Explo ing a i s -p inciples based model o zooplank on espi a ion
T.T. Packa d*†§, M. Gómez§ and M. Alca az*.
*Ins i u o de Ciencias del Ma , Paseo Ma í imo de la Ba celone a 37-49, 08003 Ba celona, Spain
†Bigelow Labo a o y o Ocean Science, W. Boo hbay Ha bo , Maine 04575, USA
§Biological Oceanog aphy Labo a o y, Facul ad de Ciencias del Ma , Uni e sidad de Las Palmas de G an Cana ia, Campus
Uni e si a io de Ta i a., 35017 Las Palmas de G.C., Cana y Islands, Spain.
This is a con ibu ion om ICM-CSIC, BLOS, ULPGC, he p ojec s:
MICROROL (CICYT CTM2004-02757/MAR), MODIVUS (CTM2005-
04795/MAR), OITHONA (CTM2007-60052).
Bu he MTE only p edic s espi a ion when he ood supply is
adequa e! Senescence espi a ion can’ be p edic ed (Fig. 3)!
Compa ing Figs. 1 and 3 shows ha clea ly. How can you
model p edic espi a ion when ood is sca ce and espi a ion
alls? No e pa allelism in Fig. 3 be ween dec eases in
espi a ion and py u a e ( ood sou ce) du ing hou 10 o 13.
Some hing in he ood limi s espi a ion. Tha ’s ou
hypo hesis! Since enzymes con ol espi a ion, ha
“some hing” is he enzyme’s subs a es (Fig.4). Consequen ly,
we a gue ha a espi a ion model should inco po a e a
Michaelis-Men en exp ession (Fig.5).
Figs. 1 & 2. Modeling espi a ion om bisubs a e
enzyme kine ics is easible in Bac e ia (1). Fo
zooplank on, should we adap his model o he MTE
model? How does he MTE (Me abolic Theo y o
Ecology 2) do his? The MTE would p edic espi a ion
(R) by he ollowing equa ion, R = i M0.75, whe e i is a
s oichiome ic ac o and M is he biomass (Fig 3).
Slide 1
Ou model is: R0 = SVmax0/(Km + S), whe e Vmax0 is, he
po en ial espi a ion (ETS). We use  a he han M0.75 because
biomass jus packages he ETS. The ETS is he eal cause o
espi a ion. Fu he mo e, he ela ionship be ween R and ETS is
be e and mo e di ec han be ween R and M (Figs 6, & 7) .
0
25
50
010 20 30
Time (h)
Measu ed
Modelled
PnPy260593
Respi a ion (mM O2 min-1)
a
Fig. 1
0
10
20
30
010 20 30
Time (h)
Respi a ion (mM CO2
min1)
PnPy100693
Measu ed
Modeled
Fig. 2
0
10
20
30
40
50
60
70
0 5 10 15 20 25 30
Time (h)
P o ein/5 (mg/L), Py u a e x 3
(mM), R-measu ed & R-
p edic ed (mM O2/min)
Measu ed Respi a ion
Cell P o ein
MTE P edic ed
Respi a ion
Nu ien
(py u a e)
PnPy260593
Fig. 3
0
10
20
30
40
50
0 5 10 15 20 25 30
Time (h)

NADPH
NADH
b
Fig. 4
0
30
60
010 20 30
TIME (h)
M O2 min-1

Measu ed
Respi a ion
Enzyme Kine ic
Model P edic ed
Respi a ion
Fig 8
y = 0.4656x - 1.5603
R2 = 0.9846
0
50
100
150
200
0 100 200 300 400
Respi a ion (ml O2 h-1animal-
 (ml O2 h-1 animal-1)
Fig 7
y = 0.9414x - 0.3444
R2 = 0.9811
-3
-2
-1
0
1
2
3
-2 -1 0 1 2 3
Log
()
Log
(Respi a ion)
-3
-2
-1
0
1
2
3
-3 -2 -1 0123
Log (D y Weigh )
Log
(Respi a ion)
y = 0.7565x + 0.1757
R2 = 0.9363
R = 1,5M0,76
Fig 6
This model ans o ms  (Time) in o R = (Time) (Fig 8).