on the applicability of computational intelligence in transcription network modelling (thesis...
Post on 27-Jan-2017
259 Views
Preview:
TRANSCRIPT
On the Applicability of Computational Intelligence in Transcription Network
Modelling
ByJorge G. Pires
Thesis Defense
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Advisor P. Palumbo
Double Diploma (Italy/Poland)
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Content
Genes, Gene Expression and Networks of genes;
Neurons and Networks of neurons (Network computation );
On the applicability of computational intelligence methods on gene expression networks;
Extras
o Numerical simulations on gene expression;
o Numerical simulations on Vitreous detachment via molecular dynamics methods;
o Samples on the packages
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Short View
Gene encodes of (poly) peptides;
Genes are self-organised on functional networks (network motifs);
Gene expression networks are divided into differential complex networks;
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Short View
Neurons are natural cells (just more one cell!) that presents the peculiar ability to conduct electrical pulses;
Neurons are simple and “useless” cells;
Neurons are self-organised into layers into similar firing patterns;
Neurons work on networks named neural networks, artificial neural networks, neural computation, neural computing or network computation;
Neural networks form functional networks;
There is not model for accounting precisely for the human’s learning paradigm;
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Gene, Gene Expression and Transcription Networks
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Gene
Genes are strands of “useless” and functional genetic code;
Genes can be simplified for dynamical modelling;
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Gene
The same way that enzymes just have a short functional part, gene is not al all necessary for performing its function;
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Gene Expression
For dynamical modelling, it can be loosely seen as a “information”-releasing box. Information is all that matters.
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Gene Expression
Two dynamical equations represents the systems: translation plus transcription , neglecting “important” biological process, such as splicing and reallocation;
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Gene Expression
Unfortunately, not all the pathway from protein request and protein production is “clear” from the point of view of measurements; it request mathematical tricks. “mathematics is lens by which we see the world” (quoted from the biofluids meeting).
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Gene Expression Networks
Source: from (Alon, ,2012, pp.5).
“….A transcription network that represents about 20% of the transcription interactions in the bacterium E. Coli. Nodes are genes (or groups of genes coded on the same mRNA called operons). An edge directed from, node X to node Y indicates that the transcription factor encoded in X regulates operon Y. ….. ” (ALON, 2006).
E. Coli transcription network.
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Transcription Networks
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Network Motifs: smaller and simpler
“...sorry Einstein, but it seems that the gods enjoy playing dices...drinking a hot tea...”
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Gene Expression NetworksNetwork Motifs: smaller and simpler
Autoregulation
Positive;
Negative;
Feed-forward Loop (Single or Multiply output);
Single input Module (SIM);
Dense overlapping regulons (DOR).
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Gene Expression NetworksNetwork Motifs: smaller and simpler
And for Developmental Transcription Networks, it may include:
Double-positive feedback loop;
Double-negative feedback loop;
Long transcription cascades.
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Network Motifs: smaller and simpler
Negative AutoregulationY
dtdy
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Network Motifs: smaller and simpler
Positive AutoregulationY
dtdy
X
A
X
A
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Network Motifs: smaller and simplerDouble-positive feedback loop
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Network Motifs: smaller and simpler
Double-negative feedback loop
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Network Motifs: smaller and simpler
Long transcription cascades
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Network Motifs: smaller and simpler
Feedforward Loops
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Network Motifs: smaller and simpler
Feedforward Loops
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Network Motifs: smaller and simpler
Feedforward Loops
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Network Motifs: smaller and simpler
Feedforward Loops
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Network Motifs: smaller and simpler
Feedforward Loops
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Network Motifs: smaller and simpler
Feedforward Loops
See: http://www.win.tue.nl/~evink/education/2IF35/PDF/2if35-alon4.pdf
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Gene Expression Dynamics
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Dynamics and response time For gene regulation
t
dil
CetY
YdtdY
)(
deg
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Dynamics and response time For gene regulation
Recollecting slide 7…….
Recollecting slide 8…….
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Dynamics and response time For gene regulation
)(
,...,1
txptXdttdX
tuXXtxdttdx
XX
nx
x(t) : mRNA concentration;
X(t): protein concentration;
λ: degradation factor;
φ : production function, this function just depends on transcription factors;
p: translation rate;
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Dynamics and response time For gene regulation
)(
,...,1
txptXdttdX
tuXXtxdttdx
XX
nx
Transcription
Translation
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Dynamics and response time For gene regulation
nXX ,...,1
Single-coupled dynamical system: The output of the translation is a Functional Protein, therefore, “…mRNA effects protein dynamics BUT the protein Dynamics DOES NOT effect the mRNA Dynamics…”
Double-coupled dynamical system: The output of the translation is a Transcription Factor, therefore, “…mRNA effects protein dynamics and protein Dynamics effects the mRNA Dynamics…”
“..Introduces all the non-linearity on the set of Ordinary Differential Equation…”
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Dynamics and response time For gene regulation Uncorrelated Transcription
Factors
Assumption 1: The action of one gene does not effect the other (for analogy, use the Coulomb's law in Electrostatic ). The transcription Factor, therefore, the gene in the same layer of control are uncorrelated
i
iii
iijnj XXVXX 01,...,
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Dynamics and response time For gene regulation Uncorrelated Transcription
Factors
Weak Assumption????
This assumption may be weak, once transcription factors are molecules and molecules in a way or another, they interact and they may deform the molecular orbital of each other. Creating a positive or negative effect on the binding of the transcription factors.
Even though, one may solve this from the statistical point of view. With some sample, one may find a uncorrelated referential and use the function on that referential. This is called Principal Component Analysis (PCA).
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Dynamics and response time For gene regulation Different Timescales
Assumption 2: The timescale for mRNA production is quite small compared to protein synthesis
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Dynamics and response time For gene regulation
Weak Assumption????
Pay attention on some proteins of fast production and on numerical simulations, give big time step (this is quite dangerous for Euler’s Method, but may not be for Runge-Kutta and Family )
Different Timescales
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Neurons and neural networks
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Neuron
Biological cell
Neural Networks
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
NeuronNeural Networks
Mathematical Model
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
i
ijij xwa , i
ijij xxa ,
Hyperplanes Hyperellipsoids
Radial Basis Function
Summation Function
NeuronNeural Networks
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
NeuronNeural Networks
Transfer Function
Some Sigmoid Functions. (α = 1 –red line-, α=3 – blue line, α=10 – black line).
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
NeuronNeural Networks
Network of Neurons
Input layerHidden layer
output layer
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
NeuronNeural Networks
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
NeuronNeural Networks
Most interesting neural Network types for applied mathematics
Multilayer Neural Networks; Radial Basis Function; Hopfield Networks; self- organizing maps (Kohonen maps); Support Vector Machines – ( Kernel Machines );
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Neural Networks: Some Examples
Associative memory: Hopfield Neural Networks
?
?
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Neural Networks: Some Examples
Function Approximation
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Neural Networks: Some Examples
Self-Organization
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Neural Networks: Some Examples
Boundaries
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Neural Networks: Some Examples
Function approximation based on laws
i
nii x
xxVtxm
,....,1
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
On the applicability of neural networks on transcription networks
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Mapping Gene Expression
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Associative Memory via Hopfield Network
Microarrays tableHopfield Network
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Self-organizing maps for finding hidden laws
Those systems can be used for finding hidden laws on genes expressing simultaneously.
This may review important information, such as correlated genes, for example, belonging to the same chromosome or having some hidden communication.
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Adaptive Resonance Theory (ART) for topology modelling
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Final Remarks and Conclusions
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Final Remarks and Conclusions
Those models were not taken from the literature, they needs to be tested and given the appropriate time for evolving;
My place here is as “pointer”, via methodological prodecures to point out the rich field for future researches on neural networks and gene expression networks;
“...who is not willing to make mistake, will never experiment the new...”. Mistakes and wrong ways are part of science; The place of science is not to give the right way, but the most probable;
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
This is the end...for me???...
My most sincere thanks for all that has given me space for working
Thanks for the attention and “think about it”
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Extras
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Gene Expression Modelling
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Gene expression Simulation, Numerical Simulations, Sample codes
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Gene expression Simulation, Numerical Simulations, Sample simulations
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Gene expression Simulation, Numerical Simulations, Sample simulations
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Gene expression Simulation, Numerical Simulations, Sample simulations
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Gene expression Simulation, Numerical Simulations, Sample simulations
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Gene expression Simulation, Numerical Simulations, Sample simulations
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Detaching Vitreous
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Vitreous Detachment Modelling via molecular dynamics methods, brief introduction to the problem
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Vitreous Detachment Modelling via molecular dynamics methods, brief introduction to the problem
Saccadic MovementsVitreous Detachment
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Vitreous Detachment Modelling via molecular dynamics methods, brief introduction to the problem
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Vitreous Detachment Modelling via molecular dynamics methods, brief introduction to the problem
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Vitreous Detachment Modelling via molecular dynamics methods, brief introduction to the problem
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Vitreous Detachment Modelling via molecular dynamics methods, Sample of the packages developed . Sample 1
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Vitreous Detachment Modelling via molecular dynamics methods, Sample of the packages developed Sample 1
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Vitreous Detachment Modelling via molecular dynamics methods, Sample of the packages developed Sample 2
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Vitreous Detachment Modelling via molecular dynamics methods, Sample of the packages developed Sample 2
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Vitreous Detachment Modelling via molecular dynamics methods, Sample of the packages developed Simulations
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Vitreous Detachment Modelling via molecular dynamics methods, Sample of the packages developed
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Vitreous Detachment Modelling via molecular dynamics methods, Sample of the packages developed
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Vitreous Detachment Modelling via molecular dynamics methods, Sample of the packages developed
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Vitreous Detachment Modelling via molecular dynamics methods, Some numerical simulations
Consider the same system before, not with 10.000 particles making a line and with spherical movements on the boundary.
Thesis Defense
On the Applicability of Computational Intelligence in Transcription Network ModellingJorge G. Pires
Faculty of Applied Physics and MathematicsGDANSK UNIVERSITY OF TECHNOLOGY
August 2012
Reference
ALON, Uri. Transcription Network: basic concepts. Formal Modeling in Cell Biology. November 18, 2009. Accessed online (May,2012) : http://www.win.tue.nl/~evink/education/2IF35/PDF/2if35-alon2.pdf.
top related