the plainness and soundness of observations on material and obvious things.”– Robert Hooke. (1635 -

1703), Micrographia 1665

Pri

nci

pia

“Induct

ion &

H

ypoth

esi

s”• “Truth being uniform and

always the same, it is admirable to observe how easily we are enabled to make out very abstruse and difficult matters, when once true and genuine Principles are obtained.”– Halley, “The true Theory of

the Tides, extracted from that admired Treatise of Mr. Issac Newton, Intituled, Philosophiae Naturalis Principia Mathematica,” Phil. Trans. 226:445,447.

• This rule we must follow, that the argument of induction may not be evaded by hypotheses.

Hypotheses non fingo.I feign no hypotheses.Principia Mathematica.

MorphogenesisMorphogenesis

Ala

n T

uri

ng:

19

52

• “The Chemical Basis of Morphogenesis,” 1952, Phil. Trans. Roy. Soc. of London, Series B: Biological Sciences, 237:37—72.

• A reaction-diffusion model for development.

“A mathematical model for the growing

embryo.”• A very general program for modeling

embryogenesis: The `model’ is “a simplification and an idealization and consequently a falsification.”

• Morphogen: “is simply the kind of substance concerned in this theory…” in fact, anything that diffuses into the tissue and “somehow persuades it to develop along different lines from those which would have been followed in its absence” qualifies.

Diffusion equation

a: concentrationDa: diffusion constant

a/ t = Da r2 a

first temporal derivative

:rate

second spatial

derivative:

flux

React

ion-D

iffusi

on

a/ t = f(a,b) + Da r2 a f(a,b) = a(b-1) –k1

b/ t = g(a,b) + Db r2 b g(a,b) = -ab +k2

reaction diffusion

a

b

Turing, A.M. (1952).“The chemical basis of morphogenesis.“ Phil. Trans. Roy. Soc. London B 237: 37

Reaction-diffusion: an example

Pearson, J. E.: Complex patterns in simple systems. Science 261, 189-192 (1993).

A+2B ! 3BB ! PA fed at rate F

B extracted at rate F,decay at rate k

d[A]/dt=F(1-[A]) d[B]/dt=-(F+k)[B]

reaction: -d[A]/dt = d[B]/dt = [A][B]2

diffusion: d[A]/dt=DA2[A]; d[B]/dt=DB2[B] [A]/ t = F(1-[A]) – [A][B]2 + DA2[A] [B]/ t = -(F+k)[B] +[A][B]2 + DB2[B]

Reaction-diffusion: an example

Genes:

19

52

• Since the role of genes is presumably catalytic, influencing only the rate of reactions, unless one is interested in comparison of organisms, they “may be eliminated from the discussion…”

Crick & Watson :1953

Genome

• Genome:– Hereditary information of

an organism is encoded in its DNA and enclosed in a cell (unless it is a virus). All the information contained in the DNA of a single organism is its genome.

• DNA molecule can be thought of as a very long sequence of nucleotides or bases:

= {A, T, C, G}

The Central Dogma• The central dogma(due to

Francis Crick in 1958) states that these information flows are all unidirectional:“The central dogma states that

once `information' has passed into protein it cannot get out again. The transfer of information from nucleic acid to nucleic acid, or from nucleic acid to protein, may be possible, but transfer from protein to protein, or from protein to nucleic acid is impossible. Information means here the precise determination of sequence, either of bases in the nucleic acid or of amino acid residues in the protein.”

DNA RNA ProteinTranscription Translation

RN

A,

Genes

and

Pro

mote

rs• A specific region of DNA that determines the

synthesis of proteins (through the transcription and translation) is called a gene– Originally, a gene meant something more

abstract---a unit of hereditary inheritance.– Now a gene has been given a physical

molecular existence.• Transcription of a gene to a messenger RNA,

mRNA, is keyed by a transcriptional activator/factor, which attaches to a promoter (a specific sequence adjacent to the gene).

• Regulatory sequences such as silencers and enhancers control the rate of transcription

Promoter

GeneTranscriptional

Initiation

Transcriptional

Termination

Terminator

10-35bp

“The Brain & the Fancy”

“Work on the mathematics of growth as opposed to the statistical description and comparison of growth, seems to me to have developed along two equally unprofitable lines… It is futile to conjure up in the imagination a system of differential equations for the purpose of accounting for facts which are not only very complex, but largely unknown,…What we require at the present time is more measurement and less theory.”– Eric Ponder, Director, CSHL

(LIBA), 1936-1941.

“Axioms of Platitudes”-E.B. Wilson

1. Science need not be mathematical.2. Simply because a subject is

mathematical it need not therefore be scientific.

3. Empirical curve fitting may be without other than classificatory significance.

4. Growth of an individual should not be confused with the growth of an aggregate (or average) of individuals.

5. Different aspects of the individual, or of the average, may have different types of growth curves.

1. Science need not be mathematical.2. Simply because a subject is

mathematical it need not therefore be scientific.

3. Empirical curve fitting may be without other than classificatory significance.

4. Growth of an individual should not be confused with the growth of an aggregate (or average) of individuals.

5. Different aspects of the individual, or of the average, may have different types of growth curves.

Genes for Segmentation

• Fertilisation followed by cell division

• Pattern formation – instructions for– Body plan

(Axes: A-P, D-V)

– Germ layers (ecto-, meso-, endoderm)

• Cell movement - form – gastrulation

• Cell differentiation

PI: Positional Information

• Positional value– Morphogen – a

substance– Threshold

concentration• Program for

development– Generative rather

than descriptive• “French-Flag Model”

bicoid

• The bicoid gene provides an A-P morphogen gradient

gap genes

• The A-P axis is divided into broad regions by gap gene expression

• The first zygotic genes• Respond to maternally-

derived instructions• Short-lived proteins, gives

bell-shaped distribution from source

Transcription Factors in Cascade

• Hunchback (hb) , a gap gene, responds to the dose of bicoid protein

• A concentration above threshold of bicoid activates the expression of hb

• The more bicoid transcripts, the further back hb expression goes

Transcription Factors in Cascade

• Krüppel (Kr), a gap gene, responds to the dose of hb protein

• A concentration above minimum threshold of hb activates the expression of Kr

• A concentration above maximum threshold of hb inactivates the expression of Kr

Segmentation

• Parasegments are delimited by expression of pair-rule genes in a periodic pattern

• Each is expressed in a series of 7 transverse stripes

Pattern Formation

– Edward Lewis, of the California Institute of Technology

– Christiane Nuesslein-Volhard, of Germany's Max-Planck Institute

– Eric Wieschaus, at Princeton• Each of the three were

involved in the early research to find the genes controlling development of the Drosophila fruit fly.

The Network of Interaction

EN

CID

WG

PTC

HH

PH

WG

PTC

HH

PHCNcid

enwg

hh

+ptc

en

Cell-to-cellinterface

a cell a neighbor

Legend:•WG=wingless•HH=hedgehog•CID=cubitus iterruptus•CN=repressor fragment

of CID•PTC=patched•PH=patched-hedgehog

complex

mRNA proteinspositiveinteracions

negativeinteracions

Completeness:von Dassow, Meir, Munro & Odell,

2000

• “We used computer simulations to investigate whether the known interactions among segment polarity genes suffice to confer the properties expected of a developmental module….

• “Using only the solid lines in [earlier figure] we found no such parameter sets despite extensive efforts.. Thus the solid connections cannot suffice to explain even the most basic behavior of the segment polarity network…

• “There must be active repression of en cells anterior to wg-expressing stripe and something that spatially biases the response of wg to Hh. There is a good evidence in Drosophila for wg autoactivation…”

Completeness

• “We incorporated these two remedies first (light gray lines). With these links installed there are many parameter sets that enable the model to reproduce the target behavior, so many that they can be found easily by random sampling.”

Model Parameters

Complete Model

Complete Model

Is this your final answer?

• It is not uncommon to assume certain biological problems to have achieved a cognitive finality without rigorous justification.

• Rigorous mathematical models with automated tools for reasoning, simulation, and computation can be of enormous help to uncover – cognitive flaws,– qualitative simplification or– overly generalized assumptions.

• Some ideal candidates for such study would include: – prion hypothesis– cell cycle machinery – muscle contractility– processes involved in cancer (cell cycle

regulation, angiogenesis, DNA repair, apoptosis, cellular senescence, tissue space modeling enzymes, etc.)

– signal transduction pathways, and many others.

The SYSTEMS BIOLOGY

Numerlogy

Astrology

Systems BiologyCombining the mathematical rigor of numerology with the predictive power of astrology.

Numeristan

AstrostanInfostan

Interpretive Biology

Integrative BiologyBioinformati

cs

Computational Biology

BioSpice

HOTzone

Cyberia

Computational Systems Biology

How much of reasoning about biology can be automated?

Why do we need a tool?

We claim that, by drawing upon mathematical approaches developed in the context of dynamical systems, kinetic analysis, computational theory and logic, it is possible to create powerful simulation, analysis and reasoning tools for working biologists to be used in deciphering existing data, devising new experiments and ultimately, understanding functional properties of genomes, proteomes, cells, organs and organisms.

Simulate Biologists! Not Biology!!

ComparisonHypotheses Revision

Experimental ResultsExperiment RunsExperiment Design

Model SimulationModel Construction

ModelODE/SDE/

Hybrid Systems

In silico Results

Symbolic AnalysisReachability Analysis

SimulationTemporal Logic Verification

Reasoning and Experimentation

Simpathica is a modular system

Canonical Form:

0)())(,),((

1

11

11

mn

j

fjlmnl

mn

j

hji

mn

j

gjii

lj

ijij

XtXtXC

niXXX

Characteristics:

• Predefined Modular Structure

• Automated Translation from Graphical to Mathematical Model

• Scalability

Demo[4.1]

Glycolysis

Glycogen

Glucose-1-PGlucose

Glucose-6-P

Fructose-6-P

P_i

Phosphorylase a

PhosphoglucomutaseGlucokinase

Phosphoglucose isomerase

Phosphofructokinase

An Artificial Clock

• Three proteins:– LacI, tetR & cI– Arranged in a cyclic

manner (logically, not necessarily physically) so that the protein product of one gene is rpressor for the next gene.LacI! : tetR; tetR! TetRTetR! : cI; cI ! cI cI! : lacI; lacI! LacI

Cycles of Repression

• The first repressor protein, LacI from E. coli inhibits the transcription of the second repressor gene, tetR from the tetracycline-resistance transposon Tn10, whose protein product in turn inhibits the expression of a third gene, cI from phage.

• Finally, CI inhibits lacI expression,completing the cycle.

Biological Model

• Standard molecular biology: Construct– A low-copy plasmid

encoding the repressilator and

– A compatible higher-copy reporter plasmid containing the tet-repressible promoter PLtet01 fused to an intermediate stability variant of gfp.

Cascade Model: Repressilator?

dx2/dt = 2 X6g26X1

g21 - 2 X2h22

dx4/dt = 4 X2g42X3

g43 - 4 X4h44

dx6/dt = 6 X4g64X5

g65 - 6 X6h66

X1, X3, X5 = constx1 x2-

x3 x4-

x5 x6-

SimPathica System

Application:Purine Metabolism

Purine Metabolism

• Purine Metabolism– Provides the organism with building blocks for the

synthesis of DNA and RNA.– The consequences of a malfunctioning purine

metabolism pathway are severe and can lead to death.

• The entire pathway is almost closed but also quite complex. It contains– several feedback loops,– cross-activations and – reversible reactions

• Thus is an ideal candidate for reasoning with computational tools.

Simple Model

Biochemistry of Purine Metabolism

• The main metabolite in purine biosynthesis is 5-phosphoribosyl-a-1-pyrophosphate (PRPP). – A linear cascade of reactions

converts PRPP into inosine monophosphate (IMP). IMP is the central branch point of the purine metabolism pathway.

– IMP is transformed into AMP and GMP.

– Guanosine, adenosine and their derivatives are recycled (unless used elsewhere) into hypoxanthine (HX) and xanthine (XA).

– XA is finally oxidized into uric acid (UA).

Biochemistry of Purine Metabolism

• In addition to these processes, there appear to be two “salvage” pathways that serve to maintain IMP level and thus of adenosine and guanosine levels as well.

• In these pathways, adenine phosphoribosyltransferase (APRT) and hypoxanthine-guanine phosphoribosyltransferase (HGPRT) combine with PRPP to form ribonucleotides.

Puri

ne M

eta

bolis

m

Queries• Variation of the initial

concentration of PRPP does not change the steady state.(PRPP = 10 * PRPP1) implies steady_state()

This query will be true when evaluated against the modified simulation run (i.e. the one where the initial concentration of PRPP is 10 times the initial concentration in the first run – PRPP1).

• Persistent increase in the initial concentration of PRPP does cause unwanted changes in the steady state values of some metabolites.

• If the increase in the level of PRPP is in the order of 70% then the system does reach a steady state, and we expect to see increases in the levels of IMP and of the hypoxanthine pool in a “comparable” order of magnitude.

Always (PRPP = 1.7*PRPP1) implies steady_state()TRUE

TRUE

Queries• Consider the following

statement:Eventually(Always (PRPP = 1.7 * PRPP1)

impliessteady_state()and Eventually

Always(IMP < 2* IMP1))and Eventually (Always (hx_pool < 10*hx_pool1)))

where IMP1 and hx_pool1 are the values observed in the unmodified trace. The above statement turns out to be false over the modified experiment trace..

• In fact, the increase in IMP is about 6.5 fold while the hypoxanthine pool increase is about 60 fold.

• Since the above queries turn out to be false over the modified trace, we conclude that the model “over-predicts” the increases in some of its products and that it should therefore be amended

False

Final Model

Puri

ne M

eta

bolis

m

Query

• This change to the model allows us to reformulate our query as shown below:

• Always(PRPP > 50 * PRPP1implies(steady_state() and Eventually(IMP > IMP1) and Eventually(HX < HX1) and Eventually(Always(IMP = IMP1)) and Eventually(Always(HX = HX1))

• An (instantaneous) increase in the level of PRPP will not make the system stray from the predicted steady state, even if temporary variations of IMP and HX are allowed.

• Demo[1.1]

TRUE

Application:ModelingApoptosis

Cell Death

Cell shrink, organelles swell, chromatin condenses, DNA fragmented, cell junctions

disintegrated, membrane blabbing, finally get engulfed ------ all within 30 minutes.

Caspase CascadeCaspases-

1~14: Major executioners of programmed cell death.

Pro Large subunit Small subunit

Cleave sites

D D

Activated Caspase

Pro

Large subunit

Small subunit

c

Active site

Killer protease, ready to cut many substrates, including other caspases and destroy cells

The activation of Casp9 needs APAF1 and cytochrome c

APAF1

Cleave downstream cellular proteins to kill cell

Cytochrome c

DEVD-Afc

Mitochondria

APAF1/cytc oligomer

dATP

APAF1/casp9 holoenzyme

Casp9

Active holoenzyme

Active site

Pro-casp3

Active casp3

DN

A

nucleus

dam

ag

e

Decreasing [APAF-1] Kill Caspase Activity

•Mix RNAi(APAF-1) treated and untreated E1A cell extract.

E1A cells

RNAi(APAF-1)

mixExtract with APAF1 Extract with

little APAF1

100% 80% 70% 60% 40% 20% 0%Measure the caspase 3 activity of the mixed cell extract

.

-50

0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90 100

Percentage of IMR90/E1A(%)

DEV

D-A

fc r

ate

(pm

ol/

min

/mg

)

DEV

D-a

fc r

ate

(fc

/min

, casp

3 a

cti

vit

y)

expected

The simple model & holoenzyme activation

pathway

Pro-casp3

DEVD-Afc

cytochrome cAPAF1

dATP

Active casp3

Afc

casp9

APAF1/cytc

APAF1/casp9 holoenzyme

Active holoenzyme

fluorescent

free casp9

Modeling pathway view in Simpathica

What happens in the real world

Simpathica recapitulate the holoenzyme formation process

Rodriguez and Lazebnik (1999)

0

5

10

15

20

25

30

35

40

0 5 10 15 20

Co

nce

ntr

atio

n o

f sp

eci

es

(nM

)

Time of Reaction (minute)

The Simulation of Apoptotic Holoenzyme Kinetics

APAF1cytc

APAF1/cytcdATP

APAF1/cytc/dATPpC9

APAF1/cytc/dATP/pC9APAF1/cytc/dATP/casp9

pC3free Casp3free Casp9DEVD-Afc

AfcAfc_rate

Where to modify the model in Simpathica?

Reversibility?

Non-Linear?

Linear

Linear

Is there cooperativity binding during holoenzyme activation?

APAF1/cytc/dATP oligomer

1st Casp9 binding:

Only APAF1/casp9 interaction.

2nd Casp9 binding:

APAF1/ casp9 interaction, plus

Casp9 / casp9 interaction.

Recruitment of a casp9 monomer promotes the binding of the second casp9.

The Non-linearity in the model can be reproduced by the Hill

moduleThe cooperativity binding can be described by the Hill Equation:

h

h

SK

SVv

][

][

5.0

Reacti

on

Rate

(n

M/m

in)

Substrate Concentration (nM)

Possible Cooperative Interaction

• Recombinant system:– cytochrome c, caspase-9, APAF1

• Purification of endogenous APAF1/cytc oligomer

Cell extract with little casp9

activation

Cell extract with little APAF

Adding back

[APAF1/cytc/dATP] caspase3 activity Linear

dependence?

• Protein X: inhibitors/modifications.

• ATP and dATP competition.• APAF1 self inhibition modeling.

ATP

XIAP

APAF1m

Self-dimer

Inhibition?

Summary

• Benchwork shows APAF1 but not the Caspase9 level plays a key role in E1A dependent activity

• The simple model built by Simpathica can recapitulate the the activation of Caspase9/APAF1 holoenzyme and downstream caspase activity.

• The non-linear dependency between caspase and [APAF1] cannot be reproduced by MM style.

• By considering Hill equation model, Simpathica shows a possibility of a cooperative interaction in the pathway.

• The experiments are in the progress to confirm the “prediction” from the modeling.

• Demo[3.1]

ComputationalIssues

State of the Project

• Simpathica Tool integrates:– Numerical Analysis

• (numerical integrator with algebraic constraints generating traces)

– Model Building• (Kripke structures, labeled finite automata, hybrid automata

etc., creating a qualitative model)– Model Reduction

• (Bisimulation & collapsing)– Symbolic Computation

• (Tarski sentences encoding of the hybrid automata in terms formulas for state transitions and temporal properties)

– Modal Logic & Model Checking• (Decision procedures for a Branching-time Propositional

Temporal Logic)– Visualization and Natural Language Interface

Simpathica

XS-Systems

Traces

XS-System Automaton

Reducing the Number of States

• The automata typically have large number of states.

• Two simple ways to reduce:– PROJECTIONPROJECTION-forget

some reactants– COLLAPSINGCOLLAPSING-

forget some intermediate states

WARNING: Too much collapsing may be dangerous to the automata.

Using Hybrid Automata

• Note that the obtained standard automata do not keep track of the variables between states…– Add information

about the continuous evolution…

– by using hybrid automata…

XS-System Hybrid Automata

Reducing States Safely

• The hybrid automata we get have the same number of states as the corresponding standard automata. Two operations reduce state space:– BisimulationBisimulation: two states are

equivalent iff they behave the same way and reach states that are equivalent.

– CollapsingCollapsing: the continuous evolution inside the states retains information

• THESE OPERATIONS PRESERVE THESE OPERATIONS PRESERVE CTL.CTL.

Semi Algebraic Representation of Hybrid

Automata

• We have formulated a semi-algebraic encoding of Hybrid Automata– Where each mode has a semi-algebraic

representation, with the flows, invariants and guard conditions represented with low degree polynomial equations, inequations and inequalities.

– The state transition is also encoded by a Tarski Sentence.

• Reachability, Model checking etc., can be encoded in terms of a Tarski sentence and is decidable.

Further Works

• Symbolic Manipulation of the differential equations (attractors, Morse theory, bifurcation analysis)– Analyze an infinite number of experiments– Infer states

• Non-determinism (Multi-Modal Logic, Perturbations)– Compare different systems– Analyze systems with memories

• Hierarchy & Modularity

TIME & FREQUENCYRAS pathway

Cell Cycle

The Cell Cycle

G1

S

G2

M(metaphase)

M(anaphase)

Cyclin

CdkCdkCdk

APCAPC

startfinis

h

cell d

ivision

The Cell Cycle

• The chromosome cycle is divided into four classes:• G1, S, G2, & M:

– During S phase, a new copy of each chromosome is synthesized…

– During M phase (mitosis) the sister chromatids are separated so that each daughter cell receives a copy of each chromosome.

• G1 and S-G2-M are separated by two transitions:• start & finish…• Cell cycle events are controlled by a network of

molecular signals– The central components are Cdks (cyclin-dependent

protein kinases), cyclin molecules and APC (anaphase-promoting complex)..

The Cell Cycle

• In the G1 phase Cdk activity is low as cyclin mRNA synthesis is inhibited and cyclin protein is degraded rapidly…

• At start, cyclin synthesis is induced and cyclin degradation is inhibited, causing a rise in Cdk activity that persists throughout S-G2-M phase– High Cdk activity is needed for DNA replication,

chromosome condensation and spindle assembly.• At finish, the proteins needed for APC complex is activated.

– APC consists of core complex of a dozen polypeptides plus two auxiliary proteins Cdc20 and Cdh1.

– Together, Cdc20 and Cdh1 label cyclins for degradation at telophase, thus returning the cell to G1.

Cyclin B/Cdk and Cdh1/APC

• A pair of nonlinear ODE (ordinary differential equations) describing the biochemical reactions at the center.

• d[CycB]/dt = k1 – (k’2 + k”2[Cdh1])[CycB]

• d[Cdh1]/dt = (k’3 + k”3 A) (1-[Cdh1])/ (J3+1

– [Cdh1]) – k4 m [CycB][Cdh1]/ (J4 + [Cdh1])

• d[CycB]/dt = k1 – (k’2 + k”2[Cdh1])[CycB]

• d[Cdh1]/dt = (k’3 + k”3 A) (1-[Cdh1])/ (J3+1

– [Cdh1]) – k4 m [CycB][Cdh1]/ (J4 + [Cdh1])

Yeast Cell Cycle Regulations

SK

CKI

CKI

CKI Cyc

B

Cdh1

Cdh1

Cdc20

Cdc20

IE

CycB

P

IE

MAD

PCDK

CDK

Simulation of Yeast Cell Cycle

Simulation of Yeast Cell Cycle

Simulation of Yeast Cell Cycle

Analysis of Experimental Traces

Queries can be made to the Queries can be made to the systemsystem

Time Course Data from simulation or interpolated wet-lab experiments can be analyzed using Temporal Logic queries

Problems

• Working biologists should not be expected to manipulate complex mathematical formalisms (ODEs, Temporal Logic,…)

• A simple query system is not exhaustive and does not help a biologist in analyzing systems discovering new facts and associations– NATURAL LANGUAGE interfaces:

• Query• Story generation

• We added a prototypical Natural Language Interface to the Simpathica Temporal Logic Query subsystem– The aim is to simplify the use of the system by

Biologists

English NL System

• Question like

“After 0.1 minutes, when CKIt is less than or equal to CycBt, does CycBt increase?”

are understood by the system and translated in the appropriate Temporal Logic query

Eventually((TICK > 0.1) and AU(not(CKIT <= CYCBT) and not(GROWING(CYCBT)) UNTIL (CKIT <= CYCBT and GROWING(CYCBT))))

The Natural Language Interface

Story generation

• Temporal Logic formulae can be rendered in English.

• Temporal Logic formulae can be generated automatically (with care).

• Each formula can be tested against a set of datasets; differences can then be noted.

DatasetDatasetDatasetDataset

FormulaGenerator

FormulaFormula

TemporalLogic Analysis

Natural LanguageStory Generation

HTMLfile

Formula

Cell Cycle Story Generation Results

(HTML rendering)

Report on "Test Experiment Tyson WT, 1 Mutant, 2 Mutants.".RESULTSThe results refer to the following datasets:¦ The first dataset is named "Ian's Experiment/Tyson Yeast Dataset WT".¦ The second dataset is named "Ian's Experiment/Tyson Yeast Dataset Mut1".¦ The third dataset is named "Ian's Experiment/Tyson Yeast

Dataset mut2".

…84. CDH1 less than or equal to 1.0071783 will always hold until CDH1

activates CYCB, is true in the first dataset, is true in the second dataset, and is false in the third dataset.

85. CDH1 represses CYCB implies CYCB is greater than or equal to 0.65, is false in the first dataset, is true in the second dataset, and is true in the third dataset.

86. eventually, CDH1 is less than or equal to CYCB, is false in the first dataset, is true in the second dataset, and is true in the third dataset.

…

Computational Algebra & Computational Algebra & Differential AlgebraDifferential Algebra

Algebraic Approaches

Differential Algebra

Example System

Input-Output Relations

Obstacles

Hooke…• “So many are the links, upon

which the true Philosophy depends, of which, if any can be loose, or weak, the whole chain is in danger of being dissolved;

• “it is to begin with the Hands and Eyes, and to proceed on through the Memory, to be continued by the Reason;

• “nor is it to stop there, but to come about to the Hands and Eyes again, and so, by a continuall passage round from one Faculty to another, it is to be maintained in life and strength.”

HookeThursday 25 May 1676

Damned Doggs.

Vindica me deus.• Commenting on

Sir Nicholas Gimcrack character inThe Virtuoso, a play by Thomas Shadwell.

HookeHookein the Royal Society, 26 June 1689in the Royal Society, 26 June 1689

• “I have had the misfortune either not to be understood by some who have asserted I have done nothing…

• “Or to be misunderstood and misconstrued (for what ends I now enquire not) by others…

• “And though many things I have first Discovered could not find acceptance yet I finde there are not wanting some who pride themselves on arrogating of them for their own…

• “—But I let that passe for the present.”

Principal Investigator• Bud Mishra

Researchers• Marco Antoniotti • Paolo Barbano • Vera Cherepinsky • Raoul-Sam Daruwala • Gilad Lerman • Joe McQuown • Toto Paxia • Archisman Rudra • Nadia Ugel

Alumni• Will Casey • Marc Rejali

Students• Fang Chen • Jiawu Feng • Ofer Gill • Matthias Heymann • Iuliana Ionita • Venkatesh P. Mysore • Marina Spivak • Bing Sun • Yi (Joey) Zhou

Visitors• Marco Isopi • Carla Piazza • Alberto Policriti • Naomi Silver • Chris Wiggins • Franz Winkler

The End

http://www.cs.nyu.edu/mishrahttp://www.cs.nyu.edu/mishra

http://bioinformatics.cat.nyu.eduhttp://bioinformatics.cat.nyu.eduValis, Gene Grammar, NYU MAD,

Cell Simulation,…