A Mathematical Model of Bacterial Aerotaxis - Humboldt State ...

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Keller-Segel chemotaxis model ∂b + ∂t ∂b− ∂t + v∂b+ ∂x = σ− b − − σ + b + − v∂b− ∂x = σ+ b + − σ − b − (1) (2)
Keller-Segel chemotaxis model ∂b + ∂t ∂b− ∂t + v∂b+ ∂x = σ− b − − σ + b + − v∂b− ∂x = σ+ b + − σ − b − Let b = b + + b− , J(x, t) = v(b + (x, t) − b− (x, t)), σ0 = 1 2 (σ+ + σ− ), ∆σ = 1 2 (σ+ − σ− ). (1) (2)
Page 1 and 2: A Mathematical Model of Bacterial A
Page 3 and 4: • Chemotaxis and Aerotaxis Outlin
Page 5 and 6: • Chemotaxis and Aerotaxis Outlin
Page 7 and 8: Concentration Conventional Chemotax
Page 9 and 10: Adaptation in conventional chemotax
Page 15: Keller-Segel chemotaxis model
Page 19 and 20: In small spatial gradients we can s
Page 21 and 22: In small spatial gradients we can s
Page 23 and 24: −1 Reversal frequency (s ) 0.7 0.
Page 25 and 26: Capillary size: 50 × 2 × 0.1mm Ox
Page 27 and 28: 8 7 6 5 4 3 2 1 0 −1 Dashed line:
Page 29 and 30: Modeling goals and assumptions Goal
Page 35 and 36: ∂r ∂t ∂l ∂t Our model = −
Page 37 and 38: Proton Motive Force (PMF) High left
Page 39 and 40: Proton Motive Force (PMF) High left
Page 41 and 42: Numerical results Invasion of oxyge
Page 43 and 44: 2.5 2 1.5 1 0.5 Bacteria: solid lin
Page 45 and 46: 7 6 5 4 3 2 1 Bacteria: solid line,
Page 47 and 48: 7 6 5 4 3 2 1 Bacteria: solid line,
Page 49 and 50: 10 9 8 7 6 5 4 3 2 1 d Quasi steady
Page 51 and 52: Summary of results • model suppor
Page 53 and 54: Summary of results • model suppor
Page 55 and 56: Slow adaptation Fast adapation Chem
Page 57 and 58: Thank you! Bori Mazzag Mathematics
Page 59 and 60: Equilibrium position for fast movin

A Mathematical Model of Bacterial Aerotaxis - Humboldt State ...

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