Abstract

To the best of the author's knowledge, this paper presents the first attempt to develop a mathematical model of the formation and growth of inclusions containing misfolded TATA-box binding protein associated factor 15 (TAF15). It has recently been shown that TAF15 inclusions are involved in approximately 10% of cases of frontotemporal lobar degeneration (FTLD). FTLD is the second most common neurodegenerative disease after Alzheimer's disease (AD). It is characterized by a progressive loss of personality, behavioral changes, and a decline in language skills due to the degeneration of the frontal and anterior temporal lobes. The model simulates TAF15 monomer production, nucleation and autocatalytic growth of free TAF15 aggregates, and their deposition into TAF15 inclusions. The accuracy of the numerical solution of the model equations is validated by comparing it with analytical solutions available for limiting cases. Physiologically relevant parameter values were used to predict TAF15 inclusion growth. It is shown that the growth of TAF15 inclusions is influenced by two opposing mechanisms: the rate at which free TAF15 aggregates are deposited into inclusions and the rate of autocatalytic production of free TAF15 aggregates from monomers. A low deposition rate slows inclusion growth, while a high deposition rate hinders the autocatalytic production of new aggregates, thus also slowing inclusion growth. Consequently, the rate of inclusion growth is maximized at an intermediate deposition rate of free TAF15 aggregates into TAF15 inclusions.

References

1.
Tetter
,
S.
,
Arseni
,
D.
, and
Murzin
,
A. G.
,
2024
, “
TAF15 Amyloid Filaments in Frontotemporal Lobar Degeneration
,”
Nature
,
625
(
7994
), pp.
345
351
.10.1038/s41586-023-06801-2
2.
Lewis
,
S.
,
2024
, “
Mistaken Identity
,”
Nat. Rev. Neurosci.
,
25
(
2
), p.
78
.10.1038/s41583-023-00787-6
3.
Kovar
,
H.
,
2011
, “
Dr. Jekyll and Mr. Hyde: The Two Faces of the FUS/EWS/TAF15 Protein Family
,”
Sarcoma
,
2011
(
1
), p.
837474
10.1155/2011/837474.
4.
Svetoni
,
F.
,
Frisone
,
P.
, and
Paronetto
,
M. P.
,
2016
, “
Role of FET Proteins in Neurodegenerative Disorders
,”
RNA Biol.
,
13
(
11
), pp.
1089
1102
.10.1080/15476286.2016.1211225
5.
Tan
,
A. Y.
, and
Manley
,
J. L.
,
2009
, “
The TET Family of Proteins: Functions and Roles in Disease
,”
J. Mol. Cell Biol.
,
1
(
2
), pp.
82
92
.10.1093/jmcb/mjp025
6.
Marko
,
M.
,
Vlassis
,
A.
, and
Guialis
,
A.
,
2012
, “
Domains Involved in TAF15 Subcellular Localisation: Dependence on Cell Type and Ongoing Transcription
,”
Gene
,
506
(
2
), pp.
331
338
.10.1016/j.gene.2012.06.088
7.
Kuznetsov
,
A. V.
,
2024
, “
Simulating Growth of TDP-43 Cytosolic Inclusion Bodies in Neuron Soma
,”
bioRxiv:2023.11.28.569118
.10.1101/2023.11.28.569118
8.
Kuznetsov
,
A. V.
,
2024
, “
Numerical and Analytical Simulation of the Growth of Amyloid-β Plaques
,”
ASME J. Biomed. Eng.
,
146
(
6
), p.
061004
10.1115/1.4064969.
9.
Kuznetsov
,
A. V.
,
2023
, “
Effect of Diffusivity of Amyloid Beta Monomers on the Formation of Senile Plaques
,”
bioRxiv:2023.07.31.551367
10.1101/2023.07.31.551367.
10.
Kuznetsov
,
A. V.
,
2024
, “
Numerical Modeling of Senile Plaque Development Under Conditions of Limited Diffusivity of Amyloid-Β Monomers
,”
J. Theor. Biol.
,
587
, p.
111823
.10.1016/j.jtbi.2024.111823
11.
Kuznetsov
,
I. A.
, and
Kuznetsov
,
A. V.
,
2022
, “
An Analytical Solution Simulating Growth of Lewy Bodies
,”
Math. Med. Biol.
,
39
(
3
), pp.
299
312
.10.1093/imammb/dqac006
12.
Kuznetsov
,
A. V.
,
2024
, “
Lewy Body Radius Growth: The Hypothesis of the Cube Root of Time Dependency
,”
J. Theor. Biol.
,
581
, p.
111734
.10.1016/j.jtbi.2024.111734
13.
Kuznetsov
,
A. V.
,
2024
, “
The Growth Rate of Senile Plaques is Determined by the Competition between the Rate of Deposition of Free Aβ Aggregates into Plaques and the Autocatalytic Production of Free Aβ Aggregates
,”
J. Theor. Biol.
,
593
, p.
111900
.10.1016/j.jtbi.2024.111900
14.
Morris
,
A. M.
,
Watzky
,
M. A.
, and
Agar
,
J. N.
,
2008
, “
Fitting Neurological Protein Aggregation Kinetic Data Via a 2-Step, Minimal/"Ockham's Razor" Model: The Finke-Watzky Mechanism of Nucleation Followed by Autocatalytic Surface Growth
,”
Biochemistry
,
47
(
8
), pp.
2413
2427
.10.1021/bi701899y
15.
Iashchishyn
,
I. A.
,
Sulskis
,
D.
,
Nguyen Ngoc
,
M.
, Smirnovas, V., and Morozova-Roche, L. A.,
2017
, “
Finke-Watzky Two-Step Nucleation-Autocatalysis Model of S100A9 Amyloid Formation: Protein Misfolding as “Nucleation” Event
,”
ACS Chem. Neurosci.
,
8
, pp.
2152
2158
.10.1021/acschemneuro.7b00251
16.
Thacker
,
D.
,
Barghouth
,
M.
, and
Bless
,
M.
,
2023
, “
Direct Observation of Secondary Nucleation Along the Fibril Surface of the Amyloid Β 42 Peptide
,”
Proc. Natl. Acad. Sci.
,
120
(
25
), p.
e2220664120
.10.1073/pnas.2220664120
17.
Chen
,
G.
,
Xu
,
T.
, and
Yan
,
Y.
,
2017
, “
Amyloid Beta: Structure, Biology and Structure-Based Therapeutic Development
,”
Acta Pharmacol. Sin.
,
38
(
9
), pp.
1205
1235
.10.1038/aps.2017.28
18.
Luo
,
Y.
,
Blechingberg
,
J.
, and
Fernandes
,
A. M.
,
2015
, “
EWS and FUS Bind a Subset of Transcribed Genes Encoding Proteins Enriched in RNA Regulatory Functions
,”
BMC Genomics
,
16
, p.
929
.10.1186/s12864-015-2125-9
19.
Rabinovici
,
G. D.
, and
Miller
,
B. L.
,
2010
, “
Frontotemporal Lobar Degeneration: Epidemiology, Pathophysiology, Diagnosis and Management
,”
CNS Drugs
,
24
(
5
), pp.
375
398
.10.2165/11533100-000000000-00000
20.
Cavicchi
,
R. E.
,
King
,
J.
, and
Ripple
,
D. C.
,
2018
, “
Measurement of Average Aggregate Density by Sedimentation and Brownian Motion Analysis
,”
J. Pharm. Sci.
,
107
(
5
), pp.
1304
1312
.10.1016/j.xphs.2018.01.013
21.
Apfelbaum
,
A. A.
,
Wrenn
,
E. D.
, and
Lawlor
,
E. R.
,
2022
, “
The Importance of Fusion Protein Activity in Ewing Sarcoma and the Cell Intrinsic and Extrinsic Factors that Regulate it: A Review
,”
Front. Oncol.
,
12
, p.
1044707
.10.3389/fonc.2022.1044707
22.
Andersson
,
M. K.
,
Ståhlberg
,
A.
, and
Arvidsson
,
Y.
,
2008
, “
The Multifunctional FUS, EWS and TAF15 Proto-Oncoproteins show Cell Type-Specific Expression Patterns and Involvement in Cell Spreading and Stress Response
,”
BMC Cell Biol.
,
9
, p.
37
.10.1186/1471-2121-9-37
23.
Isogai
,
M.
,
Suzuki
,
H.
, and
Maeda
,
R.
,
2016
, “
Ubiquitin-Proteasome-Dependent Degradation of TBP-Like Protein is Prevented by Direct Binding of TFIIA
,”
Genes Cells
,
21
(
11
), pp.
1223
1232
.10.1111/gtc.12441
24.
Boltachev
,
G. S.
, and
Ivanov
,
M. G.
,
2020
, “
Effect of Nanoparticle Concentration on Coagulation Rate of Colloidal Suspensions
,”
Heliyon
,
6
(
2
), p.
e03295
.10.1016/j.heliyon.2020.e03295
25.
DeMattos
,
R. B.
,
Lu
,
J.
, and
Tang
,
Y.
,
2012
, “
A Plaque-Specific Antibody Clears Existing Β-Amyloid Plaques in Alzheimer's Disease Mice
,”
Neuron
,
76
(
5
), pp.
908
920
.10.1016/j.neuron.2012.10.029
26.
Watzky
,
M. A.
,
Finney
,
E. E.
, and
Finke
,
R. G.
,
2008
, “
Transition-Metal Nanocluster Size vs Formation Time and the Catalytically Effective Nucleus Number: A Mechanism-Based Treatment
,”
J. Am. Chem. Soc.
,
130
(
36
), pp.
11959
11969
.10.1021/ja8017412
27.
Cascella
,
R.
,
Bigi
,
A.
, and
Riffert
,
D. G.
,
2022
, “
A Quantitative Biology Approach Correlates Neuronal Toxicity with the Largest Inclusions of TDP-43
,”
Sci. Adv.
,
8
(
30
), p.
eabm6376
.10.1126/sciadv.abm6376
28.
Beck
,
J. V.
, and
Arnold
,
K. J.
,
1977
,
Parameter Estimation in Science and Engineering
,
Wiley
,
New York
.
29.
Zadeh
,
K. S.
, and
Montas
,
H. J.
,
2010
, “
A Class of Exact Solutions for Biomacromolecule Diffusion-Reaction in Live Cells
,”
J. Theor. Biol.
,
264
(
3
), pp.
914
933
.10.1016/j.jtbi.2010.03.028
30.
Zi
,
Z.
,
2011
, “
Sensitivity Analysis Approaches Applied to Systems Biology Models
,”
IET Syst. Biol.
,
5
(
6
), pp.
336
346
.10.1049/iet-syb.2011.0015
31.
Kuznetsov
,
I. A.
, and
Kuznetsov
,
A. V.
,
2019
, “
Investigating Sensitivity Coefficients Characterizing the Response of a Model of Tau Protein Transport in an Axon to Model Parameters
,”
Comput. Methods Biomech. Biomed. Eng.
,
22
(
1
), pp.
71
83
.10.1080/10255842.2018.1534233
32.
Kacser
,
H.
,
Burns
,
J. A.
, and
Fell
,
D. A.
,
1995
, “
The Control of Flux
,”
Biochem. Soc. Trans.
,
23
(
2
), pp.
341
366
.10.1042/bst0230341
33.
He
,
Y.
,
Liu
,
B. J.
, and
Yang
,
F. Y.
,
2024
, “
TAF15 Downregulation Contributes to the Benefits of Physical Training on Dendritic Spines and Working Memory in Aged Mice
,”
Aging Cell
, p.
e14244
.10.1111/acel.14244
34.
Vogel
,
J. W.
,
Iturria-Medina
,
Y.
, and
Strandberg
,
O. T.
,
2020
, “
Spread of Pathological Tau Proteins through Communicating Neurons in Human Alzheimer's Disease
,”
Nat. Commun.
,
11
(
1
), p.
2612
.10.1038/s41467-020-15701-2
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