Dynamic Analysis of the GAL Regulatory System in Kluyveromyces lactis: A Comparative Study with Saccharomyces cerevisiae

Venkat Reddy Pannala, Ahammed Sherief K.Y., Sharad Bhartiya,* and K.V.Venkatesh*

Department of Chemical Engineering

Indian Institute of Technology, Bombay

Mumbai, INDIA 400076

*Authors to whom all correspondence should be addressed at: Department of Chemical Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai -400076, India.

Email: ;

Ph: 91022-25767225.Fax:91-22-25726895.

Supplementary material

Dynamic model development for K. lactis

Dynamic molar balance equations were written for interactions shown in Fig. 1 (in the main text) namely, protein-protein interactions, DNA-protein interactions and protein-substrate interactions. The parameter values are given in the Table S1 Parameter values were fitted by minimizing the sum of least square errors between experimental and model results. All the variables are normalized with the total variable concentrations as given in Table S2. The complete dynamic model equations and notations used are presented below.

y1 = [KlGal4p]

y2 = [KlGal4p2]

y3 = [D1]

y4 = [D2]

y5 = [D1-KlGal4p2]

y6 = [D2-KlGal4p2]

y7 = [D2-KlGal4p2-KlGal4p2]

y8 = [KlGal80pn]

y9 = [KlGal80pn2]

y10 = [KlGal4p2-KlGal80pn2]

y11 = [D1-KlGal4p2-KlGal80pn2]

y12 = [D2-KlGal4p2-KlGal80pn2]

y13 = [D2-KlGal4p2-KlGal80pn2-KlGal4p2]

y14 = [D2-KlGal4p2-KlGal80pn2-KlGal4p2-KlGal80pn2]

y15 = [KlGal1p-Galint]c

y16 = [KlGal1p-Galint]n

y17 = [KlGal1p-KlGal80p]

y18 = [KlGal1p-KlGal80p2]

y19 = [KlGal1p-KlGal80p2-KlGal1p]

y20 = [Lac12p]

y21 = [Galint]

y22 = [KlGal1p]c

y23 = [X]

y24 = [Galext]

y25 = [Gluext]

Components having DNA (D1 or D2) as their constituents do not have a dilution due to growth term or a generation term due to cell division so that the net number of DNA molecules in the system remains constant. All other intracellular components have a dilution term due to growth. Note that Anders et al. (2006) report that the binding of Gal1p in the nucleus to D-Gal4-Gal80 is negligible compared to the binding with free Gal80. Thus, the model only includes interaction between Gal1p in the nucleus and free Gal80.

Ordinary differential equations

(S1)

(S2)

(S3)

(S4)

(S5)

(S6)

(S7)

(S8)

(S9)

(S10)

(S11)

(S12)

(S13)

(S14)

(S15)

(S16)

(S17)

(S18)

(S19)

(S20)

(S21)

(S22)

(S23)

(S24)

(S25)

Algebraic equations

(S26)

(S27)

(S28)

Table S1: Model parameters of K. lactis GAL system

Parameter / Value / Source
kd / 4×108 mol-1 g h-1 / Fitted
K1
k2
k3
k4
k
k5
K
kg
kt8, kt12, kt1
K5
Ki
K0
μgalmax
μglymax
μglumax
Yx/s
Kglu
Kd
K1
K2
K3
K4
D1t
D2t
m
[KlGal4p]t0
[KlGal4p]t
KlGal80pmax
KlGal1pmax
Galint,max
n
dc
ks
Yg
Kgal
Kp / 5×108 mol-1 g h-1
5×106 mol-1 g h-1
1×1010 mol-1 g h-1
1×109 mol-1 g h-1
20 h-1
1×106 mol-1 g h-1
0.125
126 g-1dm3 h-1
5×102 g-1dm3 h-1
1×10-10 mol g-1
1.13 mM
0.6 mmol g-1
0.26 h-1
0.17 h-1
0.35 h-1
0.2 g mol-1
4 mM
6.2×10-10 mol g-1
7.3×10-7 mol g-1
1×10-10 mol g-1
5×10-10 mol g-1
8.3×10-8 mol g-1
0.072 n mol g-1
0.43 n mol g-1
10
6.95 n mol g-1
32.6 n mol g-1
170-340 n mol g-1
11000 n mol g-1
0.01 mol g-1
0.7
2×10-5 mol-1 g h-1
130 mM
60 g mol-1
160 mM
220 h-1 / Fitted
Fitted
Fitted
Fitted
Fitted
Fitted
[2]
Fitted
Fitted
Fitted
Independent Experiment
Independent Experiment
Independent Experiment
Independent Experiment
Independent Experiment
Independent Experiment
Independent Experiment
[2]
[2]
[1]
[1]
[1]
[2]
[2]
[2]
[1]c
[2]
[1]c
[1]
Assumed
[2]
[2]
Assumed
Independent Experiment
Independent Experiment
Fitted

Note that n represents the co-response coefficient used in Eq. (3) and (4) in main text

Table S2: Summary of the normalization constants used for variables in the model

Variable / Normalisation constant
KlGal4p, KlGal4p2, KlGal4p2-KlGal80p2 / KlGal4pt
All D1 Complexes / D1t
All D2 Complexes / D2t
Gal80pn, Gal80pn2, Lac12p
All [KlGal1p-KlGal80p] complexes / KlGal80pmax
KlGal1p, KlGal1p-Galint / KlGal1pmax
Galint / Galint,max


Figure S1: Sensitivity analysis of the model to the model parameters for wild-type (solid line) and the mutant (dashed line). A) Sensitivity to the parameter K0, the half saturation constant for the growth on galactose. B) Sensitivity to all other parameters except kg, kt12, kt8, kt1 and K0 when perturbed randomly.

Reference:

1. Anders A, Lilie H, Franke K, Kapp L, Stelling J, Gilles ED, Breunig KD (2006) The galactose switch in Kluyveromyces lactis depends on nuclear competition between Gal4 and Gal1 for Gal80 binding. Journal of Biological Chemistry 281 (39):29337-29348

2. Pannala VR, Bhartiya S,Venkatesh KV (2010) Experimental and steady-state analysis of the GAL regulatory system in Kluyveromyces lactis. FEBS Journal 277 (14 ): 2987-3002