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Research Papers

A Numerical Study of Sensitivity Coefficients for a Model of Amyloid Precursor Protein and Tubulin-Associated Unit Protein Transport and Agglomeration in Neurons at the Onset of Alzheimer's Disease

[+] Author and Article Information
I. A. Kuznetsov

Perelman School of Medicine,
University of Pennsylvania,
Philadelphia, PA 19104;
Department of Bioengineering,
University of Pennsylvania,
Philadelphia, PA 19104
e-mail: ivan.kuznetsov@uphs.upenn.edu

A. V. Kuznetsov

Department of Mechanical and
Aerospace Engineering,
North Carolina State University,
Raleigh, NC 27695-7910
e-mail: avkuznet@ncsu.edu

Manuscript received June 22, 2018; final manuscript received October 17, 2018; published online January 18, 2019. Assoc. Editor: Jeffrey Ruberti.

J Biomech Eng 141(3), 031006 (Jan 18, 2019) (9 pages) Paper No: BIO-18-1293; doi: 10.1115/1.4041905 History: Received June 22, 2018; Revised October 17, 2018

Modeling of intracellular processes occurring during the development of Alzheimer's disease (AD) can be instrumental in understanding the disease and can potentially contribute to finding treatments for the disease. The model of intracellular processes in AD, which we previously developed, contains a large number of parameters. To distinguish between more important and less important parameters, we performed a local sensitivity analysis of this model around the values of parameters that give the best fit with published experimental results. We show that the influence of model parameters on the total concentrations of amyloid precursor protein (APP) and tubulin-associated unit (tau) protein in the axon is reciprocal to the influence of the same parameters on the average velocities of the same proteins during their transport in the axon. The results of our analysis also suggest that in the beginning of AD the aggregation of amyloid-β and misfolded tau protein have little effect on transport of APP and tau in the axon, which suggests that early damage in AD may be reversible.

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Figures

Grahic Jump Location
Fig. 1

A schematic diagram of a neuron. The left magnified area shows various modes of fast axonal transport of APP, the central magnified area shows various modes of slow axonal transport of tau protein (in displaying modes of tau transport we followed [29], see Fig. 3 in Ref. [29]), and the right magnified area shows formation of NFTs. Note that amyloid-β plaques, which are formed by aggregation of APP fragments, are located outside the neuron.

Grahic Jump Location
Fig. 2

(a) A kinetic diagram for simulating fast axonal transport of APP. The diagram also shows a separate kinetic state for amyloid-β polymers. (b) A kinetic diagram for simulating slow axonal transport of tau protein. The diagram also shows a separate kinetic state for misfolded (aggregated) tau protein.

Grahic Jump Location
Fig. 3

Relative sensitivity coefficients showing the effects of α+*, α−*, α′+*, α′−*, Cs,i, hAPP∗, and qAPP∗ on (a) the dimensionless total APP concentration, ctot,ax, and on (b) the average APP velocity, vav,APP∗. To establish time-independence of the solution, we show the results at two times: t∗=t1∗ and t∗=t2∗, where t1∗=0.695 yr and t2∗=1 yr.

Grahic Jump Location
Fig. 4

Relative sensitivity coefficients showing the effects of v+*, v−*, and σ on (a) the dimensionless total APP concentration, ctot,ax, and on (b) the average APP velocity, vav,APP∗. To establish time-independence of the solution, we show the results at two times: t∗=t1∗ and t∗=t2∗, where t1∗=0.695 yr and t2∗=1 yr.

Grahic Jump Location
Fig. 5

Relative sensitivity coefficients showing the effects of γra*, γ10*, γ01*, vr*, A, Aax*, and Vs* on (a) the dimensionless total tau concentration, ntot,ax, and on (b) the average tau velocity, vav,tau∗. To establish time-independence of the solution, we show the results at two times: t∗=t1∗ and t∗=t2∗, where t1∗=0.695 yr and t2∗=1 yr.

Grahic Jump Location
Fig. 6

Relative sensitivity coefficients showing the effects of va*, htau*, and ndif,x=0 on (a) the dimensionless total tau concentration, ntot,ax, and on (b) the average tau velocity, vav,tau∗. To establish time-independence of the solution, we show the results at two times: t∗=t1∗ and t∗=t2∗, where t1∗=0.695 yr and t2∗=1 yr.

Grahic Jump Location
Fig. 7

Relative sensitivity coefficients showing the effects of γar*, γon,a*, γdif→st*, Dfree*, Dmt*, and T1/2,free tau* on (a) the dimensionless total tau concentration, ntot,ax, and on (b) the average tau velocity, vav,tau∗. To establish time-independence of the solution, we show the results at two times: t∗=t1∗ and t∗=t2∗, where t1∗=0.695 yr and t2∗=1 yr.

Grahic Jump Location
Fig. 8

Relative sensitivity coefficients showing the effects of γst→dif*, γfree→st*, γst→free*, γdif→free*, and jtot,tau,x=0* on (a) the dimensionless total tau concentration, ntot,ax, and on (b) the average tau velocity, vav,tau∗. To establish time-independence of the solution, we show the results at two times: t∗=t1∗ and t∗=t2∗, where t1∗=0.695 yr and t2∗=1 yr.

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