And so on 15 additional constraints physicochemical

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and so on …
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15 Additional constraints: Physicochemical constrains Osmotic Pressure Equilibrium (i nterior & e xterior, m chem. species) Electroneutrality (z = charge, C oncentration) m j ej ej m j ij ij e i C RT C RT 1 1 0 0 1 1 m j ej ej m j ij ij C z C z
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16 RBC steady-state in vivo vs calculated K PG23 GAP PG2 ATP PEP LAC PYR Na F6P ADP G6P FDP AMP PRPP ADO DHAP GSH 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 |dev/sd| |dev/av| |obs-calc| = Y sd(obs) X= metabolites (ordered by Y)
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17 -1 A+B = Constant A B K A B = K A B A&B dynamically independent A B Circular motion A B Return to steady state Phase plane diagrams: concentration of metabolite A vs B over a specific time course 1: conservation relationship. 2: a pair of concentrations in equilibrium 3: two dynamically independent metabolites 4: a closed loop trace 1 2 3 4
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18 Red 0 hours Green 0.1 Blue 1.0 Yellow 10 End 300 1 hours 300 hours ATP load Redox load ATP & Redox loads
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19 0 to 300 hour dynamics 34 metabolites calculated Redox Load ODE model Jamshidi et al. 2000 (Pub)
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20 RBC Metabolic “Machinery” Glucose Glycolysis Pyruvate Lactate ATP Nucleotide Metabolism PPP NADPH NADH 2,3 DPG Transmembrane Pumps Maintenance & Repair Oxidants Hb Met Hb 2,3 DPG HbO 2 O 2
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21 Cell Division Cycle G2 arrest to M arrest switch .
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22 Hill coefficients Response R = 1 1+(K/S) H H simple hyperbolic = 1 H (R=HbO 2 , S=O 2 ) sigmoidal = 2.8 H (R=Mapk-P, S=Mos) = 3 H (R=Mapk-P, S=Progesterone in vivo) = 42 .
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23 Progesterone AA Mos Mos-P Mek Mek-P Mapk Mapk-P k 1 k 2 k -1 k -2 “The biochemical basis of an all-or-none cell fate switch in Xenopus oocytes.” Science 1998;280:895-8 Ferrell & Machleder, (Pub) positive (a chain of enzyme modifiers close to saturation generate higher sensitivity to signals than one enzyme can)
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24 Net1: Today's story & goals Macroscopic continuous concentration rates Cooperativity & Hill coefficients Bistability Mesoscopic discrete molecular numbers Approximate & exact stochastic Chromosome Copy Number Control Flux balance optimization Universal stoichiometric matrix Genomic sequence comparisons
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25 Arkin A, Ross J, McAdams HH Genetics 1998 149(4):1633. Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected E. coli cells. Variation in level, time & whole cell effect
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26 Efficient exact stochastic simulation of chemical systems with many species & many channels "the Next Reaction Method, an exact algorithm ...time proportional to the logarithm of the number of reactions, not to the number of reactions itself". Gibson & Bruck, 1999; J. Physical Chemistry. (Pub) Gillespie J.Phys Chem 81:2340-61. 1977. Exact stochastic simulation of coupled chemical reactions
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27 Utilizing Noise Hasty, et al. PNAS 2000; 97:2075-2080, Noise-based switches and amplifiers for gene expression (Pub) Bistability ... arises naturally... Additive external noise [allows] construction of a protein switch... using short noise pulses. In the multiplicative case, ... small deviations in the transcription rate can lead to large fluctuations in the production of protein”. Paulsson, et al. PNAS 2000; 97:7148-53. Stochastic focusing: fluctuation-enhanced sensitivity of intracellular regulation. (Pub) (exact master equations)
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