[PPT] - Maintenance of Chronobiological Information by P System Mediated PowerPoint Presentation

SLIDE 1

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Maintenance of Chronobiological Information by P System Mediated Assembly of Control Units for Oscillatory Waveforms and Frequency

Thomas Hinze1,2 Benjamin Schell2 Mathias Schumann2 Christian Bodenstein2

1Brandenburg University of Technology Cottbus

Institute of Computer Science and Information and Media Technology

2Friedrich Schiller University Jena

Department of Bioinformatics at School of Biology and Pharmacy

thomas.hinze@tu-cottbus.de

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 2

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Oscillatory Signals in Biology: Range of Periodicities

spikes of firing neurons

uni−freiburg.de

heart beat

wikipedia.org

cell cycle

wikimedia.org

circadian rhythm

timeanddate.com nhs.uk

menstrual cycle

kidsgeo.com

hibernation annual cycles

1 month 1 year 6...24 hours 0.3...1.5 sec. 10 millisec.

time

1 day

An individual organism comprises a variety of regulated oscillations.

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 3

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Waveforms of Oscillatory Signals in Biology

Waveform as additional information carrier beyond frequency

signal peak for short moment fast raise or fall of signal value easy to detect average signal level can be kept low more or less bistable oscillatory behaviour almost rectangular shape towards binarisation toggling with weightable balance btw. high/low gradual and smooth alteration commonly stable limit cycle quite robust against perturbations

almost sinusoidal sinusoidal or spiking plated

Corresponding oscillators for each waveform by small or medium-sized reaction networks

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 4

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

17-years and 13-years Periodical Cicadas with Synchronous Life Cycle

1cm

magicicada.org

2004 >1,000,000 individuals appear for approx three weeks 1987 brood eggs in soil 5 larval stages nutrition in annual cycles from liquor in rootwood 17 years underground 2011 1998 1985

17−year life cycle 13−year life cycle USA

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 5

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Inspiration and Motivating Questions

No external stimulus with natural period of 17 or 13 years

known up to now

Molecular mechanism to precisely measure the passage of

17 (or 13) years?

Need of a chemical frequency divider model, ideally

configurable for distinct division ratios

Low number of slight evolutionary changes sufficient to

toggle the life cycle between a variety of years? = ⇒ Assembly of pre-defined chemical modules towards new or extended functionality

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 6

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Inspiration and Motivating Questions

No external stimulus with natural period of 17 or 13 years

known up to now

Molecular mechanism to precisely measure the passage of

17 (or 13) years?

Need of a chemical frequency divider model, ideally

configurable for distinct division ratios

Low number of slight evolutionary changes sufficient to

toggle the life cycle between a variety of years? = ⇒ Assembly of pre-defined chemical modules towards new or extended functionality

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 7

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Inspiration and Motivating Questions

No external stimulus with natural period of 17 or 13 years

known up to now

Molecular mechanism to precisely measure the passage of

17 (or 13) years?

Need of a chemical frequency divider model, ideally

configurable for distinct division ratios

Low number of slight evolutionary changes sufficient to

toggle the life cycle between a variety of years? = ⇒ Assembly of pre-defined chemical modules towards new or extended functionality

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 8

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Inspiration and Motivating Questions

No external stimulus with natural period of 17 or 13 years

known up to now

Molecular mechanism to precisely measure the passage of

17 (or 13) years?

Need of a chemical frequency divider model, ideally

configurable for distinct division ratios

Low number of slight evolutionary changes sufficient to

toggle the life cycle between a variety of years? = ⇒ Assembly of pre-defined chemical modules towards new or extended functionality

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 9

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Inspiration and Motivating Questions

No external stimulus with natural period of 17 or 13 years

known up to now

Molecular mechanism to precisely measure the passage of

17 (or 13) years?

Need of a chemical frequency divider model, ideally

configurable for distinct division ratios

Low number of slight evolutionary changes sufficient to

toggle the life cycle between a variety of years? = ⇒ Assembly of pre-defined chemical modules towards new or extended functionality

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 10

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

1. Biological Rhythms

2. P Meta Framework

Non-probabilistic P modules
Connectivity of P modules
Instructions for composition of P modules
3. Assembly of Frequency Dividers
4. Suprachiasmatic Nucleus

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 11

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Non-probabilistic P Module

is able to fulfill an elementary computational task on the fly
building block of an analog computer or in a control loop
represents a container encapsulating a formal description
f its dynamical behaviour
specifies the interface of a general real-valued system or

its approximation

aims to bridge building blocks in systems theory and

membrane systems More formally, a P module is a triple (↓, ↑, ) where ↓= (I1, . . . , Ii) . . . . . . . . . . indicates a list of input signal identifiers ↑= (O1, . . . , Oo) . . . . . . indicates a list of output signal identifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . underlying system specification with or without inherent auxiliary signals Each signal is a real-valued function over time.

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 12

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Non-probabilistic P Module

is able to fulfill an elementary computational task on the fly
building block of an analog computer or in a control loop
represents a container encapsulating a formal description
f its dynamical behaviour
specifies the interface of a general real-valued system or

its approximation

aims to bridge building blocks in systems theory and

membrane systems More formally, a P module is a triple (↓, ↑, ) where ↓= (I1, . . . , Ii) . . . . . . . . . . indicates a list of input signal identifiers ↑= (O1, . . . , Oo) . . . . . . indicates a list of output signal identifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . underlying system specification with or without inherent auxiliary signals Each signal is a real-valued function over time.

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 13

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Non-probabilistic P Module

is able to fulfill an elementary computational task on the fly
building block of an analog computer or in a control loop
represents a container encapsulating a formal description
f its dynamical behaviour
specifies the interface of a general real-valued system or

its approximation

aims to bridge building blocks in systems theory and

membrane systems More formally, a P module is a triple (↓, ↑, ) where ↓= (I1, . . . , Ii) . . . . . . . . . . indicates a list of input signal identifiers ↑= (O1, . . . , Oo) . . . . . . indicates a list of output signal identifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . underlying system specification with or without inherent auxiliary signals Each signal is a real-valued function over time.

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 14

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Non-probabilistic P Module

is able to fulfill an elementary computational task on the fly
building block of an analog computer or in a control loop
represents a container encapsulating a formal description
f its dynamical behaviour
specifies the interface of a general real-valued system or

its approximation

aims to bridge building blocks in systems theory and

membrane systems More formally, a P module is a triple (↓, ↑, ) where ↓= (I1, . . . , Ii) . . . . . . . . . . indicates a list of input signal identifiers ↑= (O1, . . . , Oo) . . . . . . indicates a list of output signal identifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . underlying system specification with or without inherent auxiliary signals Each signal is a real-valued function over time.

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 15

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Non-probabilistic P Module

is able to fulfill an elementary computational task on the fly
building block of an analog computer or in a control loop
represents a container encapsulating a formal description
f its dynamical behaviour
specifies the interface of a general real-valued system or

its approximation

aims to bridge building blocks in systems theory and

membrane systems More formally, a P module is a triple (↓, ↑, ) where ↓= (I1, . . . , Ii) . . . . . . . . . . indicates a list of input signal identifiers ↑= (O1, . . . , Oo) . . . . . . indicates a list of output signal identifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . underlying system specification with or without inherent auxiliary signals Each signal is a real-valued function over time.

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 16

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Non-probabilistic P Module

is able to fulfill an elementary computational task on the fly
building block of an analog computer or in a control loop
represents a container encapsulating a formal description
f its dynamical behaviour
specifies the interface of a general real-valued system or

its approximation

aims to bridge building blocks in systems theory and

membrane systems More formally, a P module is a triple (↓, ↑, ) where ↓= (I1, . . . , Ii) . . . . . . . . . . indicates a list of input signal identifiers ↑= (O1, . . . , Oo) . . . . . . indicates a list of output signal identifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . underlying system specification with or without inherent auxiliary signals Each signal is a real-valued function over time.

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 17

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Non-probabilistic P Module as a Processing Unit

input signals

utput signals

system providing input-output mapping on the fly

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein
metabolic P system (mP system) M
P system for cell signalling modules ΠCSM
P system for cell signalling networks ΠCSN
ordinary differential equations (ODEs) in

conjunction with numerical solver

transfer function (input-output mapping)
n its own, given explicitly or implicitly
characteristic curve, given by numeric

values along with approximation/interpolation algorithm

SLIDE 18

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Non-probabilistic P Module as a Processing Unit

input signals

utput signals

system providing input-output mapping on the fly

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein
metabolic P system (mP system) M
P system for cell signalling modules ΠCSM
P system for cell signalling networks ΠCSN
ordinary differential equations (ODEs) in

conjunction with numerical solver

transfer function (input-output mapping)
n its own, given explicitly or implicitly
characteristic curve, given by numeric

values along with approximation/interpolation algorithm

SLIDE 19

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Non-probabilistic P Module as a Processing Unit

input signals

utput signals

system providing input-output mapping on the fly

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein
metabolic P system (mP system) M
P system for cell signalling modules ΠCSM
P system for cell signalling networks ΠCSN
ordinary differential equations (ODEs) in

conjunction with numerical solver

transfer function (input-output mapping)
n its own, given explicitly or implicitly
characteristic curve, given by numeric

values along with approximation/interpolation algorithm

SLIDE 20

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Non-probabilistic P Module as a Processing Unit

input signals

utput signals

system providing input-output mapping on the fly

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein
metabolic P system (mP system) M
P system for cell signalling modules ΠCSM
P system for cell signalling networks ΠCSN
ordinary differential equations (ODEs) in

conjunction with numerical solver

transfer function (input-output mapping)
n its own, given explicitly or implicitly
characteristic curve, given by numeric

values along with approximation/interpolation algorithm

SLIDE 21

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Non-probabilistic P Module as a Processing Unit

input signals

utput signals

system providing input-output mapping on the fly

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein
metabolic P system (mP system) M
P system for cell signalling modules ΠCSM
P system for cell signalling networks ΠCSN
ordinary differential equations (ODEs) in

conjunction with numerical solver

transfer function (input-output mapping)
n its own, given explicitly or implicitly
characteristic curve, given by numeric

values along with approximation/interpolation algorithm

SLIDE 22

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Non-probabilistic P Module as a Processing Unit

input signals

utput signals

system providing input-output mapping on the fly

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein
metabolic P system (mP system) M
P system for cell signalling modules ΠCSM
P system for cell signalling networks ΠCSN
ordinary differential equations (ODEs) in

conjunction with numerical solver

transfer function (input-output mapping)
n its own, given explicitly or implicitly
characteristic curve, given by numeric

values along with approximation/interpolation algorithm

SLIDE 23

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Non-probabilistic P Module as a Processing Unit

input signals

utput signals

system providing input-output mapping on the fly

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein
metabolic P system (mP system) M
P system for cell signalling modules ΠCSM
P system for cell signalling networks ΠCSN
ordinary differential equations (ODEs) in

conjunction with numerical solver

transfer function (input-output mapping)
n its own, given explicitly or implicitly
characteristic curve, given by numeric

values along with approximation/interpolation algorithm

SLIDE 24

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

P Meta Framework: Connecting P Modules

Our P meta framework is a construct Ππ↑↓ = (M, P) where M . . . . . . denotes a finite multiset of non-probabilistic P modules P . . . . . . . . . assembly programme by its connectivity instructions

multiset of P modules interacting P modules assembly programme

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 25

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

P Meta Framework: Connecting P Modules

Our P meta framework is a construct Ππ↑↓ = (M, P) where M . . . . . . denotes a finite multiset of non-probabilistic P modules P . . . . . . . . . assembly programme by its connectivity instructions

multiset of P modules interacting P modules assembly programme

supp(M) can be interpreted as the genetic potential of

highly conserved reaction units

Multiplicity of modules −

→ limitation of resources available for module composition

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 26

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Connectivity Graph of a P Meta Framework

Each P Meta Framework Ππ↑↓ = (M, P) comes with a corresponding directed graph G = (V, E), initially V := {m[i] | m ∈ supp(M) ∧ i ∈ {1, . . . , M(m)}} E := ∅

Indexing of all instances (copies) m[i] from a P module m allows

unique identification

Let a = (a↓, a↑, a) ∈ supp(M) and b = (b↓, b↑, b) ∈ supp(M) be

two module instances derived from M.

An edge (a, b, Ra→b) ∈ E denotes a connection from a to b

where dedicated output species of a act as input species of b.

Each edge comes with a binary relation Ra→b ⊆ a↑ × b↓ in which

the mapping of a’s output species onto b’s input species is given.

Ra→b handled in an injective manner since one output species is

allowed to cover several downstream input species, but each input species must be supplied by at most one upstream output species.

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 27

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Connectivity Graph of a P Meta Framework

Each P Meta Framework Ππ↑↓ = (M, P) comes with a corresponding directed graph G = (V, E), initially V := {m[i] | m ∈ supp(M) ∧ i ∈ {1, . . . , M(m)}} E := ∅

Indexing of all instances (copies) m[i] from a P module m allows

unique identification

Let a = (a↓, a↑, a) ∈ supp(M) and b = (b↓, b↑, b) ∈ supp(M) be

two module instances derived from M.

An edge (a, b, Ra→b) ∈ E denotes a connection from a to b

where dedicated output species of a act as input species of b.

Each edge comes with a binary relation Ra→b ⊆ a↑ × b↓ in which

the mapping of a’s output species onto b’s input species is given.

Ra→b handled in an injective manner since one output species is

allowed to cover several downstream input species, but each input species must be supplied by at most one upstream output species.

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 28

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Connectivity Graph of a P Meta Framework

Each P Meta Framework Ππ↑↓ = (M, P) comes with a corresponding directed graph G = (V, E), initially V := {m[i] | m ∈ supp(M) ∧ i ∈ {1, . . . , M(m)}} E := ∅

Indexing of all instances (copies) m[i] from a P module m allows

unique identification

Let a = (a↓, a↑, a) ∈ supp(M) and b = (b↓, b↑, b) ∈ supp(M) be

two module instances derived from M.

An edge (a, b, Ra→b) ∈ E denotes a connection from a to b

where dedicated output species of a act as input species of b.

Each edge comes with a binary relation Ra→b ⊆ a↑ × b↓ in which

the mapping of a’s output species onto b’s input species is given.

Ra→b handled in an injective manner since one output species is

allowed to cover several downstream input species, but each input species must be supplied by at most one upstream output species.

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 29

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Connectivity Graph of a P Meta Framework

Each P Meta Framework Ππ↑↓ = (M, P) comes with a corresponding directed graph G = (V, E), initially V := {m[i] | m ∈ supp(M) ∧ i ∈ {1, . . . , M(m)}} E := ∅

Indexing of all instances (copies) m[i] from a P module m allows

unique identification

Let a = (a↓, a↑, a) ∈ supp(M) and b = (b↓, b↑, b) ∈ supp(M) be

two module instances derived from M.

An edge (a, b, Ra→b) ∈ E denotes a connection from a to b

where dedicated output species of a act as input species of b.

Each edge comes with a binary relation Ra→b ⊆ a↑ × b↓ in which

the mapping of a’s output species onto b’s input species is given.

Ra→b handled in an injective manner since one output species is

allowed to cover several downstream input species, but each input species must be supplied by at most one upstream output species.

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 30

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Connectivity Graph of a P Meta Framework

Each P Meta Framework Ππ↑↓ = (M, P) comes with a corresponding directed graph G = (V, E), initially V := {m[i] | m ∈ supp(M) ∧ i ∈ {1, . . . , M(m)}} E := ∅

Indexing of all instances (copies) m[i] from a P module m allows

unique identification

Let a = (a↓, a↑, a) ∈ supp(M) and b = (b↓, b↑, b) ∈ supp(M) be

two module instances derived from M.

An edge (a, b, Ra→b) ∈ E denotes a connection from a to b

where dedicated output species of a act as input species of b.

Each edge comes with a binary relation Ra→b ⊆ a↑ × b↓ in which

the mapping of a’s output species onto b’s input species is given.

Ra→b handled in an injective manner since one output species is

allowed to cover several downstream input species, but each input species must be supplied by at most one upstream output species.

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 31

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Assembly Programme Instructions (Selection)

Time-dependent changes of module connectivity
Time stamp t opens each instruction
Instruction updates graph G(V, E)

t : ModuleConnect(a → b, Ra→b) connects some or all of module a’s output species to represent b’s input species by sharing species identifiers according to the injective binary relation Ra→b ⊆ a↑ × b↓. Edge update scheme: E := E ∪ {(a, b, Ra→b)}

a a b R = {(Z, C)} ( a ModuleConnect R) , b b {B, C} Z=C {X, Y} {Z}

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 32

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Assembly Programme Instructions (Selection)

Time-dependent changes of module connectivity
Time stamp t opens each instruction
Instruction updates graph G(V, E)

t : ModuleDisconnect(a ↔ b) completely disconnects modules a and b by annihilating all cross-modular species sharings. This comes along with removing Ra→b as well as Rb→a, respectively. Edge update scheme: E := E \ {(a, b, Ra→b)} \ {(b, a, Rb→a)}

{X, Y} {Z} {B, C} a b a b b ( a ModuleDisconnect )

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 33

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

1. Biological Rhythms
2. P Meta Framework

3. Assembly of Frequency Dividers

Chemical frequency divider model 1:17
Frequency divider 1:5 by separator removal
Frequency divider 1:6 by Repressilator
Frequency divider 1:3 by Goodwin module
4. Suprachiasmatic Nucleus

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 34

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

The Repressilator Module

repressilator = (∅, {Z}, F)

, H2 k 3

2 3

k 5 k 4 k 6 k

1

Z , H X

1

k Y , H

substrate concentration time (arbitrary unit) Z

Oscillation by progressional inhibition in gene regulatory

network

Involves higher-order Hill kinetics
Velocity of decay reactions mainly determines frequency
Inherently almost sinusoidal waveform

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 35

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

The Goodwin Module

goodwin = (∅, {X}, F)

2 3, H

k 5 k 4 k 6 k

1

Z k Y X k

X substrate concentration time (arbitrary unit)

Oscillation by mutual activation and inhibition in gene

regulatory network

Involves higher-order Hill kinetics
Velocity of decay reactions mainly determines frequency
Configurable to exhibit almost sinusoidal or plated

waveforms

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 36

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

The Brusselator Module

brusselator = (∅, {S}, F)

4 k3 k1 k2 k

P Q W S T

time (arbitrary unit) substrate concentration S

Oscillation by autocatalytic feedback loops
Exclusively mass-action kinetics
Velocity of decay in concert with autocatalytic loop

determines frequency

Inherently spiking waveform

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 37

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

The Binary Signal Separator Module

separator = ({OF

0 }, {OF 3 }, F)

k k k k k, H k k k k k k k k

T

O

F

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 100 150 200 250 300 Concentration Time scale 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 100 150 200 250 300 Concentration Time scale

O

F 1

O O 3

F

O 3

T

0.5 1 1.5 2 2.5 3 3.5 4 50 100 150 200 250 300 Concentration Time scale

O 2

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 100 150 200 250 300 Concentration Time scale

F

O 2

T 1

O

T

O 1

F

O O 2

F

O 3

F F

Converts spiking or sinusoidal oscillations into plated waveform
Successive binarisation by enzymatically controlled cascade
Exclusively mass-action kinetics

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 38

Analogously implementation of other boolean functions

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 39

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

The Binary Counter Modulo 17

mod17 = ({C}, {BT

1 }, F)

NOR NOR & & NOR NOR & &

b

4

b

3

b

2

b

1

b

’ 5

b

’ 1

b

5

Based on 5-bit Gray code
Clock signal C increments counter
Exclusively mass-action kinetics

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

b′

1

= ¯ b1b2¯ b3¯ b4¯ b5 b′

2

= ¯ b1b2 ∨ ¯ b1b2¯ b3¯ b4¯ b5 b′

3

= ¯ b1¯ b2b3 ∨ ¯ b1b3¯ b4 ∨ ¯ b1b2b3b5 ∨ ¯ b1¯ b2b4¯ b5 b′

4

= ¯ b1b4¯ b5 ∨ ¯ b1b2b3b5 ∨ ¯ b1¯ b2¯ b3b5 ∨ ¯ b1¯ b2¯ b3b4 ∨ ¯ b1b2b3b4 b′

5

= ¯ b1¯ b2¯ b3¯ b4 ∨ ¯ b1¯ b2b3b4 ∨ ¯ b1b2b3¯ b4 ∨ ¯ b1b2¯ b3b4

SLIDE 40

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Composing the Original Frequency Divider 1:17

brusselator[1] separator[1] mod17[1]

0.2 0.4 0.6 0.8 1 200 400 600 800 1000 1200 concentration (a.u.) time (a.u.)

repressilator[1] goodwin[1]

0.2 0.4 0.6 0.8 1 500 1000 1500 2000 2500 3000 3500 4000 concentration (a.u.) time (a.u.)

T T 1 B B 1

C

ΠFD17 = (M, P) with M = {(brusselator, 1), (repressilator, 1), (goodwin, 1), (separator, 1), (mod17, 1)} P = {0 : ModuleConnect(brusselator[1] → separator[1], {(S, OF

0 )}),

0 : ModuleConnect(separator[1] → mod17[1], {(OF

3 , C)})} P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 41

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Frequency Divider 1:5 by Removal of Signal Separator

repressilator[1] goodwin[1] separator[1] brusselator[1] mod17[1]

0.5 1 1.5 2 2.5 3 3.5 4 200 400 600 800 1000 1200 concentration (a.u.) time (a.u.)

T B 3 T B 4 T B 5 T

B 1 T

1 1 1 B T 1 2 B 1 1 1 1 1 1 1 1 1 1 1

C C

ΠFD5 = (M, P) with M = {(brusselator, 1), (repressilator, 1), (goodwin, 1), (separator, 1), (mod17, 1)} P = {0 : ModuleConnect(brusselator[1] → separator[1], {(S, OF

0 )}),

0 : ModuleConnect(separator[1] → mod17[1], {(OF

3 , C)}),

200 : ModuleDisconnect(brusselator[1] ↔ separator[1]), 200 : ModuleConnect(brusselator[1] → mod17[1], {(S, C)})}

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 42

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Frequency Divider 1:6 by Repressilator

repressilator[1] goodwin[1] separator[1] brusselator[1] mod17[1]

0.2 0.4 0.6 0.8 1 200 400 600 800 1000 1200 concentration (a.u.) time (a.u.)

T B 3 T B 4 T B 5 T

B 1 T

B T 1 2 B 1 1 1 1 1 1 1 1 1 1 1 1 1

C

ΠFD6 = (M, P) with M = {(brusselator, 1), (repressilator, 1), (goodwin, 1), (separator, 1), (mod17, 1)} P = {0 : ModuleConnect(repressilator[1] → mod17[1], {(Z, C)})}

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 43

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Frequency Divider 1:3 by Goodwin Module

repressilator[1] goodwin[1] separator[1] brusselator[1] mod17[1]

0.5 1 1.5 2 2.5 3 3.5 4 200 400 600 800 1000 1200 concentration (a.u.) time (a.u.)

T B 3 T B 4 T B 5 T B 1 1 1 1 1 1 1 1

B 2 T

T 1 2 B

C

ΠFD3 = (M, P) with M = {(brusselator, 1), (repressilator, 1), (goodwin, 1), (separator, 1), (mod17, 1)} P = {0 : ModuleConnect(goodwin[1] → mod17[1], {(X, C)})}

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 44

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

1. Biological Rhythms
2. P Meta Framework
3. Assembly of Frequency Dividers

4. Suprachiasmatic Nucleus

Core Oscillator’s Interplay in

Suprachiasmatic Nucleus

Prospectives
Acknowledgement

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 45

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Core Oscillator’s Interplay in Suprachiasmatic Nucleus

layer master clock fourth layer

species concentrations Y for each layer Y Y

n[8] n[9] n[10] n[7] n[6] n[5] n[4] n[3] n[2] n[1] n[12] n[13] n[14]

time (arbitrary unit)

n[11]

time (arbitrary unit)

φ φ n[1],n[2] φ

n[1],n[2] n[11],n[14]

φ

n[11],n[14]

φ

n[1],n[2]

φ

n[1],n[2] time (arbitrary unit) (a full oscillation period = 360°) fd: varying coupling strength parameter effective phase difference reduction between master clock layer and fourth layer

B A

ΠSCN = (M, P) with M = {(n, 14)} P = {0 : ModuleConnect(n[1] → n[3], {(Y, X)}), 0 : ModuleConnect(n[1] → n[4], {(Y, X)}), . . . , 0 : ModuleConnect(n[10] → n[14], {(Y, X)}) 300 : ModuleConnect(n[2] → n[4], {(Y, X)}), . . . , 300 : ModuleConnect(n[6] → n[10], {(Y, X)})}

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 46

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Prospectives

Conclusions

Assembly and reassembly as well as composition and

decomposition of pre-defined reaction network modules on the fly − → promising strategy in order to achieve complex systems capable of new, extended, or unexpected functionality

Framework for an artificial evolution at a granularity of highly

conserved genetic ensembles

P system-based approach features by coping with dynamical

structures at a modular level rather than a molecular level

Simulation studies carried out using CoPaSi along with Gepasi

Model Extractor

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 47

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Prospectives

Conclusions

Assembly and reassembly as well as composition and

decomposition of pre-defined reaction network modules on the fly − → promising strategy in order to achieve complex systems capable of new, extended, or unexpected functionality

Framework for an artificial evolution at a granularity of highly

conserved genetic ensembles

P system-based approach features by coping with dynamical

structures at a modular level rather than a molecular level

Simulation studies carried out using CoPaSi along with Gepasi

Model Extractor

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 48

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Prospectives

Conclusions

Assembly and reassembly as well as composition and

decomposition of pre-defined reaction network modules on the fly − → promising strategy in order to achieve complex systems capable of new, extended, or unexpected functionality

Framework for an artificial evolution at a granularity of highly

conserved genetic ensembles

P system-based approach features by coping with dynamical

structures at a modular level rather than a molecular level

Simulation studies carried out using CoPaSi along with Gepasi

Model Extractor

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 49

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Prospectives

Conclusions

Assembly and reassembly as well as composition and

decomposition of pre-defined reaction network modules on the fly − → promising strategy in order to achieve complex systems capable of new, extended, or unexpected functionality

Framework for an artificial evolution at a granularity of highly

conserved genetic ensembles

P system-based approach features by coping with dynamical

structures at a modular level rather than a molecular level

Simulation studies carried out using CoPaSi along with Gepasi

Model Extractor

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 50

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Prospectives

Conclusions

Assembly and reassembly as well as composition and

decomposition of pre-defined reaction network modules on the fly − → promising strategy in order to achieve complex systems capable of new, extended, or unexpected functionality

Framework for an artificial evolution at a granularity of highly

conserved genetic ensembles

P system-based approach features by coping with dynamical

structures at a modular level rather than a molecular level

Simulation studies carried out using CoPaSi along with Gepasi

Model Extractor

Further work

Incorporation of Infobiotics workbench
Extension of P module library
Combining advantages of P system-based approaches with

analytical examination tools using ODEs

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 51

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Prospectives

Conclusions

Assembly and reassembly as well as composition and

decomposition of pre-defined reaction network modules on the fly − → promising strategy in order to achieve complex systems capable of new, extended, or unexpected functionality

Framework for an artificial evolution at a granularity of highly

conserved genetic ensembles

P system-based approach features by coping with dynamical

structures at a modular level rather than a molecular level

Simulation studies carried out using CoPaSi along with Gepasi

Model Extractor

Further work

Incorporation of Infobiotics workbench
Extension of P module library
Combining advantages of P system-based approaches with

analytical examination tools using ODEs

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 52

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Prospectives

Conclusions

Assembly and reassembly as well as composition and

decomposition of pre-defined reaction network modules on the fly − → promising strategy in order to achieve complex systems capable of new, extended, or unexpected functionality

Framework for an artificial evolution at a granularity of highly

conserved genetic ensembles

P system-based approach features by coping with dynamical

structures at a modular level rather than a molecular level

Simulation studies carried out using CoPaSi along with Gepasi

Model Extractor

Further work

Incorporation of Infobiotics workbench
Extension of P module library
Combining advantages of P system-based approaches with

analytical examination tools using ODEs

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 53

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Prospectives

Conclusions

Assembly and reassembly as well as composition and

decomposition of pre-defined reaction network modules on the fly − → promising strategy in order to achieve complex systems capable of new, extended, or unexpected functionality

Framework for an artificial evolution at a granularity of highly

conserved genetic ensembles

P system-based approach features by coping with dynamical

structures at a modular level rather than a molecular level

Simulation studies carried out using CoPaSi along with Gepasi

Model Extractor

Further work

Incorporation of Infobiotics workbench
Extension of P module library
Combining advantages of P system-based approaches with

analytical examination tools using ODEs

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein

SLIDE 54

Biological Rhythms P Meta Framework Assembly of Frequency Dividers Suprachiasmatic Nucleus

Acknowledgements

Jena Cottbus

Jena Centre for Bioinformatics Brandenburg University of Technology Cottbus Deutsche Forschungs- gemeinschaft, grant Hi801/3-1

P System Mediated Assembly of Control Units in Chronobiology

T. Hinze, B. Schell, M. Schumann, C. Bodenstein