# Translating Stochastic CLS into Maude

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Translating Stochastic CLS into Maude (ONGOING WORK) Thomas Anung Basuki 1 Antonio Cerone 1 Paolo Milazzo 2 1. Int. Institute for Software Technology, United Nations Univeristy, Macau SAR, China 2. Dipartimento di Informatica, Università di Pisa, Italy Iaşi September, 2008 Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

2 Introduction The Calculus of Looping Sequences (CLS) is a formalism for the description of biological systems Stochastic CLS is the stochastic extension of CLS A simulator based on Stochastic CLS has been developed Our original aim was to apply model checking to Stochastic CLS models We wanted to use Probabilistic Maude (PMaude) as a model checker unfortunately, the model checking module of PMaude seems not to be available... Consequently, we have chosen Real-Time Maude (Maude with a notion of time) we have adapted Gillespie s stochastic simulation algorithm in order to be used in Real-Time Maude we have used Real-Time Maude analysis tool to verify properties on the results of a number of simulations (statistical model checking) Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

3 Outline of the talk 1 Introduction 2 The Calculus of Looping Sequences (CLS) Definition of CLS The lac operon in CLS Stochastic CLS 3 (Statistical) model checking of Stochastic CLS models Choosing a model checker Translation of Stochastic CLS into Real-Time Maude Analysis examples Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

4 The Calculus of Looping Sequences (CLS) We assume an alphabet E. Terms T and Sequences S of CLS are given by the following grammar: T ::= S S ::= ɛ ( ) L S T T T a S S where a is a generic element of E, and ɛ is the empty sequence. The operators are: S S : Sequencing ( ) L S : Looping (S is closed and it can rotate) T 1 T 2 : Containment (T 1 contains T 2 ) T T : Parallel composition (juxtaposition) Actually, looping and containment form a single binary operator ( S ) L T. Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

5 Examples of Terms (i) (ii) (iii) ( a b c ) L ɛ ( a b c ) L ( d e ) L ɛ ( a b c ) L (f g ( d e ) L ɛ) Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

6 Structural Congruence The Structural Congruence relations S and T are the least congruence relations on sequences and on terms, respectively, satisfying the following rules: S 1 (S 2 S 3 ) S (S 1 S 2 ) S 3 S ɛ S ɛ S S S T 1 T 2 T T 2 T 1 T 1 (T 2 T 3 ) T (T 1 T 2 ) T 3 T ɛ T T ( ɛ ) L ( ) L ( ) L ɛ T ɛ S1 S 2 T T S2 S 1 T We write for T. Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

7 CLS Patterns Let us consider variables of three kinds: term variables (X, Y, Z,...) sequence variables ( x, ỹ, z,...) element variables (x, y, z,...) Patterns P and Sequence Patterns SP of CLS extend CLS terms and sequences with variables: P ::= SP SP ::= ɛ a ( ) L SP P P P X SP SP x x where a is a generic element of E, ɛ is the empty sequence, and x, x and X are generic element, sequence and term variables The structural congruence relation extends trivially to patterns Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

8 Rewrite Rules Pσ denotes the term obtained by replacing any variable in T with the corresponding term, sequence or element. Σ is the set of all possible instantiations σ A Rewrite Rule is a pair (P, P ), denoted P P, where: P, P are patterns variables in P are a subset of those in P A rule P P can be applied to all terms Pσ. Example: a x a b x b can be applied to a c a (producing b c b) cannot be applied to a c c a Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

9 CLS modeling examples: the lac operon (1) DNA i p o z y a mrna proteins R lac Repressor beta-gal. permease transacet. i p o z y a a) RNA Polimerase R NO TRANSCRIPTION i p o z y a b) RNA Polimerase R LACTOSE TRANSCRIPTION Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

10 CLS modeling examples: the lac operon (2) Ecoli ::= ( m ) L (laci lacp laco lacz lacy laca polym) Rules for DNA transcription/translation: laci x laci x repr polym x lacp ỹ x PP ỹ x PP laco ỹ x lacp PO ỹ x PO lacz ỹ x laco PZ ỹ x PZ lacy ỹ x lacz PY ỹ betagal x PY laca x lacy PA perm x PA x laca transac polym (R1) (R2) (R3) (R4) (R5) (R6) (R7) Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

11 CLS modeling examples: the lac operon (3) Ecoli ::= ( m ) L (laci lacp laco lacz lacy laca polym) Rules to describe the binding of the lac Repressor to gene o, and what happens when lactose is present in the environment of the bacterium: repr x laco ỹ x RO ỹ LACT ( m x ) L ( ) L X m x (X LACT ) x RO ỹ LACT x laco ỹ RLACT ) L ( ) L ( x (perm X ) perm x X LACT ( perm x ) L ( ) L X perm x (LACT X ) betagal LACT betagal GLU GAL (R8) (R9) (R10) (R11) (R12) (R13) Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

12 CLS modeling examples: the lac operon (4) Ecoli ::= ( m ) L (laci lacp laco lacz lacy laca polym) Example: Ecoli LACT LACT ( m ) L (laci lacp laco lacz lacy laca polym repr) LACT LACT ( m ) L (laci lacp RO lacz lacy laca polym) LACT LACT ( m ) L (laci lacp laco lacz lacy laca polym RLACT ) LACT ( perm m ) L (laci A betagal transac polym RLACT ) LACT ( perm m ) L (laci A betagal transac polym RLACT GLU GAL) Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

13 Outline of the talk 1 Introduction 2 The Calculus of Looping Sequences (CLS) Definition of CLS The lac operon in CLS Stochastic CLS 3 (Statistical) model checking of Stochastic CLS models Choosing a model checker Translation of Stochastic CLS into Real-Time Maude Analysis examples Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

14 Background: the kinetics of chemical reactions Usual notation for chemical reactions: l 1 S l ρ S ρ k k 1 l 1P l γp γ where: S i, P i are molecules (reactants) l i, l i are stoichiometric coefficients k, k 1 are the kinetic constants The kinetics is described by the law of mass action: d[p i ] dt = l i k[s 1 ] l1 [S ρ ] lρ } {{ } reaction rate l i k 1 [P 1 ] l 1 [Pγ ] l γ } {{ } reaction rate Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

15 Background: Gillespie s simulation algorithm represents a chemical solution as a multiset of molecules computes the reaction rate a µ by multiplying the kinetic constant by the number of possible combinations of reactants Example: chemical solution with X 1 molecules S 1 and X 2 molecules S 2 reaction R 1 : S 1 + S 2 2S 1 rate a 1 = ( X 1 1 )( X2 1 ) k1 = X 1 X 2 k 1 reaction R 2 : 2S 1 S 1 + S 2 rate a 2 = ( X 1 2 ) k2 = X 1(X 1 1) 2 k 2 Given a set of reactions {R 1,... R M } and a current time t The time t + τ at which the next reaction will occur is randomly chosen with τ exponentially distributed with parameter M ν=1 a ν; The reaction R µ that has to occur at time t + τ is randomly chosen a with probability µ P M. ν=1 aν At each step t is incremented by τ and the chemical solution is updated. Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

16 Stochastic CLS Stochastic CLS incorporates Gillespie s stochastic framework into the semantics of CLS Rewrite rules are enriched with a kinetic constant What is a reactant combination in Stochastic CLS? A reactant combination is an occurence (up to ) of a left hand side of a rewrite rule Two definitions of the semantics of Stochastic CLS exist The first computes the number of reactant combinations by adding unique labels to the alphabet symbols in the term The second computes the number of reactant combinations compositionally Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

17 The occ function For the sake of the translation into Maude we have defined a recursive function occ(t, T ) that gives the number of combinations of reactants T in the term T. occ(t, ɛ) = 0 j 1 + occ(s, S1 ) + occ(s, T ) if S is a prefix of E S occ(s, E S 1 T ) = 1 occ(s, S 1 ) + occ(s, T ) otherwise occ(s, (S 1 ) L (T ) T 1 ) = occ (S, S 1 ) + occ(s, T ) + occ(s, T 1 ) j occ((s) L T 1, (S 1 ) L 1 + occ((s) T T 2 ) = L T 1, T 2 ) occ((s) L T 1, T ) + occ((s) L T 1, T 2 ) occ(s T, S T 1 ) = 8 >< occ((s) L T T 1, (S 1 ) L T 2 T 3 ) = >: j (1+exactocc(S,T1 ))exactocc(t,t 1 ) 1+exactocc(S,T ) occ(s T, T 1 ) (1+exactocc((S) L T,T 3 ))exactocc(t 1,T 3 ) 1+exactocc((S) L T,T 1 ) if S S 1 and T 1 T otherwise if exactocc(t, T 1 ) > 0 otherwise if S S 1, T T 2 and exactocc(t 1, T 3 occ((s) L T T 1, T 2 ) + occ((s) L T T 1, T 3 ) otherwise.... Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

18 The occ function: examples occ ( a b, a a b b b ) = 6 ( (m ) L ( ) L ( ) L ( ) ) L occ a, m a m m a = 2 ( occ a b, ( ) L ( ) ) L m (a b) m (a b a) = 3 occ ( a b, a b c a b ) = 2 ( occ a b, ( ) ) L b a b a a b c = 3 Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

19 A Stochastic CLS model of the lac operon (1) DNA i p o z y a mrna proteins R lac Repressor beta-gal. permease transacet. i p o z y a a) RNA Polimerase R NO TRANSCRIPTION i p o z y a b) RNA Polimerase R LACTOSE TRANSCRIPTION Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

20 A Stochastic CLS model of the lac operon (2) Transcription of DNA, binding of lac Repressor to gene o, and interaction between lactose and lac Repressor: laci x 0.02 laci x Irna Irna 0.1 Irna repr polym x lacp ỹ 0.1 x PP ỹ x PP ỹ 0.01 polym x lacp ỹ x PP laco ỹ 20.0 polym Rna x lacp laco ỹ Rna 0.1 Rna betagal perm transac repr x laco ỹ 1.0 x RO ỹ x RO ỹ 0.01 repr x laco ỹ repr LACT RLACT RLACT 0.1 repr LACT (S1) (S2) (S3) (S4) (S5) (S6) (S7) (S8) (S9) (S10) Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

21 A Stochastic CLS model of the lac operon (3) The behaviour of the three enzymes for lactose degradation: ( x ) L (perm X ) 0.1 ( perm x ) L X LACT ( perm x ) L X ( perm x ) L (LACT X ) (S11) (S12) betagal LACT betagal GLU GAL (S13) Degradation of all the proteins and mrna involved in the process: perm ɛ (S14) betagal transac Irna ɛ (S16) repr 0.01 ɛ (S18) Rna RLACT LACT (S20) ɛ (S15) ɛ (S17) 0.01 ɛ (S19) Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

22 Simulation results (1) betagal perm perm on membrane Number of elements Time (sec) Production of enzymes in the absence of lactose ( m ) L (laci A 30 polym 100 repr) Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

23 Simulation results (2) betagal perm perm on membrane Number of elements Time (sec) Production of enzymes in the presence of lactose 100 LACT ( m ) L (laci A 30 polym 100 repr) Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

24 Simulation results (3) LACT (env.) LACT (inside) GLU Number of elements Time (sec) Degradation of lactose into glucose 100 LACT ( m ) L (laci A 30 polym 100 repr) Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

25 Outline of the talk 1 Introduction 2 The Calculus of Looping Sequences (CLS) Definition of CLS The lac operon in CLS Stochastic CLS 3 (Statistical) model checking of Stochastic CLS models Choosing a model checker Translation of Stochastic CLS into Real-Time Maude Analysis examples Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

26 A model checker for Stochastic CLS As candidate model checkers we have considered: PRISM Murphi PMaude All of them are probabilistic/stochastic model checkers PMaude is the most suitable It uses a language based on rewrite rules (rewrite logic) that eases the translation of Stochastic CLS rules Unfortunately, the model checking module of PMaude seems not to be available a possible alternative: Real-Time Maude Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

27 Real-Time Maude Maude is a specification language equipped with efficient analysis tools, which supports three modelling paradigms: algebraic style (via equations) rewrite logic (via rewrite rules) object oriented (via classes and messages) Real-Time Maude extends Maude with a notion of time rewrite rule applications might consume (a fixed amount of) time Real-Time Maude has two kinds of rules istantaneous rules: crl [l] : t => t if cond tick rules: crl [l] : t => t in time τ if cond Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

28 Translation of Stochastic CLS into Real-Time Maude Real-Time Maude is not stochastic we will include Gillespie s simulation algorithm (slightly changed) in the translation of Stochastic CLS models it will be used to generate single executions of the model Real-Time Maude analysis tools will be applied to the simulation results This is statistical model checking we loose exhaustivity (properties are checked on a number of runs) huge systems could be handled may allow property driven simulations Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

29 A slight modification to Gillespie s algorithm Given reactions {R 1,..., R M } and initial molecular population X 1,..., X M : Step 0 Initialize current time t = 0 and stepped time t step = 0 Step 1 Compute reaction propensities a 1,..., a n and Σ M ν=1 a ν Step 2 Choose reaction µ and reaction time τ Step 3 If t + τ t step then t step = t step + t Step 4 Execute reaction µ and set t = t + τ Step 5 If t total time then conclude, else return to Step 1 Simulations are still exact our modification doesn t change states and choices of the simulation simulation results are sampled every t time units Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

30 (Modified) Gillespie s algorthm in Real-Time Maude Every step of the simulation algorithm is translated into an instantaneous rule, apart from Step 3 (the increase of the stepped time) (set tick def 1/100.) crl [increase] : < step:3, t:r1, tau:r2, t step:r3, delta t:r4 > => < step:4, t step:r3+r4 > in time R3 if (R1+R2) >= R3 crl [no increase] : < step:3, t:r1, tau:r2, t step:r3, delta t:r4 > => < step:4 > in time R3 if (R1+R2) < R3 Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

31 Translation of Stochastic CLS into Real-Time Maude T ::= S S ::= ɛ ( ) L S T T T a S S (omod CLS is pr NAT sorts Elem Seq Term Loop subsorts Elem < Seq < Term op empty : -> Seq [ctor] op. : Seq Seq -> Seq [assoc gather (E e) id: empty ctor] op { } : Elem Nat -> Term op [ ]LContains [ ] : Seq Term -> Term [prec 41 gather (& &) ctor] op : Term Term -> Term [assoc comm prec 45 gather (E e) id: endom) empty ctor] Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

32 Translation of Stochastic CLS into Real-Time Maude Lotka reactions as Stochastic CLS rules S 1 10 S 1 S 1 S 1 S S 2 S 2 S 2 10 ɛ rl [ S1 ] : < O : CLSTerm term : (T S1), mu : 1, step : 4 > => < O : CLSTerm term : (T S1 S1), step : 5 > rl [ S2 ] : < O : CLSTerm term : (T S1 S2), mu : 2, step : 4 > => < O : CLSTerm term : (T S2 S2), step : 5 > rl [ S3 ] : < O : CLSTerm term : (T S2), mu : 3, step : 4 > => < O : CLSTerm term : T, step : 5 > Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

33 Analysis example: stochastic simulation 0.5 Simple reaction: S 1 S 2 10 Lotka reactions: S 1 S 1 S S 1 S 2 S 2 S 2 10 S 2 ɛ Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

34 Analysis example: statistical model checking Initialisation of 100 stochastic simulations rl [ initialise1 ] : < step : 0 > => < seed : random(1), step : 1 >.. rl [ initialise100 ] : < step : 0 > => < seed : random(100), step : 1 > Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

35 Analysis example: statistical model checking By using the tsearch command we can check all possible behaviours Starting with 4 x S 1 and 4 x S 2 we search 10 states where S 2 is absent (tsearch [10] INIT({S1}4 {S2}4) =>* {< O:Oid : CLSTerm term : T:Term > C:Configuration} such that occ(s2,t:term) = 0 in time <= 1/10.) Solution 1 C:Configuration --> < term: {S1}5, finaltime: e-2 >. Solution 10 C:Configuration --> < term: {S1}8, finaltime: e-2 > Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

36 Analysis example: statistical model checking The find earliest searches for the earliest time when a given state is reached Starting with 4 x S 1 and 4 x S 2 we search the earliest time when S 2 disappear (find earliest INIT({S1}4 {S2}4) =>* {< CLSTerm term:t:term > C:Configuration} such that occ(s2,t:term) == 0.) Result: {< term: {S1}8, finaltime: e-2 > in time 3/50} Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

37 Analysis example: statistical model checking Verification of properties espressed as LTL formulas. Some state formulas: vanished(t) indicates that term T has vanished from the system, IsLessThan(T,T ) indicates that the occurences of term T are less than the occurences of T. Starting with 4 x S 1 and 4 x S 2 we prove that S 2 will eventually disappear (i.e. vanished(s 2 )) that the amount of S 2 will eventually become less than the amount of S 1 (i.e. IsLessThan(S 2,S 1 )) (mc INIT({S1}4 {S2}4) =t <> vanished(s2) in time<=1.) Result Bool : true (mc INIT({S1} 4 {S2} 4) =t <> IsLessThan(S2,S1) in time<=1.) Result Bool : true Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

38 Conclusions We have presented preliminary ideas for the application of (statistical) model checking to Stochastic CLS models Many things to do: Prove the correctness of the translation into Real-Time Maude w.r.t. Stochastic CLS semantics Improve the efficiency of the computation of the occ function Model and analyse some more significant case study (e.g. the Lactose operon) Paolo Milazzo (Università di Pisa) SCLS into MAUDE Iaşi September, / 38

### Dynamics of Biological Systems

Dynamics of Biological Systems Part I - Biological background and mathematical modelling Paolo Milazzo (Università di Pisa) Dynamics of biological systems 1 / 53 Introduction The recent developments in

### Lab 9: Regulation of lactose metabolism

Lab 9: Regulation of lactose metabolism There are clearly different means and levels of regulating gene products, but the first comprehensive description of regulation of genes was that of the enzymes

### What makes cells different from each other? How do cells respond to information from environment?

What makes cells different from each other? How do cells respond to information from environment? Regulation of: - Transcription - prokaryotes - eukaryotes - mrna splicing - mrna localisation and translation

### Chapter 7 Gene Regulation in Prokaryotes

Chapter 7 Gene Regulation in Prokaryotes 1 Outline 1. Principles of Transcriptional Regulation 2. Regulation of Transcription Initiation: Lac Operon 3. The Case of Phage λ: Layers of Regulation 2 Part

### FOGA I - IS THERE SUCH A THING AS A GENE? = FORMATTING THE GENOME FOR PROTEIN SYNTHESIS

FOGA I - IS THERE SUCH A THING AS A GENE? = FORMATTING THE GENOME FOR PROTEIN SYNTHESIS Dilemma in choosing lecture style: Schematic presentation of all exceptions to classical view In-depth examination

### Lecture 1 MODULE 3 GENE EXPRESSION AND REGULATION OF GENE EXPRESSION. Professor Bharat Patel Office: Science 2, 2.36 Email: b.patel@griffith.edu.

Lecture 1 MODULE 3 GENE EXPRESSION AND REGULATION OF GENE EXPRESSION Professor Bharat Patel Office: Science 2, 2.36 Email: b.patel@griffith.edu.au What is Gene Expression & Gene Regulation? 1. Gene Expression

### Genetic Regulatory Mechanisms in the Synthesis of Proteins François Jacob and Jacques Monod. Journal of Molecular Biology (1961) 3:

Genetic Regulatory Mechanisms in the Synthesis of Proteins François Jacob and Jacques Monod. Journal of Molecular Biology (1961) 3: 318-356 " In describing genetic mechanisms, there is a choice between

### Gene Transcription in Prokaryotes

Gene Transcription in Prokaryotes Operons: in prokaryotes, genes that encode protein participating in a common pathway are organized together. This group of genes, arranged in tandem, is called an OPERON.

### Gene Switches Teacher Information

STO-143 Gene Switches Teacher Information Summary Kit contains How do bacteria turn on and turn off genes? Students model the action of the lac operon that regulates the expression of genes essential for

### Qualitative Simulation and Model Checking in Genetic Regulatory Networks

An Application of Model Checking to a realistic biological problem: Qualitative Simulation and Model Checking in Genetic Regulatory Networks A presentation of Formal Methods in Biology Justin Hogg justinshogg@gmail.com

### Regulation of Gene Expression

Chapter 18 Regulation of Gene Expression PowerPoint Lecture Presentations for Biology Eighth Edition Neil Campbell and Jane Reece Lectures by Chris Romero, updated by Erin Barley with contributions from

### The vast majority of RNA functions are concerned with protein synthesis.

RNA Structure, Function, and Synthesis RNA RNA differs from DNA in both structural and functional respects. RNA has two major structural differences: each of the ribose rings contains a 2 -hydroxyl, and

### GENE EXPRESSION Transcription (Video)

GENE EXPRESSION Is the process by which information from a gene is used in the synthesis of a functional gene product. These products are often proteins, but in non-protein coding genes such as rrna genes

### Name Class Date. Figure 13 1. 2. Which nucleotide in Figure 13 1 indicates the nucleic acid above is RNA? a. uracil c. cytosine b. guanine d.

13 Multiple Choice RNA and Protein Synthesis Chapter Test A Write the letter that best answers the question or completes the statement on the line provided. 1. Which of the following are found in both

### Ch. 12: DNA and RNA 12.1 DNA Chromosomes and DNA Replication

Ch. 12: DNA and RNA 12.1 DNA A. To understand genetics, biologists had to learn the chemical makeup of the gene Genes are made of DNA DNA stores and transmits the genetic information from one generation

### Proteins. Molecular Physiology: Enzymes and Cell Signaling. Binding. Protein Specificity. Enzymes. Enzymatic Reactions

Proteins Molecular Physiology: Enzymes and Cell Signaling Polymers of amino acids Have complex 3D structures Are the basis of most of the structure and physiological function of cells Binding Much of protein

### The Leader Election Protocol of IEEE 1394 in Maude

The Leader Election Protocol of IEEE 1394 in Maude Alberto Verdejo, Isabel Pita, and Narciso Martí-Oliet Technical Report 118.01 Dpto. de Sistemas Informáticos y Programación Universidad Complutense de

### Language-oriented Software Development and Rewriting Logic

Language-oriented Software Development and Rewriting Logic Christiano Braga cbraga@ic.uff.br http://www.ic.uff.br/ cbraga Universidade Federal Fluminense (UFF) Language-oriented Software Development and

### Overview: Conducting the Genetic Orchestra. Prokaryotes and eukaryotes alter gene expression in response to their changing environment

Overview: Conducting the Genetic Orchestra Prokaryotes and eukaryotes alter gene expression in response to their changing environment In multicellular eukaryotes, gene expression regulates development

### Controls Over Genes. Chapter 15

Controls Over Genes Chapter 15 Impacts, Issues: Between You and Eternity Mutations in some genes predispose individuals to develop certain kinds of cancer; mutations in BRAC genes cause breast cancer normal

### CellLine, a stochastic cell lineage simulator: Manual

CellLine, a stochastic cell lineage simulator: Manual Andre S. Ribeiro, Daniel A. Charlebois, Jason Lloyd-Price July 23, 2007 1 Introduction This document explains how to work with the CellLine modules

### RAF Application. The Origin of Life. E. Bingham 1 L. Hutton-Smith 2 E. Rolls 2. Oxford Summer School in Computational Biology, 2013

The Origin of Life E. Bingham 1 L. Hutton-Smith 2 E. Rolls 2 1 Department of Mathematics University of North Carolina 2 Mathematical Institute University of Oxford Oxford Summer School in Computational

### 13.4 Gene Regulation and Expression

13.4 Gene Regulation and Expression Lesson Objectives Describe gene regulation in prokaryotes. Explain how most eukaryotic genes are regulated. Relate gene regulation to development in multicellular organisms.

### GENE REGULATION. Teacher Packet

AP * BIOLOGY GENE REGULATION Teacher Packet AP* is a trademark of the College Entrance Examination Board. The College Entrance Examination Board was not involved in the production of this material. Pictures

### Software Modeling and Verification

Software Modeling and Verification Alessandro Aldini DiSBeF - Sezione STI University of Urbino Carlo Bo Italy 3-4 February 2015 Algorithmic verification Correctness problem Is the software/hardware system

### Complementary Base Pairs: A and T. DNA contains complementary base pairs in which adenine is always linked by two hydrogen bonds to thymine (A T).

Complementary Base Pairs: A and T DNA contains complementary base pairs in which adenine is always linked by two hydrogen bonds to thymine (A T). Complementary Base Pairs: G and C DNA contains complementary

### Theory of Computation Prof. Kamala Krithivasan Department of Computer Science and Engineering Indian Institute of Technology, Madras

Theory of Computation Prof. Kamala Krithivasan Department of Computer Science and Engineering Indian Institute of Technology, Madras Lecture No. # 31 Recursive Sets, Recursively Innumerable Sets, Encoding

### Testing LTL Formula Translation into Büchi Automata

Testing LTL Formula Translation into Büchi Automata Heikki Tauriainen and Keijo Heljanko Helsinki University of Technology, Laboratory for Theoretical Computer Science, P. O. Box 5400, FIN-02015 HUT, Finland

### Java+ITP: A Verification Tool Based on Hoare Logic and Algebraic Semantics

: A Verification Tool Based on Hoare Logic and Algebraic Semantics Department of Computer Science University of Illinois at Urbana-Champaign 6th International Workshop on Rewriting Logic and its Applications,

### Analysis of Algorithms I: Optimal Binary Search Trees

Analysis of Algorithms I: Optimal Binary Search Trees Xi Chen Columbia University Given a set of n keys K = {k 1,..., k n } in sorted order: k 1 < k 2 < < k n we wish to build an optimal binary search

### Module 3 Questions. 7. Chemotaxis is an example of signal transduction. Explain, with the use of diagrams.

Module 3 Questions Section 1. Essay and Short Answers. Use diagrams wherever possible 1. With the use of a diagram, provide an overview of the general regulation strategies available to a bacterial cell.

### Replication Study Guide

Replication Study Guide This study guide is a written version of the material you have seen presented in the replication unit. Self-reproduction is a function of life that human-engineered systems have

### Genetic information (DNA) determines structure of proteins DNA RNA proteins cell structure 3.11 3.15 enzymes control cell chemistry ( metabolism )

Biology 1406 Exam 3 Notes Structure of DNA Ch. 10 Genetic information (DNA) determines structure of proteins DNA RNA proteins cell structure 3.11 3.15 enzymes control cell chemistry ( metabolism ) Proteins

### Overcoming Unknown Kinetic Data for Quantitative Modelling of Biological Systems Using Fuzzy Logic and Petri Nets

Overcoming Unknown Kinetic Data for Quantitative Modelling of Biological Systems Using Fuzzy Logic and Petri Nets Jure Bordon, dr. Miha Moškon, prof. Miha Mraz June 23th 2014 University of Ljubljana Faculty

### Translation Study Guide

Translation Study Guide This study guide is a written version of the material you have seen presented in the replication unit. In translation, the cell uses the genetic information contained in mrna to

### Chapter 6: Biological Networks

Chapter 6: Biological Networks 6.4 Engineering Synthetic Networks Prof. Yechiam Yemini (YY) Computer Science Department Columbia University Overview Constructing regulatory gates A genetic toggle switch;

### Transcription recap What is translation? Short Video Activity. Initiation Elongation Termination. Short Quiz on Thursday! 6.1 and 6.

Protein Synthesis Transcription recap What is translation? Initiation Elongation Termination Short Video Activity Short Quiz on Thursday! 6.1 and 6.2 1. RNA polymerase attaches to promoter region 2. Unwinds/unzips

### Bi 8 Lecture 9. Components of Transcriptional regulatory. Ellen Rothenberg 2 February 2016

Bi 8 Lecture 9 Components of Transcriptional regulatory Machines & BACTERIAL MODES OF REGULATION, PART 1 Ellen Rothenberg 2 February 2016 Reading: Alberts 6 th edition Ch. 7, pp. 369-383 Optional: on reserve,

### INF5140: Specification and Verification of Parallel Systems

INF5140: Specification and Verification of Parallel Systems Lecture 7 LTL into Automata and Introduction to Promela Gerardo Schneider Department of Informatics University of Oslo INF5140, Spring 2007 Gerardo

### Chemical reactions allow living things to grow, develop, reproduce, and adapt.

Section 2: Chemical reactions allow living things to grow, develop, reproduce, and adapt. K What I Know W What I Want to Find Out L What I Learned Essential Questions What are the parts of a chemical reaction?

### 1 Mutation and Genetic Change

CHAPTER 14 1 Mutation and Genetic Change SECTION Genes in Action KEY IDEAS As you read this section, keep these questions in mind: What is the origin of genetic differences among organisms? What kinds

### Dynamic Process/Service Composition/Combination

INFINT 2009 - Bertinoro Workshop on Data and Service Integration Bertinoro, March 15-20, 2009 Dynamic Process/Service Composition/Combination Ugo Montanari Dipartimento di Informatica Università di Pisa

### Feed Forward Loops in Biological Systems

Feed Forward Loops in Biological Systems Dr. M. Vijayalakshmi School of Chemical and Biotechnology SASTRA University Joint Initiative of IITs and IISc Funded by MHRD Page 1 of 7 Table of Contents 1 INTRODUCTION...

### Biology Performance Level Descriptors

Limited A student performing at the Limited Level demonstrates a minimal command of Ohio s Learning Standards for Biology. A student at this level has an emerging ability to describe genetic patterns of

### [Refer Slide Time: 05:10]

Principles of Programming Languages Prof: S. Arun Kumar Department of Computer Science and Engineering Indian Institute of Technology Delhi Lecture no 7 Lecture Title: Syntactic Classes Welcome to lecture

### A Brief Introduction to Systems Biology: Gene Regulatory Networks Rajat K. De

A Brief Introduction to Systems Biology: Gene Regulatory Networks Rajat K. De Machine Intelligence Unit, Indian Statistical Institute 203 B. T. Road Kolkata 700108 email id: rajat@isical.ac.in 1 Informatics

### A Propositional Dynamic Logic for CCS Programs

A Propositional Dynamic Logic for CCS Programs Mario R. F. Benevides and L. Menasché Schechter {mario,luis}@cos.ufrj.br Abstract This work presents a Propositional Dynamic Logic in which the programs are

### Verifying Specifications with Proof Scores in CafeOBJ

Verifying Specifications with Proof Scores in CafeOBJ FUTATSUGI, Kokichi 二 木 厚 吉 Chair of Language Design Graduate School of Information Science Japan Advanced Institute of Science and Technology (JAIST)

### What happens to the food we eat? It gets broken down!

Enzymes Essential Questions: What is an enzyme? How do enzymes work? What are the properties of enzymes? How do they maintain homeostasis for the body? What happens to the food we eat? It gets broken down!

### Control of Gene Expression

Home Gene Regulation Is Necessary? Control of Gene Expression By switching genes off when they are not needed, cells can prevent resources from being wasted. There should be natural selection favoring

### Molecular Genetics. RNA, Transcription, & Protein Synthesis

Molecular Genetics RNA, Transcription, & Protein Synthesis Section 1 RNA AND TRANSCRIPTION Objectives Describe the primary functions of RNA Identify how RNA differs from DNA Describe the structure and

### Transcription Study Guide

Transcription Study Guide This study guide is a written version of the material you have seen presented in the transcription unit. The cell s DNA contains the instructions for carrying out the work of

### Some functions of most cells

Some functions of most cells Take in chemical or solar energy, turn some into mechanical activity or synthesis of molecules Manufacture more of their own internal structure, extracellular matrix, regulatory

### Lab Exercise: Transformation

Lab Exercise: Transformation Background Genetic transformation is used in many areas of biotechnology, and, at its heart, requires two things: Donor DNA and recipient cells. Cells which receive the donor

### Protein Translation. The genetic code Protein synthesis Machinery Ribosomes, trna s

Protein Translation The genetic code Protein synthesis Machinery Ribosomes, trna s Universal translation: Protein Synthesis Chemical Letters DNA A,T,G,C mrna A,U,G,C protein *ribosome * A,C,D,E,F,G,H,

### STATUS REPORT ON MAUDE-NPA TOOL

STATUS REPORT ON MAUDE-NPA TOOL Catherine Meadows Santiago Escobar Jose Meseguer September 28, 2006 1 GOAL Extend standard free algebra model of crypto protocol analysis to deal with algebraic properties

### The Mole Concept. The Mole. Masses of molecules

The Mole Concept Ron Robertson r2 c:\files\courses\1110-20\2010 final slides for web\mole concept.docx The Mole The mole is a unit of measurement equal to 6.022 x 10 23 things (to 4 sf) just like there

### CCR Biology - Chapter 8 Practice Test - Summer 2012

Name: Class: Date: CCR Biology - Chapter 8 Practice Test - Summer 2012 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What did Hershey and Chase know

### Counterexample-guided Design of Property-based Dynamic Software Updates

Counterexample-guided Design of Property-based Dynamic Software Updates Min Zhang 20141015 Min Zhang (JAIST) Counterexample-guided Design of Property-based Dynamic Software Updates 20141015 [1/45] Contents

### Chapter 18 Regulation of Gene Expression

Chapter 18 Regulation of Gene Expression 18.1. Gene Regulation Is Necessary By switching genes off when they are not needed, cells can prevent resources from being wasted. There should be natural selection

### SAM Teacher s Guide DNA to Proteins

SAM Teacher s Guide DNA to Proteins Note: Answers to activity and homework questions are only included in the Teacher Guides available after registering for the SAM activities, and not in this sample version.

### Bioinformatics: Network Analysis

Bioinformatics: Network Analysis Molecular Cell Biology: A Brief Review COMP 572 (BIOS 572 / BIOE 564) - Fall 2013 Luay Nakhleh, Rice University 1 The Tree of Life 2 Prokaryotic vs. Eukaryotic Cell Structure

### Static Program Transformations for Efficient Software Model Checking

Static Program Transformations for Efficient Software Model Checking Shobha Vasudevan Jacob Abraham The University of Texas at Austin Dependable Systems Large and complex systems Software faults are major

### Gene Regulation -- The Lac Operon

Gene Regulation -- The Lac Operon Specific proteins are present in different tissues and some appear only at certain times during development. All cells of a higher organism have the full set of genes:

### 1. Which of the following correctly organizes genetic material from the broadest category to the most specific category?

DNA and Genetics 1. Which of the following correctly organizes genetic material from the broadest category to the most specific category? A. genome chromosome gene DNA molecule B. genome chromosome DNA

### Enzymes and Metabolism

Enzymes and Metabolism Enzymes and Metabolism Metabolism: Exergonic and Endergonic Reactions Chemical Reactions: Activation Every chemical reaction involves bond breaking and bond forming A chemical reaction

### Activity 7.21 Transcription factors

Purpose To consolidate understanding of protein synthesis. To explain the role of transcription factors and hormones in switching genes on and off. Play the transcription initiation complex game Regulation

### Software Engineering

Software Engineering Lecture 04: The B Specification Method Peter Thiemann University of Freiburg, Germany SS 2013 Peter Thiemann (Univ. Freiburg) Software Engineering SWT 1 / 50 The B specification method

### Molecule Shapes. support@ingenuity.com www.ingenuity.com 1

IPA 8 Legend This legend provides a key of the main features of Network Explorer and Canonical Pathways, including molecule shapes and colors as well as relationship labels and types. For a high-resolution

### 7-5.5. Translate chemical symbols and the chemical formulas of common substances to show the component parts of the substances including:

7-5.5 Translate chemical symbols and the chemical formulas of common substances to show the component parts of the substances including: NaCl [salt], H 2 O [water], C 6 H 12 O 6 [simple sugar], O 2 [oxygen

### GenBank, Entrez, & FASTA

GenBank, Entrez, & FASTA Nucleotide Sequence Databases First generation GenBank is a representative example started as sort of a museum to preserve knowledge of a sequence from first discovery great repositories,

### Simulative Model Checking of Steady State and Time-Unbounded Temporal Operators

Simulative Model Checking of Steady State and Time-Unbounded Temporal Operators Christian Rohr Department of Computer Science Brandenburg University of Technology Cottbus June 25, 2012 Outline 1 Introduction

### Automata Theory. Şubat 2006 Tuğrul Yılmaz Ankara Üniversitesi

Automata Theory Automata theory is the study of abstract computing devices. A. M. Turing studied an abstract machine that had all the capabilities of today s computers. Turing s goal was to describe the

### NO CALCULATORS OR CELL PHONES ALLOWED

Biol 205 Exam 1 TEST FORM A Spring 2008 NAME Fill out both sides of the Scantron Sheet. On Side 2 be sure to indicate that you have TEST FORM A The answers to Part I should be placed on the SCANTRON SHEET.

### Synthetic gene networks on paper

Synthetic gene networks on paper Journal club Caihong Zhu 25.11.2014 Synthetic biology Definition: "designing and constructing biological devices and biological systems for useful purposes. _Wekipedia

### Transcription Animations

Transcription Animations Name: Lew Ports Biology Place http://www.lewport.wnyric.org/jwanamaker/animations/protein%20synthesis%20-%20long.html Protein is the making of proteins from the information found

### RNA Structure and folding

RNA Structure and folding Overview: The main functional biomolecules in cells are polymers DNA, RNA and proteins For RNA and Proteins, the specific sequence of the polymer dictates its final structure

### MICROBIAL GENETICS. Gene Regulation: The Operons

MICROBIAL GENETICS Gene Regulation: The Operons Pradeep Kumar Burma Reader Department of Genetics University of Delhi South Campus Benito Juarez Road New Delhi-110021 E-mail: pburma@hotmail.com 05-May-2006

### Discrete Mathematics, Chapter 5: Induction and Recursion

Discrete Mathematics, Chapter 5: Induction and Recursion Richard Mayr University of Edinburgh, UK Richard Mayr (University of Edinburgh, UK) Discrete Mathematics. Chapter 5 1 / 20 Outline 1 Well-founded

GCSE Additional Science Module B4 The processes of life: What you should know Name: Science Group: Teacher: R.A.G. each of the statements to help focus your revision: R = Red: I don t know this A = Amber:

### AP BIOLOGY 2009 SCORING GUIDELINES

AP BIOLOGY 2009 SCORING GUIDELINES Question 4 The flow of genetic information from DNA to protein in eukaryotic cells is called the central dogma of biology. (a) Explain the role of each of the following

### Overview Motivating Examples Interleaving Model Semantics of Correctness Testing, Debugging, and Verification

Introduction Overview Motivating Examples Interleaving Model Semantics of Correctness Testing, Debugging, and Verification Advanced Topics in Software Engineering 1 Concurrent Programs Characterized by

### The Righteous and the Wicked: Efficient high-level methods for performance analysis

The Righteous and the Wicked: Efficient high-level methods for performance analysis Stephen Gilmore Joint work with Anne Benoit, Murray Cole and Jane Hillston Enhance project, LFCS, University of Edinburgh

### 3. Recurrence Recursive Definitions. To construct a recursively defined function:

3. RECURRENCE 10 3. Recurrence 3.1. Recursive Definitions. To construct a recursively defined function: 1. Initial Condition(s) (or basis): Prescribe initial value(s) of the function.. Recursion: Use a

### Integers: applications, base conversions.

CS 441 Discrete Mathematics for CS Lecture 14 Integers: applications, base conversions. Milos Hauskrecht milos@cs.pitt.edu 5329 Sennott Square Modular arithmetic in CS Modular arithmetic and congruencies

### http://aejm.ca Journal of Mathematics http://rema.ca Volume 1, Number 1, Summer 2006 pp. 69 86

Atlantic Electronic http://aejm.ca Journal of Mathematics http://rema.ca Volume 1, Number 1, Summer 2006 pp. 69 86 AUTOMATED RECOGNITION OF STUTTER INVARIANCE OF LTL FORMULAS Jeffrey Dallien 1 and Wendy

### Formal Verification of Software

Formal Verification of Software Sabine Broda Department of Computer Science/FCUP 12 de Novembro de 2014 Sabine Broda (DCC-FCUP) Formal Verification of Software 12 de Novembro de 2014 1 / 26 Formal Verification

### A Mathematical Model of a Synthetically Constructed Genetic Toggle Switch

BENG 221 Mathematical Methods in Bioengineering Project Report A Mathematical Model of a Synthetically Constructed Genetic Toggle Switch Nick Csicsery & Ricky O Laughlin October 15, 2013 1 TABLE OF CONTENTS

Proteins play a crucial role in almost every biological process, from cell signaling to cell division. Each protein has to be uniquely suited to its particular job, yet they are all made of the same 20

### for the High-performance Modeling

1 Unifying Framework and Tool for the High-performance Modeling and Verification of Hybrid Concurrent Systems Kazunori Ueda Dept. of Computer Science and Engineering, Waseda University and National Institute

### Complex multicellular organisms are produced by cells that switch genes on and off during development.

Home Control of Gene Expression Gene Regulation Is Necessary? By switching genes off when they are not needed, cells can prevent resources from being wasted. There should be natural selection favoring

### Cells and Their Housekeeping Functions Nucleus and Other Organelles

Cells and Their Housekeeping Functions Nucleus and Other Organelles Shu-Ping Lin, Ph.D. Institute of Biomedical Engineering E-mail: splin@dragon.nchu.edu.tw Website: http://web.nchu.edu.tw/pweb/users/splin/

### Assignment 2: Option Pricing and the Black-Scholes formula The University of British Columbia Science One CS 2015-2016 Instructor: Michael Gelbart

Assignment 2: Option Pricing and the Black-Scholes formula The University of British Columbia Science One CS 2015-2016 Instructor: Michael Gelbart Overview Due Thursday, November 12th at 11:59pm Last updated

### macromolecule: monomer: polymer: a. The elements found in carbohydrates occur in a specific ratio. Describe that ratio.

NAME: DATE: Biological Macromolecule Poster Project HOUR: BIOLOGY You and your table mates will be researching and creating an informational poster on one of four biological macromolecules: carbohydrates,

### Name: Date: Period: DNA Unit: DNA Webquest

Name: Date: Period: DNA Unit: DNA Webquest Part 1 History, DNA Structure, DNA Replication DNA History http://www.dnaftb.org/dnaftb/1/concept/index.html Read the text and answer the following questions.

### Chapter 12 - Reaction Kinetics

Chapter 12 - Reaction Kinetics In the last chapter we looked at enzyme mechanisms. In this chapter we ll see how enzyme kinetics, i.e., the study of enzyme reaction rates, can be useful in learning more

### CGT 581 G Procedural Methods L systems

CGT 581 G Procedural Methods L systems Bedrich Benes, Ph.D. Purdue University Department of Computer Graphics Technology L systems Lindenmayer systems Lindenmayer system or D0L systems [d zero l system]