Dynamics of biological switches 1. Attila Csikász-Nagy King’s College London Randall Division of Cell and Molecular Biophysics Institute for Mathematical and Molecular Biomedicine

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DNA mRNA Protein Enzyme Reaction Network Cell Physiology …TACCCGATGGCGAAATGC... …AUGGGCUACCGCUUUACG... …Met -Gly -Tyr -Arg -Phe -Thr... ATP ADP -P XYZ E1E1 E2E2 E3E3 E4E4 Last Step Systems Biology

Why we need computation in biology?

The jubilant fellow will name the wire Serendipitously Recovered Component (Src) and then find that Src is required because it is the only link between a long extendable object and the rest of the radio. The object will be appropriately named the Most Important Component (Mic) of the radio. A series of studies will definitively establish that Mic should be made of metal and the longer the object is the better, which would provide an evolutionary explanation for the finding that the object is extendable.

The cell is an information processing system How it’s regulatory network is wired? We know all/most of it’s components and some about their wiring. Do we understand how it works?

Alternative definitions of systems biology - qualitative analysis of large protein / gene networks („omics“) - detailed quantitative analysis of small systems / functional modules („bottom-up approach“) - low-precision modelling of entire cells / organisms („top-down“ approach)

Jörg Stelling (ETH Zürich)

MAPK pathway

Reactions for MAPK (K) phosphorylation by MAPKK-PP (KK-PP) and K P’ase: Differential equation for MAPK (K) level: MAPK pathway – a model 7 8 9

Role of degradation in cell cycle transitions Cdk CycB synthesis Cdk degradation “Passage through three critical cell-cycle transitions - G1 → S phase, metaphase → anaphase, and anaphase → telophase and cytokinesis - is irreversible because these transitions are triggered by the regulated degradation of proteins, an irreversible process. As a consequence, cells are forced to traverse the cell cycle in one direction only.” (p. 856)

Role of degradation in cell cycle transitions Cdk CycB synthesis Cdk degradation Cdc20 Cdk CycB

Role of degradation in cell cycle transitions Cdk CycB Cdk CycB synthesis Cdk degradation Cdc20

Role of degradation in cell cycle transitions Cdc20 Cdk CycB Cdk CycB synthesis Cdk degradation Cdc20

Role of degradation in cell cycle transitions Cdk CycB Cdk CycB synthesis

Role of degradation in cell cycle transitions Cdc20 Cdk CycB Oscillator Cdk CycB synthesis Cdk degradation Cdc20

Role of degradation in cell cycle transitions Oscillator Cdk CycB synthesis Cdk degradation Cdc20 Shishi-Odoshi

Role of degradation in cell cycle transitions Cdk CycB Cdk CycB synthesis Cdk degradation Cdc20

Role of degradation in cell cycle transitions Cdk CycB Cdk CycB synthesis Cdk degradation Cdc20

Role of degradation in cell cycle transitions Cdc20 Cdk CycB Cdk CycB Cdk Cdc20 Irreversible transitions “checkpoints of the cell cycle” positive feedback Cdh1 CKI Cdk CycB

Discrete models

2 states: 1 / 0 (on / off) (probably 0 / 1 / 2) Gene: ON / OFF Immune cell: active / inactive Neuron: firing / non-firing Network elements: (E i, i= 1,...n) „State”; S i = 1 or 0 State of the system: (S 1, S 2, S 3, S 4 ) = ( 1, 0, 1, 1) time: discrete t 1, t 2... Update: serial/parallel/random a bc abc ………

States: 0 = (0,0)1 = (0,1)2 = (1,0)3 = (1,1) serial E 1 first:serial E 2 first: parallel: Random: E1E1 E2E2 - - S 1 ’ = 1,if S 2 = 0S 2 ’ = 1,if S 1 = 0 S 1 ’ = 0,if S 2 = 1S 2 ’ = 0,if S 1 = 1 S’ : updated state Random: like serial, just randomly decided which happens first E 1 or E 2

Francois Jacob & Jacques Monod Genetic regulatory mechanisms in the synthesis of proteins Journal of Molecular Biology, 3:3 (1961)

Positive feedback Inductorpermease E 1 E 2 Two steady states:[0,0] and [1,1] Lac operon: Oscillation with negative feedbacks: + E1E1 E2E

Boolean logic + E1E1 E2E2 - E3E3 + + E 2 = 1 and E 3 = 1AND gate S 1 = 1 if E 2 = 1 or E 3 = 1OR gate { Rules: a AND ba ∙ b a OR ba + b NOT aa a + 0 = aa ∙ 0 = 0a = a a + 1 = 1a ∙ 1 = aa + a = 1 a + b = b + aa ∙ b = b ∙ a a ∙ a = 0 a ∙ (b + c) = a ∙ b + a ∙ c(a + b) + c = a + (b + c) Truth table abcaba+ca(b+c)ab+ac

λ-phage lytic or lysogenic development bacteria virus lysis prophage lytic lysogenic lysogen cro R cII D cI S rd s Regulatory network: - OR R = 1 D = r S = d + s

Kinetic logic Protein from a gene: tdtd tdtd rdsRDS D d ~~ ~~ ~~ ~ ~~ ~ Parallel update (truth table)