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CDAC 2018 Mishra immune system part a

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Presentation at the CDAC 2018 Workshop and School on Cancer Development and Complexity
http://cdac2018.lakecomoschool.org

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CDAC 2018 Mishra immune system part a

  1. 1. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Immune Systems Part A: Game Theory Bud Mishra Courant, NYU Como, May 2018
  2. 2. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Outline 1 Game Theoretic Models Signaling Games Nash Equilibria Deception 2 Biological Deception Examples of Deception in Biology An Exhaustive Classification of Deception in Biology 3 Multi-Cellularity Geoffry-Cuvier Debate Cellularization: Aligning Utility Cancer & Cellular Deception 4 Immune System Overall Picture Innate System Adaptive System
  3. 3. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Self & Self-Reference What contains what? Self, Encoding of Self and Recognition of Self What cells know that they belong to a multi-cellular organism?
  4. 4. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Signaling Games Two player games with incomplete information... One player is informed ... the other player is not... 1 The informed player’s strategy set consists of signals contingent on information 2 Uninformed player’s strategy set consists of actions contingent on signals Spence 1973, Zahari 1977, Lewis 2002, Sobel 2009
  5. 5. Game Theoretic Models Biological Deception Multi-Cellularity Immune System The Model of Signaling Games Two players: S − Sender (Informed) R − Receiver (Uninformed) Roles can be shared - partial information, distributed actions TYPE: Random variable t whose support is given by T (known to Sender S). π(·) = Probability distribution over T is a prior belief of R that the sender’s type is t.
  6. 6. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Game Game 1 Player S learns t ∈ T 2 S send to R a signal s ∈ M. 3 R takes an action a ∈ A. Payoff function ui∈{S,R} : T × M × A → R.
  7. 7. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Equilibrium Behavior Strategies: 1 For S a function µ : T × M → [0, 1] such that s∈M µ(t, s) = 1, for all t. µ(t, s) = Probability that S with type t sends signal s. 2 For R a function α : M × A → [0, 1] such that a∈A α(s, a) = 1, for all s. α(s, a) = Probability that R takes action a following signal s. Subjective probability. β(t, s) = µ(t, s)π(t) t ∈T µ(t , s)π(t ) .
  8. 8. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Proposition Behavior strategies (α∗, µ∗) form a Nash equilibrium iff for all t ∈ T µ(t, s) > 0 implies a∈A US (t, s, a)α(s, a) = max s ∈S a∈A US (t, s , a)α(s , a); & for all s ∈ S (s.t. t∈T µ(t, s)π(t) > 0) α(s, a) > 0 implies t∈T UR (t, s, a)β(t, a) = max a ∈A t∈T UR (t, s, a )β(t, a ).
  9. 9. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Signaling Games in Nature Mapping Types and Actions into Signals: f S : T → A; f R : A → T. Sender US = I(T, M) + λS dS (f S (t), a). Receiver UR = I(A, M) + λRdR (t, f R (a)).
  10. 10. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Subjective Reality Note that the distribution of signals received by R is given by the probability distribution πM, where πM(s) = t∈T πT (t)µ(s|t), And the distribution of actions produced by R is given by the probability distribution πA, where πA(a) = s∈M πM(s)α(a|s). Clearly πT and πA are probability distributions on T and A respectively. If ˆπT is the probability distribution on T induced by πA under the function fR, then ˆπT (·) := πA(f −1 R (·)). (1)
  11. 11. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Deception A natural choice of measure for deception is given by the relative entropy between the probability distributions πT and ˆπT : Deception := Rel. Entropy(ˆπT |πT ) = t∈T ˆπT (t) log2 ˆπT (t) πT (t) . (2) This definition describes deception from the point of view of the receiver. To get the notion of deception from the point of view of the sender, one needs to play the game several rounds.
  12. 12. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Signaling Games Separating Equilibrium: Each type t sends a different signal Mt. f S : t → a[Mt]... Pooling Equilibrium: All types t send a single signal s∗ with probability 1. Convention & Deception: The divergence between the objective probabilities and the subjective probabilities induced by conventional equilibria. Solution: Costly Signaling; Credible and Non-credible threat; Aligned Utilities; 2 + m + n players – m Recommenders + n Verifiers
  13. 13. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Recommenders and Verifiers Recommenders aim for Liveness Verifiers aim for Safety
  14. 14. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Recommenders and Verifiers Liveness ∀Sender,S (Type t ∈ T & Signal s ∈ M) ∃Receiver,R(Action a ∈ A) AG[s → Fa US (t, s, a) > θ∗ S ] For every Uber driver with 4 or more stars, there is a passenger with 4 or more stars waiting within 4 minutes for a ride. Safety ∀Receiver,R(action a ∈ A) ∀Sender,S (Type t ∈ T & Signal s ∈ M) AG[¬a U s UR (t, s, a) > θ∗ R] For every passenger with 4 or more stars, there is no need to wait for more than 4 minutes to get a Uber driver with 4 or more stars.
  15. 15. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Outline 1 Game Theoretic Models Signaling Games Nash Equilibria Deception 2 Biological Deception Examples of Deception in Biology An Exhaustive Classification of Deception in Biology 3 Multi-Cellularity Geoffry-Cuvier Debate Cellularization: Aligning Utility Cancer & Cellular Deception 4 Immune System Overall Picture Innate System Adaptive System
  16. 16. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Thermo-Tolerance Game An example of a biochemical Lewis signaling game is provided by thermotolerance via RheA-HSP18 system: RheA is a thermosensor, thus an informed agent; but HSP18 is needed to modulate thermotolerance, thus an uninformed agent, which nonetheless acts in response to the signal consisting of RheA’s conversion to a nonDNA-binding form. They enable the cell to survive spikes in temperature in the environment, thus improving the Shapley value of all the macromolecules contained in the cells – including RheA and HSP18.
  17. 17. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Evolutionary transi- tion Type of Cooperation Signaling convention Type of subversion Replicators Between monomer subunits, forming polymers that pro- mote common inter- est of the monomer constituents The first replicators are unknown, but would have utilized molecular specificity Parasitism of replicator func- tion may have occurred by other polymers Protein translation Between mRNAs and the ribosome Genetic code ‘Deceiver’ tRNAs (tRNAs that alter the genetic code e.g. sup- pressor tRNAs) ‘Deceiver’ mR- NAs (mRNAs that benefit the sender gene, but not the host genome) Eukaryogenesis Between nucleus and mitochondrion Nuclear targeting sig- nals, mitochondrial targeting signals Bacteria can use nuclear lo- calization signals to gain entry to the nucleus (a Trojan horse strategy) Between mRNA and the spliceosome Intron splice sites Selfish elements can ‘hide’ in or mimic introns (see Table 1), viruses sequester the splicing machinery to regulate their gene expression Between DNA and hi- stones Histone code Some bacteria appear to modify the histone code
  18. 18. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Sexual reproduction Between two genders Species specific chemical, visual and auditory signaling Many examples of deception due to sexual conflict Between two gametes Gamete fusion in- volves the HAP2 protein. Sperm-egg recognition is species specific Undescribed Between two homolo- gous chromosomes Homologous recom- bination is initiated by Spo11 B chromosomes mimic sex chro- mosomes leading to chromoso- mal drive. Some examples of meiotic drive utilize molecular deception Multicellularity Between cells Has arisen a num- ber of times indepen- dently – facilitated by the evolution of cell adhesion and signal- ing, and immune sys- tems Cancers utilize a variety of molecular mechanisms that dis- rupt normal cell-cell recognition, and evade the immune system Eusociality Between related indi- viduals Has arisen a num- ber of times indepen- dently. Each has established different signaling conventions based on acoustic, vi- sual and chemical sig- nals Mimicry of acoustic signals and pheromones Humanity Between unrelated in- dividuals Spoken language Lying
  19. 19. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Outline 1 Game Theoretic Models Signaling Games Nash Equilibria Deception 2 Biological Deception Examples of Deception in Biology An Exhaustive Classification of Deception in Biology 3 Multi-Cellularity Geoffry-Cuvier Debate Cellularization: Aligning Utility Cancer & Cellular Deception 4 Immune System Overall Picture Innate System Adaptive System
  20. 20. Game Theoretic Models Biological Deception Multi-Cellularity Immune System An Old Debate – Goethe Protagonists: Biologist ´Etienne Geoffroy St Hilaire (1772 – 1844) and Anatomist Georges Cuvier (1769–1832) Time & Place: French Academy – 1830. Debate between Philosophical Anatomy (Geoffroy) vs. Empirical Anatomy (Cuvier) Geoffroy argued for the unity of animal kingdom. Cuvier argued for the existence of four ‘embranchments’ vertebrates, arthropods, molluscs and echinoderms. Who was right?
  21. 21. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Consider the Lobster Geoffroy’s Conjecture: The vertebrates were arthropods upside-down; flip the dorsal-ventral morphogenesis. An Anatomical Hurdle: It seems impossible to map arthropod’s ventral nerve cord to vertebrates’ dorsal system. It will be few centuries before we’d understand the role of genes in the development via control of morphogen gradient. Two genes sog and dpp (in arthropods) are flipped to the homologous pairs chordin and bmp (in vertebrates). sog in the fly, Drosophila, determines ventral development: chordin in the toad, Xenopus , determines dorsal development.
  22. 22. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Evo-Devo: Cell-level We work with an abstraction of a cell that: can (noisily) sense some kind of local information ι ∈ I, depending on the application can produce signals from a set S can sense its environment e ∈ E = NS, i.e., the multiset of signals produced by its neighbors has a state σ ∈ Σ, some form of (bounded) memory can perform actions a ∈ A depending on the application A strategy is a mapping s : Σ × I × E → Σ × 2S × A. We denote the individual components as sΣ, sS and sA.
  23. 23. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Segmentation: Some screenshots of an organism A one-dimensional organism after 0 & 100 steps. I is normalized to [0, 1]. The green line shows the morphogen gradient as currently sensed by the cells (i.e., noisy). The remaining lines depict the currently produced signals. Shaded regions depict sS after bias has been applied.
  24. 24. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Segmentation: More screenshots of an organism ... after 10000 & 15000 steps.
  25. 25. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Equilibria Separating Equilibrium: Each type t sends a different signal Mt. f S : t → a[Mt]... With two signals {BMP, Anti-BMP}, Arthropods (Protostomes) and Vertebretes (Deuterostomes) represent two different separating equilibria. Just as Geoffroy thought! Pooling Equilibrium: All types t send a single signal s∗ with probability 1 Are there examples of pooling equilibria in nature (on earth or some other exoplanet)?
  26. 26. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Hemichordates Saccoglossus kowalevskii (with a diffused CNS; nerve-nets) - Considered a Deuterstome
  27. 27. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Signaling Equilibria Phylogeny?
  28. 28. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Shifting Equilibria All the Renegade Cells Shifting Balance: Growth, Proliferation, Anoxia, Immune Resistance, Immortality, Metastasis...
  29. 29. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Outline 1 Game Theoretic Models Signaling Games Nash Equilibria Deception 2 Biological Deception Examples of Deception in Biology An Exhaustive Classification of Deception in Biology 3 Multi-Cellularity Geoffry-Cuvier Debate Cellularization: Aligning Utility Cancer & Cellular Deception 4 Immune System Overall Picture Innate System Adaptive System
  30. 30. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Sender and Receivers Sender = Dendritic Cells Receiver = Macrophage Recommenders = B Cells Verifiers = T Cells
  31. 31. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Senders (DC) and Receivers (Macrophage) Signaling with Cytokines; Acting by phagocytosis Different cytokines are produced depending on the type of dendritic cell (DC) involved. For example, the plasmocytoid dendritic cells can produce high levels of type 1 interferons (signal), which leads to the recruitment of another type of APC called a macrophage that can engulf and destroy (action) pathogens. DC’s also release cytokines that promote inflammation such as IL-12 and TNF-α.
  32. 32. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Safety: Educating the Verifiers (T Cells) The dendritic cells (DC) capture antigens from invading bodies, which they process and then present on their cell surface, along with the necessary accessory or co-stimulation molecules. Due to this ability to process and present antigens, dendritic cells are referred to as antigen presenting cells (APCs). Although all dendritic cells can perform antigen presentation to stimulate na¨ıve T cells, the different types of dendritic cells have distinct markers and different locations. In addition to their ability to activate na¨ıve T cells, dendritic cells play a role in aiding regulatory T cell differentiation and the development of T cell tolerance.
  33. 33. Game Theoretic Models Biological Deception Multi-Cellularity Immune System Liveness: Learning by Recommenders (B Cells) Variations: B cells explore recommendations (obliviously) by undergoing V(D)J recombination as they develop. Positive selection occurs through antigen-independent signaling involving both the pre-BCR and the BCR. If these receptors do not bind to their ligand, B cells do not receive the proper signals and cease to develop. Negative selection occurs through the binding of self-antigen with the BCR; If the BCR can bind strongly to self-antigen, then the B cell undergoes one of four fates: clonal deletion, receptor editing, anergy, or ignorance (B cell ignores signal and continues development). Memory: Upon antigen binding, the memory B cell takes up the antigen through receptor-mediated endocytosis, degrades it, and presents it to T cells as peptide pieces in complex with MHC-II molecules on the cell membrane. Interaction between Macrophage and B Cells (?)
  34. 34. Game Theoretic Models Biological Deception Multi-Cellularity Immune System End La fin Die Ende Shuryou Slutten Wakas Sfarsit Samapta El fin Son Ukuphela

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