Arun S. Moorthy Investigating the colon-diet-flora system using modeling and simulation June 17th, 2015 Biophysics Interdepartmental Program, University of Guelph guts, bugs, and dietary fiber
microbiota affects health, has been a topic of significant discussion for the past several years? prevalent: Overview ▶ How diet impacts gut microbiota, and subsequently, how ▶ Many hypotheses relating microbiota state to health concerns are ▶ neural developmental disorders (autism spectrum) ▶ anxiety and depression ▶ obesity ▶ cancer
to its physical inaccessibility. digestive system through diet or exiting as feces. individuals and within a single person, posing clinical challenges. Overview ▶ The human colon is inherently difficult to investigate in vivo due ▶ Assessment is usually done using only the materials entering the ▶ Large variability exists in microbiota composition between
models maintain analytical value. x low complete x x Models B Mathematical moderate high x Reactor Systems high moderate x Animal Models Clinical Trials very high limited x x Overview Cost A Experimental Tool Microbial Host Phys- Experimental Ecology iology Control A: Cost includes financial considerations, as well as ethical concerns and experimental time. B: Mathematical models will often focus on either microbial ecology or host physiology to ensure
To design and develop a widely accessible software tool(s), grounded in physical modeling and deterministic approaches, to aid in exploring mechanical aspects of colon-diet-flora behavior through supporting the rapid design, execution and analysis of simulation experiments. Research Objectives
http://compugut.sourceforge.net
Mathematical Formulation
Model
F (1) S (2) Model φ h = µ KX + FX φ f = µ K + SX
12 4 S 1 X 1 3 Lactate utilization S 2 X 2 -1 Homoacetogenesis 4 Methanogenesis Homoacetogenesis S 3 X 3 5 Methanogenesis S 3 X 4 IpH -1 5 -1 3 13 X 1 I 1 X 4 j 1 14 For soluble components Glucose utilization 11 10 Hydrolysis For particulate components -1 I 1 X 1 2 Lactate utilization 1 X 3 8 S 2 S 1 9 pr Decay of X 4 9 7 S 4 6 5 4 3 2 1 -1 S 3 S 5 6 Glucose utilization Decay of X 1 -1 7 Decay of X 2 -1 8 -1 2 S 6 Decay of X 3 -1 Hydrolysis 1 S 9 S 8 S 7 X 2 Model Component i Kinetic Rate Process φ 1 ( c ) Y 1 , 1 φ 2 ( c ) Y 2 , 2 Y 3 , 2 Y 4 , 2 Y 5 , 2 Y 6 , 2 Y 8 , 2 Y 9 , 2 φ 3 ( c ) Y 3 , 3 Y 4 , 3 Y 5 , 3 Y 6 , 3 Y 8 , 3 Y 9 , 3 φ 4 ( c ) Y 4 , 4 Y 8 , 4 Y 9 , 4 φ 5 ( c ) Y 7 , 5 Y 8 , 5 Y 9 , 5 Component i Kinetic Rate Process φ 1 ( c ) = κ 1 K 1 X 1 + I 1 φ 2 ( c ) = κ 2 Y 11 , 2 K 2 + S 1 φ 3 ( c ) = κ 3 Y 12 , 3 K 3 + s 2 φ 4 ( c ) = κ 4 Y 13 , 4 K 3 + S 3 φ 5 ( c ) = κ 5 Y 14 , 5 K 5 + S 3 exp ( − 3 ( pH − pHU ) 2 ) if pH < pHU , pHU − pHL with IpH = if pH ≥ pHU φ 6 ( c ) = κ 6 , 1 X 1 φ 7 ( c ) = κ 7 , 1 X 2 φ 8 ( c ) = κ 8 , 1 X 3 φ 9 ( c ) = κ 9 , 1 X 4
(4) i S F i n n (3) Model P i , j = N ( P i , σ ) ∑ φ h = µ i X i F + ∑ n i K i X i ∑ φ f = µ i K i + SX i
Model
Model
methanogenic biomass 7. 14. acetogenic biomass 13. lactate utilizing biomass 12. sugar utilizing biomass 11. fiber 10. water 9. carbon dioxide 8. methane butyrate 6. propionate 5. acetate 4. hydrogen 3. lactate 2. sugar 1. materials in the colon-complex (5) Model ∂ t c + ∂ x f ( c ) = r ( c ) + e ( c ) where c = concentration of
System Details colon-complex (diet-flora-colon) 3 28-100 34 56 10 9 Model Process Model: Sub-processes: Number of State Variables: Biochemical Parameters (BP): Spatial Exchange Parameters (SEP): Physical Parameters (PP): Operation Parameters (OP):
compuGUT
compuGUT
compuGUT
compuGUT
compuGUT
Time 24 h 72 h 168 h 211.2 h 216 h Lumen Mucus Preliminary Results
nine subsequent substrates/metabolites, four biomass functional groups with up to ten subdivisions per group. result of three factors: (1) the total amount of fiber consumed, (2) the number of meals in which the fiber is distributed, and (3) the length/intensity of the meal. the measured output. diet and low-fiber diet simulation is amplified when meals are less frequent, and diminished when meals are consumed more frequently. Preliminary Summary ▶ Able to simulate a model system with primary substrate of fiber, ▶ We investigated how the colon microbiota composition varies as a ▶ The length of meal (15 minutes versus 30 minutes) has limited effect on ▶ Difference between measured output generated through a high-fiber
colon, suggesting that using single (CSTR-type) lumped assumptions may be in adequate. process proceeds, during a period of distress is tempered by having a diverse microbial community present. However, the composition of the microbial community after a distress/perturbation period is often not the same as it was prior to that period. Preliminary Summary ▶ Measurements of state variables vary along the length of the ▶ Overall system performance, judging how the anaerobic digestion
(9) A 1 V m X 2 A 2 A 1 X 1 (8) V m V l A 2 X 2 (6) (7) V l X 1 Antimicrobial Extension − γ 3 , a ∂ t A 1 + ¯ v l ∂ x A 1 = − Y a κ a ( A 1 − A 2 ) , K a + A 1 ( ) ∂ t X 1 + ¯ = Y x µ f ( S 1 , X 1 ) − + κ d + γ 1 , 1 v l ∂ x X 1 κ a K a + A 1 ( V m ) + γ 4 , 1 X 2 , + γ 3 , a ∂ t A 2 = − Y a κ a ( A 1 − A 2 ) , K a + A 2 ( ) ∂ t X 2 = Y x µ f ( S 2 , X 2 ) − κ a + κ d + γ 4 , 1 K a + A 2 ( V l ) + γ 1 , 1 X 1 ,
IpH -1 -1 Methanogenesis 5 1 Glucose utilization -1 Decay of X 4 Homoacetogenesis 10 4 S 1 X 1 9 3 Lactate utilization -1 Decay of X 3 2 I 1 X 1 -1 j X 4 X 3 X 2 X 1 A 1 I 1 -1 For soluble components SAT 15 14 13 12 11 10 -1 For particulate components S 2 X 2 Lactate utilization Hydrolysis 8 S 3 S 2 S 1 Decay of X 1 pr S 3 X 4 9 7 S 5 6 5 4 3 2 1 6 S 4 S 6 3 5 8 4 Homoacetogenesis -1 Decay of X 2 S 3 X 3 7 -1 S 7 Glucose utilization 2 Methanogenesis -1 Hydrolysis 1 S 9 S 8 1 Antimicrobial Extension Component i Kinetic Rate Process φ 1 ( c ) Y 1 , 1 φ 2 ( c ) Y 2 , 2 Y 3 , 2 Y 4 , 2 Y 5 , 2 Y 6 , 2 Y 8 , 2 Y 9 , 2 φ 3 ( c ) Y 3 , 3 Y 4 , 3 Y 5 , 3 Y 6 , 3 Y 8 , 3 Y 9 , 3 φ 4 ( c ) Y 4 , 4 Y 8 , 4 Y 9 , 4 φ 5 ( c ) Y 7 , 5 Y 8 , 5 Y 9 , 5 Component i Kinetic Rate Process φ 1 ( c ) = κ 1 K 1 X 1 + I 1 φ 2 ( c ) = κ 2 Y 11 , 2 K 2 + S 1 φ 3 ( c ) = κ 3 Y 12 , 3 K 3 + s 2 φ 4 ( c ) = κ 4 Y 13 , 4 K 3 + S 3 φ 5 ( c ) = κ 5 Y 14 , 5 K 5 + S 3 exp ( − 3 ( pH − pHU ) 2 ) if pH < pHU , pHU − pHL with IpH = if pH ≥ pHU φ 6 ( c ) = κ 6 , 1 X 1 φ 7 ( c ) = κ 7 , 1 X 2 φ 8 ( c ) = κ 8 , 1 X 3 φ 9 ( c ) = κ 9 , 1 X 4 φ A , 1 ( c ) Y 11 , 10
designed to resemble a pre-treatment flora is consumed compliment consumed for a total period of 10 days 7 3 Same as control, except following antibiotic treatment (day 20) - 2 g/d of a generic probiotic supplement are consumed for a total period of 20 days 8 4 Same as control, except following antibiotic treatment (day 20) - a single 40 g dosage of a generic probiotic supplement is consumed 9 Flora re- 1 2 Same as control, except following antibiotic treatment (day 20) - 2 g/d of a probiotic supplement designed to resemble a pre-treatment flora are consumed for a total period of 10 days 10 2 Same as control, except following antibiotic treatment (day 20) - 4 g/d of a probiotic supplement designed to resemble a pre-treatment flora are consumed for a total period of 10 days 11 3 Same as control, except following antibiotic treatment (day 20) - 2 g/d of a probiotic supplement designed to resemble a pre-treatment flora are consumed for a total period of 20 days 12 4 Same as control, except following antibiotic treatment (day 20) - a single 40 g dosage of a probiotic supplement Same as control, except following antibiotic treatment (day 20) - 4 g/d of a generic probiotic supplement are 6 10 days 2 1 compuGUT is initially simulated for 14 days with standard diet from default initial conditions. After initial period, system receives 2.5 mL of targeted antibiotic ever 4 hours for 5 days. After day 20, system is simulated at standard operating conditions for 312 days (recovery). 2 Fiber 1 Same as control, except following antibiotic treatment (day 20) fiber intake is increased to 40 g per meal for total period of 10 days 3 Same as control, except following antibiotic treatment (day 20) fiber intake is increased to 80 g per meal for 1 10 days 4 3 Same as control, except following antibiotic treatment (day 20) fiber intake is increased to 40 g per meal for 20 days 5 Competitive Culture 1 except following antibiotic treatment (day 20) - 2 g/d of a generic probiotic supplement are consumed for a Control Antimicrobial Extension Sim Category Case Description No.
Antimicrobial Extension
locations in eliminating the targeted biomass strain, alter the long-term composition of the microflora if there is no external intervention. of recovery after an unwanted shift in flora composition. Antimicrobial Summary ▶ Simulation results suggest: ▶ Dynamic effect of antimicrobial treatment varies between colon ▶ Low dosages and short duration treatment regimes, though ineffective ▶ Probiotic-type intervention may be an effective method to improve rate
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