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Neuroenergetics

Neuroenergetics. Students: Idrizi Elita, Tscherrig Jennifer, Pattaroni C é line 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!

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Neuroenergetics

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  1. Neuroenergetics Students: Idrizi Elita, Tscherrig Jennifer, Pattaroni Céline Supervisors: Pellerin Luc, Aitana Morton de Lachapelle

  2. 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

  3. Biological aspects

  4. 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

  5. Aspects biologiques détaillés

  6. 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

  7. Mathematical aspects • Analytical and numerical methods • 1st part: transport and metabolism of glucose • 2nd part: transport and metabolism of lactate

  8. Analytical and numerical methods Example: production of a protein dP/dt = a*P analytical numerical P(t) = Po * eatno formula

  9. 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] Geextracellular glucose T transporter (GLUT) Gn neuronalglucose E hexokinase * phosphorylation

  10. 1) Metabolism Gn+H [GnH] Gn*+H k1, k-1 k2 • Hypotheses: 1. Hypothesis of pre-equilibrium: rapid equilibration of GnH 2. 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

  11. 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, GnT 2. 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))

  12. Our graphics

  13. Graphics (Barros)

  14. Conclusions: analytical and numerical methods Analytical results: • Advantages: simple formula • Desadvantages: many hypotheses Numerical simulations: To follow (lactate)…

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