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![Nonlinear dynamics
of biochemical inhibition in cells
Chemical Species
Chemical Complex
Enzymatic reaction
Enzymatic Inhibition
L c SRC
pMEK MEKi
ppERK
[MEKi] [MEKi]
In preparation
for publication](https://image.slidesharecdn.com/finaldemo-150701134931-lva1-app6892/85/Final-demo-47-320.jpg)
![Nonlinear dynamics
of biochemical inhibition in cells
Chemical Species
Chemical Complex
Enzymatic reaction
Enzymatic Inhibition
L c SRC
SRCi
pMEK
ppERK
[SRCi] [SRCi]
L c SRC
pMEK MEKi
ppERK
[MEKi] [MEKi]
In preparation
for publication](https://image.slidesharecdn.com/finaldemo-150701134931-lva1-app6892/85/Final-demo-48-320.jpg)
Final demo
- 1. infervote.org Democratizing democracy: aresource for political engagement Robert Vogel
- 2. Why? • We areconstantly bombarded with political rhetoric that shape our political views. • How are we ACTUALLY represented by our elected officials? • How does and will our congress vote on topics we care about? • Do senator voting records exhibit polarized behavior? • How can we find misbehaving and polarized senators? • What action can we take?
- 3.
- 4. The Polarity Index Senatori Votes Republican Senator j Votes
- 5. The Polarity Index Senatori Votes Republican Senator j Votes Votes in common
- 6. The Polarity Index Senatori Votes Republican Senator j Votes Votes in common Jij = Votes in common All votes
- 7. The Polarity Index Senatori Votes Republican Senator j Votes Votes in common Jij = Votes in common All votes Ji1 = ~1
- 8. The Polarity Index Senatori Votes Republican Senator j Votes Votes in common Jij = Votes in common All votes Ji1 = ~1 Ji2 = + ~0
- 9. The Polarity Index Senatori Votes Republican Senator j Votes Votes in common Jij = Votes in common All votes + Polarity= Ji1 = ~1 Ji2 = + ~0
- 10. The Polarity Index Senatori Votes Republican Senator j Votes Votes in common Jij = Votes in common All votes + Polarity= Ji1 = ~1 Ji2 = + ~0
- 11. Clustering Senator Votingwith Jaccard distance
- 12. Democrat RepublicanInd Clustering SenatorVoting with Jaccard distance
- 13. Democrat RepublicanInd Clustering SenatorVoting with Jaccard distance d Mitch McConnell (KY) John McCain (AZ)
- 14. Democrat RepublicanInd Clustering SenatorVoting with Jaccard distance Elizabeth Warren (MA) Dianne Feinstein (CA) d Mitch McConnell (KY) John McCain (AZ)
- 15. Democrat RepublicanInd Clustering SenatorVoting with Jaccard distance Elizabeth Warren (MA) Dianne Feinstein (CA) Bernie Sanders (VT) d Mitch McConnell (KY) John McCain (AZ)
- 16. Democrat RepublicanInd Clustering SenatorVoting with Jaccard distance Elizabeth Warren (MA) Dianne Feinstein (CA) Bernie Sanders (VT) d Mitch McConnell (KY) John McCain (AZ) Rand Paul (KY) Marco Rubio (FL) Ted Cruz (TX)
- 17. Democrat RepublicanInd Clustering SenatorVoting with Jaccard distance Elizabeth Warren (MA) Dianne Feinstein (CA) Bernie Sanders (VT) d Mitch McConnell (KY) John McCain (AZ) Rand Paul (KY) Marco Rubio (FL) Ted Cruz (TX)
- 18. Do votes alignwith bill sponsors? Republican Sponsor • The bill sponsor is the member of congress that introduces the document for consideration. Democrat Sponsor
- 19. Infer directionality ofbiochemical reactions using Langevin dynamics Robert Vogel Developed new parameterization of therapeutic drugs using insight from nonlinear dynamical systems
- 20. Voting Distributions andthe Simulated Senate • Sample 5000 experimental senates using parameters from data • Data exhibit a more diverse distribution then simulation • Potential next step, use the Ising model to model pairwise interactions Republican SponsorDemocrat Sponsor
- 21. The Jaccard Indexand Political Polarity
- 22. Jaccard Index forMeasuring Polarity • Jaccard Index measures the number identical votes between Senator i and Senator j normalized to total votes • Polarity index is the average Jaccard index between Senator i and all Senators in party R. Jij = |vi vj| |vi [ vj| JiR = 1 NR X j2R Jij
- 23. Distribution of polarityindex • If party politics were not a factor, these distributions would overlap
- 24. Jaccard Distance forSenator Clustering • Jij 1 the more similar Senator i votes to Senator j. • Hierarchical clustering utilizes a dissimilarity measure. Standard solution 1 - Jij dJ (i, j) = 1 |vi vj| |vi [ vj| | {z } Jij
- 25. Votes are strictlypartisan • Fraction of votes along party line, most votes are partisan
- 26.
- 27. Topic modeling oflegislative summaries Wordspaceperbill TopicSpace Bills Topics T S = S’ Y N0 Congress person Topic Probabilities P T’ = P’ New bill in topic space Probability of vote P Y N 0 Prediction Clustering
- 28. Can we makepredictions of senator votes from legislative documents? Topic 1 Topic 2 Topic 3 Senator 1 Vote Document 1 Document 2 Document N Topic M
- 29. Can we makepredictions of senator votes from legislative documents? Topic 1 Topic 2 Topic 3 Senator 1 Vote Document 1 Document 2 Document N Topic M VoteSenator 2
- 30. Can we makepredictions of senator votes from legislative documents? Topic 1 Topic 2 Topic 3 Senator 1 Vote Document 1 Document 2 Document N Topic M Senator L Vote VoteSenator 2
- 31. Legislative document reductionto topics • 2559 legislative summaries • Constructed 6403 word basis from text by: • removing stop words (e.g and, that, this, a) • removing non-english words • stemming (e.g. rested equal to rest) • TF-IDF • Cosine similarity to group topics
- 32. Legislative document reductionto topics • 2559 legislative summaries • Constructed 6403 word basis from text by: • removing stop words (e.g and, that, this, a) • removing non-english words • stemming (e.g. rested equal to rest) • TF-IDF • Cosine similarity to group topics • Result: No structure in bill data, more data needed! Documents Documents
- 33. Document dimensionality reductionnot sufficient with PCA 95% of the variablity corresponds to > 1000 dimensions A small topic space, represents a small portion of the variability
- 34. tSNE dimensionality reductionsuggests no structure in bill data • Each point is a document in the reduced space defined by tSNE • t-distributed Stochastic Neighborhood Embedding maps points from a high to a low dimensional space by minimizing the Kullback-Leibler Divergence (minimize information loss).
- 35.
- 36. Why only chooseBills and Amendments? • In general, these documents can become law • Other votes are for approving nominations for office and resolutions. • Resolutions can be very diverse as shown below.
- 37. Graduate Research: Anoverview • Langevin Dynamics to: • figure out direction in biochemical reactions, and • testing isolation of a network motif. • Bifurcation analysis to identify: • nodes in a network sensitive to therapeutic inhibition
- 38. Biochemical Noise • Flowcytometry measures the relative quantity of <= 12 biochemical species per cell at a rate of 20,000 cells per second. • Fluorescent molecules are coupled to antibodies that specifically bind to a biochemical species. • Quantity of molecules is proportional to fluorescent signal −2 −1 0 1 2 −4 −3 −2 −1 0 1 2 3 4 PMA 1 PMA 2 PMA 3 Log2 Normalized pMEK Log2NormalizedppERK PMA 1 PMA 2 PMA 3 PMA 1 PMA 2 PMA 3 −2 −1 0 1 2 −4 −3 −2 −1 0 1 2 3 4 PMA : 1 Log2 pMEK Log2ppERK PMA : 1 −2 −1 0 1 2 −4 −3 −2 −1 0 1 2 3 4 PMA : 2 Log2 pMEK Log2ppERK PMA : 2 −2 −1 0 1 2 −4 −3 −2 −1 0 1 2 3 4 PMA : 3 Log2 pMEK Log2ppERK PMA : 3
- 39. Fluctuations break symmetry ofaverage measurements Variance of Y > X Y X𝜉x 𝜉y O O • Fluctuations from source node propagates to target X Y𝜉y 𝜉x O O Variance of X > Y True Model False Model
- 40. Fluctuations break symmetry ofaverage measurements Variance of Y > X 0.2 0.3 0.4 0.5 0.6 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Cov(pMEK, ppERK) Variance True Model pMEK ppERK 0.2 0.3 0.4 0.5 0.6 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Cov(pMEK, ppERK) Variance False Model pMEK ppERK 0.2 0.3 0.4 0.5 0.6 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Cov(pMEK, ppERK) Variance True Model pMEK ppERK 0.2 0.3 0.4 0.5 0.6 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Cov(pMEK, ppERK) Variance False Model pMEK ppERK Y X𝜉x 𝜉y O O • Fluctuations from source node propagates to target X Y𝜉y 𝜉x O O Variance of X > Y True Model False Model
- 41. Nonlinear dynamics ofbiochemical inhibition
- 42. Inhibition of biochemicalsignaling in cells, a new parameter 𝛼 L c SRC pMEK MEKi ppERK In preparation for publicationChemical SpeciesChemical Complex Enzymatic reaction Enzymatic Inhibition
- 43. Inhibition of biochemicalsignaling in cells, a new parameter 𝛼 L c SRC pMEK MEKi ppERK L c SRC SRCi pMEK ppERK In preparation for publicationChemical SpeciesChemical Complex Enzymatic reaction Enzymatic Inhibition
- 44. Inhibition of biochemicalsignaling in cells, a new parameter 𝛼 L c SRC pMEK MEKi ppERK L c SRC SRCi pMEK ppERK In preparation for publicationChemical SpeciesChemical Complex Enzymatic reaction Enzymatic Inhibition
- 45. Inhibition of biochemicalsignaling in cells, a new parameter 𝛼 L c SRC pMEK MEKi ppERK L c SRC SRCi pMEK ppERK In preparation for publicationChemical SpeciesChemical Complex Enzymatic reaction Enzymatic Inhibition
- 46. Nonlinear dynamics of biochemicalinhibition in cells Chemical Species Chemical Complex Enzymatic reaction Enzymatic Inhibition In preparation for publication
- 47. Nonlinear dynamics of biochemicalinhibition in cells Chemical Species Chemical Complex Enzymatic reaction Enzymatic Inhibition L c SRC pMEK MEKi ppERK [MEKi] [MEKi] In preparation for publication
- 48. Nonlinear dynamics of biochemicalinhibition in cells Chemical Species Chemical Complex Enzymatic reaction Enzymatic Inhibition L c SRC SRCi pMEK ppERK [SRCi] [SRCi] L c SRC pMEK MEKi ppERK [MEKi] [MEKi] In preparation for publication
- 49. Finding dysfunctional components intumor samples
- 50. Single cell measurementsfind abnormalities in tumor patient profiles • Kullback-Leibler divergence measures the dissimilarity of the single cell distribution of biochemical signaling features between patient and healthy donor samples. Sjk = X i2HD DKL (Pj(xk)||Pi(xk)) = X i2HD Pj(xk) log ✓ Pj(xk) Pi(xk) ◆ • k = Biochemical species • j = patient id • i = Healthy donor