Mathematical Modeling in Molecular Biology - Vision at IME-USP
Mathematical Modeling in Molecular Biology - Vision at IME-USP
Mathematical Modeling in Molecular Biology - Vision at IME-USP
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<strong>M<strong>at</strong>hem<strong>at</strong>ical</strong> <strong>Model<strong>in</strong>g</strong> <strong>in</strong><br />
<strong>Molecular</strong> <strong>Biology</strong><br />
Junior Barrera<br />
DCC-<strong>IME</strong>-<strong>USP</strong>/BIOINFO-<strong>USP</strong>
Cell cycle,<br />
Tripanosoma-cruzi,<br />
Dictyostelium<br />
....<br />
CAGE<br />
Bioquímica-<strong>USP</strong><br />
Projects<br />
Cancer<br />
Virus<br />
NHGRI<br />
Hemocentro<br />
Agriculture<br />
Ribeirão-<strong>USP</strong><br />
VGDN<br />
ICB-<strong>USP</strong><br />
BIOINFO-<strong>USP</strong><br />
Agriculture<br />
ESALQ<br />
OMS<br />
ICB-<strong>USP</strong><br />
Malária<br />
ICB-<strong>USP</strong><br />
Cancer<br />
Ludwig
Layout<br />
• Economics perspective<br />
• Fundamentals of <strong>Molecular</strong> <strong>Biology</strong><br />
• Experimental techniques<br />
• D<strong>at</strong>a m<strong>in</strong><strong>in</strong>g environments<br />
• Some Biological problems<br />
• Formaliz<strong>in</strong>g Biological problems<br />
• A family of <strong>M<strong>at</strong>hem<strong>at</strong>ical</strong> problems<br />
• Other areas with similar problems
Economics Perspective<br />
• Atomic program (1930-1945)<br />
• Space program (1960-1975)<br />
• Genetics (1990- ...): <strong>in</strong>tern<strong>at</strong>ional<br />
<strong>in</strong>vestment, public and priv<strong>at</strong>e<br />
Brazilian <strong>in</strong>vestment is proportionally gre<strong>at</strong>er<br />
than the <strong>in</strong>vestment of some developed countries
Fundamentals of <strong>Molecular</strong><br />
<strong>Biology</strong>
Popul<strong>at</strong>ion<br />
organism<br />
Prote<strong>in</strong> structure<br />
and dynamics<br />
tissue<br />
DNA, Prote<strong>in</strong>,<br />
Gene Expression,<br />
Gene Networks<br />
molecule<br />
cell
Heredity - Mendel (1866)<br />
The phenotypes of an <strong>in</strong>dividual depends on genes of his<br />
parents.
Chromosome Theory - Morgan (1910)<br />
Genes were situ<strong>at</strong>ed <strong>in</strong> chromosomes
The molecular structure of chromosomes (W<strong>at</strong>son and Crick -<br />
1953)<br />
DNA structure: the double helix<br />
Four basis: aden<strong>in</strong>e(A), guan<strong>in</strong>e(G), thym<strong>in</strong>e(T), cytos<strong>in</strong>e(C)<br />
genes are sequences of nucleotides
DNA manipul<strong>at</strong>ion<br />
cut, replic<strong>at</strong>ion and decod<strong>in</strong>g
Genes control the metabolism<br />
Metabolism occurs by sequences of enzyme-c<strong>at</strong>alyzed<br />
reactions.<br />
Enzymes are specified by one or more genes
Gene expression
species modific<strong>at</strong>ion, diagnostics, drug production
Experimental techniques
Áreas de <strong>at</strong>uação
Microarrays
Image Analysis
Signal<br />
gene 1<br />
gene 2
D<strong>at</strong>a M<strong>in</strong><strong>in</strong>g Environments
Objected oriented d<strong>at</strong>abase<br />
P1<br />
P2<br />
Pn<br />
Pi : analytical and m<strong>in</strong><strong>in</strong>g procedures (kernel parallel)
Integr<strong>at</strong>ed Environment<br />
Genbank<br />
d<strong>at</strong>abase<br />
Another<br />
d<strong>at</strong>abases<br />
Access control<br />
module<br />
Cl<strong>in</strong>ical d<strong>at</strong>a<br />
Sequence module<br />
P1<br />
microarray module<br />
P1<br />
analitical<br />
oper<strong>at</strong>ional<br />
P2<br />
P3<br />
analitical<br />
oper<strong>at</strong>ional<br />
P2<br />
P3<br />
query<br />
Pn<br />
Pn<br />
query<br />
query
Users<br />
1<br />
Analysis tools writer SpreadSheet D<strong>at</strong>am<strong>in</strong>ig<br />
2<br />
M_d<strong>at</strong>abase<br />
MOLAP/ROLAP server<br />
3<br />
Metad<strong>at</strong>a<br />
D<strong>at</strong>a Warehouse<br />
D<strong>at</strong>a<br />
Mart<br />
Integr<strong>at</strong>or<br />
Wrapper Wrapper Wrapper<br />
4<br />
IMS<br />
RDMS<br />
Others
System Architecture<br />
Slice 1<br />
Appl. 1<br />
Java<br />
Appl. 2<br />
PB<br />
Appl. 3<br />
Delphi<br />
Consulte rules and<br />
libraries<br />
Slice N<br />
Oracle<br />
Sybase<br />
DB/2<br />
Appl. n<br />
MATLA<br />
N-2 slices<br />
Informix
Some Biological problems<br />
• Modific<strong>at</strong>ion of Sugar Cane, Eucalyptus<br />
and chickens<br />
• Cancer diagnostics<br />
• Drug performance aga<strong>in</strong>st HIV and Malaria<br />
• Understand<strong>in</strong>g of the cell division cycle<br />
• Reconstitution of nervous tissue<br />
• Design of drugs<br />
• Prediction of new virus
Formaliz<strong>in</strong>g Biological Problems
Σ<br />
Wh<strong>at</strong> genes regul<strong>at</strong>e the<br />
p<strong>at</strong>hway A->B->C->D ?<br />
Wet Lab<br />
Proteome<br />
Transcriptome<br />
Genome<br />
P<strong>at</strong>hways
Choice of adequ<strong>at</strong>e cluster<strong>in</strong>g<br />
technique
Cluster<strong>in</strong>g<br />
measurement<br />
Class 2<br />
[high variance]<br />
measurement<br />
Class 1<br />
[low variance]
Looser clusters due<br />
to large variance<br />
Cluster<strong>in</strong>g
Design classifier<br />
v−erb−b2 avian erythroblastic leukemia viral oncogene homolog 2<br />
2<br />
1.5<br />
1<br />
0.5<br />
0<br />
−0.5<br />
−1<br />
−1.5<br />
LINEAR CLASSIFIER (DISPERSED−GAUSSIAN) w/ σ = 0.600<br />
the tumor sample from P<strong>at</strong>ient 20<br />
7−th (0.416607)<br />
BRCA1<br />
BRCA2/sporadic<br />
1−th (0.389593)<br />
−3.5 −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 1<br />
phosphofructok<strong>in</strong>ase, pl<strong>at</strong>elet
Dimensionality Reduction<br />
x2<br />
Wh<strong>at</strong> is the m<strong>in</strong>imum number<br />
of genes th<strong>at</strong> is enough to<br />
dist<strong>in</strong>guish two Biological<br />
st<strong>at</strong>es?<br />
x1
Filter Design
Applic<strong>at</strong>ion
<strong>Model<strong>in</strong>g</strong> Dynamical Systems
Cell<br />
peptide<br />
other signals
peptide<br />
other signals<br />
mRNA<br />
Transcr.<br />
Transl<strong>at</strong>.<br />
Prote<strong>in</strong>s<br />
Pool<br />
Metabolic<br />
P<strong>at</strong>hways
peptide<br />
other signals<br />
GENES<br />
NETWORK<br />
mRNA<br />
Transcr.<br />
Transl<strong>at</strong>.<br />
Prote<strong>in</strong>s<br />
Pool<br />
Metabolic<br />
P<strong>at</strong>hways
x1fp<br />
.<br />
.<br />
.<br />
x1<br />
Division Steps<br />
z<br />
u1<br />
y1fp<br />
x1f<br />
y1f<br />
I<br />
u2<br />
u5<br />
p<br />
w1fp<br />
vfp<br />
w2fp<br />
w1f<br />
v w2f<br />
y2fp<br />
w1<br />
w2<br />
x3f<br />
x4f<br />
y1f<br />
y2f<br />
y2f<br />
y1<br />
y2<br />
z<br />
Forward Signal<br />
Feedback to p<br />
Feedback to previous layer<br />
.<br />
.<br />
.<br />
x6fp<br />
x6f<br />
x6
Knockout<br />
x1fp<br />
.<br />
.<br />
.<br />
x1<br />
Division Steps<br />
z<br />
u1<br />
y1fp<br />
x1f<br />
y1f<br />
I<br />
u2<br />
u5<br />
p<br />
w1fp<br />
vfp<br />
w2fp<br />
w1f<br />
v w2f<br />
y2fp<br />
w1<br />
w2<br />
x3f<br />
x4f<br />
y1f<br />
y2f<br />
y2f<br />
y1<br />
y2<br />
z<br />
Forward Signal<br />
Feedback to p<br />
Feedback to previous layer<br />
.<br />
.<br />
.<br />
x6fp<br />
x6f<br />
x6
System identific<strong>at</strong>ion
peptide<br />
Cell<br />
other signals<br />
GENES<br />
NETWORK<br />
mRNA<br />
Transcr.<br />
Transl<strong>at</strong>.<br />
Prote<strong>in</strong>s<br />
Pool<br />
Metabolic<br />
P<strong>at</strong>hways<br />
microarray<br />
proteome
F<strong>in</strong>d the architecture of a gene regul<strong>at</strong>ion network from<br />
microarray d<strong>at</strong>a.<br />
NMSE 2<br />
Predictor 2<br />
NMSE 1<br />
Target Gene Predictor 1<br />
NMSE 3<br />
Predictor 3
System dynamics simple
System identified
A family of <strong>M<strong>at</strong>hem<strong>at</strong>ical</strong><br />
problems
Design of classifier, filter or<br />
dynamical system<br />
Optimiz<strong>at</strong>ion<br />
Comb<strong>in</strong><strong>at</strong>ory<br />
or cont<strong>in</strong>uos<br />
St<strong>at</strong>istical<br />
Estim<strong>at</strong>ion<br />
Algebraic<br />
Represent<strong>at</strong>ion
The constra<strong>in</strong>ed estim<strong>at</strong>ion problem<br />
Error<br />
ψ opt<br />
Ψ<br />
Sample size
Other areas with similar<br />
problems<br />
• F<strong>in</strong>ances<br />
• Market<strong>in</strong>g<br />
• Digital TV<br />
• Petrol Industry<br />
• Neuro Sciences<br />
• ...
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