Cell Quota Based Population Models and their Applications Aaron Packer School of Mathematical & Statistical Sciences Arizona State University November 17, 2014 A. Packer Cell Quota Based Models + Applications Nov 17, 2014 1 / 72
Outline Introduction 1 Neutral Lipid Synthesis in Green Microalgae 2 Introduction Model Results Conclusion Applications to Stoichiometric Producer-Grazer Models for Aquaculture 3 Introduction Model Equilibria Linear Functional Response Holling Type II Functional Response Prostate Cancer and Androgen Deprivation Therapy 4 Mechanistic derivation Uptake Single population model Results Future Work A. Packer Cell Quota Based Models + Applications : — 2 / 72
Introduction Introduction 1 Neutral Lipid Synthesis in Green Microalgae 2 Introduction Model Results Conclusion Applications to Stoichiometric Producer-Grazer Models for Aquaculture 3 Introduction Model Equilibria Linear Functional Response Holling Type II Functional Response Prostate Cancer and Androgen Deprivation Therapy 4 Mechanistic derivation Uptake Single population model Results Future Work A. Packer Cell Quota Based Models + Applications : — 3 / 72
Introduction Cell Quota Model In 1968, phycologist M.R. Droop published his famous discovery on the functional relationship between growth rate and internal nutrient status of algae in chemostat culture. � � 1 − q µ ( Q ) = µ m Q Q : cell quota (nutrient/biomass) q : subsistence quota µ m : maximum specific growth rate A. Packer Cell Quota Based Models + Applications : — 4 / 72
Introduction Cell Quota Model, cont’d � � 1 − q µ ( Q ) = µ m Q Leadbeater, B., “The ‘Droop Equation’–Michael Droop and the legacy of the ‘Cell- Quota Model’ of phytoplankton growth”, Protist 157 , 3, 345 (2006). A. Packer Cell Quota Based Models + Applications : — 5 / 72
Introduction Summary Problems Why do certain oleaginous algae produce so many neutral lipids, and how can their cultivation for biofuels be improved? What role does ammonia- (and to lesser extend nitrite-) induced toxicity play in the dynamics of producer-grazer systems for aquaculture? Can cell-quota based population models be applied to prostate cancer in a mechanistic way? Solutions The nitrogen cell quota quantifies the metabolic shift to neutral lipids in green microalgae and gives rise to a mechanistic modeling framework. Nitrogen toxicity can be modeled by adding new feedback into producer-grazer systems with nutrient recycling. A mechanistically derived model follows naturally via application of the “cell quota” concept to androgens. A. Packer Cell Quota Based Models + Applications : — 6 / 72
Introduction Summary Problems Why do certain oleaginous algae produce so many neutral lipids, and how can their cultivation for biofuels be improved? What role does ammonia- (and to lesser extend nitrite-) induced toxicity play in the dynamics of producer-grazer systems for aquaculture? Can cell-quota based population models be applied to prostate cancer in a mechanistic way? Solutions The nitrogen cell quota quantifies the metabolic shift to neutral lipids in green microalgae and gives rise to a mechanistic modeling framework. Nitrogen toxicity can be modeled by adding new feedback into producer-grazer systems with nutrient recycling. A mechanistically derived model follows naturally via application of the “cell quota” concept to androgens. A. Packer Cell Quota Based Models + Applications : — 6 / 72
Introduction Summary Problems Why do certain oleaginous algae produce so many neutral lipids, and how can their cultivation for biofuels be improved? What role does ammonia- (and to lesser extend nitrite-) induced toxicity play in the dynamics of producer-grazer systems for aquaculture? Can cell-quota based population models be applied to prostate cancer in a mechanistic way? Solutions The nitrogen cell quota quantifies the metabolic shift to neutral lipids in green microalgae and gives rise to a mechanistic modeling framework. Nitrogen toxicity can be modeled by adding new feedback into producer-grazer systems with nutrient recycling. A mechanistically derived model follows naturally via application of the “cell quota” concept to androgens. A. Packer Cell Quota Based Models + Applications : — 6 / 72
Neutral Lipid Synthesis in Green Microalgae Introduction 1 Neutral Lipid Synthesis in Green Microalgae 2 Introduction Model Results Conclusion Applications to Stoichiometric Producer-Grazer Models for Aquaculture 3 Introduction Model Equilibria Linear Functional Response Holling Type II Functional Response Prostate Cancer and Androgen Deprivation Therapy 4 Mechanistic derivation Uptake Single population model Results Future Work A. Packer Cell Quota Based Models + Applications : — 7 / 72
Neutral Lipid Synthesis in Green Microalgae Introduction Outline Introduction 1 Neutral Lipid Synthesis in Green Microalgae 2 Introduction Model Results Conclusion Applications to Stoichiometric Producer-Grazer Models for Aquaculture 3 Introduction Model Equilibria Linear Functional Response Holling Type II Functional Response Prostate Cancer and Androgen Deprivation Therapy 4 Mechanistic derivation Uptake Single population model Results Future Work A. Packer Cell Quota Based Models + Applications : — 8 / 72
Neutral Lipid Synthesis in Green Microalgae Introduction Motivation Theoretical Why do certain species of green microalgae produce such large quantities of neutral lipids, particularly triacylglycerols, during stressed conditions? Mathematical Is a mechanistic model possible, and what insight can be gained? A. Packer Cell Quota Based Models + Applications : — 9 / 72
Neutral Lipid Synthesis in Green Microalgae Introduction Motivation Theoretical Why do certain species of green microalgae produce such large quantities of neutral lipids, particularly triacylglycerols, during stressed conditions? Compensate for lack of electron/carbon sink during uncoupling of photosynthesis from growth. Transient energy storage during stressful times Mathematical Is a mechanistic model possible, and what insight can be gained? A. Packer Cell Quota Based Models + Applications : — 9 / 72
Neutral Lipid Synthesis in Green Microalgae Introduction Motivation Theoretical Why do certain species of green microalgae produce such large quantities of neutral lipids, particularly triacylglycerols, during stressed conditions? Compensate for lack of electron/carbon sink during uncoupling of photosynthesis from growth. Transient energy storage during stressful times Mathematical Is a mechanistic model possible, and what insight can be gained? Yes! Mechanistic modeling helps validate current theory explaining the NL phenomenon in oleaginous algae A. Packer Cell Quota Based Models + Applications : — 9 / 72
Neutral Lipid Synthesis in Green Microalgae Introduction Key Observations - Nitrogen & Light Nitrogen Starvation Increases neutral lipid synthesis. Decreases cellular growth and production of non–neutral lipid biomass. Decreases capacity of certain mechanisms that prevent and repair both photoinhibition and photooxidation. Light Intensity Increasing light intensity... Increases neutral lipid synthesis. Increases susceptibility to photoinhibition and photooxidation. A. Packer Cell Quota Based Models + Applications : — 10 / 72
Neutral Lipid Synthesis in Green Microalgae Introduction Key Observations - Nitrogen & Light Nitrogen Starvation Increases neutral lipid synthesis. Decreases cellular growth and production of non–neutral lipid biomass. Decreases capacity of certain mechanisms that prevent and repair both photoinhibition and photooxidation. Light Intensity Increasing light intensity... Increases neutral lipid synthesis. Increases susceptibility to photoinhibition and photooxidation. A. Packer Cell Quota Based Models + Applications : — 10 / 72
Neutral Lipid Synthesis in Green Microalgae Introduction Key Observations - Nitrogen & Light Nitrogen Starvation Increases neutral lipid synthesis. Decreases cellular growth and production of non–neutral lipid biomass. Decreases capacity of certain mechanisms that prevent and repair both photoinhibition and photooxidation. ց ր ⇒ NLs are defense from the dangers of photosynthesis–growth uncoupling Light Intensity Increasing light intensity... Increases neutral lipid synthesis. Increases susceptibility to photoinhibition and photooxidation. A. Packer Cell Quota Based Models + Applications : — 10 / 72
Neutral Lipid Synthesis in Green Microalgae Introduction Case Study: Pseudochlorococcum sp. (Li et al. 2011) 0.25 8 100% 7 25% 0.2 0% 6 5 0.15 100% g N/L g/L 25% 4 0% 0.1 3 2 0.05 1 0 0 2 4 6 8 10 0 2 4 6 8 10 12 days days Figure 1: Extracellular N Figure 2: Biomass 100% culture: 0.24 g N L -1 . 25% culture: 0.06 g N/L. 0% culture: 0.0 g N L -1 . Li, Y., D. Han, M. Sommerfeld, and Q. Hu. “Photosynthetic carbon partitioning and lipid production in the oleaginous microalga Pseudochlorococcum sp. (Chlorophyceae) under nitrogen-limited conditions.” Bioresource Technology 102 , 1 (2011): 123–129. A. Packer Cell Quota Based Models + Applications : — 11 / 72
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