Neuroenergetics
Students:
Idrizi Elita, Tscherrig Jennifer, Pattaroni Céline
Supervisors:
Pellerin Luc, Aitana Morton de Lachapelle
Goals of the project
- Transport / metabolism of glucose and lactate rate-limiting for the brain?
-> Glucose: Barros
-> Lactate: our project!
- Using mathematical tools (matlab) to enforce the hypothesis of lactate
Biological aspects
Glucose - lactate
Glucose: principal energetic substrat of the brain
Lactate: energetic substrat of neurones
Hypothesis of lactate: glucose transformed into lactate by the astrocytes to feed the neurones in extreme conditions of necessity of energy
Aspects biologiques détaillés
Main problems
The transport of glucose is important to define its metabolism and contrariwise
Solve mathematically the transport and metabolism of lactate in the neurones like Barros did it for the glucose
Mathematical aspects
1. Analytical and numerical methods
2. 1st part:
transport and metabolism of glucose
1. 2nd part:
transport and metabolism of lactate
Example: production of a protein
dP/dt = a*Panalytical numerical
P(t) = Po * eat
no formula Analytique
Temps
[P]
P(t)
Numérique
Temps
[P]
Analytical and numerical methods
Transport and metabolism of glucose
Ge+T [GeT] [GnT] Gn+T+E [GnE] Gn*+E
k1, k-1 k2, k-2
d[GeT]/dt = k1* Ge * T - k-1 * [GeT] - k2 * [GeT] + k-2 * [GnT]
Ge extracellular glucose T transporter (GLUT)Gn neuronal glucose E hexokinase
* phosphorylation
1) Metabolism
Gn+H [GnH] Gn*+H k1, k-1 k2
- Hypotheses:1. Hypothesis of pre-equilibrium: rapid equilibration of GnH2. Hypothesis of total hexokinase concentration : Htot = H+[GnH]3. Max speed reached when all enzymes form a complex with Glc:
Vmax = k2*Htot
M-M constant : Km = k2+k-1 / k1
- Solution:vm = (Gn*Vmax)/(Gn+Km) irreversible Michaelis-Menten kinetics
2) Transport
Ge+T [GeT] [GnT] Gn+T k1, k-1 k2, k-2 k3, k-3
- Hypotheses:1. Hypothesis of pre-equilibrium: rapid equilibration of GeT, GnT2. Hypothesis of transport speed: dissociation of GeT and GnT faster than transport (reversible Michaelis-Menten kinetics)dissociation constants : ke=k-1/k1 and kn=k3/k-3
3. Hypothesis of total GLUT transporters concentration: Ttot = T + [GeT] + [GnT]
4. Max speeds for Glc transport inside and outside the neuron : VmaxIN = k2*Ttot and VmaxOUT = k-2*Ttot
- Solution: vt = k2[GeT] – k-2[GnT] =
(VmaxIN*(Ge/ke) - VmaxOUT*(Gn/kn))/(1+(Ge/ke)+(Gn/kn))
Our graphics
Graphics (Barros)
Conclusions: analytical and numerical methods
Analytical results:- Advantages: simple formula
- Desadvantages: many hypotheses
Numerical simulations:To follow (lactate)…