Rumen Modeling:

Rumen Input-Output

Balance Models ~ J. R. REICHL ~ and R. L. BALDWIN Department of Animal Science University of California, Davis 95616

ABSTRACT

Two models of rumen fermentative relationships expressed as systems of simultaneous linear equations and based on requirements for maintenance of balances of elementary input and output and metabolic pathways are presented in matrix format consistent with solution by linear programs. Matrix entries defining the two models were verified carefully based upon a survey of the literature, and conceptual bases of the models were validated by comparisons of model outputs with experimental data not used in model construction. The models then were used to evaluate interactions among feed composition, volatile fatty acid yields and patterns, microbial growth yields and efficiencies, and microbial metabolic pathways. INTRODUCTION

Rapid accumulation of data regarding physiological and metabolic processes of animals requires construction of quantitative models for efficient use of data in selection and design of experiments and for evaluation and explanation of experimental results. Complexity of the animal and uses of quantitative data vary with each type of problem, indicating a need for several mathematical and computer techniques in constructing properly descriptive, useful, and inclusive quantitative models. Calculations by hand of overall balances for metabolic systems and of patterns of metabolite flow (flux) via alternate pathways within the constraints of experimental data are laborious, subject to error, and usually lead to

Received April 5, 1974. 1This research was supported in part by USPHS Grant AMO7672~ 2Present address: Department of Animal Nutrition, Hohenheim University, 7000 Stuttgart 70, Germany.

formulation of only one of several feasible solutions (5, 27). Computations of optimum or most efficient relationships among rumen microbes (27, 28), among metabolic pathways (5), and between ruminant digestive and metabolic functions are expensive to compute iteratively in dynamic simulation models. These several problems suggest that linear programming techniques which provide for computation of balance and flux patterns for complex systems of linear equations, for computation of alternate feasible solutions, and for computation of optimum relationships within or among metabolic (or other) functions, might be useful in quantitative modeling. Quantitative models of rumen fermentation are presented in this paper. They provide a means for computation of elemental balances and balances among metabolic pathways based on experimental observations specified as constraints on the right hand side (RHS) of the linear programming matrix. Entries in the matrixes of the models are based upon experimental data and were validated further by comparing computed balance relationships with data obtained in a detailed balance study published separately (22). In addition, due to current interest in relationships between microbial growth yields and balances among other products of digestion, these relationships were evaluated by the models. The proposed use of linear programming for computation of balances for rumen fermentation is trivial since other computerized methods for solving simultaneous linear equations are available. Optimization capacity of linear programming is not used, i.e., equal weightings are specified for all terms in the objective function. We elected linear programming for computing balance relationships because we wished the models in computing balance relationships to be compatible in format with more complex models which can be used to evaluate optimum digestive or animal metabolic relationships. These latter applications of linear programming will be discussed in subsequent papers.

879

880

REICHL AND BALDWIN MODELING PROCEDURE

Assumptions of microbial cell compositions are central because they influence not only estimates of elementary balances in the rumen but also the quantitative contributions of single synthetic equations. They also affect predicted balances of fermentation products. Compositions of rumen microbes in the models agree with the literature (21, 23, 26, 32, 36) but differ from high lipid (25%) and low carbohydrate (8%) compositions found by Hoogenraad and Hird (17). We considered storage polysaccharide in protozoal ceils but not in bacterial cells because our 10% for nitrogen content of bacterial cells is close to the 10.5% which is usually used as a basis for estimating bacterial storage polysaccharide (19). Our 20.16% for total bacterial polysaccharide is close to the 18% reserve polysaccharide reported for continuous cultures and differs from 35% reported for batch cultures. Both of these values were reported for Ruminococcus albus by Hungate (19). Weller (36), in dry tureen bacteria, found 9.3 to 12.4% nitrogen and in dry rumen protozoa 3.8 to 7.9% nitrogen. There is considerable nucleotide nitrogen in microbial cells, and nitrogen occurs also in lipid fractions. From our calculations, a factor of 5.45 instead of 6.25 should be used to calculate microbial protein from nitrogen content. The factor 6.25 is valid for most plant cells but not microbial

Two rumen models are described in the paper, elementary balance and pathway balance. Model of Rumen Elemental Balance

This model is based on elementary compositions of microbial cells, of digestible feed nutrients, and of fermentation products. Composition of rumen bacterial and protozoal dry cells is in Table 1. Without storage polysaccharide protozoa composition was considered the same as bacteria. Nucleic acid content was based on data of Smith (32). Lipid content was calculated from values reported by Allison et al. (2) on the proportional incorporations of radioactive isovalerate into protein and lipid in rumen bacteria. The elementary composition of microbial protein (average amino acid) was calculated from data of Purser and Buechler (26) for pure strains of rumen bacteria. For calculation of elemental composition of microbial nucleic acid, an average of compositions of AMP, CMP, GMP, and UMP was used. Calculation of microbial lipid composition is based approximately on analytical data of Abraham (1) and reflects a generalized composition of 20% of phospholipid with palmitate, a branched fatty acid, and serinophosphate.

TABLE 1. Calculated compositions of rumen microbes and their components.

Protein

Bacteria or protozoa Protozoa + storage polysaccharide Molecular weight

54.46

9,08

38.81 115

6.47 322

Bacteria or protozoa Protozoa + storage polysaccharide C H O N S P

Nucleic Acid

.474

.028

.338

.020

5.04 7.59 1.77 1.25 .03 ...

Journal of Dairy Science Vol. 58, No. 6

9.05 12.0 7.0 3.8 . . 1.0

Polysacch.

Lipid

(g/lO0 g dry cells) 20.16 43.10 162 (mol/lOO g cells) ,124

.

.

4.76

8.22 614

3.39

.013

(atoms/tool) 6.0 10.0 5.0 . . . . . . . . . . .

11.54

.019

.266

.

.

Ash

30.2 55.8 10.0 8 8

RUMEN MODELING cells because of their high nucleic acid content. Using 5.45 with Weller's (36) nitrogen values, estimates of 50.7 to 67.6% protein in bacterial and 20.7 to 43.1% protein in protozoal cells are obtained. These are consistent with assumed compositions in Table 1. The elementary composition in Table 1 is similar to that computed independently by Henderickx et al. (14). The input matrix for the model of elementary balance is in Table 2. The objective in setting up the matrix was to enable computation of input (nutrients fermented or converted in the rumen) from complete or partial experimental data on output. We accomplished this by assigning negative values to matrix entries describing rumen inputs (diet carbohydrate, diet protein, diet lipid, water, and diet or secreted urea). We then assigned positive values to matrix entries describing rumen outputs (ammonia, protozoa, bacteria, acetate, propionate, butyrate, valerate, carbon dioxide, and methane) and specified the input ( - ) must equal o u t p u t (+) on the right hand side by imposing the constraint equal zero, for the C, H, O, and N rows. The remainder of the matrix is constructed to equate (entries of 1.0) column values for the products with corresponding row values, e.g., C2 = acetate, etc. This enables exact specification of amounts of products formed as constraints (BHS). All values in the table are tool except the elemental compositions for protozoa and bacteria which are mol/100 g dry weight of cells with the phosphate contents of the protein and lipid fractions subtracted. Matrix values for columns PROTO and BACT (Table 2) are sums of products obtained by multiplying mol/100 g cells (Table 1) times atoms per mol (Table 1) of C, H, O, and N. Thus, the BHS specification of 2.0 for bacterial growth (CBACT) indicates that 200 g of bacteria were produced in the example in the matrix. No preference for components of diet is specified in the objective statement (Z), and exact requests were set for all products. Under these conditions no slack exists in the solution and an exact, required balance between inputs and outputs is computed whether specification of RHS for objective functions is maximized or minimized. The elementary compositions for feed components (Table 2) were calculated as: alfalfa protein (average amino acid) was calculated from the data of Wilson and Tilley (37); lipid

881

composition of feed was based approximately on the data of DiCostanzo et al. (10) for forage lipid (13.3% of phosphotipid, 33.3% of triglyceride, and 53.3% of monoglyceride - glycerides mostly with linolenic acid, phospholipid with lecithin); and feed carbohydrates were 50% each of hexose and pentose. Urea secretion into the rumen and formation of fermentation end-products also are represented in the matrix. The program used to compute the elementary balance was ALPSI (Burroughs Co.; AA 924 386) with the maximization feature. No preference in the objective function was used in the model. Computation was accomplished by setting exact requests on the RHS of the matrix. In Table 2 is an example RHS wherein constraints on all products and on protein input were made. Other inputs were calculated by computer. Model of Rumen Pathways Balance

This model is based on calculation of biosynthetic and fermentation equations for rumen microbiota. Equations for synthesis of microbial nucleic and amino acids are based on metabolic pathways published by Dawes and Large (9). The technique of calculation was essentially the same as used before (4, 5) with the differences that no additional carbohydrates were used to provide carbon dioxide and formate. Synthesis of average nucleic acid 1.5 hexose + 10.0 ATP + 3.8 NH 3 + 2.7 NAD + .5 HCOOH -+ nucleic acid + 10.0 ADP + 2.7 NADH 2 Synthesis of average amino acid .535 hexose + .714 ATP + .271 BCFA + 1.25 NH 3 + .03 H2S + .208 NADH 2 + .383 CO2 ~ amino acid + .714 ADP + .208 NAD Three possibilities for lipid synthesis are considered: Lipid synthesis from glucose 5.7 hexose + 2.4 ATP + 1.0 BCFA + .8 NH 3 + 2.2 NAD ~ lipid +2.4 ADP + 2.2 NADH 2 + 9.6 CO 2 ; Journal of Dairy Science Vol. 58, No. 6

882

REICHL AND BALDWIN Lipid synthesis from acetate

.9 hexose + 21.6 ATP + 9.6 acetate + 1.0 BCFA + .8 NH 3 + 17.0 NADH 2 ~ lipid + 21.6 ADP + 17.0 NAD; and, Lipid synthesis from fatty acid .9 hexose + 4.8 ATP + 1.2 FA + 1.0 BCFA + .8 NH 3 + .2 NADH 2 ~ lipid + 4.8 ADP + .2 NAD Equations for amino acid (AA) uptake (.5 ATP/average AA), for protein synthesis from AA (5.0 ATP/average AA) and for polysaccharide synthesis (2.0 ATP/polysaccharide) were used as published before (4, 5). Equations for the model of complete pathways balance are in matrix format in Table 3. The objective of this model was the same as that for the model of elementary balance as described above, i.e., to enable computation of balances among biosynthetic and fermentative rumen microbial metabolic pathways based on our knowledge of metabolic pathways and experimental data on diets and products of fermentation (specified RHS). All values in the model are in tool except for biosynthetic reactions as specified on the RHS which were set to yield the amount of each cell component in 100 g of dry microbial cells. Thus, in the example RHS in Table 3, the 1.0 request for NASYNT specifies the synthesis of the amount of nucleic acid in 100 g of dry microbial cells; this is 9.08 g or (9.08/322) .028 tool as calculated from data in Table 1. To simplify the matrix resulting from conversion of the biosynthetic pathway equations to matrix entries, HCOOH was equal to H 2 + CO 2 ; H 2 was equal to NADH2; and ATP was equal to the ~ P which distinguishes it from ADP. As an example of how matrix entries for biosynthetic process were calculated, values for the NAS column are calculated below: Equation for synthesis of average nucleic acid (above) x .0281 = .042 hexose + .281 ATP + .107 NH 3 + .076 NAD + .014 HCOOH (= .014 H 2 + .014 CO2) -+ .0281 nucleic acid + .281 ADP + .076 NADH2; at ATP -- ADP = % P (notated as ATP as is common) and NADH 2 -- NAD = H2; this equation simplifies to --.042 hexose Journal of Dairy Science Vol. 58, No. 6

(= + .042 carbohydrate uptake) - . 2 8 1 ATP --.017 NH 3 --.014 CO2 ~ 1.0 (.0281mol) NASYNT + .062 (.076 -- .014) H2 . Coefficients for this revised equation agree with those in matrix Column 1 (Table 3). Similar simplifications were made in computing matrix entries for the other (AAS etc.) columns. The matrix values of 2.11 (1/.473) and 8.065 (1/.124) were used to equate AAUPT and AAU and CAPOLY and CAP, respectively, in the matrix because AAUPT and CAPOLY are specified in moll100 g cells. This was done so that computed utilizations of diet protein and carbohydrate for microbial growth would be output as column values in mol used for microbial growth instead of as moll100 g cells. The METHB column accommodates both formation of methane from CO2 and H 2 and growth of methanobacteria. Thus, the entries in the METHB column represent the sum of biosynthesis equations for all cell components with CO2, ACET, and BCFA as carbon sources plus the equation for reduction of CO2 to CH 4 by H 2 (5, 27). An implicit assumption was that one ATP is formed per tool of CH 4 formed. The exact amount of methanobacterial growth computed to occur can vary dependent upon availability of nutrients for growth and H 2 availability as determined by amounts of fermentative products formed by and growth yields of other organisms. This is achieved by setting the RHS constraint for methane at > 0 in the example RHS of Table 3. Alternately, an exact request for methane can be imposed if appropriate data are available for a given experiment for which one desires to compute a balance. A new equation for fermentation of a tool of average amino acid of alfalfa (AAF) was calculated by taking a weighted average of the fermentation products formed from the individual amino acids (5). The equation for carbohydrate fermentation (CAF) provides simply for the conversion of carbohydrate to pyruvate, NADH 2 [set equal to H 2 as described above to simplify the matrix; this can be justified on the basis of experimental data (4, 5)] and ATP (~P). In specific tests, the column for the phosphoketolase pathway (CA5F) was used to evaluate effects of this alternate pathway of carbohydrate fermentation in the rumen. The stoichio-

T A B L E 2. M a t r i x f o r r u m e n e l e m e n t a r y b a l a n c e m o d e l a , b. CHO

AA

Z

1.0

1.0

C H O N

-5.5 -9.0 -4.5

-5.09 -7.72 -1.53 -1.28

PRTAA AMMON CPROTO CBACT

LI

H20

UREA

1.0

1.0

1.0

-36.0 -60.0 -5.3 -.1

-2.0 -1.0

-1.0 -4-.0 -1.0 -2.0

NH 3

PROTO

C2

C3

C4

C5

CO 2

CH 4

RHS1 =

3.0 1.0

3.893 6.18 2.079 .509

3.968 6.182 1.672 .714

2.0 4.0 2.0

3.0 6.0 2.0

4.0 8.0 2.0

5.0 10.0 2.0

1.0

1.Q 4.0

2.0

1.0 1.0

CARBDI METH

1.0 1.0 1.0 1.0 1.0 1.0 1.0

MAXIMIZE

= = = =

.0 .0 .0 .0

= = =

1.05 .3 .0 2.0

= = = =

3.1 .62 .31 .07

= =

2.26 1.53

1.0

ACET PROP BUT VAL

o~

BACT

Z

O

Z g3

a C H O = f e e d c a r b o h y d r a t e , A A a n d P R T A A = f e e d p r o t e i n ( a v e r a g e a m i n o a c i d ) , L I = f e e d lipid, N H 3 a n d A M M O N = a m m o n i a , P R O T O a n d C P R O T O = p r o t o z o a , B A C T a n d C B A C T -- b a c t e r i a , C 2 a n d A C E T = a c e t a t e , C 3 a n d P R O P = p r o p i o n a t e , C 4 a n d B U T = b u t y r a t e , C 5 a n d V A L = v a l e r a t e , C O 2 a n d C A R B D I = c a r b o n d i o x i d e , C H 4 a n d M E T H = m e t h a n e , R H S 1 = r i g h t h a n d s i d e N o . 1, % = m a x i m i z e d f u n c t i o n . b V a l u e s in t o o l , e x c e p t i n g t h a t P R O T O a n d B A C T are e x p r e s s e d in 1 0 0 g o f d r y cells.

¢0

Z

.o

Ox

oo Oo tao

0o 0~ 4~

t:::

T A B L E 3. M a t r i x f o r r u m e n p a t h w a y s balance m o d e l a. NAS

< o

Z o o~

Z

1.0

NASYNT AASYNT AAUPT CAPOL¥

1.0

LISYGL L1SVAC LISYFA CAU PVA ATP FA N H 3-

p L C

AAU

1.0

1.0

CAP

LI1

LI2

LI3

METHB

1.0

1,0

1.0

1.0

1.0

AAF

CAF

CA5F

LIF

1.0

1.0

1.0

1.0

PC 2

PC 3

PC 4

PC 5

UREA

SFA

2.11 8.065 1.0 1.0 .042

.253

.107

.017

-.281

-2.706

-.045

-.406

-.107

-.592

-.015

-.014 -.128

-.019

-2.605

-.248

1.0 .017 .43 .54

-.O15

-.090 -,023 -.015

-.714

1.07

-.019

-.019

-.014 -.147

.0B .30

2.0 2.0

1.0 2.0

1.0 -1.0 1.0 1.0 1.805

-1.0 1.0

-2.0 2.0

-2,0 1,0 -1.0 2.0

1.0 1.0 1.0

.062 -.014

-.098 -.181

.041 .180

-.180 -.320

-1.058 -,004 -30.433 -8.152 7.08

,21 .89 .60

2.0

1.0 1.0

2.0

1.0 1.0 1.0

RHS1 = MAXIM

1.0

H2S BCFA BUT PROP ACET H2 CO 2 CH 4

AAS

1,0 1,0 1.0

-2.0 2.0

-3.0 1.0

-1.0 1.0

= = = =

1.0 1.0 .0 1.0

= = = >

1.0 .0 .0 ,0

= 3> = >

,0 .0 .0 .0

> > = =

.0 .0 .31 .62

= = > >

3.10 .0 .0 .0

= = =

1.05 .024 .0

a A b b r e v i a t i o n s are as follows: N A S and N A S N Y T = nucleic acid s y n t h e s i s ; A A S a n d A A S Y N T = a m i n o acid s y n t h e s i s a n d i n c o r p o r a t i o n into p r o t e i n ; A A U a n d A A U P T = a m i n o acid u p t a k e and i n c o r p o r a t i o n i n t o p r o t e i n ; CAP and C A P O L Y = p o l y s a c c h a r i d e s y n t h e s i s ; LI1 a n d L I S Y G L = lipid s y n t h e s i s f r o m glucose; LI2 a n d L I S Y A C = lipid s y n t h e s i s f r o m acetate; LI3 and L I S Y F A = lipid s y n t h e s i s f r o m F A ; C A U = c a r b o h y d r a t e u p t a k e ; M E T H B = M e t h a n o b a c t e r i u m sp.; C A F = c a r b o h y d r a t e f e r m e n t a t i o n ; CA5 F a n d C = f e r m e n t a t i o n v i a p h o s p h o k e t o l a s e p a t h w a y ; A A F and P = p r o t e i n f e r m e n t a t i o n ; L I F a n d L = lipid f e r m e n t a t i o n ; P V A = p y r u v a t e ; F A = f a t t y acid; S F A = s a t u r a t e d FA; B C F A = b r a n c h e d chain FA; PC 2 = P V A -~ acetate; PC 3 = P V A -~ p r o p i o n a t e ; PC 4 = P V A -~ b u t y r a t e ; PC 5 = P V A -~ B C F A ; R H S 1 = r i g h t h a n d side n u m b e r 1; Z = maximized function.

-r

Z >. .~ Z

RUMEN MODELING metry for this pathway was calculated according to Dawes and Large (9). The column for lipid fermentation (LIF) provides for the fermentation of glycerol and release of 1.8 fatty acids per mol of forage lipid degraded (10). The Columns PC2-PC5 provide for the conversion of pyruvate to acetate, propionate, butyrate, and branched chain fatty acids (equated to valerate for simplicity), respectively, according to welldocumented pathways discussed previously (4, 5). The urea column simply reflects urea secretion into the rumen. The S F A column provides for the reduction of one double bond per fatty acid (FA). The rows denoted P, L, and C provide for specification on the RHS of extents of protein and lipid fermentation ( A A F and LIF) and participation of the phosphoketolase pathway in the rumen fermentation. The model of pathway balance (Table 3) discussed above, accommodates or incorporates most of our current knowledge of rumen metabolic pathways and enables computation of many interrelationships among rumen substrates and rumen digestion products. These computations may be undertaken in analyses of experimental data or for analyses of possible theoretical interrelationships among substrates and pathways' with specification of artificial or theoretical constraints. Additional columns or rows can be added to the matrix to accommodate additional biosynthetic or fermentative pathways and additional fermentation products or to enable specification of additional constraints. The ALPSI computer program (linear programming software available at most university

885

computer centers will solve the system just as readily) was used for solutions in the same way as for the model of rumen elementary balance. In the RHS, exact constraints for microbial cell yield are specified. If, for example, a yield of 100 g dry cells is desired, NASYNT and CAPOLY should equal 1.0, the sum of AASYNY and AAUPT should equal 1.0, and the sum of the three possibilities for lipid synthesis (LI1, LI2 and LI3) should equal 1.0. Also in the example RHS in Table 3, volatile fatty acid production and protein and lipid fermentation are specified; no accumulations of pyruvate, unsaturated fatty acids, or hydrogen were allowed (=0); and, several substances such as ammonia were allowed to accumulate (>o.o). RESULTS A N D DISCUSSION

The model of elementary balance was tested by comparing results from this model with experimental results from a sheep fed alfalfa pellets at 2-h intervals (22). The elementary balance computed for the sheep fed at 2-h intervals is in Table 4. Feed composition, cell yields, and fermentation products were determined directly in the experiment (22). With these values as inputs to the model and, in addition, specifying amino acids and lipid fermentations as RHS constraints as in Table 2, amounts of carbohydrate digested in the rumen were calculated. These values agree with results in the literature for animals fed at 1 to 3 h intervals (7, 12, 16, 18, 25) indicating that elemental balances from our model sheep experiment (22) and the model of elementary

TABLE 4. Elementary substrate-product balance for an experimental sheep fed at 2-h intervals per daya. Mol input Protein Carbohydrates Lipid Urea H20

Mol output 1.050 2.376 .024 .181 2.085

Elementary input 19.434 35.800 14.672 1.706

197.33 g .510 1.420 .781

Cells NH 3 CO 2 CH4

C H O N

Valerate Butyrate Propionate Acetate

.061 .304 .578 3.113

Elementary output 19.434 35.813 14.673 1.706

aCell yields expressed in grams, all other values in mol or gram atoms. More detailed data are in Reference 22. Journal of Dairy Science Vol. 58, No. 6

886

REICHL AND BALDWIN

balance are internally consistent and agree with literature (see also Discussion). Example results of a number of computations using the model of elementary balance are in Table 5. Compared are two proportions among the volatile fatty acids, six cell yields, and two gas productions. Computed amounts of feed nutrients are in ranges close to those provided by a kilogram of alfalfa per day as is described in the input section of Table 4. When approximately the same amount of urea secretion (if no protozoal cell yield is considered) was maintained at constant intake of feed protein, negative ammonia productions were obtained when high cell yields (300 g) were programmed. Higher cell yields must be balanced by higher carbohydrate and lipid inputs. If both bacterial and protozoal cell yields are considered, the proportion of lipid to carbohydrate required at high

cell yields is less. Also, the urea required to balance nitrogen use is less. The two yields and proportions of VFA's in Table 5 were each calculated to provide approximately 9 mol of ATP. The specified yields of 100, 200, and 300 microbial cells correspond to 11.11, 22.22, and 33.33 g of cells per mol of ATP. The value of 33.33 g is identical with the theoretical maximum value reported by Gunsalus and Shuster (13). On the assumptions of 100% efficiency of utilization of ATP for growth and of substrates for both growth and fermentation, and minimal gas production, maximal theoretical cell yields are realizable from the standpoint of elementary balance. The high values for CO2 and C H 4 production specified in Table 5 were calculated from theoretical fermentation equations in the literature (4, 5, 20). The lower values specified were

TABLE 5. Example results from rumen elementary balance model a. Input values Protozoa

Bacteria

Computed values CO 2

CH 4

Carbohydrate

Lipid

Urea

NH 3

.011 .026 .041 .005 .014 .022 .041 .056 .070 .035 .043 .052

.184 .191 .197 .133 .089 .044 .183 .189 .195 .132 .087 .043

1.0 .3 -.4 1.0 .3 -.4 1.0 .3 -.4 1.0 .3 -.4

.026 .041 .055 .020 .028 .037 .067 .082 .096 .061 .069 .078

.184 .190 .196 .133 .088 .043 .182 .188 .194 .131 .086 .041

1.0 .3 -.4 1.0 .3 -.4 1.0 .3 -.4 1.0 .3 -.4

Constant values: Protein 1.05, Acet 3.10, Prop .62, But .31, Val .07

.5 1.0 1.5

.5 1.0 1.5

1.0 2.0 3.0 .5 1.0 1.5 1.0 2.0 3.0 .5 1.0 1.5

2.26 2.26 2.26 2.26 2.26 2.26 1.13 1.13 1.13 1.13 1.13 1.13

1.53 1.53 1.53 1.53 1.53 1.53 .765 .765 .765 .765 .765 .765

2.086 2.710 3.335 2.129 2.796 3.464 1.598 2.172 2.796 1.591 2.258 2.925

Constant values: Protein 1.05, Acet 2.16, Prop 1.08, But .54, Val .07

.5 1.0 1.5

.5 1.0 1.5

1.0 2.0 3.0 .5 1.0 1.5 1.0 2.0 3.0 .5 1.0 1.5

2.16 2.16 2.16 2.16 2.16 2.16 1.08 1.08 1.08 1.08 1.08 1.08

1.1.5 1.15 1.15 1.15 1.15 1.15 .575 .575 .575 .575 .575 .575

1.980 2.604 3.228 2.023 2.690 3.357 1.411 2.035 2.659 1.459 2.121 2.788

avalues in mol excepting that microbial yields are expressed as g dry cells × 10-2. Journal of Dairy Science Vol. 58, No. 6

RUMEN MODELING

set at 50% of these. This was done to accommodate H 2 utilization in cell component biosynthesis as has been discussed by Henderickx et al. (14). Example results from the model of rumen pathways balance are in Table 6. Compared at constant VFA production are three cell yields, two pathways for carbohydrate fermentation and microbial protein synthesis, and three possible routes of microbial lipid synthesis. Productions of NH 3, H2S, BCFA, CO 2, and CH 4 w e r e greater than zero. To simplify presentation and interpretation, values for NH 3 and CO2 output by the model were corrected to zero urea secretion. Thus, ammonia production from dietary protein was not sufficient to accommodate high microbial growth. Cell yields are expressed as programmed cell yields (1 to 300 g) plus cell yields of Methanobacterium. Higher contributions of the phosphoketolase pathway (CASF) to total carbohydrate fermentation (CAF + CA5F) resulted in less CO2. The C H 4 and ATP were higher when the 200 g cell yield was requested. High protein fermentation as compared to normal resulted in less carbohydrate fermentation, in higher excesses of NH 3, H2S and BCFA but approximately the same CH4 and ATP productions (for example compare runs A4 and D1 where total cell yields were 222 g). Comparison of three different ways of lipid synthesis indicated that when preformed fatty acids were used, total carbohydrate utilization and CO 2 production were less. No other effects were observed (Runs B or C). When protein synthesis based on 100% AA uptake was compared to 100% AA synthesis, less carbohydrate uptake, higher carbohydrate fermentation, and higher ATP production were observed. No serious effect on gas production was observed (Runs B and C). Cell yields per mol of ATP in Table 6 for normal feed protein (1.05 mol) varied between 11.5 and 13.6 at 100 g cell yields and 20.5 to 25.1 at 200 g cell yields (Runs A). At 300 g cell yields and with normal protein, carbohydrate fermentation was abnormal and unbalanced (Runs A). At higher protein, cell yields per mol of ATP increased toward the theoretical maximum (Run D2). Different routes of lipid synthesis didn't affect cell yields per ATP (Runs B and C). Amino acid uptake for protein synthesis decreased cell yields per mol of ATP from 20.5 to 15.6 when 200 g cell yields were

887

requested (Runs A4 and C1). With columns "ATP total" and "ATP excess" of Table 6 it is possible to calculate efficiencies of ATP utilization for growth. If 100 g cells were produced, efficiencies were 46 to 50%; if 200 g cell yields were specified, efficiencies were 75 to 88% (Runs A). The higher values in these ranges correspond to more carbohydrate fermentation via the phosphoketolase pathway. The amino acid uptake system decreased efficiencies from 75 to 58% as compared in Runs A4 and C1. These efficiencies are invalid because of the artificially programmed limits on cell yields but clearly indicate the complex interactions among substrate availability, fermentation products, and cell yields. This problem will be discussed in a subsequent paper. The 200 g daily cell yields in both models of elementary and pathways balance and the daily feed inputs, are approximately the same as for the sheep fed at 2-h intervals (22). With our assumption on microbial cell composition (Table 1) for analysis of the data from the sheep experiment (22), a microbial nitrogen yield was 16.7 g. This was 70.8% of the total nitrogen intake in feed. Hume (18) in sheep fed at 3-h intervals and at similar dairy feed intakes found 14.3 to 16.7 g microbial nitrogen outflow from the rumen. This was 75.2 to 91.5% of the total nitrogen intake in feed. For the model sheep experiment, our elementary balance model was used (Table 4) to calculate a net urea secretion of 21.5% of total feed nitrogen input. This agrees with experimental estimates from numerous laboratories (7, 24, 34). Daily intake of true lipid for the experimental sheep (Table 4) and for our model computations was 13.94 g (with content in mmol: glycerol, 24.06; higher fatty acids, 43.43; and cholin, 2.29) from our composition data. Daily microbial lipid yield in a sheep fed at 2-h intervals was 19.33 g (with content in mmol: glycerol, 31.28; branched fatty acids, 31.48; higher fatty acids, 37.78; and phosphoserin, 25.18). This estimate agrees with estimates in the literature (29, 33) that lipid and fatty acids outputs are higher than inputs in continuously fed sheep. In batch culture, Bauchop and Elsden (6) found dry cell yields of Streptococcus faecalis and other microbes of 8.3 to 12.6 g per tool of ATP. From the values Hungate (19) obtained in Journal of Dairy Science Vol. 58, No. 6

0o 00 0o

T A B L E 6. E x a m p l e results f r o m r u m e n p a t h w a y s b a l a n c e m o d e l a , b. I n p u t values

o

RunC, d

Cell yields

AAF

CAF

A 1 2 3 4 5 6 7 8 9

100 100 100 200 200 200 300 300 300

1.05 1.05 1.05 1.05 1.O5 1.05 1.05 1.05 1.05

1.938 1.191 .445 1.950 1.195 .445 8.060 5.900 3.740

B 1 2 3

200 200 200

1.05 1.05 1.05

C 1 2 3

200 200 200

D 1 2

200 300

.102 .102 .102 2.05 2.05

C o m p u t e d values

BCFA

.72 1.44

.14 .14 .15

Cells

Cells

ATP

CHO e

OM e

5.76 4.93 4.10 2.73 1.88 1.04 17.88 12.84 7.80

11.5 12.4 13.6 20.5 22.5 25.1 10.8 13.2 17.0

33.7 32.7 31.6 50.3 49.8 49.1 21.2 24.9 30.2

24.7 23.9 23.0 38.7 38.2 27.6 19.4 22.4 26.7

ATP excess

10.60 9.41 8.22 10.85 9.64 8.44 27.72 22.68 17.68

CAU+CAP

NH 3

H2S

CO 2

CH 4

.526 .526 .526 1.052 1.052 1.052 1.578 1.578 1.578

.25 .29 .33 -.46 -.43 -.39 -1.02 -1.02 -1.02

.014 .015 .016

2.55 2.20 1.84 2.55 2.18 1.82 10.32 8.16 6.00

1.56 1.20 .84 1.56 1.20 .84

1.950 2.129 1.948

1.052 .872 .872

-.46 -.46 -.46

2.55 2.55 2.20

1.56 1.56 1.55

10.85 10.57 10.83

2.73 2.62 2.63

20.5 21.0 20.5

50.3 50.3 53.5

38.7 38.7 40.6

2.284 2.464 2.283

.546 .366 .366

-.29 -.29 -.29

2.54 2.54 2.17

1.59 1.59 1.58

14.21 14.10 14.11

6.06 5.95 5.97

15.6 15.7 15.7

53.4 53.4 57.1

40.5 40.5 42.6

1.052 1.578

1.62 -.10

2.92 3.19

1.57 1.51

10.52 11.35

2.39

21.1 28.3

56.5 63.8

34.9 43.0

1.619 1.846

CA5F

Cells

ATP total

.72 1.44

.72 1.44

6.11 4.67 3.23

.29 .37

.001 .001

.030 .017

a A b b r e v i a t i o n s are d e f i n e d in T a b l e 3. b c o n s t a n t values: U R E A = 0, L I F = . 0 2 4 , A C E T = 3.10, P R O P = .62, B U T = .31, V A L - see B C F A c o l u m n f o r values s p e c i f i e d . Cln r u n s C, A A U = . 9 4 8 ; in all o t h e r r u n s A A U w a s set t o zero. d L i p i d s y n t h e s i s : LI3 in r u n s B3 a n d C3, LI2 in r u n s B2 a n d C2, in all o t h e r r u n s is LI1. e C H O -- 1 0 0 g c a r b o h y d r a t e , OM - 1 0 0 g o r g a n i c m a t t e r .

m t" > Z >

Z

RUMEN MODELING continuous culture of Ruminococcus albus, it is possible t o calculate an average of 12.8 g cells per tool of ATP and a m a x i m u m value of 14.5 g without, or 17.5 g with storage polysaccharide. The values o f 20 g cells per mol ATP for t h e r u m e n bacteria Bacteroides amylopbilus and Selenomonas ruminatium found by Hobs0n and Summers (15) in c o n t i n u o u s culture agree with our calculation for continuously fed sheep in the m o d e l experiment. In general, estimates of growth yields in batch culture are close to results for sheep fed twice daily while results in continuous culture are close to results with sheep fed each 2 h. C o m p u t a t i o n s o f elementary and pathways balance with absolute yields 100 g or 200 g and corresponding yields per mol of ATP agree with results on sheep fed at 12-h and 2-h intervals, respectively. Walln6fer et al. (35) reported a 25% contrib u t i o n of the phosphoketolase p a t h w a y to xylose f e r m e n t a t i o n in r u m e n contents. Operation of this pathway has an effect n o t o n l y of increasing cell yields per ATP b u t also of decreasing gas p r o d u c t i o n (Table 6). Seeley et al. (30) found that 14 to 45% higher theoretical m e t h a n e productions were estimated f r o m the balance equations o f Hungate (20) than were observed experimentally. The p h o s p h o k e t o l a s e pathway could n o t be the only reason for this difference. However, of the factors in Table 6, no others were found. In the elemental balance c o m p u t a t i o n (Table 5), lower gas p r o d u c t i o n was related to higher lipid inputs. This agrees with the e x p e r i m e n t of Czerkawski et al. (8) and others, but in relation to alfalfa (Table 4) and computations of pathways balance (Table 6), an absolute difference of only .01 mol of CH 4 could be attributed to lipid. In our computations, protein f e r m e n t a t i o n did n o t influence m e t h a n e p r o d u c t i o n (Table 6). However, this estimate is d e p e n d e n t on the stoichiom e t r y o f protein f e r m e n t a t i o n and this has n o t been studied extensively. Our protein fermentation pattern with high acetic acid p r o d u c t i o n agrees with e x p e r i m e n t s of Annison (3) and E1-Shazly (11) for casein. The balance approach in this paper is similar to the i n p u t - o u t p u t m o d e l of Shapiro (31). However, c o m p u t e r techniques and models are different. A linear p r o g r a m m i n g analysis o p t i m i z i n g interrelationships a m o n g diet, cell yields, and f e r m e n t a t i o n products as influenced or as a

889

reflection of the balance of microbial species in the r u m e n will be presented in a subsequent paper. These m o r e detailed analyses are based u p o n the c o n c e p t and parameter verifications accomplished through e l e m e n t a l and p a t h w a y s balance models.

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