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− | <p>The aim of our mathematical model is to simulate the growth of neurons towards our biofilm in response to the presence of pro Nerve Growth Factor (proNGF) (Figure 1). proNGF is part of a family of proteins called neurotrophins. They are responsible for the development of new neurons, and for the growth and maintenance of mature ones. We created a deterministic model to help the wet lab establish the optimal concentration gradients of proNGF needed for the regrowth of the nerves. proNGF concentration and concentration gradient are key parameters affecting the growth rate and direction of neurites. Neurites growth has shown to be proNGF dose-dependent: if proNGF concentration is too low or too high, the growth rate is attenuated. In order to visualize the results of the model on a micro channel, we used MATLAB | + | <p>The aim of our mathematical model is to simulate the growth of neurons towards our biofilm in response to the presence of pro Nerve Growth Factor (proNGF) (Figure 1). proNGF is part of a family of proteins called neurotrophins. They are responsible for the development of new neurons, and for the growth and maintenance of mature ones. We created a deterministic model to help the wet lab establish the optimal concentration gradients of proNGF needed for the regrowth of the nerves. proNGF concentration and concentration gradient are key parameters affecting the growth rate and direction of neurites. Neurites growth has shown to be proNGF dose-dependent: if proNGF concentration is too low or too high, the growth rate is attenuated. In order to visualize the results of the model on a micro channel, we used MATLAB and Python. This is an important part of our project since it creates the link between the wet lab and dry lab. </p> |
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Revision as of 01:56, 18 October 2018
First aspect modeled : secretion, diffusion and influence of proNGF
The aim of our mathematical model is to simulate the growth of neurons towards our biofilm in response to the presence of pro Nerve Growth Factor (proNGF) (Figure 1). proNGF is part of a family of proteins called neurotrophins. They are responsible for the development of new neurons, and for the growth and maintenance of mature ones. We created a deterministic model to help the wet lab establish the optimal concentration gradients of proNGF needed for the regrowth of the nerves. proNGF concentration and concentration gradient are key parameters affecting the growth rate and direction of neurites. Neurites growth has shown to be proNGF dose-dependent: if proNGF concentration is too low or too high, the growth rate is attenuated. In order to visualize the results of the model on a micro channel, we used MATLAB and Python. This is an important part of our project since it creates the link between the wet lab and dry lab.
We divided our model in three parts:
- Production of proNGF by the genetically modified Escherichia coli
- Simulation of the diffusion of proNGF in a given environment
- Neurons growth in the presence of proNGF
Context of our model
Our project aims at creating a biofilm composed of genetically modified E. coli able to release a neurotrophic factor: proNGF. It helps to accelerate the connection between the neurons and the implant of the prosthesis; hence aiming at connecting the prosthesis and the amputee's neurons directly. This will enable the patient to have a more instinctive control of his prosthetic device. The nerves will be guided towards a conductive membrane surrounding our genetically modified biofilm (Figure 2). This membrane will then pass the neural signal of the regenerated nerves towards the electronic chip of the implant through wires. It will allow the patient to have a more instinctive and natural control than any other current prosthesis, and a reduced re-education time.
The aim of the wet lab is to test the biofilm on a microfluidic chip as a proof of concept. The chip is composed of two compartments: one contains the genetically modified E. coli that produce proNGF and the other one contains neurons (Figure 3). Microchannels link the two compartments in the middle of the chip, allowing the diffusion of proNGF and the growth of the neurites. Our model will hence be established on a microfluidic chip shape in order to share our results with the wet lab and indicate them the optimal concentration of proNGF needed according to our model. All the codes we used in this part are available here.
We introduce different parameters in order to create our model :
g | Length of the neurite outgrowth |
dg/dt
|
Neurite outgrowth rate |
u(x,t) | Concentration of proNGF at the position x and time t |
du/dt
|
proNGF concentration gradient at the position x and time t |
Cdiff | Diffusion coefficient of proNGF |
K | Gradient factor (growth rate of the neurite under the stimulation of the proNGF concentration gradient) |
Gθ | Baseline growth rate (neurite growth rate in absence of proNGF concentration gradient) |
L | Length of the conduit |
proNGF production by genetically modified E. coli
proNGF diffusion simulation in a given environment
Neurons growth in the presence of proNGF
Second aspect modeled : mechanical modeling
Neuronarch aims at making the prosthesis of the future and making it more comfortable and protective for the patient. For this sake and to facilitate surgical interventions we modeled the behavior of a bone under mechanical stress. We presented our tools and scripts to Dr. Laurent Sedel, an orthopedic surgeon at Hôpital Lariboisière and researcher at the Hôpital Ambroise Paré – Hôpitaux universitaires Paris Ile-de-France Ouest, in the hopes of using our tools to improve the life span of prosthesis.
REFERENCES
- M. Stamatakis and N. V. Mantzaris, "Comparison of deterministic and stochastic models of the lac operon genetic network," Biophys. J., vol. 96, no. 3, pp. 887-906, 2009.
- A. Y. Weiße, D. A. Oyarzún, V. Danos, and P. S. Swain, "Mechanistic links between cellular trade-offs, gene expression, and growth," Proc. Natl. Acad. Sci., vol. 112, no. 9, pp. E1038-E1047, 2015.
- R. Milo, "Useful fundamental BioNumbers handout.doc," pp. 1-2, 2008.
- M. S. Packer, H. A. Rees, and D. R. Liu, "Phage-assisted continuous evolution of proteases with altered substrate specificity," Nat. Commun., vol. 8, no. 1, 2017.
- H. Benabdelhak et al., "A specific interaction between the NBD of the ABC-transporter HlyB and a C-terminal fragment of its transport substrate haemolysin A," J. Mol. Biol., vol. 327, no. 5, pp. 1169-1179, 2003.
- Defining the concentration gradient of nerve growth factor for guided neurite outgrowth, XCao M.SShoichet, March 2001
- Immobilized Concentration Gradients of Neurotrophic Factors Guide Neurite Outgrowth of Primary Neurons in Macroporous Scaffolds, Moore K, MacSween M, Shoichet M, feb 2006
- Mathematical Modeling of Guided Neurite Extension in an Engineered Conduit with Multiple Concentration Gradients of Nerve Growth Factor (proNGF), Tse TH, Chan BP, Chan CM, Lam J, sep 2007
- Mathematical modeling of multispecies biofilms for wastewater treatment, Maria Rosaria Mattei, november 2005