bioRxiv (Cold Spring Harbor Laboratory),
Journal Year:
2023,
Volume and Issue:
unknown
Published: Nov. 30, 2023
Abstract
This
paper
introduces
a
mathematical
model
for
the
growth
of
transactive
response
DNA
binding
protein
43
kDa
(TDP-43)
inclusion
bodies
in
neuron
soma.
The
model’s
equations
enable
numerical
determination
concentrations
TDP-43
dimers,
monomers,
and
aggregates.
Assuming
all
aggregates
integrate
into
bodies,
predicts
size
bodies.
An
approximate
solution
to
is
derived
scenario
which
degradation
machinery
dysfunctional,
resulting
infinite
half-lives
solution,
valid
large
times,
that
body’s
radius
increases
proportionally
cube
root
time.
To
best
author’s
knowledge,
this
study
presents
first
attempt
relationship
between
sensitivity
analysis
indicates
monomers
aggregates,
as
well
body
radii,
are
independent
kinetic
constants.
While
full
continues
work
with
finite
half-lives,
becomes
invalid
scenarios
physiologically
relevant
(finite)
In
contrast
situation
shows
various
values
constants,
curves
representing
depicting
converge
distinct
constant
values.
Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences,
Journal Year:
2025,
Volume and Issue:
481(2309)
Published: March 1, 2025
The
paper
develops
a
criterion
to
quantify
the
accumulated
neurotoxicity
of
extracellular
amyloid
beta
(Aβ)
oligomers
in
Alzheimer's
disease
(AD).
Accumulated
is
determined
by
integrating
concentration
Aβ
within
control
volume
(CV)
over
time.
In
scenario
low
rate
free
oligomer
deposition
into
senile
plaques
and
dysfunctional
degradation
machinery,
resulting
an
infinitely
long
half-life
monomers
aggregates,
obtained
analytical
solution
reveals
quadratic
relationship
between
This
suggests
that
initially,
increases
slowly
but
accelerates
as
time
progresses.
could
help
understand
prolonged
delay
onset
AD
symptoms.
Furthermore,
model
indicates
with
duration
aggregation
process,
it
implies
if
protein
system
compromised,
becomes
unavoidable.
Eventually,
neuronal
death
only
question
way
prevent
this
outcome
ensure
machinery
for
peptides
their
aggregates
remains
functional.
A
threshold
value
suggested.
developed
theory
exceeded,
nearby
neurons
will
die.
progression
analysed.
An
S-shaped
growth
pattern,
half-deposition
increases,
revealed.
addition,
sensitivity
different
parameter
values
examined.
bioRxiv (Cold Spring Harbor Laboratory),
Journal Year:
2024,
Volume and Issue:
unknown
Published: Aug. 20, 2024
Abstract
The
paper
develops
a
criterion
to
quantify
the
accumulated
neurotoxicity
of
Aβ
oligomers
in
Alzheimer’s
disease
(AD).
Accumulated
is
determined
by
integrating
concentration
within
control
volume
over
time.
In
scenario
low
rate
free
oligomer
deposition
into
senile
plaques
and
dysfunctional
degradation
machinery,
resulting
an
infinitely
long
half-life
monomers
aggregates,
obtained
analytical
solution
reveals
quadratic
relationship
between
This
suggests
that
initially,
increases
slowly
but
accelerates
as
time
progresses.
could
help
understand
prolonged
delay
onset
AD
symptoms.
Furthermore,
model
indicates
with
duration
aggregation
process,
it
implies
if
protein
system
compromised,
becomes
unavoidable.
Eventually,
neuronal
death
only
question
way
prevent
this
outcome
ensure
machinery
for
peptides
their
aggregates
remains
functional.
A
threshold
value
suggested.
developed
theory
exceeded,
nearby
neurons
will
die.
progression
analyzed.
An
S-shaped
growth
pattern
half-deposition
revealed.
Additionally,
sensitivity
different
parameter
values
examined.
bioRxiv (Cold Spring Harbor Laboratory),
Journal Year:
2023,
Volume and Issue:
unknown
Published: Aug. 2, 2023
Abstract
Alzheimer’s
disease
(AD)
presents
a
perplexing
question:
why
does
its
development
span
decades,
even
though
individual
amyloid
beta
(Aβ)
deposits
(senile
plaques)
can
form
rapidly
in
as
little
24
hours,
recent
publications
suggest?
This
study
investigated
whether
the
formation
of
senile
plaques
be
limited
by
factors
other
than
polymerization
kinetics
alone.
Instead,
their
may
diffusion-driven
supply
Aβ
monomers,
along
with
rate
at
which
monomers
are
produced
from
precursor
protein
(APP)
and
undergo
degradation.
A
mathematical
model
incorporating
nucleation
autocatalytic
process
(via
Finke-Watzky
model),
well
monomer
diffusion,
was
proposed.
The
obtained
system
partial
differential
equations
solved
numerically,
simplified
version
analytically.
computational
results
predicted
that
it
takes
approximately
7
years
for
aggregates
to
reach
neurotoxic
concentration
50
μM.
Additionally,
sensitivity
analysis
performed
examine
how
diffusivity
production
impact
aggregates.
bioRxiv (Cold Spring Harbor Laboratory),
Journal Year:
2024,
Volume and Issue:
unknown
Published: Jan. 11, 2024
Abstract
This
paper
introduces
a
method
to
simulate
the
progression
of
senile
plaques,
focusing
on
scenarios
where
concentrations
amyloid
beta
(Aβ)
monomers
and
aggregates
vary
between
neurons.
Extracellular
variations
in
these
may
arise
due
limited
diffusivity
Aβ
high
rate
monomer
production
at
lipid
membranes,
requiring
substantial
concentration
gradient
for
diffusion-driven
transport
monomers.
The
dimensionless
formulation
model
is
presented,
identifying
four
key
parameters
governing
solutions
aggregate
concentrations,
as
well
radius
growing
plaque
within
control
volume.
These
include
monomers,
production,
half-lives
aggregates.
A
parameter
introduced
assess
validity
lumped
capacitance
approximation.
An
approximate
solution
derived
scenario
involving
large
dysfunctional
protein
degradation
machinery,
resulting
infinitely
long
In
this
scenario,
depend
solely
single
that
characterizes
production.
According
solution,
linearly
dependent
an
directly
proportional
cube
root
However,
when
departing
from
conditions
(e.g.,
finite
half-lives),
aggregates,
along
with
radius,
exhibit
complex
dependencies
all
parameters.
For
instance,
under
physiological
half-life
conditions,
reaches
maximum
value
stabilizes
thereafter.
bioRxiv (Cold Spring Harbor Laboratory),
Journal Year:
2024,
Volume and Issue:
unknown
Published: Nov. 3, 2024
Abstract
A
criterion
characterizing
the
combined
neurotoxicity
of
amyloid
beta
and
tau
oligomers
is
suggested.
mathematical
model
that
makes
it
possible
to
calculate
a
value
this
during
senile
plaque
NFT
formation
proposed.
Computations
show
for
physiologically
relevant
parameter
values,
increases
approximately
linearly
as
time
increases.
Once
neurofibrillary
tangles
starts
in
addition
formation,
slope
rate
at
which
becomes
larger.
The
critical
upon
reaching
neuron
dies
estimated.
predict
unless
production
rates
monomers
are
very
large,
order
accumulated
toxicity
reach
value,
degradation
machinery
responsible
must
become
dysfunctional.
after
20
years
aggregation
process
strongly
influenced
by
deposition
into
plaques
NFTs.
This
suggests
NFTs
may
reduce
sequestering
more
toxic
oligomeric
species
less
insoluble
aggregates.
Mathematical Medicine and Biology A Journal of the IMA,
Journal Year:
2024,
Volume and Issue:
unknown
Published: Oct. 15, 2024
Abstract
Alzheimer’s
disease
(AD)
presents
a
perplexing
question:
why
does
its
development
span
decades,
even
though
individual
amyloid
beta
(Aβ)
deposits
(senile
plaques)
can
form
rapidly
in
as
little
24
hours,
recent
publications
suggest?
This
study
investigated
whether
the
formation
of
senile
plaques
be
limited
by
factors
other
than
polymerization
kinetics
alone.
Instead,
their
may
diffusion-driven
supply
Aβ
monomers,
along
with
rate
at
which
monomers
are
produced
from
precursor
protein
and
undergo
degradation.
A
mathematical
model
incorporating
nucleation
autocatalytic
process
(via
Finke–Watzky
model),
well
monomer
diffusion,
was
proposed.
The
obtained
system
partial
differential
equations
solved
numerically,
simplified
version
analytically.
computational
results
predicted
that
it
takes
approximately
7
years
for
aggregates
to
reach
neurotoxic
concentration
50
μM.
Additionally,
sensitivity
analysis
performed
examine
how
diffusivity
production
impact
aggregates.
bioRxiv (Cold Spring Harbor Laboratory),
Journal Year:
2024,
Volume and Issue:
unknown
Published: April 10, 2024
Abstract
The
formation
of
amyloid
beta
(Aβ)
deposits
(senile
plaques)
is
one
the
hallmarks
Alzheimer’s
disease
(AD).
This
study
investigates
what
processes
are
primarily
responsible
for
their
formation.
A
model
developed
to
simulate
diffusion
monomers,
production
free
Aβ
aggregates
through
nucleation
and
autocatalytic
processes,
deposition
these
into
senile
plaques.
suggests
that
efficient
degradation
monomers
alone
may
suffice
prevent
growth
plaques,
even
without
degrading
existing
because
interrupts
supply
reactants
needed
plaque
impact
monomer
diffusivity
demonstrated
be
small,
enabling
application
lumped
capacitance
approximation
derivation
approximate
analytical
solutions
limiting
cases
with
both
small
large
rates
aggregate
It
found
rate
governed
by
two
competing
processes.
One
If
this
grows
slowly.
However,
if
plaques
very
large,
removed
from
intracellular
fluid
leaving
insufficient
catalyze
new
aggregates.
under
certain
conditions,
offer
neuroprotection
impede
own
growth.
Additionally,
it
indicates
there
exists
an
optimal
at
which
attain
maximum
size.
Abstract
To
the
best
of
author’s
knowledge,
this
paper
presents
first
attempt
to
develop
a
mathematical
model
formation
and
growth
inclusions
containing
misfolded
TATA-box
binding
protein
associated
factor
15
(TAF15).
It
has
recently
been
shown
that
TAF15
are
involved
in
approximately
10%
cases
frontotemporal
lobar
degeneration
(FTLD).
FTLD
is
second
most
common
neurodegenerative
disease
after
Alzheimer’s
(AD).
characterized
by
progressive
loss
personality,
behavioral
changes,
decline
language
skills
due
frontal
anterior
temporal
lobes.
The
simulates
monomer
production,
nucleation
autocatalytic
free
aggregates,
their
deposition
into
inclusions.
accuracy
numerical
solution
equations
validated
comparing
it
with
analytical
solutions
available
for
limiting
cases.
Physiologically
relevant
parameter
values
were
used
predict
inclusion
growth.
influenced
two
opposing
mechanisms:
rate
at
which
aggregates
deposited
production
from
monomers.
A
low
slows
growth,
while
high
hinders
new
thus
also
slowing
Consequently,
maximized
an
intermediate
