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)…