Cell Process
3. Metabolic reactions and C-13 validation
4. Enzyme and molecular simulation
Liang Yu
Department of Biological Systems Engineering
Washington State University
02. 28. 2013
Main topics
Cell and transport phenomena
High performance computation
Metabolic reactions and C-13 validation
Enzyme and molecular simulation
Metabolic reactions and C-13 validation
Overview of this talk
Introduction
Fluxomics approach
Flux balance analysis (FBA)
13C-Metabolic flux analysis (13C-MFA)
Software for 13C-MFA
Challenges for 13C-MFA
Technical limitations of fluxomics for
industrial application
Introduction
The goal of metabolic engineering is the development of
targeted methods to improve the metabolic capabilities of
industrially relevant microorganisms.
Metabolic flux analysis (Fluxomics) quantitatively depicts the
systematic response to perturbations from gene modification
or growth condition changes
13C-Metabolic flux analysis (13C-MFA) is a standard technique
to probe cellular metabolism and elucidate in vivo metabolic
fluxes
By measuring the proteinogenic amino acids or intracellular metabolite
isotopomer pattern, in vivo flux can be determined without decoupling
the interaction among genome, proteins and metabolites
13C flux analysis has been used for microbes, plants, and higher
organisms under various conditions
Metabolic flux analysis
Metabolic flux analysis (Fluxomics)
Fluxomics is the cell-wide
quantification of intracellular
metabolite turnover rates
Fluxomics can not only provide genetic
engineers with strategies for “rationally
optimizing” a biological system, but
also reveal novel enzymes useful for
biotechnology applications
Major approaches for fluxomics
Flux balance analysis (FBA)
Uses measured extracellular and biomass fluxes (such as substrate
uptake rate, production secret rate, and biomass composition profiling)
with the stoichiometric constraints from mass balances for a determined
system - while quick, determined networks rarely capture actual
network functioning in real biological systems
In case of the underdetermined systems, additional constraints are
needed in order to make the system solvable
The constraints include the cofactor balance, or an objective function,
which usually will be biomass flux maximization or cofactor optimization
The results will be less reliable and accurate as they are largely
dependent on the assumptions not experimental data
Major approaches for fluxomics
13C-based metabolic flux analysis (13C-MFA)
has been developed for addressing pitfalls for FBA by obtaining
intracellular information, i.e. measuring the proteinogenic amino
acids isotopomer fraction to solve the mathematical construction
for the biological system
The key to 13C-MFA is isotopic labeling, whereby microbes are
cultured using a carbon source with a known distribution of 13C.
By tracing the transition path of the labeled atoms between
metabolites in the biochemical network, one can quantitatively
determine intracellular fluxes
allows for precise determinations of metabolic status under a
particular growth condition
An iterative approach of fluxomic analysis and
rational metabolic engineering
The iterative flux analysis and genetic engineering of microbial
hosts can remove competitive pathways or toxic byproducts,
amplify genes encoding key metabolites, and balance energy
metabolism
Methodologies for FBA and 13C-MFA
Share two key characteristics
The use of a metabolic network
The assumption of a steady metabolic state (for internal
metabolites)
have different purposes
FBA profiles the “optimal” metabolism for the desired
performance
13C-MFA measures in vivo operation of a metabolic network
The two approaches to flux analysis are
complementary when developing a rational
metabolic engineering strategy
Fluxomics Tools
13C-assisted cellular metabolism analysis
13C Flux Analysis Protocol
Experiments and Modeling
13C-Pathway and Flux Analysis: Flowchart
13C-Pathway and Flux Analysis: Demo
Applications of 13C Flux Analysis
Investigate regulation of metabolism under
various conditions
Identify unknown pathways and confirm
gene functions
Reveal the bottleneck pathways for
genetic manipulation
OpenFLUX: efficient modelling
software for 13C-MFA
Compared with other popular software
FiatFlux and 13C-FLUX, OpenFLUX is:
Simple, flexible, transparent and fast computation
Good for both non-expert and export users
Provides the user a versatile and intuitive
spreadsheet-based interface to control the underlying
metabolite and isotopomer balance models used for
flux analysis and allowing for the implementation of
large-scale metabolic networks
L. Quek, C. Wittmann, L. K Nielsen and J. O Krömer. OpenFLUX: efficient modelling
software for 13C-based metabolic flux analysis. Microbial Cell Factories 2009, 8:25.
Workflow of OpenFLUX
Algorithm for weighted least-square parameter
System Requirements for OpenFLUX
OpenFlux parser was built on JAVA SE
Development Kit (JDK) (version 6). It is made
available for WINDOWS, MAC and LINUX
platforms, but requires JAVA to be installed for
the respective platforms
MATLAB 7 (should also be compatible with
earlier version of MATLAB, but this was not
checked) and Optimization Toolbox
MS EXCEL (or any compatible software that can
set up tab-delimited text tables)
Challenge for 13C-MFA
Steady State Culture
Bio-reactor fermentation: best control, but expensive
Shaking flask: cheap but growth condition is not stable
Large-scale metabolic network
Current reactions are only about hundreds
It is difficult for rapid sampling and precise measurements
of metabolites at short time intervals throughout the entire
culture period
Mixed Culture Flux Analysis
Overcome Computational Bottlenecks
Improving Searching Method: Grid searching(very
inefficient); Nonlinear solvers (prone to fall in local minima);
Genetic algorithms (not fooled by local minima).
Technical Limitations of Fluxomics for
Industrial Application
Biological systems (e.g., Bacillus subtilis) seem to display
suboptimal growth performance
A previous study examined 11 objective functions in E. coli and
found no single objective function that can perfectly describe flux
states under various growth conditions
Flux determination assumes that enzymatic reactions are
homogenous inside the cell and that there are no transport
limitations between metabolite pools. However, eukaryotes have
organelles (compartments) that may have diffusion limitations or
metabolite channeling
Some industrial hosts and the great majority of environmental
microbes resist cultivation in minimal media, and introducing other
nutrient sources often significantly complicates metabolite labeling
measurements and flux analyses
Enzyme and molecular simulation
Overview of this talk
Introduction
Protein, enzyme and molecular modeling
Molecular modeling methods
Results for molecular dynamics
Introduction
Biological processes are commonly studied by
experimental techniques (X-ray, NMR, etc.). However, to
gain deeper insights in terms of atomic interactions we
try to model biological macromolecules (proteins, DNA,
carbohydrates, etc.) and simulate their behavior by
Monte Carlo (MC) methods or molecular dynamics (MD)
techniques that obey the rules of physics
Biomolecular simulation is application of computational
models to understand the structure, dynamics, and
thermodynamics of biological molecules
Why study protein ensembles?
Protein flexibility is crucial for function. One “average”
structure is not enough. Proteins constantly sample
configurational space.
Transport - binding and moving molecules (ex: molecular oxygen
binding to hemoglobin)
Enzyme catalysis - substrate entry and produce release
Allosteric regulation - regulation of enzyme activity. Enzyme
must be able to flip-flop between on (active) and off (inactive)
states
Molecular associations - induced fit (ex: transcription complexes)
Protein Function in Cell
Enzymes
Catalyze biological reactions
Structural role
Cell wall
Cell membrane
Cytoplasm
Enzyme
Catalyze nearly all important chemical reactions
in the cell
Involve in the control of the transcription of
genetic information, signal transduction, and cell
regulation
The catalytic activity is associated with the
structures
The structure-function relation constitutes the
main dogma of structural biology
Enzyme modeling
The fundamental mechanisms of enzyme catalysis was
proposed by Fischer (1894) of a “lock and key” model.
The induced-fit hypothesis was introduced in 1958 by
Koshland
Such models fail to describe allostericity (change of a
protein conformation resulting in change of function as,
for instance, noncompetitive inhibition) and cooperative
effects. Currently, it is widely accepted that proteins in
the intracellular environment permanently undergo
conformational fluctuations which span a wide range of
timescales and amplitudes
Enzyme modeling
Modern computational methodologies represent a
precious contributor to the study of enzyme reactivity,
enabling the identification and characterization of the
transition state and transiently formed, scarcely
populated conformers.
It is possible to provide in-depth atomistic insights into
protein motions along a wide range of timescales thus
allowing to assess in which degree do those motions
impact enzyme catalysis.
Two of the most used in silico methods are quantummechanical/molecular-mechanical (QM/MM) and
molecular dynamics (MD).
Theoretical Foundations
Schrödinger equation
Born-Oppenheimer approximation (fixed
nuclei)
Force field parameters for families of
chemical compounds
System modeled using Newton’s
equations of motion
History for molecular dynamics
Theoretical milestones:
Newton (1643-1727): Classical equations of motion: F(t)=m a(t)
Schroinger (1887-1961): Quantum mechanical equations of motion: -ih δt ψ(t)=H(t) ψ(t)
Boltzmann(1844-1906): Foundations of statistical mechanics
Molecular dynamics milestones:
Metropolis (1953): First Monte Carlo (MC) simulation of a liquid (hard spheres)
Wood (1957): First MC simulation with Lennard-Jones potential
Alder (1957): First Molecular Dynamics (MD) simulation of a liquid (hard spheres)
Liquid
Rahman (1964): First MD simulation with Lennard-Jones potential
Karplus (1977) & McCammon (1977): First MD simulation of proteins
Karplus (1983): The CHARMM general purpose FF & MD program
Kollman(1984): The AMBER general purpose FF & MD program
Car-Parrinello(1985): First full QM simulations
Kollmann(1986): First QM-MM simulations
Protein
Experimental Foundations
X-ray crystallography
Analysis of the X-ray diffraction pattern produced when a beam
of X-rays is directed onto a well-ordered crystal. The phase has
to be reconstructed.
Phase problem solved by direct method for small molecules
For larger molecules, sophisticated Multiple Isomorphous
Replacement (MIR) technique used.
Protein crystallography
Difficult to grow well-ordered crystals
Early success in predicting alpha helices and beta sheets
NMR Spectroscopy
Nuclear Magnetic Resonance provides structural and dynamic
information about molecules.
Quantum Mechanics
Modeling the motion of a complex
molecule by solving the wave functions of
the various subatomic particles would be
accurate (Schrödinger equation)
But it would also be very hard to program
and take more computing power than
anyone has.
 2 2
   U ( x, y, z ) ( x, y, z )  E ( x, y, z )
2m
Classical Mechanics
Instead of using Quantum mechanics, we
can use classical Newtonian mechanics to
model our system.
This is a simplification of what is actually
going on, and is therefore less accurate.
To alleviate this problem, we use numbers
derived from QM for the constants in our
classical equations.
Molecular Modeling
For each atom in every molecule, we need:
Position (r)
Momentum (m + v)
Charge (q)
Bond information (which atoms, bond
angles, etc.)
Molecular Mechanics: energy minimization
U
Torsion angles
Are 4-body
Non-bonded
pair
1
2


K
b

b

b
0
2
all bonds
1
2
 
K    0 
all angles 2

 K 1  cosn 
all torsions
Angles
Are 3-body
Bonds
Are 2-body
 R 12  R 6 
   ij  ij   2 ij  
r  
 rij 
i , j nonbonded
 ij  



i , j nonbonded
qi q j
40rij
U is a function of the conformation C of the protein. The problem of
“minimizing U” can be stated as finding C such that U(C) is minimum.
Molecular Dynamics
Movement on the potential energy surface
Newton’s second law
propagate the structure
through time:
dxi
 vi
dt
dvi
 m 1Fi
dt
Force: Fi  i E
Brownian Dynamics
Monte Carlo
In molecular simulations, ‘Monte Carlo’ is an
importance sampling technique
Make random move and produce a new conformation
Calculate the energy change E for the new conformation
Accept or reject the move based on the Metropolis criterion
E
P  exp(
)
kT
Boltzmann factor
If E<0, P>1, accept new conformation;
Otherwise: P>rand(0,1), accept, else reject.
k is Boltzmann constant.
P is the probability that a system is in a state E.
Towards molecular simulations of
biological cells
time scale
maximal system size
Molecular Dynamics
1ns - 1s
100,000 atoms = (10 nm)3
Brownian Dynamics
1s – 1ms
1 – 100 rigid proteins = (100 nm)3
Random Walk
1s – 1ms
Diffusion equation1s – 1ms
(e.g. Virtual Cell)
cell subcompartments (1 - 10 m)3
Dynamic Monte Carlo
1 ns – 1 s
10,000 reactions
Network models
no time scale
no length scale
Methods for multi-scale
Molecular dynamics: internal dynamics of proteins
Molecular dynamics: protein unfolding
http://www.stanford.edu/group/pandegroup/folding/results.html
Molecular dynamics: membrane dynamics
Selective translocation of water across a membrane
S. Hub and Bert L. de Groot. Mechanism of selectivity in aquaporins and aquaglyceroporins PNAS. 105:1198-1203 (2008)
Molecular dynamics: membrane dynamics
Selective translocation of water across a membrane
http://www.mpibpc.mpg.de/abteilungen/071/bgroot/gallery.html