Example models for ruminant

digestion and metabolism

Heidi Rossow, PhD

UC Davis School Of Veterinary Medicine,

VMTRC Tulare, CA

Intro to Molly

Representation of milk production

Short demo using BST

Exercise

WEBSITE:

http://www.vmtrc.ucdavis.edu/laboratories/metabolic/molly.cfm

Publications:Baldwin RL, France J, Gill M. 1987. Metabolism of the lactating cow I-III.

J Dairy Research 54:77-145.

Baldwin RL. 1995. Modeling ruminant digestion and metabolism.

Chapman & Hall:London.

Johnson HA, Maas JA, Calvert CC, Baldwin RL. 2008. Use of computer

simulation to Teach systems approach to Nutrition and Metabolism.

JAS 86:483-499

Neal & Thornley 1983 J Ag Sci Cambridge 101:389-400

OBJECTIVE

Bridge gap between basic knowledge

of cow digestion and metabolism,

and animal performance

Nutrients

Milk

Nutrients

Digestion

Absorption

Metabolism

Reproduction Genetics

Environment

Management

Health

State Variables

Animal Element

Amino acids

(Lys His Met/Cys Other)

Glucose

Acetate

Fatty Acids

Adipose TG

Body Protein

Visceral Protein

Uenz

Milk lactose

Milk Protein

Milk Fat

Milk

Digestive ElementLarge Particles

Small Particles

Microbes

Rumen VFAs

DMI

Soluble Ash

Cellulose

Hemicellulose

Soluble, Insoluble Protein

Soluble Carbohydrates

Alpha, Beta Hexoses

Total Absorbed

Amino Acids (TAbsAa)

Absorbed

Propionic Acid (AbsPr)

Absorbed

Glucose (AbsGl)

Absorbed

Acetate (AbsAc)

Absorbed

Fatty Acids (AbsFa)Butyrate

(AbsBu)

ABSORBED NUTRIENTS

Oxidation

(BuCd)

O2

CO2

Plasma Total Amino Acids (TAa)

Made up of His, SAa, Lys, Other Aa (Aa)

Body Protein

(Pb)Visceral Protein

(Pv)

Ammonia (Am)

Urea

MILK

Protein (Pm) Lactose (Lm) Triacylglyceride (Tm)

Saliva

Pregnancy

(PRG)

Plasma Glucose

(Gl)

Oxidation

(PrCd)

O2

CO2

UreaTAaDEG TAaGlV

PrGlV

Absorbed

Lactate (AbsRLa)

Lactate in Body

(LaGlB)

Lactate in Adipose

(LaGlF)

LaGlV

LaGlV

O2

CO2

O2

CO2

Lactate in Gut

(GGlLa)

GlLmV

Storage Triglyceride (Ts)

Triose Phosphate (TpF), NADPH2 (HyF),

Fatty Acids (TsF)

Viscera

Triose Phosphate (TpV)

NADPH2 (HyV)

Oxidation

(GlCd)

O2

CO2

TAaPm, TAaLAV

Plasma Acetate

(Ac)

Oxidation

(AcCd)

O2

CO2

Glycerol

(Gy)

GlHyV GlTpV

GyGlV

TAaSal

TAaPbB

TPbAaB

TAaPvV

TPvAaV

TAaPRG

TAaAcTAaDEG

AcTsFGlTpF GlHyF

GlLaB

Plasma Fatty Acids

(Fa)

TsFaF

AcTmV FaTmV

Oxidation

(FaCd)

O2

CO2

Urea

O2

CO2

NADPH2

CO2

NADPH2

FaTsF

TpTmV

UpGl

Equations

dFa/dt = absFa + TsFaF1

-FaTsf – FaTmV – FaCd

Units = Mol/d

Integrate dFa/dt = Mol Fa

cFa = Fa / Blood volume

= Mol/L

dAc/dt = absAc + TAaAc

-AcTsF – AcTmV - AcCd

0

0.5

1

1.5

2

2.5

3

0 0.005 0.01 0.015 0.02

[S]

U (

mo

l/d

) Baseline

V

k

Example: U = Vm / (1 + Km/[S])

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.002 0.004 0.006 0.008 0.01

[S]

Ac

Tm

V

[Ac]

[Gl]

AcTmV = VAcTmV

*uenz*Kminh*INS

/(1.0+kAcTmV

/[Ac] + k1AcTm

/[Gl])

AV Difference (Mammary)

Miller et al., 1991

AV Difference (Mammary)

Miller et al., 1991

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.002 0.004 0.006 0.008 0.01

[S]

Ac

Tm

V

[Ac]

[Gl]

AcTmV = VAcTmV

*uenz*Kminh*INS

/(1.0+kAcTmV

/[Ac] + k1AcTm

/[Gl])

Representation of milk production

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

0 500 1000 1500 2000 2500 3000

UCELLS

To

tal M

ilk 3

08 d

ays (

kg

)

DDMIN=15

DDMIN=19

DDMIN=23

DDMIN=27

Molly Milk Production vs. DMI

Potential milk = UCELLS

Molly milk production assumptions

1. Lactose is 4.8% of milk yield

2. Lactose production is dependent on

a-lactalbumin production

3. Relative proportion of milk fat from de

novo (Ac) and body, diet (Fa) are 50/50

4. Milk protein yield is determined by

limiting amino acid theory.

duenz = usyn - udeg

usyn = Vusyn*UCELLS*Lhor*BST/

(kusyn+Lhor*BST)

udeg = uenz*(Kudeg + KudegM*

((umave/Kmdeg)10

/(1+umave/Kmdeg)10

))

= retained milk effects

Lhor is integrated

Neal & Thornley 1983 J Ag Sci Cambridge 101:389-400

Representation of milk production

duenz = usyn - udeg

Milk Components

1. GlLmV = VGlLmf

*(VAaLA

*uenz*kminh/

(1+((kAaLA

/[Aa])EXP

))/fLAAa

2. FaTmV = VFaTmV

*uenz*INS*kminh/

(1+kFaTmV

/[Fa]+k1FaTm

/[Gl])

3. AcTmV = VAcTmV

*uenz*INS*kminh/

(1+kAcTmV

/[Ac]+k1AcTm

/[Gl])

4. AaPmV1 = VAaPm

*uenz*kminh/

(1+(kAaPm

/[Aa])EXP

)/fPmAa

GlLmV = VGlLmf

*(VAaLA

*uenz*kminh/

(1+((kAaLA

/[Aa])EXP

))/fLAAa

0

0.001

0.002

0.003

0.004

0.005

0.006

0 0.002 0.004 0.006 0.008 0.01

cAa

GlL

m

FaTmV = VFaTmV

*uenz*INS*kminh/

(1+kFaTmV

/[Fa]+k1FaTm

/[Gl])

0

1

2

3

4

5

6

0 0.002 0.004 0.006 0.008 0.01

[S]

FaT

mV

[Fa]

[Gl]

[Fa], Uenz

[Gl], Uenz

AcTmV = VAcTmV

*uenz*INS*kminh/

(1+kAcTmV

/[Ac]+kAcTm

/[Gl])

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.002 0.004 0.006 0.008 0.01

[S]

Ac

Tm

V

[Ac]

[Gl]

AaPmV1 = VAaPm

*uenz*kminh/

(1+(kAaPm

/[Aa])EXP

)/fPmAa

Demo using BST

1. Control

Go until day 308

Diet1

BST 1.0

Save data….

Model load

Model reset to T=0

Model run

2. BST lactation

Go until day 70

Diet1

BST 1.0

Save data….

Model reset to T=0

Model run

Demo using BST

3. Give BST

Go until day 308

Diet1

BST 3.0

Save data….

Model Continue

View Plot

Dmilk

Dmlktm

dmlkpm

Demo using BST

Results

Modeling ExerciseAdjust ucells to match the cow’s milk production

Total milk = 10042, total fat=355, total protein=293

iBW = 550, fBW=612, tot DMI=6197

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0

10

20

30

40

50

60

0 50 100 150 200 250

kgkg

DIM

DMILK

DDMin

DMlkTm

DMlkPm

Modeling Exercise

Screen clipping taken: 6/17/2017 6:54 PM

Modeling Exercise - Solution

Modeling Exercise - Solution

Thanks…

http://www.vmtrc.ucdavis.edu/laboratories/metabolic/molly.cfm