Falk Schreiber

Modelling and Visualising

Biological Systems

Bioinformatics

IPK Gatersleben

Institute of Computer Science

Martin Luther University

Halle-Wittenberg

IPK Gatersleben & MLU Halle-Wittenberg

Outline

1. Modelling metabolism

- Basics

- Constraint-based modelling: FBA

- Mathematical representation

- Application of constraints

- Example

- Resources and tools

2. Visualising models and networks

- Basics

- Standard graphical representation

- Process Description Language

- Resources and tools

Metabolic Modelling

Comprises the reconstruction,

simulation, and analysis of

metabolic models

Metabolic model

list of reactions and

associated properties,

assumed to be present in the

system under investigation,

along with

description of the environment

within which the biological

system is assumed to reside

Provides a basis for system-level

analysis of metabolism for

different organisms

Source: http://www.hydroponicist.com/pages/p69-oxygen-air.htm

Methods in Metabolic Modelling M

od

el s

ize

Mo

de

l d

eta

ils

+ kinetic rate laws

+ kinetic parameters

+ metabolite

concentrations

Topology

only network

structure

Petri Nets

+ stoichiometric

constraints

+ thermodynamics

Flux

Balance

+ mass balance

+ capacity

constraints

Kinetic

Flux Balance Analysis

Constraint-based stoichiometric modelling approach to predict

and analyse the metabolic steady state conversion rates (fluxes)

Advantages

No kinetic parameters required

Quantitative predictions

Applicable to large systems

Applications

Prediction of optimal metabolic yields and flux distributions

Prediction of phenotype/viability of knockout-mutants

Prediction of pathway redundancies

…

History of FBA

Principles of Flux Balance Analysis

Simulation

Oxygene level

Reaction Network Formalism

b: exchange fluxes

v: internal fluxes plast

b

plast

b

b

ext

v

v

v

BBR

CCR

AAR

CBR

CAR

BAR

3

6

5

4

3

2

1

:

:

:

:

:

:

2

1

3

2

1

Stoichiometric Matrix

010110

100101

001011

654321

C

B

A

RRRRRR

plast

b

plast

b

b

ext

v

v

v

BBR

CCR

AAR

CBR

CAR

BAR

3

6

5

4

3

2

1

:

:

:

:

:

:

2

1

3

2

1

Stoichiometric Matrix

Stoichiometric Matrix

010110

100101

001011

654321

C

B

A

RRRRRR

plast

b

plast

b

b

ext

v

v

v

BBR

CCR

AAR

CBR

CAR

BAR

3

6

5

4

3

2

1

:

:

:

:

:

:

2

1

3

2

1

Dynamic Mass Balance

vSdt

dM

S

v

Mass balance equations Matrix form

b: exchange fluxes

v: internal fluxes

Steady State

Steady state mass balance

Steady state assumption

0dt

dM0vSthus

Metabolic Modelling

Mass balance:

Thermodynamic: directionality of reaction

Capacity: enzymatic capacity,

nutrient availability

Constraints

FluxB

Flu

xC

Feasible

solution space

FluxB

Flu

xC

iii v

0 vSdt

dM

iv0

Metabolic Modelling

Optimization problem: maximize/minimize Z

Solved using linear programming

FluxB

Flu

xC

FluxB

Flu

xC

Optimization

Max./Min. Z Optimal solution

Direction of

increasing Z

Feasible

solution space

Example

System of two metabolites A and B

Production constrains

0 < A < 60 and 0 < B < 50

Capacity for simultaneous production

A + 2B < 120

Objective function

Z = 20A + 30B

FluxA

Flu

xB

50

60

Feasible set

A + 2B = 120

FluxA

Flu

xB

50

60

Feasible set Z = 2100

Z = 20A + 30B

Z = 1500

Optimal value within

feasible set

Linear Programming: Types of Solutions

Objective Function

How to identify plausible physiological states?

Question Objective

What are the biochemical production

capabilities?

Maximize metabolite product

What is the maximal growth rate and

biomass yield?

Maximize growth rate

What is the trade-off between

biomass production and metabolite

overproduction?

Maximize biomass production for

a given metabolite production

How energetically efficient can

metabolism operate?

Minimize ATP production or

minimize nutrient uptake

Model Simulation and Analysis

Flux balance analysis

Robustness analysis

Knockout analysis

Flux variability analysis

Yield / flux

predictions

under varying

environmental

conditions

- multi parameter

variation

Yield / flux

predictions under

varying genetic

backgrounds

- complete

- specified

Obj. function

sensitivity to flux

variation of

specific reaction

- complete

- specified

Predictions of

min/ max flux

values

- complete

Objective Function: Growth Objective

Objective Function: Growth Objective

Metabolite Demand (mmol)

ATP 41.2570

NADH -3.5470

NADPH 18.2250

G6P 0.2050

F6P 0.0709

R5P 0.8977

E4P 0.3610

T3P 0.1290

3PG 1.4960

PEP 0.5191

PYR 2.8328

AcCoA 3.7478

OAA 1.7867

AKG 1.0789

Metabolic demands of precursors and cofactors required for

1 g of biomass of E. coli.

Z = 41.2570 vATP - 3.547vNADH +

18.225vNADPH + ….

Summary Flux Balance Analysis

Metabolism in the Hordeum vulgare Seed

FBA model of seed storage metabolism in

developing endosperm of Hordeum vulgare

Metabolism in the Hordeum vulgare Seed

FBA model of seed storage metabolism in

developing endosperm of Hordeum vulgare

Size

257 reactions, 234 metabolites

Pathways

Glyc, TCA, PPP, oxP, Ferm,

Rubisco, AA, Starch, CW, and

others

Case Study

Non-invasive imaging uncovers metabolic compartmentation

in the endosperm

Primary site of alanine synthesis is the central endosperm

Alanine gradients reflect local oxygen state of the

endosperm

13C-Ala gradient can be used as in vivo marker for hypoxia

Source of images:

L. Borisjuk and

H. Rolletschek, IPK

Case Study

Alanine-AT: critical branch point separating aerobic from

anaerobic metabolism

Modelling purpose: to elucidate role of alanine metabolism for

seed tissues with varying oxygen supply

Source of images:

L. Borisjuk and

H. Rolletschek, IPK

Simulation of Region-specific Metabolism

A

B

Central endosperm

(hypoxic region)

Peripheral endosperm

(aerobic region)

Regulation of Alanine-AT

Regulation of Alanine-AT in the endosperm in response to

changing oxygen supply

Current Research Directions

Model coupling

(different organs)

Multiscale modelling

(different modelling

methods)

Software Tools for FBA

CellNetAnalyzer (CNA)

http://www.mpi-magdeburg.mpg.de/projects/cna/cna.html

COBRA Toolbox

http://gcrg.ucsd.edu/downloads/COBRAToolbox

FBA-SimVis

http://fbasimvis.ipk-gatersleben.de/

Model Reconstruction: Metabolic Model

1. Model definition

Organism, organ, dev. stage, pathways, model boundaries

2. Model reconstruction & data retrieval

Top-down: metabolism – pathways – reactions

Integration of heterogeneous data types

Data types: biochemical, physiological, genomic data

Data basis: literature, databases

Missing data

Data referring to closely related species/organs/dev. stages

Inferred reactions: indirect, inferred from BM requirements

Unknown reaction directionality: rev; unknown compartment:

cytosol

Additional Parameters

Maximum uptake/excretion rates

Literature, experimental data, approximations

(e.g. related taxa)

Growth objective

Biomass composition

Energy requirements (growth, maintenance)

Literature, experimental data, approximations

(e.g. dev. stage)

Outline

1. Modelling metabolism

- Basics

- Constraint-based modelling: FBA

- Mathematical representation

- Application of constraints

- Example

- Resources and tools

2. Visualising models and networks

- Basics

- Standard graphical representation

- Process Description Language

- Resources and tools

Question 1 – Can you Read this?

A network with

102 nodes

Protein interaction network,

source: Jeong et al. Nature,

2001

Question 1 – Can you Read this?

A network with

103 nodes

Metabolic network,

source: KEGG, 2012

Question 1 – Can you Read this?

A network with

104 nodes

Protein interaction network,

source: DIP, 2013

Part 1

A network with

104 nodes

Protein interaction network,

source: DIP, 2013

Automatic

layout of large

networks and

circuit-boards

Question 2 – Can you Understand this?

Question 2 – Can you Understand this?

Is degraded?

Stimulates gene

transcription?

Associates into?

Translocates?

Reciprocal stimulation?

Part 2

Standardisation

of graphical

representation

Is degraded?

Stimulates gene

transcription?

Associates into?

Translocates?

Reciprocal stimulation?

Part 1

A network with

104 nodes

Protein interaction network,

source: DIP, 2013

Automatic

layout of large

networks and

circuit-boards

Automatic Layout of Networks

Force-based approaches

Simulate a system of physical forces Eades. Congressus Numerantium, 1984.

Fruchterman & Reingold. Software - Practice and Experience,1991.

Layered approaches

Decycling - layering - crossing

reduction - coordinate assignment Sugiyama et al. IEEE Transactions on Systems, Man and

Cybernetics, 1981.

Orthogonal / grid-based approaches Tamassia. SIAM Journal on Computing, 1987.

Biedl et al. Graph Drawing, LNCS 1353, 1997.

Many Special Layout Algorithms

Commonly extensions of the three classes of layout algorithms

Force-based

Layered

Orthogonal / grid-based

Examples

Source: Genc & Dogrusoz.

Graph Drawing LNCS 2912,

2004.

Source: Schreiber. In

Silico Biology, 2002.

Source: Becker & Rojas.

Bioinformatics, 2001.

Source: Karp & Paley. Conf.

Bioinformatics and Genome

Research, 1994.

Good Network Layout

Better layouts have

Fewer edge crossings

Large crossing angles

Straighter edges

Horizontal and vertical edges

Symmetrical parts shown symmetrically

…

Special layout algorithms

Part 2

Standardisation

of graphical

representation

Ambiguity in Conventional Representation

Standardised Symbols are Important

Most English

speaking country

Quebec Iran China Israel

Singapore Norway Poland USA and

Canada

Pathway Diagrams has been Used a Long Time Ago

From Hodgkin AL and Huxley AF (1952) A quantitative

description of membrane current and its application to

conduction and excitation in nerve. J. Physiol. 117: 500-544.

From the wall chart of Biochemical Path-ways

created by Gerhard Michal (1968)

A metabolic pathway diagram Electrical circuit diagram

representing cell membrane

What is SBGN?

A way to unambiguously describe biochemical and

cellular events in graphs

Limited amount of symbols (~30) Smooth learning curve

Can graphically represent quantitative models,

biochemical pathways, at different levels of granularity

Developed since 2006 by a growing community, part of

COMBINE

Three languages

Process Descriptions one state = one glyph

Entity Relationships one entity = one glyph

Activity Flow conceptual level

Graph Trinity: Three Languages in One

Process Description

maps

Entity Relationships

maps

Activity Flow

maps

Unambiguous

Mechanistic

Sequential

Combinatorial

explosion

Unambiguous

Mechanistic

Non-Sequential

Ambiguous

Conceptual

Sequential

Graph Trinity: Three Languages in One

Process Description

Entity Relationships

Activity Flow

SBGN Process Description Language

A Process Description (PD) Diagram represents all molecular

processes and interactions occurring between various

biochemical entities

It depicts how entities transition forms as a result of biochemical

reactions (including non-covalent modifications such as binding)

Most of the classic metabolic pathways (e.g., glycolysis and

TCA cycle) in biochemistry textbooks were drawn in this

approach

Though not the conventional approach for drawing signaling

pathways, this approach captures the details of biochemical

reactions within the pathway network and provides, in most

cases, unambiguous interpretation of pathway mechanisms

Graph Trinity: Three Languages in One

Process Description

maps

Entity Relationships

maps

Activity Flow

maps

Unambiguous

Mechanistic

Sequential

Combinatorial

explosion

Unambiguous

Mechanistic

Non-Sequential

Ambiguous

Conceptual

Sequential

SBGN Process Description L1 V1.2 Reference Card

Pools of Entities

Collection of molecules

indistinguishable in some

sense

Non-overlapping

Characterized by

concentration

Entity Types

LABEL LABEL LABEL LABEL

Unspecified

entity Simple

chemical Macromolecule Nucleic acid

feature

Material Type

Unit of information

Controlled vocabulary (SBO)

Indicates its chemical structure

(physical composition)

Name Label

Non-macromolecular ion mt:ion

Non-macromolecular radical mt:rad

Ribonucleic acid mt:rna

Deoxribonucleic acid mt:dna

Protein mt:prot

Polysaccharide mt:psac

pre:label PhyA

mt:prot

Conceptual Type

Unit of information

Controlled vocabulary (SBO)

Indicates its function within the

context of a given PD map

pre:label

Name Label

Gene ct:gene

Transcription start site ct:tss

Gene coding region ct:coding

Gene regulatory region ct:grr

Messenger RNA ct:mRNA

crp

ct:grr

Macromolecular Pools: State Variables

Pool is set of molecules

somehow undistinguishable

Molecules can be in different

state

(Non)phosphorylated

Open/close channel

Modified at some state

R R P R

Ch

Close

Ch

Open

Kinase

P@237

2P

Stateless and State-full Entity Types

Not all entities can have states

Stateless

Simple chemicals

Unspecified entity

State-full entities

Macromolecule

Nucleic acid feature

Complex

State is defined as combination of state values

Once defined state variable should be always visible

PhyA

mt:prot

Pr/Prf

Example 1: LEC1/AFL-B3 Network

Macromolecules: biochemical substances that are built up from the

covalent linking of pseudo-identical units. Examples of

macromolecules include proteins, nucleic acids (RNA, DNA), and

polysaccharides (glycogen, cellulose, starch, etc.).

Complex and Multimer

Represents complexes of molecules held together by non-covalent

bonds

Multimer require cardinality

Can have state variables

In multimer it means that all monomers have same state

Use complex if not the same states

N:3

LABEL

N:5

LABEL LABEL

N:2 LABEL

LABEL

Multimers Complex

Key Concept: Process

Process: conversion of

element of one pool to

another

Special cases

Non-covalent binding

Association

Dissociation

Incompleteness

Uncertain process

Omitted process ?

//

Association

Dissociation

Process

Uncertain

process

Omitted

process

LEC1/AFL-B3 Network

Omitted processes are processes that are known to exist, but

details are omitted from the map for the sake of clarity or parsimony.

A single omitted process can represent any number of actual

processes.

Arcs

Using pools by process

Consumption/production

Stoichiometry (optional)

Regulating process rate

Stimulation

Inhibition

Catalysis

Requirement for process

Necessary stimulation

production

catalysis

stimulation

inhibition

necessary

stimulation

modulation

consumption 2

Laying out Process Arcs

Production can represents consumption

Reversible process

Substrates and products should come to opposite sides of process shape (two connectors)

Regulatory arcs should come to other two sides of the process

If you have separate regulation of forward and backward process, you have to split

LEC1/AFL-B3 Network

A stimulation affects positively the flux of a process represented by

the target process.

Sink/source: Creation and Destruction

Represents creation and destruction of entities

Shape to represent source of materials and sink of degraded

entities

LEC1/AFL-B3 network

A submap is used to encapsulate processes (including all types of

nodes and edges) within one glyph. The submap hides its content

to the users, and display only input terminals (or ports).

LEC1/AFL-B3 Factors and Maturation Gene Control

Environmental Influence

External influences: Perturbing agent

Light

Temperature change

Mutation/disease

System manifestation: Phenotype

Apoptosis

Phenotype

LABEL LABEL

Perturbing

agent Phenotype

LEC1/AFL-B3 Factors and Maturation Gene Control

The phenotype glyph represents biological processes or phenotypes

that are affected or generated by a biochemical/regulatory network.

Such processes can take place at different levels and are

independent of the biochemical network itself.

Clone Marker

Each entity pool is only once represented on the map

Layout problems

Clone marker as visual indicator of duplication

Stateless nodes carry unnamed marker

State-full nodes carry named marker to simplify recognition

marker

LABEL

LEC1/AFL-B3 Factors and Maturation Gene Control

If an EPN is duplicated on a map, it is necessary to indicate this fact by

using the clone marker auxiliary unit. The purpose of this marker is to

provide the reader with a visual indication that this node has been

cloned, and that at least one other occurrence of the EPN can be

found in the map.

Discrimination Between Knowledge Levels

Transcription

factor +

Target

gene

DNA

complex

transcription

translation

Discrimination Between Knowledge Levels

Transcription factors

and target gene DNA

together stimulate

transcription,

translation

Transcription factor

stimulates the

transcription of

several putative target

genes

Compartments

Container to represent physical or logical structure

Free form

Visually thicker line

The same entity pools in different compartments are different

Compartments are independent

Overlapping do not mean containment

Compartments

Neuro-muscular junction

Logical Gates

Encode of network logic

To simplify layout

If there are many activators for the

process

To include uncertain information

Combination of TF with unknown or

combinatorial binding kinetics

Three main logic operations

AND: all are required

OR: any combination is required

NOT: prevent influence

Strength and Weakness of SBGN-PD

Strength

Easy translation into

mathematical model

Natural mapping to

SBML

A lot of information in DBs

KEGG

Panther

Timeline is easily extractable

Weakness

Full explicit definition of state

Combinatorial complexity

Additional assumption to

include uncertain

information

Laborious creation

SBGN Process Description L1 V1.2 Reference Card

SBGN Process Description - Entity Pool Nodes

SBGN Process Description - Process Nodes

SBGN Process Description - Connecting Arcs

Software Tools for SBGN

SBGN

http://www.sbgn.org

SBGN-ED

http://www.sbgn-

ed.org

Source: Demir et. al. Nature Biotechnology, 2012.

Standards in Systems Biology

High Throughput Modelling and Visualisation

Path2Models: A

pipeline to produce

models that

combine data

from different

sources

140.000 kinetic,

logical and

constraint-based

models

Part of

BioModelsDB

Path2Models team: F. Büchel, T. Czauderna, C. Chaouiya, A. Dräger, M. Glont, H. Hermjakob, M. Hucka,

S. Keating, D.B. Kell, R. Keller , C. Laibe, N. Le Novère, P. Mendes, F. Mittag, M. Rall, N. Rodriguez, J. Saez-

Rodriguez, F. Schreiber, M. Schubert, N. Swainston, M. van Iersel, C. Wrzodek, M. Wybrow, A. Zell