European Journal of Applied Mathematics,
Journal Year:
2024,
Volume and Issue:
unknown, P. 1 - 27
Published: Nov. 7, 2024
Abstract
We
introduce
a
free
boundary
model
to
study
the
effect
of
vesicle
transport
onto
neurite
growth.
It
consists
systems
drift-diffusion
equations
describing
evolution
density
antero-
and
retrograde
vesicles
in
each
coupled
reservoirs
located
at
soma
growth
cones
neurites,
respectively.
The
allows
for
change
length
as
function
concentration
cones.
After
establishing
existence
uniqueness
time-dependent
problem,
we
briefly
comment
on
possible
types
stationary
solutions.
Finally,
provide
numerical
studies
biologically
relevant
scales
using
finite
volume
scheme.
illustrate
capability
reproduce
cycles
extension
retraction.
bioRxiv (Cold Spring Harbor Laboratory),
Journal Year:
2024,
Volume and Issue:
unknown
Published: May 23, 2024
ABSTRACT
Axonal
outgrowth,
cell
crawling,
and
cytokinesis
utilize
actomyosin,
microtubule-based
motors,
cytoskeletal
dynamics,
substrate
adhesions
to
produce
traction
forces
bulk
cellular
motion.
While
it
has
long
been
appreciated
that
growth
cones
resemble
crawling
cells
the
mechanisms
drive
help
power
they
are
typically
viewed
as
unique
processes.
To
better
understand
relationship
between
these
modes
of
motility,
here,
we
developed
a
unified
active
fluid
model
cytokinesis,
amoeboid
migration,
mesenchymal
neuronal
axonal
outgrowth
in
terms
flow,
adhesions,
viscosity,
force
generation.
Using
numerical
modeling,
fit
subcellular
velocity
profiles
motions
structures
docked
organelles
from
previously
published
studies
infer
underlying
patterns
generation
adhesion.
Our
results
indicate
that,
during
there
is
primary
converge
zone
at
cleavage
furrow
drives
flow
towards
it;
symmetric
across
cell,
result,
stationary.
In
mesenchymal,
amoeboid,
site
shifts,
differences
adhesion
front
back
crawling.
During
migration
convergence
lies
within
cone,
which
actin
retrograde
P-domain
anterograde
shaft.
They
differ
body
weakly
attached
thus
moves
forward
same
axon.
contrast,
strongly
adheres
remains
stationary,
resulting
decrease
away
cone.
The
simplicity
with
can
be
modeled
by
varying
coefficients
simple
suggests
deep
connection
them.
Briefings in Bioinformatics,
Journal Year:
2024,
Volume and Issue:
25(4)
Published: May 23, 2024
Abstract
The
development
of
the
human
central
nervous
system
initiates
in
early
embryonic
period
until
long
after
delivery.
It
has
been
shown
that
several
neurological
and
neuropsychiatric
diseases
originate
from
prenatal
incidents.
Mathematical
models
offer
a
direct
way
to
understand
neurodevelopmental
processes
better.
modelling
neurodevelopment
during
is
challenging
terms
how
‘Approach’,
initiate
propose
appropriate
equations
fit
underlying
dynamics
while
including
variety
elements
are
built-in
naturally
process
neurodevelopment.
imperative
answer
where
start
modelling;
other
words,
what
‘Approach’?
Therefore,
one
objective
this
study
was
tackle
mathematical
issue
broadly
different
aspects
approaches.
approaches
were
divided
into
three
categories:
cell
division,
neural
tube
growth
plate
growth.
We
concluded
approach
provides
suitable
platform
for
simulation
brain
formation/neurodevelopment
compared
division
devised
novel
equation
designed
algorithms
include
geometrical
topological
could
most
necessary
period.
Hence,
proposed
defined
structure
would
be
generate
an
artificial
network
autonomously
grows
develops.
Frontiers in Cell and Developmental Biology,
Journal Year:
2024,
Volume and Issue:
12
Published: Oct. 17, 2024
While
the
structural
organization
and
molecular
biology
of
neurons
are
well
characterized,
physical
process
axonal
elongation
remains
elusive.
The
classic
view
posited
occurs
through
deposition
cytoskeletal
elements
in
growth
cone
at
tip
a
stationary
array
microtubules.
Yet,
recent
studies
reveal
microtubules
docked
organelles
flow
forward
bulk
elongating
axons
European Journal of Applied Mathematics,
Journal Year:
2024,
Volume and Issue:
unknown, P. 1 - 27
Published: Nov. 7, 2024
Abstract
We
introduce
a
free
boundary
model
to
study
the
effect
of
vesicle
transport
onto
neurite
growth.
It
consists
systems
drift-diffusion
equations
describing
evolution
density
antero-
and
retrograde
vesicles
in
each
coupled
reservoirs
located
at
soma
growth
cones
neurites,
respectively.
The
allows
for
change
length
as
function
concentration
cones.
After
establishing
existence
uniqueness
time-dependent
problem,
we
briefly
comment
on
possible
types
stationary
solutions.
Finally,
provide
numerical
studies
biologically
relevant
scales
using
finite
volume
scheme.
illustrate
capability
reproduce
cycles
extension
retraction.
