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Neuroenergetics

This project aims to investigate the rate-limiting factors of glucose and lactate metabolism in the brain using mathematical tools. The focus is on the transport and metabolism of lactate, which is hypothesized to be transformed from glucose by astrocytes to provide energy to neurons in extreme conditions. Analytical and numerical methods will be used to model and simulate these processes.

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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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