Investigating Glucose and Lactate Metabolism in the Brain: A Neuroenergetics Approach
This project explores the transport and metabolism of glucose and lactate in the brain, focusing on whether lactate can be a significant energy substrate for neurons. Using advanced mathematical tools, specifically MATLAB, we aim to analyze and validate hypotheses about glucose transformation into lactate by astrocytes, particularly during energy shortages. Our study employs both analytical and numerical methods to model the dynamics of glucose and lactate transport, addressing critical biological aspects and establishing a comprehensive understanding of cerebral energy metabolism.
Investigating Glucose and Lactate Metabolism in the Brain: A Neuroenergetics Approach
E N D
Presentation Transcript
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
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
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 • Analytical and numerical methods • 1st part: transport and metabolism of glucose • 2nd part: transport and metabolism of lactate
Analytical and numerical methods Example: production of a protein dP/dt = a*P analytical numerical P(t) = Po * eatno formula
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
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
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))
Conclusions: analytical and numerical methods Analytical results: • Advantages: simple formula • Desadvantages: many hypotheses Numerical simulations: To follow (lactate)…
