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INTRODUCTION TO SYSTEMS BIOLOGY
Corso di Biochimica
Laurea Magistrale in Medicina e Chirurgia
SOME INTERESTING BOOKS
Eberhard O. Voit
Uri Anon
B.O. Palsson
SOME FREELY AVAILABLE MATERIALS
URI ALON'S lectures on Systems Biology on the WWW (Weizmann Institute of Science)
Lecture 1: Introduction http://www.youtube.com/watch?v=Z__BHVFP0Lk
Lecture 2: Autoregulation http://www.youtube.com/watch?v=w7oaCxaKfcA
Lecture 3: Feed Forward Loop http://www.youtube.com/watch?v=7AS4mW4Qwl0
Lecture 4: Timing Memory and Global structure http://www.youtube.com/watch?v=3pPgPyS5ceQ
Lecture 5: Robustness http://www.youtube.com/watch?v=YGB0OblGQ00
Lecture 6: Pattern formation http://www.youtube.com/watch?v=GoE-k3-8W1E
Lecture 7: Robust Patterning http://www.youtube.com/watch?v=nJLu6GuCE0Q
Lecture 8: Optimality http://www.youtube.com/watch?v=PxjibEIs3MY
Lecture 9: Optimal gene regulation http://www.youtube.com/watch?v=yzQdxNSJXik
Preprint of “Mathematical modelling in Systems Biology” by Brian Ingalls (University of Waterloo, Canada)
http://www.math.uwaterloo.ca/~bingalls/MMSB/
What is a system?
Which systems do you know?
When do we need to introduce the concept of system?
SOME FEATURES OF A SYSTEM
It consists of many distinguishable parts
The part of the system strongly interact with each other
The parts of the systems can (more weakly or differently) interact with the environment surrounding the system
EXAMPLES OF SYSTEMS
Planetary system
Molecular systems
Thermodynamic systems
Cellular systems
Ecosystems
Organism systems
SYSTEMS
System (from Latin systēma, in turn from Greekσύστημα systēma, "whole compounded of several parts or members, system", literary "composition)
A System is a set of interacting or interdependent entities forming an integrated whole.
The concept of an 'integrated whole' can also be stated in terms of a system embodying a set of relationships which are differentiated from relationships of the set to other elements.
Wikipedia: systems
SYSTEMS
Systems have structure, defined by parts and their composition;
Systems have behavior, which involves inputs, processing and outputs of material, energy or information;
Systems have interconnectivity: the various parts of a system have functional as well as structural relationships between each other.
Wikipedia: Systems
THE SYSTEMS EXHIBIT PECULIAR BEHAVIOR
Temperature, pression…….
Metabolism, self-replication,….
“Emergent” properties
Is it possible to predict the behavior of the system
starting from the laws controlling the interaction
between the parts?
Approach to understand the nature of complex things by reducing them to the interactions of their parts, or to simpler or more fundamental things
Newton reduced celest motions to gravity
Study in vitro the enzyme activity or Nucleic Acid pairing interactions
REDUCTIONISM
Wikipedia: Reductionism
REDUCTIONIST APPROACH IN BIOLOGY
The organism is completely explained by (is reduced to) its elementary constituents: biological macromolecules and metabolites.
All the information for governing the process is written in the Genome
Genes/proteins are entities performing a specific function
FROM REDUCTIONIST TO SYSTEMS VIEW
Gene centrism: the genome is the program of the life
The gene-centric view is insufficient to account for phenotype: Gene expression depends on the cellular
environment
Gene expression depends on external signals
Genes are the pipes of the organ of the life [Noble]
WHO IS THE PLAYER?
The mechanism of gene expression that are hardwired in: The so called non coding regions of the genome
The cytoplasmic engines for the maturation of the transcripts
The cytoplasmic engines for translation of the gene in proteins
The physics of protein folding and protein-protein or protein-ligand interaction
The cytoplasmic and cellular mechanism for external signal transduction
COMPLEXITY IN SYSTEMS
Warren Weaver has posited that the complexity of a particular system is the degree of difficulty in predicting the properties of the system if the properties of the system’s parts are given.
Wikipedia: Complexity
Weaver "Science and Complexity", American Scientist, 36: 536 (1948).
http://www.ceptualinstitute.com/genre/weaver/weaver-1947b.htm
“Prediction is very difficult, especially about
the future”. Niels Bohr
FROM WHERE DOES THE COMPLEXITY ARISE?
Number of parts?
Form of the interactions?
Pattern of the relationship?
Noise?
FROM WHERE DOES THE COMPLEXITY ARISE?
COMPLEXITY IS NOT THE “AMOUNT” OF
ORDER/DISORDER
Gas system
-) Random interactions between
the gas molecules
-) The system properties can be
derived with statistical methods
(ideal gas law)
Lattice system
-) ordered pattern of interactions
-) the system properties can be
derived neglecting the internal
structure (rigid body) or applying
simple statistical models
(thermodynamic properties)
Max
disorder
Max
order
BOTH SYSTEMS ARE SLIGHTLY COMPLEX
THE PATTERN OF INTERACTION IN COMPLEX
SYSTEMS IS NOT RANDOM NOR REGULAR
In Weaver's view, complexity comes in two forms: disorganized complexity, and organized complexity.
Wikipedia: Complexity
Weaver "Science and Complexity", American Scientist, 36: 536 (1948).
http://www.ceptualinstitute.com/genre/weaver/weaver-1947b.htm
THE PATTERN OF INTERACTION IN COMPLEX
SYSTEMS IS NOT RANDOM NOR REGULAR
In Weaver's view, complexity comes in two forms: disorganized complexity, and organized complexity.
Wikipedia: Complexity
Weaver "Science and Complexity", American Scientist, 36: 536 (1948).
http://www.ceptualinstitute.com/genre/weaver/weaver-1947b.htm
Random (gas)Non Random (Caos)
COMPLEXITY IS NOT DUE (ONLY) TO THE NUMBER OF
PARTS
The three-body problem
Taking an initial set of data that specifies the
positions, masses and velocities of three bodies
for some particular point in time, determine the
motions of the three bodies, in accordance with
the laws of classical mechanics
Henri Poincaré showed that there is no general
analytical solution for the three-body problem.
The motion of three bodies is generally non-
repeating, except in special cases.
It is difficult to predict the behavior of the system
(e.g. is it a bound system or not?)
FOLLOWING THE SAME EXAMPLE, COMPLEXITY IS NOTDUE (ONLY) TO THE IGNORANCE OR TO THECOMPLICACY OF THE INTERACTION LAWS.NOTICE, HOWEVER, THAT IN THIS CASE THEINTERACTION IS NONLINEAR
• Even physical systems composed of few bodies can give origin to:
• SYMMETRY BREAKING
• DETERMINISTIC CHAOS
.
NON LINEAR TERMS IN INTERACTIONS LEAD TO COMPLEX (=DIFFICULT TO PREDICT) EFFECTS
SYMMETRY BREAKING
In physics it describes a phenomenon where (infinitesimally) small fluctuations acting on a system crossing a critical point decide a system's fate, by determining which branch of a bifurcation is taken. For an outside observer unaware of the fluctuations (the "noise"), the choice will appear arbitrary.
Symmetry breaking is supposed to play a major role in pattern formation.
Wikipedia: Symmetry Breaking
SYMMETRY BREAKING: FERROMAGNETISM
SYMMETRY BREAKING: POLYA’S URN
A large urn contains a red ball and a green one: one ballis extracted and then replaced in the urn with anotherball of the same colour. The process is iterated manytimes.
SYMMETRY BREAKING: POLYA’S URN
Initial random events can have a very large effect on the outcome
Positive feedback governs the phenomenon
DETERMINISTIC CHAOS
A systems of elementary units governed by non linear laws can exhibit an extreme dependence from the initial conditions: a little difference can lead to a big difference after short time
The system is still deterministic but its evolution becomes unpredictable
The butterfly effect
Branislav K. Nikolić, University of Delaware
NON LINEARITY DRIVES THE CHAOTICITY
LINEAR AND NON LINEAR EFFECTS
A US penny weighs 2.5 grams and a Euro cent coin weighs 2.3 grams. Therefore, two pennies and two cents weigh 9.6 grams, and 4,000 pennies and 6,000 cent coins weigh (10,000 + 13,800) grams = 23,800 grams. The weights simply add up in a linear manner,
a pinch of salt may improve the taste of a bowl of soup, and two pinches could possibly even further enhance the taste. However, a hundred spoons of salt might just make the soup inedible: taste is a nonlinear phenomenon.
NON LINEARITY
Much of the nonlinearity and unpredictability of biological systems is caused by regulatory control mechanisms that operate in distinctly different ways and at different time scales.
A good example is the regulation of metabolic processes, which are biochemical reactions that convert food into energy and into a vast number of chemical compounds our body needs.
NON LINEARITY
Suppose both A and B are in a steady state
Now let’s try to predict what happens if we increase A, let’s say by 20 per cent.
More B means more inhibition of the production of A, which now fights the activation of this same process by A. Who will win? Will A go up or down? And what about B? Will it go up or down?
it is impossible to predict the outcome! Unless we set up a mathematical model with actual numbers that specify the magnitudes of production and utilization and the strengths of all activation and inhibition signals.
Both A and B may keep on growing without end. For other numbers,
both A and B decrease to 0, either immediately, or after some ups and downs.
both A and B may oscillate for a while and then return to the steady state.
Finally, for yet other constellations of numbers, both A and B may start to oscillate and keep on oscillating until some outside force puts an end to it.
The sobering conclusion is that our brain by itself is insufficient to solve the puzzle, and even hard thinking is not enough.
INTERACTION WITH THE ENVIRONMENT: NON
EQUILIBRIUM SYSTEMS
Complex systems operate under far from equilibrium conditions. There has to be a constant flow of energy to maintain the organization of the system
Ideal Gas system
-) the system is isolated from the
environment (apart from forces
opposing to the internal pressure)
-) laws can be written and solved
Atmospheric gas dynamics
-) the system exchange energy
and matter with the environment.
Forces arise from heating and
from earth motions.
-) laws can be written but difficultly
solved.
NON EQUILIBRIUM SYSTEMS CAN LEAD TO SELF-ORGANIZATION BEHAVIOR (DIFFICULT TO PREDICT)
Belousov-Zhabotinsky reaction.
The reaction is far from equilibrium and
remain so for a significant length of time.
Reaction creates patterns and oscillations
https://www.youtube.com/watch?v=IBa4kgXI4Cg
Figure 1
Nature, Nurture, or Chance: Stochastic Gene Expression and Its Consequences
Arjun Raj, Alexander van
Cell 2008 135, 216-226DOOudenaardenI: (10.1016/j.cell.2008.09.050)
THE SYSTEMS SOMETIMES BEHAVES IN A STOCHASTIC WAY
Elowitz et al.
(Science 2002)
quantified the
variability in the
expression from a
promoter in E.
coli by introducing
two copies of the
same promoter
into the genome
of E. coli, one
driving the
expression of cyan
fluorescent protein
(CFP) and the
other driving the
expression of
yellow fluorescent
protein (YFP)
Extrinsic fluctuations are those that affect the expression of
both copies of the gene equally in a given cell, such as
variations in the numbers of RNA polymerases or ribosomes.
Intrinsic fluctuations are those due to the randomness
inherent to transcription and translation; being random, they
should affect each copy of the gene independently, adding
uncorrelated variations in levels of CFP and YFP levels
Both sources of noise can be significant dependent on the
promoter.
Later time-lapse measurements showed that in bacteria, the time scale
for intrinsic fluctuations is less than 9 min, whereas extrinsic fluctuations
exert their effects on time scales of about 40 min, or roughly the length of
the cell cycle (Rosenfeld et al., 2005).
Nature, Nurture, or Chance: Stochastic Gene Expression and Its Consequences
Arjun Raj, Alexander van
Cell 2008 135, 216-226DOOudenaardenI: (10.1016/j.cell.2008.09.050)
The systems sometimes behaves in a stochastic way
COMPLEXITY IS DUE TO ONE OR MORE OF
THESE FEATURES :
Presence of many parts, with different features
Presence of specific interactions among the different parts, organized in non random and non completely ordered way
Presence of non linear terms in interactions
Interaction with the environment in a non-equilibrium state
Stochasticity and noise
FEATURES OF COMPLEX SYSTEMS
Nonlinearity
Small perturbation may cause a large effect, proportional
effect, or no effect at all.
Jonathan Wren
FEATURES OF COMPLEX SYSTEMS
Feedback loops
Jonathan Wren
FEATURES OF COMPLEX SYSTEMS
Open systems (dissipation of energy)
Flagella uses energy:
Jonathan WrenTend towards entropy
FEATURES OF COMPLEX SYSTEMS
Can have memory (response history dependent)
e.g. New protein may
remain in
cell after initial response,
shifting the rate of reaction
the next time the cell is
exposed to a chemical
Chemical concentration
Response
Jonathan Wren
FEATURES OF COMPLEX SYSTEMS
Nested (modules have complexity)
Jonathan Wren
FEATURES OF COMPLEX SYSTEMS
There are no precise boundaries
Jonathan Wren
BIOLOGICAL SYSTEMS: GENOTYPE VS PHENOTYPE
Two poles: Genotype: information coded in the genetic material
that is transmitted from parents to offspring
Phenotype: complex of somatic characters of an organism, of or an individual
The final goals of Life Sciences are focused on phenotypes: Biology: understanding the emergence of phenotypes
Biotech: controlling phenotypes
Medicine: correcting pathological phenotypes
SYSTEMS BIOLOGY
WHAT IS “SYSTEMS BIOLOGY”?
The study of the mechanisms underlying complex biological processes as integrated systems of many interacting components. Systems biology involves
(1) collection of large sets of experimental data
(2) proposal of mathematical models that might account for at least some significant aspects of this data set,
(3) accurate computer solution of the mathematical equations to obtain numerical predictions, and
(4) assessment of the quality of the model by comparing numerical simulations with the experimental data.
-(Leroy Hood, 1999)
Is this just another name for “physiology”?
SYSTEMS BIOLOGY IS AN INTEGRATION
OF DATA & APPROACHES
SYSTEMS BIOLOGY
Systems biology is a new specialty area that actually has exactly the same goals and purposes as general biology, namely, to understand how life works. But in contrast to traditional biology, systems biology pursues these goals with a whole new arsenal of tools that come from mathematics, statistics, computing, andengineering, in addition to biology, biochemistry, and biophysics.
Voit, Eberhard O.. Systems Biology: A Very Short Introduction (Very Short Introductions) OUP Oxford..
Experimental systems biologists use many different types of laboratory techniques to fill some of the holes with new measurements, while computational systems biologists, or systems modelers for short, depend on mathematics and computing to infer what is most likely happening in the holes.
TECHNOLOGIES TO STUDY SYSTEMS AT
DIFFERENT LEVELS
Genomics (HT-DNA sequencing) Mutation detection (SNP methods) Transcriptomics (Gene/Transcript measurement,
SAGE, gene chips, microarrays) Proteomics (MS, 2D-PAGE, protein chips, Yeast-2-
hybrid, X-ray, NMR) Metabolomics (NMR, X-ray, capillary electrophoresis)
COMPUTATIONAL SYSTEMS BIOLOGY
CSB uses a pipeline from data to understanding that consists of two toolsets:
machine learning (ML) that extract as much true information as possible from large sets of raw data, while filtering out spurious results and errors in the datasets.
The second toolset analyzes mathematical models, which span the spectrum from very simple to extremely complicated (static networks models, dynamical models)
MACHINE LEARNING
“My CPU is a neural-
net processor; a
learning computer. The
more contact I have
with humans, the more
I learn .”*
* Arold Schwarzenegger in
Terminator 2: The judgment day
Types of Learning
54
UnsupervisedSupervised Reinforcement
Learning from labelled
data
E.g., Image classification
Discover structure in unlabeled
data
E.g., Clustering, compression
Learning by “doing” with delayed
reward
E.g.,in games such as chess,
checkers, new treatment
strategies, etc.
Recommender Learning to recommend
E.g., suggestions for new
items to buy, alternative
treatments, etc.
(Semisupervised)
Supervised Learning
55
Supervised
Classification Regression
?
x=0.8
y=12.5 ?
Unsupervised Learning
56
Unsupervised
Clustering Compression Pattern Mining
Some examples
ALPHAFOLD
HTTPS://DEEPMIND.COM/BLOG/ARTICLE/ALPHAFOLD-USING-AI-FOR-SCIENTIFIC-DISCOVERY
STATIC NETWORK MODELING
Nodes, direct edges, indirect edges
STATIC NETWORK MODELING: GRAPHS
The paper written by Leonhard Euler on the Seven Bridges
of Königsberg and published in 1736 is regarded as the first
paper in the history of graph theory
STATIC NETWORK MODELING: GRAPHS
The paper written by Leonhard Euler on
the Seven Bridges of Königsberg and
published in 1736 is regarded as the first
paper in the history of graph theory
STATIC NETWORK MODELING: GRAPHS
An Eulerian circuit in a graph G is a circuit that includes all vertices and edges of G. A graph which has an Eulerian circuit is an Eulerian graph. (easy!)
A Hamiltonian circuit in a graph G is a circuit that includes every vertex (except first/last vertex) of G exactly once. ... (difficult!)
A Hamiltonian path is therefore not a circuit.
STATIC NETWORK MODELING
Nodes, direct edges, indirect edges
DYNAMIC MODELING
The adjective dynamic is used when some aspect of the system changes with time.
DYNAMIC MODELING
𝐸 𝑡 = 𝐸 ∙ 𝑒𝑟∙𝑡
𝑑𝐿(𝑡)
𝑑𝑡= 𝑟 ∙ 𝐿 1 −
𝐿
𝐾⇒ 𝑠𝑡𝑒𝑎𝑑𝑦 𝑠𝑡𝑎𝑡𝑒
𝑑𝐿 𝑡
𝑑𝑡= 0 ⇒
𝑟 ∙ 𝐿 1 −𝐿
𝐾= 0 ⇒ 𝐿 = 𝐾
ODEs= Ordinary Differential Equations
CENTRAL DOGMA
The central dogma dissects the complex machinery of life into distinct subsystems, which interact in ways that are often quite well understood, although nature always has surprises in store.
Gene Regulation Networks
Abdollahi A et al., PNAS 2007
TRANSCRIPTION NETWORKS
PROTEINS
The Protein Interaction Network of Yeast
Yeast two hybrid
Uetz et al., Nature 2000
SIGNALLING
Many such cascades work side by side inside the cell and cross-talk,
METABOLIC PATHWAYS -ENZYMES
METABOLIC PATHWAYS -ENZYMES
Source: ExPASy
Metabolic Networks
From Genotype to Phenotype
…code for
proteins...
>protein kinase
acctgttgatggcgacagggactgtatgctgatct
atgctgatgcatgcatgctgactactgatgtgggg
gctattgacttgatgtctatc....
Genes in
DNA...
(about 30,000 in the human genome)
Proteins
interact
…proteins correspond to
functions...
…when they are expressed
From 5000 to 10000
proteins per tissue
…with
different effects
depending on
variabilityOver 3.5 millions of
single mutations are
known
….in metabolic pathways
The Gene Ontology classification is a controlled dictionarythat describe gene function under three aspects:
-) Molecular Function
-) Biological Process
-) Cellular Component
WHAT FUNCTION MEANS FOR A
GENE/PROTEIN?
CELLULAR FUNCTION ARE NOT ENCODED
(ONLY) IN THE GENES
Functions at the cell level are the effect of the cooperation of different combinations of genes
Not all combinations of genes perform a function Consider the 30,000 human genes, counting the modules of
100 genes would lead to 10 278 functions
Counting any possible combination would lead to 10 72403
functions [Noble, Music of life, 2006]
The number of possible functions exponentially increases with the number of genes
Only a tiny subset of these interaction corresponds to real functions and this information is not encoded in genes
Different levels of analysis
Proteomics
>protein kinase
acctgttgatggcgacagggactgtatgctgatct
atgctgatgcatgcatgctgactactgatgtgggg
gctattgacttgatgtctatc....
Genomics
InteractomicsTransciptomics
The different levels are not directly encoded in the
preceding ones
We need experimental data for each one.
Metabolomics
GENE EXPRESSION DEPENDS ON HIGHER
LEVELS IN THE HIERARCHY Gene functions make sense only with respect to
the systems they participate• Genes
• Proteins
• Metabolic pathways
• Cellular functions
• Cells
• Tissues
• Organs
• Apparatus
• Organisms
Transcription
Control of expression
WHY MODELS?
Testing whether the model is accurate, in the sense that it reflects—or can be made to reflect—known experimental facts
Analyzing the model to understand which parts of the system contribute most to some desired properties of interest
Kell, Knowles (2006) The Role of Modeling in Systems Biology
WHY MODELS?
Hypothesis generation and testing, allowing one rapidly to analyze the effects of manipulating experimental conditions in the model without having to perform complex and expensive experiments (or to restrict the number that are performed)
Testing what changes in the model would improve the consistency of its behavior with experimental observations
Kell, Knowles (2006) The Role of Modeling in Systems Biology
C.Piazza, Università di Udine http://iclp08.dimi.uniud.it/PRESENTAZIONI/Piazza.pdf
AS WE BEGIN TO CONNECT SYSTEMS WE
CAN ENGAGE IN INFERENCE
We move up the chain from data to knowledge by questioning, observing and then hypothesizing These X genes are upregulated together, but
are they interacting? PPI network data suggests Y are Are these Y part of a complex? If they are always expressed together, that
suggests maybe yes
As more data is integrated and systems linked together, this becomes easier
EXAMPLE OF INFERENCE
(a) An interaction network of Snz–Sno proteins of S.
cerevisiae. The nodes represent proteins and the
lines represent yeast two-hybrid (Y2H) interactions.
The red nodes represent proteins that correspond to
genes in one transcriptome cluster, whereas the
green nodes represent proteins that correspond to
genes belonging to a different cluster. The existence
of two stable complexes can be hypothesized based
on the integrated data.
(b) The genes NTH1 and YLR270W have similar
expression profiles (upper panel). Red indicates
upregulation and green indicates downregulation.
mRNA expressions of both genes are upregulated
during heat shock and other forms of stress.
Deletions of NTH1 and YLR270W each confer
similar heat-shock sensitive phenotypes (lower
panel).
EACH SYSTEM HAS METHODS FOR
MODELING
Pi Calculus Petri Nets
Flux Balance Analysis Differential Eqs
SO HOW CAN WE MEANINGFULLY
INTEGRATE THE DATA?
SYSTEM HETEROGENEITY IN SIZE & TIMESCALE
Atomic Scale
0.1 - 1.0 nm
Coordinate data
Dynamic data
0.1 - 10 ns
Molecular dynamics
Molecular Scale
1.0 - 10 nm
Interaction data
Kon, Koff, Kd
10 ns - 10 ms
Interactions
Cellular Scale
10 - 100 nm
Concentrations
Diffusion rates
10 ms - 1000 s
Fluid dynamics
SYSTEM HETEROGENEITY IN SIZE & TIMESCALE
Tissue Scale
0.01m - 1.0 m
Metabolic input
Metabolic output
1 s – 1 hr
Process flow
Organism scale
0.01m – 4.0 m
Behaviors
Habitats
1 hr – 100 yrs
Mechanics
Ecosystem scale
1 km – 1000 km
Environmental impact
Nutrient flow
1 yr – 1000 yrs
Network Dynamics
EACH OF THE SCALES DOES NOT FIT
TOGETHER SEAMLESSLY
If one scale (e.g., protein-protein interactions) behaves deterministically and with isolated components, then we can use plug-n-play approaches
If it behaves chaotically or stochastically, then we cannot
Most biological systems lie between this deterministic order and chaos: Complex systems
SB IS SPRINGING OUT OF EXISTING EFFORTS
ANYWAY
E-cell (Keio University, Japan)
BioSpice Project (Arkin, Berkeley)
Metabolic Engineering Working Group (Palsson & Church, UCSD, Harvard)
Silicon Cell Project (Netherlands)
Virtual Cell Project (UConn)
Gene Network Sciences Inc. (Cornell)
Project CyberCell (Edmonton/Calgary)
PRINCIPLE 1: MODULARITY
Module Interacting nodes w/
common function
Constrained pleiotropy
Feedback loops, oscillators, amplifiers
PRINCIPLE 2: RECURRING CIRCUIT
ELEMENTS
Network motifs Common methods to achieve an effect
PRINCIPLE 3: ROBUSTNESS
Robustness Insensitivity to
parameter variation
Severe constraints on design Robustness not
present in most designs
STOCHASTIC VS DETERMINISTIC MODELS
Stochastic: Monte Carlo methods or statistical distributions
Deterministic: equations such as ODEs
Phenomena are not of themselves either stochastic or deterministic; large-scale, linear systems can be modeled deterministically, while a stochastic model is often more appropriate when nonlinearity is present.
Kell, Knowles (2006) The Role of Modeling in Systems Biology
DISCRETE VS CONTINOUS (IN TIME)
Discrete: Discrete event simulation, for example, Markov chains, cellular automata, Boolean networks.
Continuous: Rate equations.
Discrete time is favored when variables only change when specific events occur (modeling queues). Continuous time is favored when variables are in constant flux.
Kell, Knowles (2006) The Role of Modeling in Systems Biology
MACROSCOPIC VS MICROSCOPIC
Microscopic: Model individual particles in a system and compute averaged effects as necessary.
Macroscopic: Model averaged effects themselves, for example, concentrations, temperatures, etc.
Are the individual particles or subsystems important to the evolution of the system, or is it enough to approximate them by statistical moments or ensemble averages?
Kell, Knowles (2006) The Role of Modeling in Systems Biology
HIERARCHICAL VS MULTI-LEVEL
Hierarchical: Fully modular networks.
Multi-level: Loosely connected components.
Can some processes/variables in the system be hidden inside modules or objects that interact with other modules, or do all the variables interact, potentially?
Kell, Knowles (2006) The Role of Modeling in Systems Biology
FULLY QUANTITATIVE VS PARTIALLY
QUANTITATIVE VS QUALITATIVE
Qualitative: Direction of change modeled only, or on/off states (Boolean network).
Partially quantitative: Fuzzy models.
Fully quantitative: ODEs, PDEs, microscopic particle models.
Reducing the quantitative accuracy of the model can reduce complexity greatly and many phenomena may still be modeled adequately
Kell, Knowles (2006) The Role of Modeling in Systems Biology
SUMMARY
Systems Biology can be done by breaking down each system into modules
Integrating them to study emergent behaviours
Many problems remain unsolved in exactly how to do this, but independent efforts are being developed in most areas that may one day merge together
THAT’S ALL, THANK YOU FOR THE ATTENTION!
