Dynamic balance between vesicle transport and microtubule growth enables neurite
growth
by
Arjun Singh Yadaw, Mustafa Siddiq, Vera Rabinovich, Ravi Iyengar and Jens Hansen
Supplementary Methods:
Identification of the dependency of average dynamic MT length and dynamic MT
degradation rates on the effective tubulin concentration
To generate two formulas that describe the behavior of dynamic MTs that can be incorporated
into our main model we simulated dynamic MT growth profiles under varying effective tubulin
concentrations using the model of Margolin and co-workers (Margolin et al., 2011). We selected
this model, since it offers a desirable balance between computational performance and biological
detail. To estimate the length distribution of dynamic microtubules, we simulated the behavior of
one microtubule (i.e. 13 interacting protofilaments) over a long time period and calculated the
frequency of all microtubule lengths over this time period (Suppl. figure 2). We assume that the
growth dynamics of all dynamic microtubules in the neurite are independent of each other. Based
on this assumption the frequency of a certain microtubule length within this time period is also
proportional to the frequency of a certain microtubule length among multiple microtubules at one
time point. In other words, the length distribution of one microtubule over an infinite time period
equals the length distribution of infinitive microtubules at one time-point, i.e. at every time point.
In consequence we estimate the length distribution of all dynamic microtubules based on the
simulation of the growth and catastrophic behavior of one dynamic microtubule.
We used the model of Margolin et al to generate different length distributions of the
microtubules in dependence of different effective tubulin concentrations. We calculated the
microtubule length by averaging the length of the 13 protofilaments at each time point. The
higher the effective tubulin concentration the longer the dynamic microtubules. Effective tubulin
concentration is defined to be the concentration of free tubulin that is available for the
incorporation into dynamic microtubules. For each effective tubulin concentration, we
interpolated the length distributions with a gamma function, since the gamma function
distribution allows the description of a multiple-step process that leads to catastrophic
breakdown (Gardner et al., 2011). The gamma function is described by a rate and a scale
parameter. Consequently, we obtained one shape and one scale parameter for each effective
tubulin concentration. To allow the prediction of the length distribution of dynamic microtubules
in dependence of any effective tubulin concentration, we used this data to generate two formulas:
one that describes the dependency of the shape parameter on the effective tubulin concentration
and one that describes the dependency of the scale parameter on the effective tubulin
concentration.
𝑆𝑐𝑎𝑙𝑒𝑃𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟 = 𝑎1 × 𝑒 𝑎2 𝑥 + 𝑏1 × 𝑒 𝑏2 𝑥
𝑆ℎ𝑎𝑝𝑒𝑃𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟 = 𝑚𝑥 + 𝑏
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐷𝑦𝑛𝑎𝑚𝑖𝑐 𝑀𝑇 𝐿𝑒𝑛𝑔𝑡ℎ = 𝑆𝑐𝑎𝑙𝑒𝑃𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟 × 𝑆ℎ𝑎𝑝𝑒𝑃𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟 .
Where 𝑎1 , 𝑎2 , 𝑏1 and 𝑏2 are power fitting parameter of scale parameter and 𝑚 and 𝑏 are power
fitting parameter of shape function. x : Effective tubulin concentration.
The same dynamic MT growth profiles were used to identify the dependency of the dynamic MT
degradation rate on the effective tubulin concentration. We assumed that a dynamic MT
undergoes complete catastrophic breakdown, if its length is below 8 tubulin dimers. Based on
this assumption, we counted how often the dynamic MT of each growth profile undergoes
complete catastrophic breakdown. The dynamic MT degradation rate for each effective tubulin
concentration was obtained by dividing this number by the simulation time. A power fitting
method was used to obtain a formula that describes the dependence of the degradation rate on the
effective tubulin concentration.
𝐷𝑒𝑔𝑟𝑎𝑑𝑎𝑡𝑖𝑜𝑛𝑟𝑎𝑡𝑒 = 𝑑1 × 𝑥 𝑑2
Where 𝑑1 and 𝑑2 are power fitting parameter of degradation rate.
Image Analysis: MetaMorph software was used for image stitching of individual image tiles.
Neurites were manually pseudo colored. Neurite lengths were quantified using MetaMorph.
Supplementary Figure 1A
Bright field images of neurites at varying times and distribution and gamma fitting of neurites
lengths at different time points
16hrs
22hrs
28hrs
34hrs
40hrs
46hrs
52hrs
58hrs
64hrs
70hrs
Supplementary Figure 1B
Supplementary Figure 1: Neurites grow with different outgrowth velocities. Neurons were
dissected from rat cortical brain, incubated for 16h to allow initial growth, followed by Image
acquisition every 6h up to 70h after plating. (A) Images were pseudo colored and subjected to
neurite length quantification via Metamorph. (B) The length distribution of the longest neurite
shifts towards higher values over the experiment time. For each dataset we identified the length
of the top and bottom 10% and 25% quantile as well as the median length. These values were
used to calculate the outgrowth velocity for the selected quantiles (Fig. 2B).
Supplementary Figure 2
Supplementary Figure 2: Dynamic model of microtubule growth. Using the model by
Margolin et al (Margolin et al., 2012) we generated growth profiles of single dynamic
microtubules over a time period of mins as a function of varying effective tubulin concentrations
ranging from 8 to 10 µM. 4 examples are shown in (A). We identified the length distribution for
each growth profile and interpolated it with a gamma function (B). The gamma function is
described by a shape and a scale parameter. We identified two formulas that allow the prediction
of the shape and the scale parameter in dependence of the effective tubulin concentration (C).
The product of both parameters gives the average length of the dynamic microtubule (D). To
determine the degradation rate of dynamic MTs in dependence of the effective tubulin
concentration, we counted how often the dynamic MT of each growth profile falls below the
length of 8 tubulin dimers that we defined as the threshold for complete catastrophic breakdown.
(E) The obtained degradation rates were interpolated with power fitting method to obtain a
formula that was incorporated into our main model. (F) The formulas for the average dynamic
MT lengths and the degradation rates were incorporated into the main model. New dynamic MTs
enter the pool of dynamic MTs with a certain nucleation rate. Dynamic MTs are either degraded
at the specified degradation rate (D) or are converted into stable MTs at a specified conversion
rate. The tubulin dependent average length of dynamic MTs is calculated via the formula that
was obtained in (E). The length increase of the stable MTs is the product of the average length of the
dynamic MTs and the count of converted dynamic MTs. The length of the dynamic MTs is the product of
the dynamic MTs and the count of dynamic MTs.
2
Surface area [m ]
OR
# vesicles
Supplementary Figure 3A
# molecules
Time [min]
Time [min]
# molecules
Time [min]
Time [min]
# molecules
# molecules
Time [min]
Time [min]
# molecules
# molecules
Time [min]
Time [min]
# molecules
Length
[m]
# MTs
Concentration
[M]
Time [min]
Time [min]
# molecules
Molecule flux [# / min]
2
Membrane flux [m /min]
Suppl. Figure 3B
Time [min]
Time [min]
Molecule flux [# / min]
Time [min]
Time [min]
Molecule flux [# / min]
Molecule flux [# / min]
Time [min]
Time [min]
Molecule flux [# / min]
Molecule flux [# / min]
Time [min]
Time [min]
Molecule flux [# / min]
Molecule flux [# / min]
Time [min]
Supplementary Figure 3: Steady state distribution of proteins and membrane vesicles and
fluxes.(A) At steady state all protein and membrane amounts stay constant in the different
compartments, except in the Microtubule Transport Compartment (MTC) and the neurite shaft.
Neurite shaft growth is facilitated by continuous membrane addition, so the membrane surface
area of the neurite shaft grows over the time. The MTC grows parallel to the neurite shaft,
'consuming' some of the vesicles i.e. membrane and transmembrane proteins. The figure shows
the membrane surface areas or protein amounts in each compartment within each set of vesicles
(in contrast to Fig 3C that shows the number of vesicles). B1 refers to anterograde vesicles that
bud from the TGN with the coat protein B, A1 refers to anterograde vesicles that bud from the
TGN with the coat A, B2 refers to retrograde vesicles that bud from the GC with coat protein B
and A2 refers to retrograde vesicles that bud from the GC with coat protein A. Green lines refer
to TGN or growth cone (GC), orange lines refer to anterograde moving vesicles (B1, A1) and
blue lines to retrograde moving vesicles (B2, A2). Solid lines represent those vesicles that are
mainly responsible for membrane transport in the indicated direction (i.e. B1 in the anterograde
direction and A2 in the retrograde direction). (B) All fluxes, i.e. membrane or protein transfers
from one compartment into the other are shown. Colors and line styles are the same as in (A).
Supplementary Figure 4
A
B
C
D
E
F
G
H
I
Supplementary Figure 4: Comparison of the predicted steady state conditions with the
numerically identified steady state conditions. (A) Results that were obtained for (A) no NOG
and fixed NOG velocities of (B) 2.5 µm/h, (C) 5 µm/h, (D) 7.5 µm/h, (E) 10 µm/h, (F) 12.5
µm/h, (G) 15 µm/h, (H) 17.5 µm/h and (I) 20 µm/h. See figure 4C and 4D for details.
Supplementary Figure 5
A
B
C
D
E
F
G
Supplementary Figure 5: Dependency of the various transmembrane protein amounts on
the growth velocity and the tethering rate at the growth cone. The start amount of cycling
trans membranous proteins that are involved in anterograde vesicular transport (Fig 5A: vSNARE V, here B: kinesin receptor) increases with increasing velocity, since more vesicle are
generated at the TGN that need to have the same amount of these molecules per vesicle.
Similarly, the production rates for these molecules increase over proportionally. The starting
amount of cycling transmembrane proteins that are involved in retrograde transport decreases
with increasing velocities ((A) v-SNARE U, (C) dynein receptor). Increased outgrowth velocity
at a constant membrane cycling rate depends on an increase of net membrane transfer to the
growth cone, i.e. the anterograde membrane, but not on an increase of the retrograde transport
rate. The total amount of v-SNARE U and dynein receptor that needs to be loaded on the
retrograde vesicles during endocytosis at the growth cone stays the same. A higher anterograde
transport rate offers more binding sites for the same amount of SNARE U and dynein receptor,
lowering the needed concentration of these proteins at the TGN. The production rate increases
over proportionally for the proteins that are involved in anterograde transport (Fig. 5B: vSNARE V, here B: kinesin receptor), while it only increases linearly for the proteins that are
involved in retrograde transport (A, C). The initial amount of stationary proteins (D-G) does not
increase with increased NOG velocity and the production rates for these proteins are very small,
since only a small percentage of stationary proteins cycle between the TGN and the GC and are
consumed by the MTC.
Supplementary Table S1: Percentage of active vesicles movement in MTC and GC.
Postulates governing SCP dynamics
Trans Golgi Network size
50 mm2
Percentage of anterograde vesicles in MTC that are actively transported along microtubules
10
Percentage of anterograde vesicles in GC cytoplasm that fuse with the growth cone
10
Percentage of retrograde vesicles in MTC that are actively transported along microtubules
90
Percentage of retrograde vesicles in CB cytoplasm that fuse with the TGN
90
Table S2: Symbols for dependent and independent variables of the model
SL.
No.
Symbols
Description
1.
2.
3.
4.
5.
6.
7.
8.
𝑆𝐺
𝑆𝑃𝑀
𝐴𝐺
𝐵𝐺
𝐴𝑃𝑀
𝐵𝑃𝑀
𝑓1
𝑓2
9.
𝑓3
10.
𝑓4
11.
𝑓5
12.
𝑓6
13.
𝑓7
14.
15.
16.
𝑓8
𝑆𝑋𝐺
𝑠𝑥𝐺
17.
18.
𝑅1𝐺
𝑟1𝐺
19.
20.
𝐾𝑖𝑛𝐺
𝑘𝑖𝑛𝐺
21.
22.
𝐷𝑦𝑛𝐺
𝑑𝑦𝑛𝐺
Total amount of Dynein motor protein in Golgi compartment.
Concentration of Dynein motor protein Dyn in Golgi compartment. Where
𝐷𝑦𝑛𝐺
𝑑𝑦𝑛𝐺 =
23.
𝐵𝐺
𝑆𝑋𝐺𝐶𝐶
24.
𝐺
𝑠𝑥𝐺𝐶𝐶
Amount of SNAREs SX in the vesicles originated from Golgi with coat B in
Growth Cone Cytoplasm (GCC) compartment
Average concentration of SNARE SX in the vesicles originated from Golgi
with coat protein B in Growth Cone Cytoplasm (GCC) compartment. Where
Size of Golgi Compartment
Size of Growth Cone Plasma Membrane Compartment
Coat A budded vesicles from Golgi
Coat B budded vesicles from Golgi
Coat A budded vesicles from Growth Cone Plasma Membrane
Coat B budded vesicles from Growth Cone Plasma Membrane
Forward rate of vesicles movement from Golgi to Cell Body Cytoplasm
Forward rate of vesicles movement from Cell Body Cytoplasm to Motor
Transport Compartment
Forward rate of vesicles movement from Motor Transport Unit to Growth
Cone Cytoplasm
Forward rate of vesicles movement from Growth Cone Cytoplasm to
Growth Cone Plasma Membrane
Forward rate of vesicles movement from Growth Cone Plasma Membrane to
Growth Cone Cytoplasm
Forward rate of vesicles movement from Growth Cone Cytoplasm to
Motor Transport Unit
Forward rate of vesicles movement from Motor Transport Unit to
Cell Body Cytoplasm
Forward rate of vesicles movement from Cell Body Cytoplasm to Golgi
Total amount of SNARE X in Golgi compartment.
Concentration of SNARE X in Golgi compartment. Where 𝑠𝑥𝐺 =
𝑆𝑋𝐺
𝑆𝐺
Total amount of Recruitment factor 1 in Golgi compartment
Concentration of Recruitment factor 1 in Golgi compartment. Where 𝑟1 𝐺 =
𝑅1 𝐺 /𝑆𝐺
Total amount of Kinesin motor protein in Golgi compartment.
Concentration of Kinesin motor protein Kin in Golgi compartment. Where
𝐾𝑖𝑛
𝑘𝑖𝑛𝐺 = 𝑆 𝐺
𝐺
𝐵
𝑆𝐺
𝐵
𝐵
𝐵
𝐺
𝐺
𝐺
𝑠𝑥𝐶𝐵𝐶
= 𝑆𝑋𝐶𝐵𝐶
/ 𝑁𝐶𝐵𝐶
25.
𝐵
𝐺
𝐾𝑖𝑛𝑀𝑇𝐶
Amount of Kinesin motor protein Kin in the vesicles originated from Golgi
compartment with coat B in MTC compartment.
𝐵
26.
𝐺
𝑘𝑖𝑛𝑀𝑇𝐶
27.
𝐺
𝐷𝑦𝑛𝑀𝑇𝐶
28.
𝐺
𝑑𝑦𝑛𝑀𝑇𝐶
29.
𝐺
𝑅1 𝐵𝐶𝐵𝐶
30.
𝐺
𝑟1 𝐶𝐵𝐶
𝐴
𝐴
𝐵
Be the average concentration of Kinesin Kin in vesicles originated in
compartment G with coat protein B in MTC compartment. Where
𝐵𝐺
𝐵𝐺
𝐵𝐺
𝑘𝑖𝑛𝐶𝐵𝐶
= 𝐾𝑖𝑛𝐶𝐵𝐶
/ 𝑁𝐶𝐵𝐶
Amount of Dynein motor protein Dyn in the vesicles originated from Golgi
compartment with coat A in MTC compartment.
Average concentration of Dynein Dyn in vesicles originated in compartment
G with coat protein A in MTC compartment. Where
𝐴𝐺
𝐴𝐺
𝐴𝐺
𝑑𝑦𝑛𝐶𝐵𝐶
= 𝐷𝑦𝑛𝐶𝐵𝐶
/ 𝑁𝐶𝐵𝐶
Total amount of recruitment factor 1 (R1) in the vesicles originated from
Golgi compartment with coat B in CBC compartment.
Average concentration recruitment factor 1 (R1) in the vesicles originated
from Golgi compartment with coat B in CBC compartment. Where
𝐵
𝐺
𝑟1 𝐶𝐵𝐶
= 𝑅1
31.
𝐺
𝑅2 𝐵𝐶𝐵𝐶
32.
𝐺
𝑟2 𝐶𝐵𝐶
𝐵
𝐵
𝐵
𝐺
𝑁𝐶𝐵𝐶
34.
35.
36.
𝐵
𝑘𝑠𝑥
37.
38.
39.
𝐴
𝑘𝑘𝑖𝑛
𝐴
𝑘𝑑𝑦𝑛
𝑘𝑟𝐴1
𝑘𝑟𝐴2
𝐵
𝜙𝑆𝑉𝐺
𝐵
40.
𝐺
𝜙𝑘𝑖𝑛
41.
𝐺
𝜙𝑑𝑦𝑛
42.
𝜙𝑟1𝐺
43.
𝜙𝑟2𝐺
44.
𝑤𝐺𝐴
45.
𝐴
𝑤𝑃𝑀
46.
𝑤𝐺𝐵
47.
𝐵
𝑤𝑃𝑀
𝐵
𝐵
𝐵
𝐶𝐵𝐶
𝐵
𝐺
/ 𝑁𝐶𝐵𝐶
Total amount of recruitment factor 2 (R2) in the vesicles originated from
Golgi compartment with coat B in CBC compartment.
Average concentration recruitment factor 2 (R2) in the vesicles originated
from Golgi compartment with coat B in CBC compartment. Where
𝐺
𝑟2 𝐶𝐵𝐶
= 𝑅2
33.
𝐵𝐺
𝐵𝐺
𝐶𝐵𝐶
𝐵
𝐺
/ 𝑁𝐶𝐵𝐶
Number of vesicles originated from Trans Golgi Network with coat protein
B in Cell Body Cytoplasm (CBC) compartment.
Dissociation constant of SNARE SX with coat protein B.
Dissociation constants of motor 𝑘𝑖𝑛𝐺 from coat protein A
Dissociation constants of motor 𝑑𝑦𝑛𝐺 from coat protein A
Dissociation constants of recruitment factor 1 (𝑟1 ) from coat protein A
Dissociation constants of recruitment factor 2 (𝑟2 ) from coat protein A
Denotes a saturation function for carrying SNARE SV to vesicles that
are initiated by coat B from Golgi
Denotes a saturation function for carrying motor protein kin to vesicles that
are initiated by coat B from Golgi
Denotes a saturation function for carrying motor protein dyn to vesicles that
are initiated by coat B from Golgi
Denotes a saturation function for carrying recruitment factor 𝑟1 to vesicles
that are initiated by coat B from Golgi
Denotes a saturation function for carrying recruitment factor 𝑟2 to vesicles
that are initiated by coat B from Golgi
Vesicles budding rate at Golgi with coat A
Vesicles budding rate at Plasma Membrane with coat A
Vesicles budding rate at Golgi with coat B
Vesicles budding rate at Plasma Membrane with coat B
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
𝜅𝑋𝑈
𝜅𝑌𝑉
Fusion rate constant of vesicles (X,U) to target compartment
Fusion rate constant of vesicles (Y,V) to target compartment
𝑣𝑘
𝑣𝑑
𝑘𝑀𝑃
Velocity of vesicle movement by one Kinesin receptor protein
Velocity of vesicle movement by one Dynein receptor protein
Membrane lipid production rate
𝑆𝜓
𝑀𝜓
𝑅𝜓
SNARE binding spots per vesicle area
Motor protein binding spots per vesicle area
Cargo binding spots per vesicle area
𝑁1
𝑁2
𝛽1
𝛽2
a
b
𝜃1
𝜃2
𝐿1
γ
𝐿𝑠𝑡𝑏𝑙
𝐿𝑑𝑦𝑛
𝐿𝑀𝑇𝐵
𝑇𝐶𝐵𝐶
𝑇𝑀𝑇𝐶
𝐿𝐶𝐵𝐶
𝐿𝑀𝑇𝐶
𝐵𝐺
#𝑘𝐶𝐵𝐶
77.
𝐺
#𝑘𝑀𝑇𝐶
78.
𝑘𝑖𝑛
𝑓𝐶𝐵𝐶
Number of dynamic microtubules
Number of microtubules in neurite shaft cross section
Nucleation rate of dynamic microtubule
Degradation rate of dynamic microtubules
Scale parameter of power series method of degradation rate
Exponent parameter of power series method of degradation rate
Shape Parameter ( Gamma distribution)
Scale parameter ( Gamma distribution)
Average dynamic microtubule length
Rate of conversion from dynamic microtubules to stable microtubules
Increase in length of Stable Microtubules
Combined length of Dynamic Microtubules
Microtubule scaffold length
Average time taken by a vesicle to cross CBC compartment
Average time taken by a vesicle to cross MTC compartment
Microtubule scaffold length in CBC compartment
Microtubule scaffold length in MTC compartment
Number of kinesin motor receptor per vesicle in CBC compartment which is
budded with Coat B from Golgi
Number of kinesin motor receptor per vesicle in MTC compartment which is
budded with Coat B from Golgi
Fraction of bound kinesin motor receptor in CBC compartment
79.
𝑘𝑖𝑛
𝑓𝑀𝑇𝐶
Fraction of bound kinesin motor receptor in MTC compartment
80.
𝐺
𝑓𝑁𝐶𝐵𝐶
𝐵
Fraction of bound coat B budded vesicles in CBC compartment
81.
𝐺
𝑓𝑁𝑀𝑇𝐶
𝐵
Fraction of bound coat B budded vesicles in MTC compartment
82.
𝐺
𝑓𝑁𝐺𝐶𝐶
𝐵
Fraction of bound coat B budded vesicles in GCC compartment
83.
84.
𝐵
𝑆𝐴𝑉𝑆𝐴
𝑅𝑆𝐶𝑃𝑉𝐹
Anterograde vesicle surface area
Required snare complex per vesicle fusion
𝑺𝒖𝒑𝒆𝒓𝒔𝒄𝒓𝒊𝒑𝒕𝒔𝒖𝒃𝒔𝒄𝒓𝒊𝒑𝒕 𝒐𝒇 𝒔𝒖𝒑𝒆𝒓𝒔𝒄𝒓𝒊𝒑𝒕
𝒁𝒔𝒖𝒃𝒔𝒄𝒓𝒊𝒑𝒕
where, Superscript = Coat Protein
Subscript of superscript = Compartment
Subscript = Compartment
Table S3: Parameters and Initial values
Parameter
Number of microtubules per cross-section
Diameter of neurite
Length of growth cones
Kinesin motor protein anterograde velocity
Dynein motor protein retrograde velocity
Vesicle diameter
Growth cone surface area
Dissociation constant of SNARE SX with
𝐴
coat protein B. (𝑘𝑠𝑥
)
Dissociation constant of SNARE SU with
𝐴
coat protein B. (𝑘𝑠𝑢
)
Dissociation constant of SNARE SX with
𝐵
coat protein B. (𝑘𝑠𝑥
)
Dissociation constant of SNARE SU with
𝐵
coat protein B. (𝑘𝑠𝑢
)
Dissociation constant of SNARE SY with
𝐴
coat protein B. (𝑘𝑠𝑦
)
Dissociation constant of SNARE SV with
𝐴
coat protein B. (𝑘𝑠𝑣
)
Dissociation constant of SNARE SY with
𝐵
coat protein B. (𝑘𝑠𝑦
)
Dissociation constant of SNARE SV with
𝐵
coat protein B. (𝑘𝑠𝑣
)
Dissociation constants of recruitment factor
1 from coat protein A (𝑘𝑟𝐴1 )
Value
20
(10 – 100)
1.0
(1.0 – 3.0)
10
1
Units
#
Reference
Fadic et al., 1985
µm
Harris et al., 1989
µm
µm/s
0.65
µm/s
39.7 ± 6.6
70 - 200
1.00
nm
µm2
Molecules
1.00
Molecules
10000
Molecules
100
Molecules
10000
Molecules
100
Molecules
1.00
Molecules
1.00
Molecules
1.00
Molecules
Beller et al., 2013
Vale et al., 1996
Carter et al., 2005
King et al., 2000
Nishiura et al, 2004
Zhang et al., 1998
Kunda et al., 2001
Margolin et al.,
2012
Margolin et al.,
2012
Margolin et al.,
2012
Margolin et al.,
2012
Margolin et al.,
2012
Margolin et al.,
2012
Margolin et al.,
2012
Margolin et al.,
2012
Assumed
Dissociation constants of recruitment factor
1 from coat protein A (𝑘𝑟𝐵1 )
Dissociation constants of recruitment factor
2 from coat protein A (𝑘𝑟𝐴2 )
Dissociation constants of recruitment factor
2 from coat protein A (𝑘𝑟𝐵2 )
Cargo binding spots per vesicle surface area
Dissociation constants of motor kinesin
𝐴
𝑘𝑖𝑛𝐺 from coat protein A (𝑘𝑘𝑖𝑛
)
Dissociation constants of motor kinesin
𝐵
𝑘𝑖𝑛𝐺 from coat protein B (𝑘𝑘𝑖𝑛
)
Dissociation constants of motor Dynein
𝐴
𝐷𝑦𝑛𝐺 from coat protein B (𝑘𝑑𝑦𝑛
)
Dissociation constants of motor Dynein
𝐵
𝐷𝑦𝑛𝐺 from coat protein B (𝑘𝑑𝑦𝑛
)
Length of CBC compartment
Length of GCC compartment
Length of MTC compartment
Scale parameter multiplier (a1)
Scale parameter exponent (a2)
Scale parameter multiplier (b1)
Scale parameter exponent (b2)
Shape multiplier (m)
Shape constant (b)
Degradation multiplier (d1)
Degradation exponent (d2)
Anterograde vesicle surface area
Retrograde vesicle surface area
Snare binding spots per vesicle surface area
Motor binding spots per vesicle surface area
SNARE Y production rate at TNG
SNARE V production rate at TNG
SNARE X production rate at TNG
SNARE U production rate at TNG
Motor K production rate at TNG
Motor D production rate at TNG
Recruitment factor 1 production rate at TNG
Recruitment factor 2 production rate at TNG
Vesicles budding rate at TGN with coat A
( 𝑤𝐺𝐴 )
Vesicles budding rate at Plasma Membrane
𝐴
with coat A ( 𝑤𝑃𝑀
)
Vesicles budding rate at TGN with coat B
( 𝑤𝐺𝐵 )
10000
Molecules
Assumed
10000
Molecules
Assumed
1.00
Molecules
Assumed
2
10
#
Molecules
Assumed
0.1
Molecules
Assumed
0.1
Molecules
Assumed
10
Molecules
Assumed
1
2
20
0.00016757
1.0311
8.7342e-19
4.2122
0.089898
0.15547
-12.78
2.93e10
0.05
0.05
1400
140
0.13789
3.1011
0.26133
4.5833
0.30746
0.20475
4.9616e-07
3.2591e-07
1.0024e-05
µm
µm
µm
µm2
µm2
#
#
1/ min
1/ min
1/ min
1/ min
1/ min
1/ min
1/ min
1/ min
µm2
Assumed
Assumed
Assumed
Calculated
Calculated
Calculated
Calculated
Calculated
Calculated
Calculated
Calculated
Calculated
Calculated
Predicted
Predicted
Predicted
Predicted
Predicted
Predicted
Predicted
Predicted
Predicted
Predicted
Predicted
0.00010024
µm2
Predicted
µm2
Predicted
0.00015472
Vesicles budding rate at Plasma Membrane
𝐵
with coat A ( 𝑤𝑃𝑀
)
1.5472e-05
µm2
Tethering rate constant of vesicles (X,U) to
target compartment Golgi (𝜅𝑋𝑈 𝐺 )
8e-06
1/(molecules
min)
Predicted
Tethering rate constant of vesicles (X,U) to
target compartment Growth Cone Plasma
Membrane (𝜅𝑋𝑈 𝑃𝑀 )
8e-07
1/(molecules
min)
Predicted
Tethering rate constant of vesicles (Y,V) to
target compartment Golgi (𝜅𝑌𝑉 𝐺 )
2e-07
1/(molecules
min)
Predicted
Tethering rate constant of vesicles (Y,V) to
target compartment Growth Cone Plasma
Membrane (𝜅𝑌𝑉 𝑃𝑀 )
2e-06
1/(molecules
min)
Predicted
Required snare complex per vesicle fusion
(𝑅𝑆𝐶𝑃𝑉𝐹 )
Fraction of bound kinesin motor with
microtubules in CBC compartment
Fraction of bound kinesin motor with
microtubules in MTC compartment
Fraction of bound kinesin motor with
microtubules in GCC compartment
Fraction of bound dynein motor with
microtubules in CBC compartment
Fraction of bound dynein motor with
microtubules in MTC compartment
Fraction of bound dynein motor with
microtubules in CBC compartment
Membrane production rate at TGN
Nucleation rate of microtubules
Stabilization rate of dynamic microtubules
5.00
#
Predicted
95
percent
Assumed
8.15
Percent
Assumed
0
Percent
Assumed
0
Percent
Assumed
84
Percent
Assumed
95
percent
Assumed
0.27358
5.2032
0.0041667
µm2
1/min
1/min
Predicted
Predicted
Predicted
50
µm2
Predicted
Predicted
Coat B budded vesicles membrane surface
area from TGN in CBC
0.03
µm2
Predicted
Coat B budded vesicles membrane surface
area from TGN in MTC
2.5433
µm2
Predicted
Initial Values
Trans Golgi Network (TGN)
Predicted
Coat B budded vesicles membrane surface
area from TGN in GCC
Growth cone plasma membrane
Coat A budded vesicles membrane surface
area from TGN in CBC
Coat A budded vesicles membrane surface
area from TGN in MTC
7.6299
µm2
Predicted
50
µm2
Predicted
2.2911e-06
µm2
Predicted
µm2
Predicted
0.0008038
µm2
Coat A budded vesicles membrane surface
area from TGN in GCC
0.0067794
Predicted
Coat B budded vesicles membrane surface
area from plasma membrane in CBC
0.01252
µm2
Predicted
Coat B budded vesicles membrane surface
area from plasma membrane in MTC
6.5014e-05
µm2
Predicted
Coat B budded vesicles membrane surface
area from plasma membrane in GCC
4.0126e-05
µm2
Predicted
Coat A budded vesicles membrane surface
area from plasma membrane in CBC
0.55556
µm2
Predicted
Coat A budded vesicles membrane surface
area from plasma membrane in MTC
0.2849
µm2
Predicted
Coat A budded vesicles membrane surface
area from plasma membrane in GCC
0.14
µm2
Predicted
Neurite shaft surface area
62.8319
µm2
Predicted
SNAREs Y in TGN compartment
22.0942
molecules
Predicted
Total vesicle snare Y with Coat B budded
from TNG in CBC
0.33348
molecules
Predicted
Total vesicle snare Y with Coat B budded
from TNG in MTC
28.2713
Molecules
Predicted
Total vesicle snare Y with Coat B budded
from TNG in GCC
84.8139
Molecules
Predicted
SNAREs Y in GC compartment
20000
Molecules
Predicted
Total vesicle snare Y with Coat A budded
from TNG in CBC
1.9228e-11
Molecules
Predicted
Total vesicle snare Y with Coat A budded
from TNG in MTC
6.746e-09
Molecules
Predicted
Total vesicle snare Y with Coat A budded
from TNG in GCC
0.00011986
Molecules
Predicted
Total vesicle snare Y with Coat B budded
from GC in CBC
10.449
Molecules
Predicted
Total vesicle snare Y with Coat B budded
from GC in MTC
0.054339
Molecules
Predicted
Total vesicle snare Y with Coat B budded
from GC in GCC
0.033537
Molecules
Predicted
Total vesicle snare Y with Coat A budded
from GC in CBC
9.4014
Molecules
Predicted
Total vesicle snare Y with Coat A budded
from GC in MTC
4.8213
Molecules
Predicted
Total vesicle snare Y with Coat A budded
from GC in GCC
2.3692
Molecules
Predicted
SNAREs V in TGN compartment
20.6316
Molecules
Predicted
Total vesicle snare V with Coat B budded
from TNG in CBC
7.5
Molecules
Predicted
Total vesicle snare V with Coat B budded
from TNG in MTC
635.8221
Molecules
Predicted
Total vesicle snare V with Coat B budded
from TNG in GCC
1907.4662
Molecules
Predicted
SNAREs V in GC compartment
4498.003
Molecules
Predicted
Total vesicle snare V with Coat A budded
from TNG in CBC
1.2923e-07
Molecules
Predicted
Total vesicle snare V with Coat A budded
4.5337e-05
molecules
Predicted
from TNG in MTC
Total vesicle snare V with Coat A budded
from TNG in GCC
0.00049928
Molecules
Predicted
Total vesicle snare V with Coat B budded
from GC in CBC
7.0517
Molecules
Predicted
Total vesicle snare V with Coat B budded
from GC in MTC
0.036543
Molecules
Predicted
Total vesicle snare V with Coat B budded
from GC in GCC
0.022554
Molecules
Predicted
Total vesicle snare V with Coat A budded
from GC in CBC
211.4387
Molecules
Predicted
Total vesicle snare V with Coat A budded
from GC in MTC
108.4301
Molecules
Predicted
Total vesicle snare V with Coat A budded
from GC in GCC
53.2826
Molecules
Predicted
19999.7387
Molecules
Predicted
Total vesicle snare X with Coat B budded
from TNG in CBC
0.63204
Molecules
Predicted
Total vesicle snare X with Coat B budded
from TNG in MTC
53.5819
Molecules
Predicted
Total vesicle snare X with Coat B budded
from TNG in GCC
160.7458
Molecules
Predicted
2
Molecules
Predicted
Total vesicle snare X with Coat A budded
from TNG in CBC
0.0019236
Molecules
Predicted
Total vesicle snare X with Coat A budded
from TNG in MTC
0.67487
Molecules
Predicted
Total vesicle snare X with Coat A budded
from TNG in GCC
5.6971
Molecules
Predicted
Total vesicle snare X with Coat B budded
0.00048599
molecules
Predicted
SNAREs X in TGN compartment
SNARE X in GC compartment
from GC in CBC
Total vesicle snare X with Coat B budded
from GC in MTC
5.4461e-10
Molecules
Predicted
Total vesicle snare X with Coat B budded
from GC in GCC
3.3613e-10
Molecules
Predicted
Total vesicle snare X with Coat A budded
from GC in CBC
17.8183
Molecules
Predicted
Total vesicle snare X with Coat A budded
from GC in MTC
9.1376
Molecules
Predicted
Total vesicle snare X with Coat A budded
from GC in GCC
4.4902
Molecules
Predicted
3503.0379
Molecules
Predicted
Total vesicle snare U with Coat B budded
from TNG in CBC
11.0848
Molecules
Predicted
Total vesicle snare U with Coat B budded
from TNG in MTC
939.7258
Molecules
Predicted
Total vesicle snare U with Coat B budded
from TNG in GCC
2819.1774
Molecules
Predicted
SNARE U in GC compartment
66.4791
Molecules
Predicted
Total vesicle snare U with Coat A budded
from TNG in CBC
0.001279
Molecules
Predicted
Total vesicle snare U with Coat A budded
from TNG in MTC
0.44874
Molecules
Predicted
Total vesicle snare U with Coat A budded
from TNG in GCC
3.7795
Molecules
Predicted
Total vesicle snare U with Coat B budded
from GC in CBC
0.0011828
Molecules
Predicted
Total vesicle snare U with Coat B budded
from GC in MTC
3.6171e-06
Molecules
Predicted
Total vesicle snare U with Coat B budded
2.2324e-06
Molecules
Predicted
SNAREs U in TGN compartment
from GC in GCC
Total vesicle snare U with Coat A budded
from GC in CBC
312.5
Molecules
Predicted
Total vesicle snare U with Coat A budded
from GC in MTC
160.2564
Molecules
Predicted
Total vesicle snare U with Coat A budded
from GC in GCC
78.75
Molecules
Predicted
Kinesin receptors K in TGN compartment
1.0757
Molecules
Predicted
Total kinesin receptors K with Coat B
budded from TNG in CBC
0.7436
Molecules
Predicted
Total kinesin receptors K with Coat B
budded from TNG in MTC
63.04
Molecules
Predicted
Total kinesin receptors K with Coat B
budded from TNG in GCC
189.12
Molecules
Predicted
184.4922
Molecules
Predicted
Total kinesin receptors K with Coat A
budded from TNG in CBC
7.0251e-07
Molecules
Predicted
Total kinesin receptors K with Coat A
budded from TNG in MTC
0.00024645
Molecules
Predicted
Total kinesin receptors K with Coat A
budded from TNG in GCC
0.0020644
Molecules
Predicted
Total kinesin receptors K with Coat B
budded from GC in CBC
1.6756
Molecules
Predicted
Total kinesin receptors K with Coat B
budded from GC in MTC
0.0087054
Molecules
Predicted
Total kinesin receptors K with Coat B
budded from GC in GCC
0.0053728
Molecules
Predicted
Total kinesin receptors K with Coat A
budded from GC in CBC
20.9636
Molecules
Predicted
Total kinesin receptors K with Coat A
10.7505
Molecules
kinesin receptors K in GC compartment
budded from GC in MTC
Predicted
Total kinesin receptors K with Coat A
budded from GC in GCC
5.2828
Molecules
Predicted
Dynein receptor D in TGN compartment
66.8333
Molecules
Predicted
Total dynein receptor D with Coat B budded
from TNG in CBC
0.49521
Molecules
Predicted
Total dynein receptor D with Coat B budded
from TNG in MTC
41.9818
Molecules
Predicted
Total dynein receptor D with Coat B budded
from TNG in GCC
125.9454
Molecules
Predicted
1.0938
Molecules
Predicted
Total dynein receptor D with Coat A budded
from TNG in CBC
0.00030677
Molecules
Predicted
Total dynein receptor D with Coat A budded
from TNG in MTC
0.10763
Molecules
Predicted
Total dynein receptor D with Coat A
budded from TNG in GCC
0.90727
Molecules
Predicted
Total dynein receptor D with Coat B budded
from GC in CBC
0.0038582
Molecules
Predicted
Total dynein receptor D with Coat B budded
from GC in MTC
1.9925e-05
Molecules
Predicted
Total dynein receptor D with Coat B budded
from GC in GCC
1.2297e-05
Molecules
Predicted
Total dynein receptor D with Coat A budded
from GC in CBC
13.9608
Molecules
Predicted
Total dynein receptor D with Coat A budded
from GC in MTC
7.1594
Molecules
Predicted
Total dynein receptor D with Coat A budded
from GC in GCC
3.5181
Molecules
Predicted
100
Molecules
Predicted
Dynein receptor D in GC compartment
Recruitment factor 1 in TGN compartment
Total recruitment factor 1 with Coat B
budded from TNG in CBC
1.2e-06
Molecules
Predicted
Total recruitment factor 1 with Coat B
budded from TNG in MTC
0.00010173
Molecules
Predicted
Total recruitment factor 1 with Coat B
budded from TNG in GCC
0.00030519
Molecules
Predicted
recruitment factor 1 in GC compartment
0.0015224
Molecules
Predicted
Total recruitment factor 1 with Coat A
budded from TNG in CBC
3.0544e-05
Molecules
Predicted
Total recruitment factor 1 with Coat A
budded from TNG in MTC
0.010716
Molecules
Predicted
Total recruitment factor 1 with Coat A
budded from TNG in GCC
0.090358
Molecules
Predicted
Total recruitment factor 1 with Coat B
budded from GC in CBC
7.4581e-11
Molecules
Predicted
Total recruitment factor 1 with Coat B
budded from GC in MTC
3.6518e-13
Molecules
Predicted
Total recruitment factor 1 with Coat B
budded from GC in GCC
2.2539e-13
Molecules
Predicted
Total recruitment factor 1 with Coat A
budded from GC in CBC
3.383e-05
Molecules
Predicted
Total recruitment factor 1 with Coat A
budded from GC in MTC
1.7348e-05
Molecules
Predicted
Total recruitment factor 1 with Coat A
budded from GC in GCC
8.525e-06
Molecules
Predicted
Recruitment factor 2 in TGN compartment
0.00065687
Molecules
Predicted
Total recruitment factor 2 with Coat B
budded from TNG in CBC
7.8823e-07
Molecules
Predicted
Total recruitment factor 2 with Coat B
budded from TNG in MTC
6.6824e-05
Molecules
Predicted
Total recruitment factor 2 with Coat B
budded from TNG in GCC
0.00020047
Molecules
Predicted
100
Molecules
Predicted
Total recruitment factor 2 with Coat A
budded from TNG in CBC
1.1325e-14
Molecules
Predicted
Total recruitment factor 2 with Coat A
budded from TNG in MTC
3.9661e-12
Molecules
Predicted
Total recruitment factor 2 with Coat A
budded from TNG in GCC
3.829e-11
Molecules
Predicted
Total recruitment factor 2 with Coat B
budded from GC in CBC
0.16687
Molecules
Predicted
Total recruitment factor 2 with Coat B
budded from GC in MTC
0.00086636
Molecules
Predicted
Total recruitment factor 2 with Coat B
budded from GC in GCC
0.0005347
Molecules
Predicted
Total recruitment factor 2 with Coat A
budded from GC in CBC
2.2222e-05
Molecules
Predicted
Total recruitment factor 2 with Coat A
budded from GC in MTC
1.1396e-05
Molecules
Predicted
Total recruitment factor 2 with Coat A
budded from GC in GCC
5.5999e-06
Molecules
Predicted
9
µM
Assumed
Recruitment factor 2 in GC compartment
Effective tubulin
References:
1. Beller, J.A., Kulengowski, B., Kobraei, E., Curinga, G., Calulot, C.M., Bahrami, A.,
Hering, T.M., Snow, D.M. (2013). Comparison of sensory neuron growth cone and
filopodial responses to structurally diverse aggrecan variants, in vitro. Exp. Neurol. 247,
143–157.
2. Carter, N.J., Cross, R.A. (2005). Mechanics of the kinesin step. Nature 435, 308–312.
3. Fadić R, Vergara J, Alvarez J. (1985). Microtubules and caliber of central and peripheral
processes of sensory axons. J. Comp. Neurol 236, 258-264.
4. Harris, K. M., and Stevens, J. K. (1989). Dendritic spines of CA1 pyramidal cells in the
rat hippocampus: serial electron microscopy with reference to their biophysical
characteristics. J. Neurosci. 9, 2982-2997.
5. King, S.J., Schroer, T.A.,(2000). Dynactin increases the processivity of the cytoplasmic
dynein motor. Nat Cell Biol. 2, 20-4.
6. Kunda, P., Paglini, G., Quiroga, S., Kosik, K., Caceres, A. (2001 Evidence for the
Involvement of Tiam1 in Axon Formation, The Journal of Neuroscience 21, 2361–2372.
7. Margolin, G., Gregoretti, I.V., Cickovski, T.M., Li, C., Shi, W., Alber, M.S., and Goodson,
H.V. (2012). The mechanisms of microtubule catastrophe and rescue: implications from
analysis of a dimer-scale computational model. Molecular biology of the cell 23, 642-656.
8. Nishiura, M., Kon, T., Shiroguchi, K., Ohkura, R., Shima, T., Toyoshima, Y.Y., Sutoh,
K.,(2004). A single-headed recombinant fragment of Dictyostelium cytoplasmic dynein can
drive the robust sliding of microtubules. J. Biol. Chem. 22, 22799–22802.
9. Vale, R. D., Funatsu, T.S., Pierce, D.W., Romberg, L., Harada, Y., Yanagida, T.(1996).
Direct observation of single kinesin molecules moving along microtubules. Nature 380,
451-3.
10. Zhang, B., Koh, Y.H., Beckstead, R.B., Budnik, V., Ganetzky, B., Bellen, H.J. (1998).
Synaptic Vesicle Size and Number are Regulated by a Clathrin Adaptor Protein Required
for Endocytosis. Neuron 21, 1465–1475.