Utilization of the bootstrap method for determining confidence intervals of parameters for a model of MAP1B protein transport in axons

Abstract

This paper develops a model of axonal transport of MAP1B protein. The problem of determining parameter values for the proposed model utilizing limited available experimental data is addressed. We used a global minimum search algorithm to find parameter values that minimize the discrepancy between model predictions and published experimental results. By analyzing the best fit parameter values it was established that some processes can be dropped from the model without losing accuracy, thus a simplified version of the model was formulated. In particular, our analysis suggests that reversals in MAP1B transport are infrequent and can be neglected. The detachment of anterogradely-biased MAP1B from microtubules (MTs) and the attachment of retrogradely-biased MAP1B to MTs can also be neglected. An analytical solution for the simplified model was obtained. Confidence intervals for the determined parameters were found by bootstrapping model residuals. The resultant analysis heavily constrained the values of some parameters while showing that some could vary without significantly impacting model error. For example, our analysis suggests that, above a certain threshold value, the kinetic constant determining the rate of MAP1B transition from the retrograde pausing state to the off-track state has little impact on model error. On the contrary, the kinetic constant describing MAP1B transition from a pausing to a running state has great impact on model error.

Simulating tubulin-associated unit transport in an axon: using bootstrapping for estimating confidence intervals of best-fit parameter values obtained from indirect experimental data

“…The method suggested in [34] for simulating transport of MAP1B protein in axons was further developed and applied to the model of tau transport. The sensitivity of model parameters to noise (discrepancies between model predictions and published experimental data) was estimated by using a bootstrapping approach.…”

“…Our main goal was then to develop a method to estimate the values of these eight parameters, and their confidence intervals, from indirect experimental data reported in the literature, such as the tau distribution along the axon and average tau transport velocity. The method suggested in [34] for simulating transport of MAP1B protein in axons was further developed and applied to the model of tau transport. The sensitivity of model parameters to noise (discrepancies between model predictions and published experimental data) was estimated by using a bootstrapping approach.…”

Bidirectional, unlike unidirectional transport, allows transporting axonal cargos against their concentration gradient

“…(42). For optimizing the fit, the Least Square Regression (LSR) was utilized, as described in [40,54,55]. 1)-( 5) using Eqs.…”

“…( 55) estimates how well the average velocity of -syn predicted by the model, , We also used 1  =1 s 2 /µm 2 . This value was selected by numerical experimentation to avoid overfit in terms of either -syn concentration or average velocity, as described in Kuznetsov and Kuznetsov (2017b).…”

Modeling tau transport in the axon initial segment

“…For example, a very large value of ω 1 would cause an overfit in terms of tau average velocity, which would be forced to approach exactly 0.00345 µm/s. This would ignore the natural variance of the velocity [57]. Also, setting ω 1 to a very large value would put more weight on the tau velocity at the cost of tau concentration, and would lead to predicting a total tau concentration that would fit the experimentally measured tau concentration reported in [49] worse.…”