systems biology1 introduction (55p)
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Systems Biology (I)Introduction
André Leier
Advanced Computational Modelling CentreThe University of Queensland
comp4006/7011: Introduction to Complex SystemsSemester II, 2006
Systems Biology: A New Science (?)
“Systems biology is the science of discovering, modeling, understanding and ultimately engineering at the molecular level the dynamic relationship between the biological molecules that define living organisms.”
Leroy Hood, President ISB(from systemsbiology.org)
“Organisms function in an integrated manner[…] But biologists have historically studied organisms part by part and celebrated the modern ability to study them molecule by molecule, gene by gene.” Systems biology is “a new science, a critical sciences of the future that seeks to understand the integration of the pieces to form biological systems.”
David Baltimore, Nobel Laureate, President CalTech(from systemsbiology.org)
Systems Biology: An Integrative Approach
“Systems biology is an academic field that seeks to integrate different levels of information to understand how biological systems function. By studying the relationships and interactions between various parts of a biological system […] it is hoped that eventually an understandable model of the whole system can be developed.”
Wikipedia
Transcriptomics Machine LearningChemical KineticsGenomics Numerical
MathematicsProteomicsMetabolomics Systems Biology Data Analysis
ModellingThermo-dynamics
MolecularCell Biology
SystemsAnalysisSimulationNonlinear
dynamics EngineeringSignal Processing
Systems Biology: Key Aspects
Interacting network of components and processes (spatiotemporal);Integrative approach (sources of data on different levels/scales, such as genomic, proteomic, metabolic, etc.);
Genes nfκb1, H. sapiens ATGGCAGAAGATGATCCATAT…
Proteins
Signalling pathwayHoffmann and Baltimore, Immun Rev 210, 171–186(2006).
Hoffmann et al., Science 298, 1241–1245 (2002).
Lodish et al., Molecular Cell Biology, 5th Edition (2003).
Systems Biology: Key Aspects (cont.)
Aimed at a quantitativeunderstanding of the function;
Ultimate goal: understanding structure, development, dynamics, functioning and control of cells and entire organisms(→ medical applications).
Hoffmann and Baltimore, Immun Rev 210, 171–186(2006).
Overview (Systems Biology I – IV)
Introduction Cell Biology Review & Chemical Kinetics Basics
Modelling Genetic Regulatory Networks
Modelling Noise and Delays
Multi-scale and Spatial Modelling
What We Will Learn Today
Basics of molecular cell biology
Introduction to chemical kinetics
DNA
ProteinCellEukaryote
Prokaryote mRNA Transcription
Translation
Promoter
Transcription Factor
InhibitionActivation
Regulation
Concentration
Reaction
Quasi-Steady State Assumption
EquilibriumProducts
Stoichiometric Coefficients
Molecularity
Order
Substrate
Enzyme
Conservation Law
Michaelis-Menten
Cooperativity
Hill functionSpecies Reactants Rate Equations
Part I
Basics of Molecular Cell Biology- A Review -
Why Are We Studying the Basics of Cell Biology?
The biological cell is the subject of our study! We are interested in the functioning of biological processes within (intracellular) and between cells (intercellular).
A biological cell is an example of a highly complex system. It consists of a huge number of different components that interact in a non-trivial way. Researchers usually focus on specific subsystems (pathways / modules). The systems approach shall help us to gain a better understanding of biological processes.
From Complex Systems to Systems Biology: We need to understand the basic biological principles first (before we can analyse, model, simulate, etc.).
All Living Things Are Made of Cells
Cells
have a variety of different shapes, sizes and functions,
grow and divide (reproduce themselves),
convert energy / digest, sense and respond to their environment,
are able to cooperate to form complex organisms,
…
HOW DOES THIS WORK?
All Living Things Are Made of Cells (cont.)
Alberts et al., Molecular Biology of the Cell, 4th Edition (2002).
Cell Structure
Prokaryotic cell
Eukaryotic cell
Lodish et al., Molecular Cell Biology, 5th Edition (2003).
DNA and its Building Blocks
Genetic information is encoded in the nucleotide sequence. Prokaryotes: DNA in the cytoplasm; Eukaryotes: DNA in the nucleus (packaged into chromosomes).Genome: all cell DNA.
Alberts et al., Molecular Biology of the Cell, 4th Edition (2002).
The Cell – A Chemical Factory
Basic constituents inside cells aresugars (monosaccharides)fatty acidsnucleotidesamino acids
plus some ions, water (~70%), other organic molecules.These are linked into macromolecules
All cells are governed by the same chemical machinery. Alberts et al., Molecular Biology of the Cell, 4th Edition (2002).
From DNA to Proteins: Transcription and Translation
Genes are expressed with different efficiencies
Alberts et al., Molecular Biology of the Cell, 4th Edition (2002).
From DNA to Proteins: Transcription and Translation (cont.)
Differences in eukaryotic and prokaryotic cells:
Alberts et al., Molecular Biology of the Cell, 4th Edition (2002).
From DNA to Proteins:Transcription and Translation (cont.)
Alberts et al., Molecular Biology of the Cell, 4th Edition (2002).
A ribosometranslates mRNA (using tRNA).
Transcription initiationby RNA polymerase (RNAP) II in an eukaryotic cell.
The genetic code
codon
aminoacid
Alberts et al., Molecular Biology of the Cell, 4th Edition (2002).
Proteins
Primary structure = amino acid sequenceSecondary structure = local folding patternTertiary structure = 3D organization
Alberts et al., Molecular Biology of the Cell, 4th Edition (2002). Lodish et al., Molecular Cell Biology, 5th Edition (2003).
Gene Control Region
Promoter: DNA sequence to which RNAP binds to begin transcription.Transcription factor (TF): protein required to initiate or regulate transcription.
Alberts et al., Molecular Biology of the Cell, 4th Edition (2002).
Regulation Of Gene Expression - In Prokaryotes
Alberts et al., Molecular Biology of the Cell, 4th Edition (2002).
Regulation Of Gene Expression - In Eukaryotes
Alberts et al., Molecular Biology of the Cell, 4th Edition (2002).
Regulation Of Gene Expression
Alberts et al., Molecular Biology of the Cell, 4th Edition (2002).
Controlled by environmental signals(ligands bind to receptors)
What you should keep in mind!
For a deeper understanding of cell functioning we need an integrative approach. In other words: We can identify the pieces, now we have to put the picture together! (→ Systems Biology)
Be familiar with the biological terms.
Biological “standard” processes: transcription, translation, translocation, different regulatory mechanisms.
Regulatory mechanisms lead to complex, nonlinear behaviour (concentration dynamics).
Part II
Brief Introduction toChemical Kinetics
Why Are We Studying Chemical Kinetics?
Cell functioning is based on biochemical machineries(the cell as a huge biochemical reaction network).
Chemical kinetics deals with the time course of chemical reactions (reaction velocity) and the influence of pressure, temperature, concentrations, catalysts, etc.
To understanding cell functioning, we have to understand the underlying biochemistry.
We need this background to understand modelling examples shown in the upcoming lectures.
Chemical Reactions
Molecules change/convert/”interact” via chemical reactions.
Example for a (symbolic) reaction equation:
a A + b B → c C + d D
A,B: reactants (are “consumed”); C,D: products;a,b,c,d: stoichiometric coefficients
of A, B, C and D
Chemical species: any sort of particle involved.
Reactions are governed by specific reaction mechanisms.These can be found only experimentally!
Rate equations describe how fast concentrations of participating reactants change (i.e., a velocity).
Concentrations
smol: amount of substance, unit is mol (“mole”)
1 mol contains Avogadro’s number of particles (of any substance)Avogadro’s number: NA = 6.02205 · 1023 mol -1
The number of molecules is then: s = smol · NA
Molar concentration [S]: [S] = smol / VV: volume (in litre)unit of [S] is 1 mol/L ≡ 1M (“molar”)
Rate Equations
Assume a closed system with constant temperature, pressure & volume.
We start with a very simple reaction: S → Ps = s(t): number of molecules of species S at time t,∆s: change in the number of s in the time interval ∆t.
Then ∆s ∝ s · ∆t,hence ∆s = k · s · ∆tor ∆s / ∆t = k · s(with negative ∆s as s is consumed over time!)
Assuming a large number of molecules we can rewrite this in terms of concentrations [S]=[S(t)]: ∆[S] / ∆t = k · [S]
Rate Equations (cont.)
With ∆t → 0 we obtain:
d[S(t)]/dt = - k [S(t)]
For the given reaction, the reaction rate is:r(t) = - d[S(t)]/dt = k · [S(t)] = d[P(t)]/dt
The reaction rate is defined as the amount of substrate that changes per unit time and per unit volume.
k is called the rate coefficient or rate constant of the reaction.
mol / litre sec-1
Rate Equations (cont.)
The analytical solution of the ordinary differential equation (ODE)
d[S]/dt = - k [S]
is [S(t)] = [S0] e-kt
with [S0] = [S(0)], the concentration at time t=t0.
Rate Equations (cont.)
For a more general system written as:α1 A1 + α2 A2 + … + αn An = 0
with stoichiometric coefficients αi and αi > 0 for products, αi < 0 for reactants,the reaction rate is
r(t) = 1/αi d[Ai(t)]/dt .The reaction rate (at fixed temperature and pressure) is usuallyexpressed as a function of the species concentrations:
r(t) = k [A1(t)]ν1 [A2(t)]
ν2 … [An(t)]νn
νi is not necessarily equal to αi
The νi are called partial reaction orders. ν = ν1 + ν2 + … + νn is the order of the reaction.
Elementary Chemical Reactions
Elementary reactions are irreducible.
A reaction that is elementary follows the law of mass action that states:
“The rate of a chemical reaction is directly proportional to theproduct of the effective concentrations of each participating molecule.” Hence: νi = αI
Elementary reactions are often characterized due to their molecularity (total number of molecules of reactants).
There are no known elementary reactions of molecularity >3.
Rate Equations for Elementary Reactions (Examples)
0th-order reaction:r = k = dS/dt
1st-order reaction (monomolecular):e.g. S → P or S → P1 + P2
r(t) = - dS/dt = dP/dt = k [S(t)]
2nd-order reaction (bimolecular):S1+S2 → P
r(t) = - dS1/dt = - dS2/dt = dP/dt = k [S1(t)] [S2(t)]2S → P
r(t) = k [S(t)]2
litre mol -1 sec-1
sec-1
mol litre-1 sec-1
More About Reactions
Two or more elementary reactions can combine to build a more complex reaction mechanisms that is observed.(reactive intermediates, reversible reactions, competitive reactions, etc.)
In those cases it is often not possible to analytically integrate the reaction rate equations to obtain explicit solutions for the concentration dynamics – numerical integration methods help here!
We can also try to simplify the rate equations by using specificassumptions (conservation laws, steady states / quasi-steady states).
Chemical reactions in cells are often catalysed by proteins (called enzymes) by change of the reaction rates.In general, an enzyme specifically catalyses one type of reaction on one type of substrate (the catalysed species).Example: RNAP catalyses transcription of DNA into mRNA
Typical scheme: E + S ⇌ ES → E + P
E: EnzymeS: SubstrateES: complex of E and SP: Product
k1: forward rate constant, k-1: reverse rate constant
k1
k-1
k2
E + S → ESES → E + SES → E + P
Michaelis-Menten Kinetics
Michaelis-Menten Kinetics (cont.)
The kinetic rate equations are:
To analyse the system we reduce it by using a conservation law!
k1
k-1
k2
E + S → ESES → E + SES → E + P
- k1 [E] [S]
- k1 [E] [S]
k1 [E] [S]
+ k-1 [ES]
+ k-1 [ES]
- k-1 [ES]
+ k2 [ES]
- k2 [ES]
k2 [ES] ≡ r
d[S]/dt =
d[E]/dt =
d[ES]/dt =
d[P]/dt =
= - k1 [E] [S] + (k-1+ k2) [ES]
= - d[E] / dt
Conservation Laws
In a closed system matter is conserved. We can use this to formulate conservation laws that allow us to simplify the system.
The enzyme E is only the catalyst and is not consumed; it is either free or bound in the complex ES; hence:
E0 + ES0 = [E(t)] + [ES(t)]
with E0 = [E(t=0)], ES0 = [ES(t=0)].The substrate S is either free, bound by ES or consumed (present in form of the product P); hence:
S0 + ES0 = [S(t)] + [ES(t)] + [P(t)]
with S0 = [S(t=0)].
Michaelis-Menten Kinetics (cont.)
Assuming [ES0] = P0 = 0 and using [E(t)] = E0 - [ES(t)] the four differential equations reduce to:
d[S]/dt = - k1 [E] [S] + k-1 [ES]
d[E]/dt = - k1 [E] [S] + (k-1+ k2) [ES]
d[ES]/dt = k1 [E] [S] - (k-1+ k2) [ES]
d[P]/dt = k2 [ES]
d[S]/dt = - k1 [E0] [S] + k1 [ES] [S] + k-1 [ES]
d[ES]/dt = k1 [E0] [S] - k1 [ES] [S] - (k-1+ k2) [ES]
d[P]/dt = k2 [ES]
d[S]/dt = - k1 E0 [S] + (k1 [S] + k-1) [ES]
d[ES]/dt = k1 E0 [S] - (k1 [S] + k-1 + k2) [ES]
d[P]/dt = k2 [ES] ≡ r
Results:
Michaelis-Menten Kinetics (cont.)
k1= 103
k-1= 1k2 = 10-1
E0=0.5*10-3
S0=10-3
log scale
Chemical Equilibrium
At the (chemical) equilibriumthe forward and backward fluxof reacting molecules are equal.
Alberts et al., Molecular Biology of the Cell, 4th Edition (2002).
The Quasi-Steady-State Assumption
The (chemical) equilibrium of the Michaelis-Menten reaction is:[S]=[ES]=0, [E]=E0 and [P]=S0
This steady state will occur when t → ∞.
A quasi-steady state (quasi-equilibrium, pseudo-steady state) is a state where the concentration of reactive intermediates is relatively constant (over some time range).
For the Michaelis-Menten reaction, the quasi-steady state assumption reads as follows:there is a balance between ES formation and dissociation;
mathematically: d[ES]/dt = d[E]/dt ≈ 0
The Quasi-Steady-State Assumption(cont.)
For our example of a Michaelis-Menten kinetics, we can identify the time range of the quasi steady state by looking at the graph:
In the marked timeframe the concentration of E and ES is almost constant.
log scale
trans
ient
quas
i ste
ady
stat
e
subs
trate
depl
etio
n
stea
dy s
tate
Michaelis-Menten Kinetics (cont.)
With d[ES]/dt = d[E]/dt = 0, it is [ES] = k1 [S] E0 / (k1 [S] + k-1 + k2)
and we obtain the reduced system:
with Km = (k-1 + k2) / k1
Km is called the Michaelis constant (unit M)Using the quasi steady state assumption reduces the original enzymatic reaction with reactive intermediate ES to a reaction: S + E → E + P
r ≡ d[P]/dt = k2 [ES] = k2 [S] E0 / (Km + [S])
d[S]/dt = - d[P]/dt
Michaelis-Menten Kinetics (cont.)
Michaelis-Menten equation:with rmax ≡ k2 E0
rmax is called the limiting rate (or maximum rate) for the reaction;it describes the rate limit for [S] ›› Km, when all enzymes are bound and [ES]=E0 (the maximal ES-concentration); then r ≈ rmax ≡ k2 E0 (a constant).
Km describes the concentration of [S] at which r = 0.5 rmax
In other words: at [S]=Km half of the total enzyme concentration E0 is bound by S, half is free.
r = rmax [S] / (Km + [S])
Cooperativity
“Cooperativity results from the interactions between binding sites [of a macromolecule]. If the binding of ligand at one site increases the affinity for ligand at another site, the macromolecule exhibits positive cooperativity. Conversely, if the binding of ligand at one site lowers the affinity for ligand at another site, the protein exhibits negative cooperativity. If the ligand binds at each site independently, the binding is non-cooperative.“
Wikipedia
Cooperativity (cont.)
“Cooperativity: Phenomenon in which the binding of one ligand molecule to a target molecule promotes the binding of successive ligand molecules. Seen in the assembly of large complexes, as well as in enzymes and receptors composed of multiple allosteric subunits, where it sharpens the response to a ligand.”
Alberts et al., Molecular Biology of the Cell, 4th Edition (2002).
Two identical interacting binding sites
Enzymes often have (at least) two binding sites on their surface.For simplicity we assume enzymes E with two (identical) binding sites for substrate molecules S and two reactions
E0 + S ⇌ E1; E1 + S ⇌ E2
Define K ≡ k1/k-1 and K’ ≡ k2/k-2 (intrinsic association constants)
Time evolution of unbound E: dE0/dt = -2k1E0S+k-1E1
k1
k-1
k2
k-2
There are 2 possible binding sites for binding the first substrate and only onepossibility for E1 to loose the substrate.
Two identical interacting binding sites (cont.)
Similarly, the time evolution of E1: dE1/dt = -k2E1S+2k-2E2
In steady state, dE0/dt=dE1/dt=0: K = E1/(2E0S) and K’ = 2E2/(E1S)
Let b(t) be the avg. number of substrates bound to an enzyme at time t (E1 binds one, E2 binds two substrates):
b ≡ (E1 + 2 E2) / (E0 + E1 + E2)
Using K and K’, b can be written as
b ≡ (2KS+2KK’S2) / (1+2KS+KK’S2)
The saturation function Y is then defined as:Y = b/2 = (KS+KK’S2) / (1+2KS+KK’S2)
(Y is the fraction of binding sites that are occupied)
Two identical interacting binding sites (cont.)
For K=K’: Y’ = KS/(1+KS)(this is function is very similar to the Michaelis-Menten equation)
Definition:Y-Y’ > 0: positive cooperativityY-Y’ < 0: negative cooperativity
Positive: sequential binding (here: binding the second ligand) is enhanced; the binding affinity for a second is larger than for the first ligand (K’>K) Negative: sequential binding is inhibited; the binding affinity for the first is larger than for the second ligand (K>K’)
Two identical interacting binding sites (cont.)
Consider the reaction: E0 + 2S ⇌ E2
it is assumed that the reactive intermediates E1 can be neglected
Then, b reduces to b = 2 E2 / (E0+E2).
In steady-state: dE0/dt = -k1E0S2+k-1E2 = 0thus: K = k1/k-1 = E2 / (E0 S2) and b = 2KS2/(1+KS2)
And the saturation function is: Y = KS2/(1+KS2) = S2 / (Kd + S2)with Kd = 1/K (dissociation constant)
k1
k-1
Hill functions
A.V. Hill (Nobel laureate) was one of the first to consider cooperative effects and ways to quantify them!
Functions of type h(x,k,m) = xm / (k + xm)are often called Hill functions
m is called the Hill coefficient (Hill number) and is considered as an estimate of the number of binding sites of a protein
More specifically, the Hill number nH is defined as the slope of the Hill plot, ln [Y/(1-Y)] against ln[S] : nH = d/d(ln[S]) ln(Y/1-Y)
Hill functions are also used as regulatory functions when modelling gene activation and inhibition (cooperativity in terms of transcription factor binding)
What you should keep in mind!
Remember
the terms, e.g. stoichiometric coefficient, steady-state assumption, elementary reactions, Hill coefficients, etc,
the Michaelis-Menten reaction scheme;
the concepts of equilibrium and cooperative binding.
Further Reading
Molecular Cell Biology:Alberts et al., Essential Cell Biology, 2nd Edition (2003).Alberts et al., Molecular Biology of the Cell, 4th Edition (2002).(Glossary)Lodish et al., Molecular Cell Biology, 5th Edition (2003).
Chemical/Biological Kinetics:Segal, Biological Kinetics (1991).Bisswanger, Enzyme Kinetics (2002).IUPAC Compendium of Chemical Terminology
Systems Biologywww.systemsbiology.orgParts of this lecture are based on the lecture notes“Systems Biology” by A. van Oudenaarden, MIT, Sept. 2004
Further Reading (Hyperlinks)
Alberts et al., (2002) – Glossary:http://www.ncbi.nlm.nih.gov/books/bv.fcgi?call=bv.View..ShowTOC&rid=mboc4.TOC
&depth=2
Lodish et al., (2003)http://www.ncbi.nlm.nih.gov/books/bv.fcgi?call=bv.View..ShowTOC&rid=mcb.TOC
IUPAC Compendium of Chemical Terminologyhttp://www.iupac.org/publications/compendium/index.html
www.systemsbiology.org
Systems Biology, lecture noteshttp://ocw.mit.edu/OcwWeb/Physics/8-591JFall2004/LectureNotes/index.htm