model results (actin dynamics)

Results and Observations

Model considering actin polar filaments

This model has already been discussed in “Actively Contracting Bundles of Polar Filaments”,PRL

(Vol. 85 No. 8).However the model that we have used to describe dynamics includes treadmmilling

(current: ∂x(vtrc+-) ).So In this model as it's straightforward to see from the graph that αc >0 for all

parameters (when vtr=0), which means unstability is due to interaction between parallel filaments

with α≥ αc

Also it can be easily seen that αc increases with increasing D, diffusion coeff.(As

(magnitude only) in graph (is actually β*Ɩ/D where Ɩ is length of filament (both filaments were

assumed of same length)) is decreasing , αc increases).As soon as we decrease size of system L, αc

increases(shortening of bundles gives stability).Also αc decreases with increasing c22 w.r.t. i.e.

increasing filaments of same orientation.(graph 1)Also When treadmilling is accounted,αc

decreases which means treadmilling is also responsible for destabilization of system.Now it might

be said for that region when αc decreases with increase in D is due to dominance of treadmilling in

those region.(see graph 2).

Graph 1 (Here coordinates on X-axis is and coordinates on Y-axis is .Curves

with green color indicate more fraction of c22 compared to c11 and and red color indicate lesser fraction

c22 compared to c11.)


Graph 2(Here in this case c11=.3 and c22=.7,Here coordinates on X-axis is and coordinates on Y-axis is

)

Model considering actin polar filaments and Bipolar filaments

This model is an extension of previous model with consideration of Bipolar filaments which has

been mentioned in "Self-organization and mechanical properties of active filament bundles",

Physical Review E 67 051913. However the model that we have used to describe dynamics includes

treadmmilling (current: ∂x(vtrc+-) ).

Also it can be easily seen that αc decreases with increasing wd ,rate of splitting of bipolar

filaments to result in polar ones.(As (magnitude only) in graph (is actually β/wd*Ɩ where Ɩ is

length of filament (both filaments were assumed of same length)) is decreasing , α c decreases).As

soon as we decrease size of system L, αc first decreases then increases(shortening of bundles for

stabiltiy now has barrier ).Also αc may increase with increase in β(not always! In green curve,for β

(negatvie part), αc has very random patterns) and sometimes function is multivalued, So no

certainity for all α<αc is stable region , while in previous model (only polar filaments) , αc decreases

with increase in β and with certainity. So In this model, more anti parallel filament interactions

causes stability to system(as β increases,more stabiltiy to system).Also αc decreases with

increasing c22 w.r.t. i.e. increasing filaments of same orientation.It stabilizes(αc increases) with

increase in D,diffusion coefficient.


Constant Prameters: (C0+ =.3 , C0

- =.7, D=2, β=.5 ,wd=.7 ,wc=.3 ,Ɩ=1)

Also αc decreases with increase in wc ,So combination of polar filaments(antiparallel) resulting in

bipolar filament causes unstability to system( wc is rate of combination of polar filaments).If this

result is in consistence with other observations, then it can be understood physically that "As

antiparallel filaments may cause stability to system,so making of bipolar filaments by

combination will bring unstability to system."(however this argument seems to be

mathematically wrong when wc<wd ,as for these values of wc ,we get polar filaments efectively as

wc>wd which is not happening as you can see from graph curve with lesser β has lesser stability for

all times.By looking at graph ,one thing that is needed to be observed,for system to have stability

with lesser L (contraction) is not so straightforward.as it can be seen that for wc lesser than certain

value,system has more stability than system of lesser size(really ???).


As we have seen earlier that for bundles of small size have bigger αc i.e. shortening of bundles lead to

inhomogeneous stable state(generally happens beacause of unstable homogeneous state).As we

can see tfrom previous results that these unstabilities occur due to more filament interactions

which leads to shortening.However for shortening of these bundles,someone has to perform

mechanical work which is coming from these interactions in terms of stress produced by forces

generated by motors and hydrodynamic forces of these fluids.If we ignore interaction b/w different

filaments due to friction force,considering filament to be rigid-rod like filamentmoving in a viscous

environment with velocity v and mobility μ ,if there is a force on filament at point smot ,then we can

write explicitly force balance neglecting mass momentum of rod,

∂sσ =fmot + v/μ

After using this knowledge ,we can write it's tension profile which piecewise linear.

Image Source: K. Kruse

Stress is positive in the rear end as it is being pulled and negative as it is being stretched.To get total stress

profile along the bundle, we need to sum all stresses in all filaments.Using above stress profile,we calculate

an average stress profile along a filament a x by summing over all contributions due to interactions.We then

can calculate stress in bundle at position y,by summing over average stress of filaments with their '+'ve end

within the certain interval (for '+' ve actin filament [y-Ɩ ,y],for '-'ve actin filament [y,y+ Ɩ] & for bipolar

ones [y- Ɩ,y+ Ɩ]).

model results (actin dynamics)

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