1. Logical Analysis and Invariants

2. Outline Golden thread of science Induction Deduction Triumph of logic
Bet on the beans
De-noise PPI networks
Abduction
Identify homologs
Make computer systems more secure
Induction
Improve database design
Infer key mutations
Diagnose pediatric leukemias
Triumph of logic

3. Three types of reasoning

4. Three types of reasoning
Deduction
Socrates is a man
All men are mortal
Socrates is mortal
Induction
Socrates is a man
Socrates is mortal
All men are mortal
Abduction
All men are mortal
Socrates is mortal
Socrates is a man

5. Task
Try drawing the logical flow of deduction, abduction and induction
Now, try the following example:

6. Pierce’s logic

7. The Golden Thread of Science
Science is characterized by
Observing an invariant
Proving that it is true, i.e., a law
Exploiting it to solve problems
An invariant is something that remains unchanged.
Biology/Chemistry is no more about Petri dish & test tube than Computer Science is about programming

8. In the following examples you will see the intertwining of logic and invariants in scientific problem solving

9. Deduction
What is an invariant

10. Shall we bet on the color of the bean that is left behind?
Suppose you have a bag of x red beans and y green beans
Repeat the following:
Remove 2 beans
If both green, discard both
If both red, discard one, put back one
If one green and one red, discard red, put back green
If one bean is left behind, can you predict its colour?
Shall we bet on the color of the bean that is left behind?

11. Bet on the last green bean
Suppose you have a bag of x red beans and y green beans
Repeat the following:
Remove 2 beans
If both green, discard both
If both red, discard one, put back one
If one green and one red, discard red, put back green
If one bean is left behind, can you predict its colour?
When the parity of # of green beans (y) is odd, …
Start with y=2n+1
y=2n+1  y=2n-1
y=2n+1  y=2n+1
y remains odd
Last bean must be green!

12. Bet on the last red bean
Suppose you have a bag of x red beans and y green beans
Repeat the following:
Remove 2 beans
If both green, discard both
If both red, discard one, put back one
If one green and one red, discard red, put back green
If one bean is left behind, can you predict its colour?
When the parity of # of green beans (y) is even, …
Start with y=2n
y=2n  y=2n-2
y=2n  y=2n
y remains even
Last bean must be red!

13. Bet on color of the last bean … and win!
If you start w/ odd # (even #) of green beans, there will always be an odd # (even #) of green beans in the bag
Parity of green beans is invariant
Bean left behind is green iff you start with odd # of green beans
Suppose you have a bag of x red beans and y green beans
Repeat the following:
Remove 2 beans
If both green, discard both
If both red, discard one, put back one
If one green and one red, discard red, put back green
If one bean is left behind, can you predict its colour?

14. What have we just seen?
Problem solving by (deductive) logical reasoning on invariants

15. Science is characterized by …
Observing an invariant:
Parity of green beans is invariant
Proving it:
Exploit it to solve problems:
Predict colour of the last bean

16. Removing noise from PPI experiments
Deduction
Removing noise from PPI experiments

17. Protein-protein interaction detection
Many high-throughput assays for PPIs
Generating large amounts of expt data on PPIs can be done with ease
High-throughput
approaches
sacrifice quality for quantity: (a) limited or biased coverage:
false negatives, & (b) high error rates:
false positives
But …
Growth of BioGrid
In order to decipher the “interactome”, which is far more complex than the genomes and proteomes, scientists have developed many high throughput methods for detecting protein-protein interactions experimentally.
Here are some of the most popular methods. Yeast-two-hybrid detects direct binary relationships between two protein molecules. The mass spectrometry purification methods, such as TAP, or Tandem Affinity Purification, detects multi-protein relationships in protein complexes.
Protein-protein interactions can also be detected indirectly, and probably less accurately, by measuring the interactions between gene, since proteins are products of genes. For example, correlated mRNA expression with gene chips or microarray experiments, measures co-expression of genes to infer potential interactions between proteins that are products of the co-expressed genes. There are also more direct experimental methods to measure gene interactions: for example, synthetic lethality can be used to measure direct interactions between two genes instead of just their co-expressions.
In any case, the fact is that we do not have any problem generate lots of data on protein-protein interactions using current technologies.

18. Noise in PPI networks High level of noise
Large disagreement betw methods
Sprinzak et al., JMB, 327: , 2003
High level of noise
Need to clean up before making inference on PPI networks

19. Chua & Wong. Increasing the reliability of protein interactomes
Chua & Wong. Increasing the reliability of protein interactomes. Drug Discovery Today, 13(15/16): , 2008
Time for Exercise #1
Can you think of things a biologist can do to remove PPIs that are likely to be noise?

20. De-noising PPI networks using Reproducibility
If a PPI is reported in a few independent expts, it is more reliable than those reported in only one expt
Good idea. But you need to do more expts  More time & more $ has to be spent

21. De-noising PPI networks using localization coherence
Two proteins should be in the same place to interact. Agree?
Good idea. But the two proteins in the PPI you are looking at may not have localization annotation

22. Liu et al. Complex discovery from weighted PPI networks.
Bioinformatics, 25(15): , 2009
Time for Exercise #2
Do you really need to know where two proteins are, in order to know whether they are in the same place? If not, how?

23. Topology of neighbourhood of real PPIs
Suppose 20% of putative PPIs are noise
≥ 3 purple proteins are real partners of both A and B
A and B are likely localized to the same cellular compartment (Why?) A B ?

24. Czekanowski-Dice distance
Brun, et al. Genome Biology, 5(1):R6, 2003
Czekanowski-Dice distance
Given a pair of proteins (u, v) in a PPI network
Nu = the set of neighbors of u
Nv = the set of neighbors of v
CD(u,v) =
Consider relative intersection size of the two neighbor sets, not absolute intersection size
Case 1: |Nu| = 1, |Nv|= 1, |NuNv|=1, CD(u,v)=1
Case 2: |Nu| = 10, |Nv|= 10, |NuNv|=10, CD(u,v)=1 24

25. Liu et al. Complex discovery from weighted PPI networks.
Bioinformatics, 25(15): , 2009
Adjusted CD-distance
Variant of CD-distance that penalizes proteins with few neighbors
wL(u,v) =
u = max{0, }, v = max{0, }
Suppose average degree is 4, then
Case 1: |Nu| = 1, |Nv|= 1, |NuNv|=1, wL(u,v)=0.25
Case 2: |Nu| = 10, |Nv|= 10, |NuNv|=10, wL(u,v)=1
Beware of strength of small numbers

26. The triumph of logic Impact:
Two proteins should be in same place to interact A B ?
Impact:
PPI networks can be cleansed based purely on topological info, w/o needing location etc info on proteins

27. Identifying homologous proteins
Abduction
Identifying homologous proteins

28. Proteins perform a wide variety of activities in the cell
A protein is a ...
A protein is a large complex molecule made up of one or more chains of amino acids
Proteins perform a wide variety of activities in the cell

29. Function assignment to protein seq
SPSTNRKYPPLPVDKLEEEINRRMADDNKLFREEFNALPACPIQATCEAASKEENKEKNR
YVNILPYDHSRVHLTPVEGVPDSDYINASFINGYQEKNKFIAAQGPKEETVNDFWRMIWE
QNTATIVMVTNLKERKECKCAQYWPDQGCWTYGNVRVSVEDVTVLVDYTVRKFCIQQVGD
VTNRKPQRLITQFHFTSWPDFGVPFTPIGMLKFLKKVKACNPQYAGAIVVHCSAGVGRTG
TFVVIDAMLDMMHSERKVDVYGFVSRIRAQRCQMVQTDMQYVFIYQALLEHYLYGDTELE VT
How do we attempt to assign a function to a new protein sequence?

30. In the course of evolution…

31. Time for Exercise #3
How can we guess the function of a protein?

32. Abductive reasoning
Law: Two proteins inheriting their function from a common ancestor have very similar amino acid sequences
Observation: Proteins X and Y are very similar in their sequence
Abduction: Proteins X and Y are descended from the same ancestor and inherit their function from this ancestor
Proteins X and Y have a common function

33. Guilt by association Compare T with seqs of known function in a db
Assign to T same
function as homologs
Confirm with suitable
wet experiments
Discard this function
as a candidate

34. Earliest research in seq comparison
Source: Ken Sung
Doolittle et al. (Science, July 1983) searched for platelet-derived growth factor (PDGF) in his own DB. He found that PDGF is similar to v-sis oncogene
PDGF SLGSLTIAEPAMIAECKTREEVFCICRRL?DR?? 34 p28sis 61 LARGKRSLGSLSVAEPAMIAECKTRTEVFEISRRLIDRTN 100

35. Inferring key mutations: Why some PTP are inefficient
Induction
Inferring key mutations: Why some PTP are inefficient

36. Protein tyrosine phosphatase
Sequence from a typical PTP
Some PTPs are much less efficient than others
Why? And how do you figure out which mutations cause the loss of efficiency?

37. Reasoning based on an invariant…
This site is conserved in D1, but is not consistently missing in D2
 Not a likely cause of D2’s loss of function
This site is conserved in D1, but is consistently missing in D2
 Possible cause of D2’s loss of function
present
absent

38. Key mutation site: PTP D1 vs D2
Positions marked by “!” and “?” are likely places responsible for reduced PTP activity
All PTP D1 agree on them
All PTP D2 disagree on them
Lim et al. Journal of Biological Chemistry 273: ,1998.

39. Confirmation by mutagenesis expt
Wet expts confirmed the predictions
Mutate D  E in D1
i.e., check if D  E can cause efficiency loss
Mutate E  D in D2
i.e., show D  E is the cause of efficiency loss
Impact:
Hundreds of mutagenesis expts saved by simple reasoning on (violation of) invariants!

40. Time for Exercise #4
Is this abductive, deductive, or inductive reasoning?

41. The triumph of logic
Induction/hypothesis: A site that is critical for PTP efficiency is present in all efficient PTPs and absent in all inefficient PTPs
Observation: A site X is present in all efficient PTPs and absent in all inefficient PTPs
Abduction: Site X is critical for PTP efficiency

42. Diagnosing pediatric leukemias
Induction
Diagnosing pediatric leukemias

43. Some Patient Samples Does Mr. A have cancer? genes samples Mr. A:
malign
benign
genes
samples
???
Mr. A:
Does Mr. A have cancer?

44. Let’s rearrange the rows…
genes
benign
benign
samples
benign
benign
malign
malign
malign
malign
???
Mr. A:
Does Mr. A have cancer?

45. and the columns too…
genes
malign
benign
samples
???
Mr. A:
Induction/hypothesis: Benign (malignant) tumour has lots of red (blue) genes on the left and blue (red) genes on the right

46. The triumph of logic
Induction/hypothesis: Benign (malignant) tumour has lots of red (blue) genes on the left and blue (red) genes on the right
Observation: Mr A’s tumour has lots of blue genes on the left and red genes on the right
Abduction: Mr A’s tumour is malignant

47. Invariant profile of leukemia subtypes

48. What have we just seen?
Guilt by association of invariants

49. Childhood ALL
6 Major subtypes: T-ALL, E2A-PBX, TEL-AML, BCR-ABL, MLL genome rearrangements, Hyperdiploid>50
Diff subtypes respond differently to same Tx
Over-intensive Tx
Development of secondary cancers
Reduction of IQ
Under-intensiveTx
Relapse: suffer deterioration after a period of improvement.
The subtypes look similar
Conventional diagnosis
Immunophenotyping
Cytogenetics
Molecular diagnostics
Unavailable in most ASEAN countries

50. The situation in ASEAN, circa 2000

51. Exploit invariant gene expr profiles
Low-intensity treatment applied to 50% of patients
Intermediate-intensity treatment to 40% of patients
High-intensity treatment to 10% of patients
Reduced side effects
Reduced relapse
75-80% cure rates
US$36m (US$36k * 2000 * 50%) for low intensity
US$48m (US$60k * 2000 * 40%) for intermediate intensity
US$14.4m (US$72k * 2000 * 10%) for high intensity
Total US$98.4m/yr
Save US$51.6m/yr, compared to applying intermediate-intensity treatment to everyone
Yeoh et al, Cancer Cell 2002 51

52. Remarks

53. What have we learned? Three types of logical reasoning
Invariant is a fundamental property of many problems
Paradigms of problem solving
Problem solving by logical reasoning on invariants
Problem solving by rectifying/monitoring violation of invariants
Guilt by association of invariants
Computer Science is no more about programming than Biology/Chemistry is about Petri dish & test tube

54. Acknowledgements
This lecture is based on notes originating from the following person:
Professor Limsoon Wong
National University of Singapore