Code documentation: ampartrafficking

rate_model

Created on Wed Nov 4 11:43:38 2020

@author: Moritz

class ampartrafficking.rate_model.Parameter(base_value)

This class defines some basic properties and functionality for parameters that change during LTP induction.

Attributes

base_valuefloat

Base value of the correspconding model parameter, i.e. before LTP-induction.

Methods

timecourse(function,pars)	Sets up time course of the parameter during LTP-induction. Requires a function and the parameters of that function to be passed.
update(t)	Updates the parameter to the current value according to the function passed to timecourse.

timecourse(function, pars)

Sets up time course of the parameter during LTP-induction. Requires a function and the parameters of that function to be passed.

Parameters

functionfunction

A function that describes the time course of the parameter during LTP-induction

parsarray_like

List of parameters for the function.

Returns

out:

update(t)

Sets up time course of the parameter during LTP-induction. Requires a function and the parameters of that function to be passed.

Parameters

tfloat

Time passed since the LTP induction stimulus.

Returns

out: Updates current value of the partameter.

class ampartrafficking.rate_model.Model_system

This class contains the set of differential equations that describe AMPAR trafficking at spines.

Methods

odes(Init,t,Vspine,P,kin,kout,kexo,kendo,kUB,kBU,Cooperativity,sLTP,kin_RE,kout_RE)

Defines the ODEs that describe the synapse.

odes(Init, t, Vspine, P, kin, kout, kexo, kendo, kUB, kBU, Cooperativity, sLTP, kin_RE, kout_RE)

Defines the ODEs that describe the AMPAR dynamics at the spine.

Parameters

Init[U(0),B(0),Sexo(0)]

Initial conditions for the three variables of the system.

tarray_like

Time.

Vspinefloat

Describes the spine volume and spine volume change during E-LTP.

Pfloat

Number of binding site/slots at the PSD.

kinfloat

Rate at which receptors hop from the dednritic membrane compartment onto the spine membrane compartment.

koutfloat

Rate at which receptors hop from the spine membrane compartment onto the dendritic membrane compartment.

kexofloat

Rate of exocytosis events occuring at the spine.

kendofloat

Rate at which receptors are endocytosed at the spine.

kUBfloat

Rate at which AMPARs bind to PSD slots.

kBUfloat

Rate at which AMPARs unbind from PSD slots.

Cooperativity: 1,0

States whether binding is cooperative (1) or not cooperative (0).

sLTP1,0

States whether slTP does occur (1) or does not occur (0).

kin_REfloat

Rate at which AMPAR containing endosomes enter the spine (dynamics of exocytosis event size Sexo).

kout_REfloat

Rate at which AMPAR containing endosomes leave the spine.

Returns

out: [dU,dB,dS_exo]

ampartrafficking.rate_model.kUB_(B, kUB, Cooperativity, P)

Returns the receptor binding rate kUB for either the cooperative or the non-cooperative binding model.

Parameters

Bfloat

Number of bound receptors.

kUBfloat

Rate at which AMPARs bind to PSD slots.

Cooperativity0, 1

Specifies whether cooperative recepotr binding is accounted for (=1) or not (=0).

Pfloat

Number of binding site/slots at the PSD.

Returns

float

kUB.

ampartrafficking.rate_model.kBU_(B, kBU, Cooperativity, P)

Returns the receptor unbinding rate kUB for either the cooperative or the non-cooperative binding model.

Parameters

Bfloat

Number of bound receptors.

kBUfloat

Rate at which AMPARs unbind from PSD slots.

Cooperativity0, 1

Specifies whether cooperative recepotr binding is accounted for (=1) or not (=0).

Pfloat

Number of binding site/slots at the PSD.

Returns

float

kUB.

ampartrafficking.rate_model.Stim_Resp(t, a0, a, b, c)

This function describes the response of a parameter to the LTP induction-stimulus.

Parameters

tfloat

time passed since induction of LTP

a0float

baseline of the parameter (Should usually be set to 1).

afloat

Parameter amplitude during LTP induction

bfloat

time constant

cfloat

time constant

Returns

float

current factor of parameter change.

Examples

Import libraries:

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> import ampartrafficking.rate_model as rm
>>> import seaborn as sns

Set parameters:

>>> t=np.linspace(0,10*60,100)
>>> kexo0=0.0018
>>> exocytosis=True

Plot:

>>> plt.figure(figsize=(4,3), dpi=150)
>>> plt.plot(t/60,kexo0*rm.Stim_Resp(t,1,5,25,60), linewidth=2)
>>> plt.xlabel('Time (min.)')
>>> plt.ylabel('$k_{exo}$ ($s^{-1}$)')
>>> sns.despine()

Output:

ampartrafficking.rate_model.DV(t, V0, exocytosis)

This function describes the evolution of the spine volume during sLTP.

Parameters

tfloat

time passed since induction of LTP

V0float

initial spine volume.

exocytosisTrue, False

States whether exocytosis is blocked or not. Make sure that the boolean value is chosen in agreement with the definition of kexo.

Returns

float

current factor of spine volume change.

Examples

Import libraries:

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> import ampartrafficking.rate_model as rm
>>> import seaborn as sns

Set parameters:

>>> t=np.linspace(0,120*60,1000)
>>> exocytosis=True
>>> spineVolumes=[0.04,0.08,0.2]

Plot:

>>> plt.figure(figsize=(4,3), dpi=150)
>>> for V0 in spineVolumes:
>>>     plt.plot(t/60,rm.DV(t,V0,exocytosis)*100, linewidth=2, label='$V_{spine}^0=$'+'{:1.2f} $\mu m^3$'.format(V0))
>>> plt.legend()
>>> plt.xlabel('Time (min.)')
>>> plt.ylabel('$V_{spine}$ (%)')
>>> sns.despine()

Output:

ampartrafficking.rate_model.kUB0_(Init, kBU, P, Aspine, Cooperativity)

Returns the receptor binding rate at baseline, which is calculated from the fixed point equation of the AMPAR trafficking model.

Parameters

Initarray_like

Initial state values for U, B and Sexo ([U(0),B(0),Sexo(0)]) .

kBUfloat

Rate at which AMPARs unbind from PSD slots.

Pfloat

Number of binding site/slots at the PSD.

Aspinefloat

Spine surface area.

Cooperativity0, 1

Specifies whether cooperative recepotr binding is accounted for (=1) or not (=0).

Returns

float

Receptor binding rate at baseline kUB0.

ampartrafficking.rate_model.kendo_(Init, kexo0, kin, kout, Aspine)

Returns the receptor endocytosis rate, which is calculated from the fixed point equation of the AMPAR trafficking model.

Parameters

Initarray_like

Initial state values for U, B and Sexo ([U(0),B(0),Sexo(0)]) .

kexo0float

Rate of exocytosis events occuring at the spine under basal conditions.

kinfloat

Rate at which receptors hop from the dednritic membrane compartment onto the spine membrane compartment.

koutfloat

Rate at which receptors hop from the spine membrane compartment onto the dendritic membrane compartment.

Aspinefloat

Spine surface area.

Returns

float

Receptor endocytosis rate kendo.

ampartrafficking.rate_model.SexoFP_(kin_RE, kout_RE, Vspine)

Returns the fixed point of the exocytosis event size Sexo, i.e. the number of AMPARs delivered to the spine membrane during one exocytosis event.

Parameters

kin_REfloat

Rate at which AMPAR containing endosomes enter the spine (dynamics of exocytosis event size Sexo).

kout_REfloat

Rate at which AMPAR containing endosomes leave the spine.

Vspinefloat

Spine volume.

Returns

float

Fixed point of the exocytosis event size Sexo.

ampartrafficking.rate_model.UFP_(kexo, Sexo, kendo, kin, kout, Aspine)

Returns the fixed point of the mobile receptor pool.

Parameters

kexofloat

Rate of exocytosis events occuring at the spine.

Sexofloat

Exocytosis event size.

kendofloat

Rate at which receptors are endocytosed at the spine.

kinfloat

Rate at which receptors hop from the dednritic membrane compartment onto the spine membrane compartment.

koutfloat

Rate at which receptors hop from the spine membrane compartment onto the dendritic membrane compartment.

Aspinefloat

Spine surface area.

Returns

float

Fixed point of the mobile receptor pool.

ampartrafficking.rate_model.BFP_(UFP, kUB, kBU, P, Aspine, Cooperativity)

Returns the fixed point of the bound receptor pool.

Parameters

UFPfloat

Fixed point of the mobile receptor pool.

kUBfloat

Rate at which AMPARs bind to PSD slots.

kBUfloat

Rate at which AMPARs unbind from PSD slots.

Pfloat

Number of binding site/slots at the PSD.

Aspinefloat

Spine surface area.

Cooperativity0, 1

Specifies whether cooperative recepotr binding is accounted for (=1) or not (=0).

Returns

float

Fixed point of the bound receptor pool.

parameter_sampling

Created on Tue Nov 10 17:12:34 2020

@author: Moritz

ampartrafficking.parameter_sampling.parameterSampling(t, Init, sLTP, Cooperativity, P, kin, kout, Trials, kBU_max, aUB_max, TUB_max, kexo_max, aexo_max, Texo_max)

Returns evolution over time of bound AMPARs for normal E-LTP and LTP with exocytosis blockage for various Trials. Parameter values for exocytosis event, receptor binding and unbinding rate are drawn randomly for each Trial. Also, evolution over time of mobile receptors, binding rate and exocytosis event rate and spine area are returned as well as values for the baseline exocytosis event rate kexo0, the factor of change in exocytosis event rate amplitide during LTP-induction aexo and amplitude decay time constant Texo are returned for each Trial.

Parameters

tarray_like

Time over which the model is integrated.

Initarray_like

Initial state values for U, B and Sexo ([U(0),B(0),Sexo(0)]) .

sLTP0, 1

Specifies whether sLTP is accounted for (=1) or not (=0).

Cooperativity0, 1

Specifies whether cooperative recepotr binding is accounted for (=1) or not (=0).

Pfloat

Number of receptor binding sites

kinfloat

Rate at which receptors hop from the dednritic membrane compartment onto the spine membrane compartment.

koutfloat

Rate at which receptors hop from the spine membrane compartment onto the dendritic membrane compartment.

Trialsinteger

Number of trials.

kBU_maxfloat

Maximum of the receptor unbinding rate. Values are drawn randomly between 0 and kBU_max. kUB0 is calculated from the unbinding rate (kUB0_(kBU)).

aUB_maxfloat

Maximum of the factor by which the receptor binding rate increases during LTP-induction. Values are drawn randomly between 0 and aUB_max.

TUB_maxfloat

Maximum of the decay time by which the receptor binding rate decreases to the baseline after LTP-induction. Values are drawn randomly between 0 and TUB_max.

kexo_maxfloat

Maximum of the baseline receptor exocytosis event rate kexo0. Values are drawn randomly between 0 and kexo_max. kendo is calculated from the exocytosis event rate (kendo_(kexo0)).

aexo_maxfloat

Maximum of the factor by which the receptor exocytosis event rate increases during LTP-induction. Values are drawn randomly between 0 and aexo_max.

Texo_maxfloat

Maximum of the decay time by which the receptor exocytosis event rate decreases to the baseline after LTP-induction. Values are drawn randomly between 0 and Texo_max.

Returns

B_Trarray_like

Time evolution of bound receptors during normal E-LTP for different Trials; shape(Trials, len(t))

B_ne_Trarray_like

Time evolution of bound receptors during E-LTP with exocytosis blockage for different Trials; shape(Trials, len(t))

U_Trarray_like

Time evolution of mobile receptors for different Trials; shape(Trials, len(t))

kUB_Trarray_like

Time evolution of the receptor binding rate for different Trials; shape(Trials, len(t))

kexo_Trarray_like

Time evolution of the receptor exocytosis event rate for different Trials; shape(Trials, len(t))

Aspine_Trarray_like

Time evolution of the spine surface area for different Trials; shape(Trials, len(t))

kexo0_Trarray_like

Values of the receptor exocytosis event rate at baseline for different Trials; shape(Trials)

aexo_Trarray_like

Values of the factor by which the receptor exocytosis event rate increases during LTP-induction for different Trials; shape(Trials)

Texo_Trarray_like

Values of the decay time by which the receptor exocytosis event rate decreases to the baseline after LTP-induction for different Trials; shape(Trials)

ampartrafficking.parameter_sampling.ELTP(Time)

Returns time evolution of EPSPs during E-LTP in % of baseline. The function has been fitted to data from Barco et al. 2002.

Parameters

Timearray_like

Time in s.

Returns

float

Time evolution of EPSPs during E-LTP in % of baseline.

ampartrafficking.parameter_sampling.LTPnoExo(Time)

Returns time evolution of EPSPs during LTP with exocytosis blockage in % of baseline. The function has been fitted to data from Penn et al. 2017.

Parameters

Timearray_like

Time in s.

Returns

float

Time evolution of EPSPs during LTP with exocytosis blockage in % of baseline.

ampartrafficking.parameter_sampling.Matching(B_Basal, B_nE, Trials, Time, BFP, Percentage=0.005)

Returns the indices and distance measure for the 0.5% of Trials that best match with experimental data from Barco et al. 2002 and Penn et al. 2017.

Parameters

B_Basalarray_like

Time evolution of bound AMPARs during normal E-LTP for different Trials (shape(Trials,t)).

B_nEarray_like

Time evolution of bound AMPARs during LTP with exocytosis blockage for different Trials (shape(Trials,len(Time))).

Trialsint

Number of trials.

Timearray_like

Time in s.

BFPfloat

Fixed point/Basline level of the number of bound receptors.

Percentagefloat, optional

By default Percentage=0.005. Percentage of Trials that are returned that best match with experimental data.

Returns

GoodMatch_indexarray_like

Indices of the 0.5% of Trials that best match with experimental data.

GoodMatch_Valuearray_like

Distance measure of the 0.5% of Trials that best match with experimental data.

stochastic_model

Created on Wed Nov 4 11:48:22 2020

@author: Moritz

ampartrafficking.stochastic_model.nearestNeighbours(PSD)

Returns the number of nearest neighbours on a grid.

Parameters

PSDarray_like

Grid with occupied and free elements, shape(N, N)

Returns

out: array_like

Matrix containing the number of nearest neighbors for each element of the grid matrix.

Examples

Import libraries:

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> import ampartrafficking.stochastic_model as sm

Create and populate grid and calculate nearest neighbour matrix:

>>> N=10
>>> PSD=np.zeros((N,N))
>>> PSD[np.random.randint(0,N,20),np.random.randint(0,N,20)]=1
>>>
>>> NN=sm.nearestNeighbours(PSD)

Plot:

>>> plt.figure(figsize=(3,3), dpi=150)
>>> plt.imshow(PSD)
>>> plt.colorbar()
>>> plt.xlabel('position')
>>> plt.ylabel('position')
>>>
>>> plt.figure(figsize=(3,3), dpi=150)
>>> plt.imshow(NN)
>>> plt.colorbar()
>>> plt.xlabel('position')
>>> plt.ylabel('position')

Output:

ampartrafficking.stochastic_model.kBUcoop(kBU, NN, PSD, typeID, beta=1.0)

Returns the cooperative unbinding rate per bound receptor.

Parameters

kBUfloat

unbinding rate

betafloat, optional

By default beta=1.0. Factor by which the fraction of occupied nearest neighbours lowers the unbinding rate.

NNarray_like

Matrix that contains the number of nearest neighbours for each grid element.

PSDarray_like

Matrix representing the PSD grid

typeIDfloat>0

Receptor-type ID.

Returns

out: array_like

Matrix containing the unbinding rates at each occupied grid element.

Examples

Import libraries:

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> import ampartrafficking.stochastic_model as sm

Create and populate grid and calculate nearest neighbour matrix:

>>> kBU=0.1
>>> typeID=2
>>> N=10
>>> PSD=np.zeros((N,N))
>>> PSD[np.random.randint(0,N,20),np.random.randint(0,N,20)]=typeID
>>> NN=sm.nearestNeighbours(PSD)

Plot:

>>> plt.figure(figsize=(4,3), dpi=150)
>>> plt.plot(sm.kBUcoop(kBU, np.arange(0,9), np.array([typeID]*9), typeID))
>>> plt.xlabel('number of nearest neighbours')
>>> plt.ylabel('unbinding rate $k_{BU}^{coop}$')
>>>
>>> fig=plt.figure(figsize=(3,2.25), dpi=150)
>>> plt.imshow(PSD)
>>> cbar=plt.colorbar()
>>> cbar.set_label('occupied (type)', rotation=90, labelpad=10, y=0.5)
>>> plt.xlabel('position')
>>> plt.ylabel('position')
>>>
>>> fig=plt.figure(figsize=(3,2.25), dpi=150)
>>> plt.imshow(NN)
>>> cbar=plt.colorbar()
>>> cbar.set_label('nearest neighbours', rotation=90, labelpad=10, y=0.5)
>>> plt.xlabel('position')
>>> plt.ylabel('position')
>>>
>>> fig=plt.figure(figsize=(3,2.25), dpi=150)
>>> plt.imshow(sm.kBUcoop(kBU, NN, PSD, typeID))
>>> cbar=plt.colorbar()
>>> cbar.set_label('unbinding rate $k_{BU}^{coop}$', rotation=90, labelpad=10, y=0.5)
>>> plt.xlabel('position')
>>> plt.ylabel('position')

Output:

ampartrafficking.stochastic_model.kUBcoop(kUB, NN, PSD, alpha=16)

Returns the cooperative binding rate per mobile receptor.

Parameters

kUBfloat

binding rate

alphafloat, optional

By default alpha=16. Factor by which the fraction of occupied nearest neighbours increases the binding rate.

NNarray_like

Matrix that contains the number of nearest neighbours for each grid element.

PSDarray_like

Matrix representing the PSD grid

Returns

out: array_like

Matrix containing the binding rates at each unoccupied grid element.

Examples

Import libraries:

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> import ampartrafficking.stochastic_model as sm

Create and populate grid and calculate nearest neighbour matrix:

>>> kUB=0.0005
>>> N=10
>>> PSD=np.zeros((N,N))
>>> PSD[np.random.randint(0,N,20),np.random.randint(0,N,20)]=1
>>> NN=sm.nearestNeighbours(PSD)

Plot:

>>> plt.figure(figsize=(4,3), dpi=150)
>>> plt.plot(sm.kUBcoop(kUB, np.arange(0,9), np.array([0]*9)))
>>> plt.xlabel('number of nearest neighbours')
>>> plt.ylabel('binding rate $k_{UB}^{coop}$')
>>>
>>> fig=plt.figure(figsize=(3,2.25), dpi=150)
>>> plt.imshow(PSD)
>>> cbar=plt.colorbar()
>>> cbar.set_label('occupied (type)', rotation=90, labelpad=10, y=0.5)
>>> plt.xlabel('position')
>>> plt.ylabel('position')
>>>
>>> fig=plt.figure(figsize=(3,2.25), dpi=150)
>>> plt.imshow(NN)
>>> cbar=plt.colorbar()
>>> cbar.set_label('nearest neighbours', rotation=90, labelpad=10, y=0.5)
>>> plt.xlabel('position')
>>> plt.ylabel('position')
>>>
>>> fig=plt.figure(figsize=(3,2.25), dpi=150)
>>> plt.imshow(sm.kUBcoop(kUB, NN, PSD))
>>> cbar=plt.colorbar()
>>> cbar.set_label('binding rate $k_{UB}^{coop}$', rotation=90, labelpad=10, y=0.5)
>>> plt.xlabel('position')
>>> plt.ylabel('position')

Output:

ampartrafficking.stochastic_model.probabilityEval(Mub, Mbu, PSD, ID_basal, Mub_notBleached=None, Mbu_notBleached=None, ID_notBleached=None)

Returns the updated PSD Matrix and the corresponding number of receptors that got bound and unbound. To types, “basal” and “not bleached” can be considered, which is necessary when simulation FRAP.

Parameters

Mubarray_like

Matrix containing binding probabilities for the type “basal”.

Mbuarray_like

Matrix containing unbinding probabilities for the type “basal”.

Mub_notBleachedarray_like, optional

By default None. Matrix containing binding probabilities for the type “not bleached”.

Mbu_notBleachedarray_like, optional

By default None. Matrix containing unbinding probabilities for the type “not bleached”.

PSDarray_like

Matrix representing the PSD grid and its bound receptors.

ID_basalfloat

Receptor ID of the basal pool.

ID_notBleached: float

Receptor ID of the not bleached pool.

Returns

out: float, float, float, float, array_like

Number of receptors that got bound and unbound of the two types “basal” and “not bleached” and the updated PSD matrix.

Examples

Import libraries:

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> import ampartrafficking.stochastic_model as sm

Set parameters:

>>> U=10
>>> U_notBleached=10
>>> kUB=0.005
>>> kBU=1
>>> N=10
>>> ID_basal=1
>>> ID_notBleached=2
>>> dt=0.5

Create and populate grid and calculate nearest neighbour matrix:

>>> PSD=np.zeros((N,N))
>>> while np.sum(PSD)<20*ID_basal:
>>>     i=np.random.randint(0,N)
>>>     j=np.random.randint(0,N)
>>>     if PSD[i,j]==0:
>>>         PSD[i,j]=ID_basal
>>>
>>> while np.sum(PSD)<20*ID_basal+20*ID_notBleached:
>>>     i=np.random.randint(0,N)
>>>     j=np.random.randint(0,N)
>>>     if PSD[i,j]==0:
>>>         PSD[i,j]=ID_notBleached
>>>
>>> NN=sm.nearestNeighbours(PSD)

Plot PSD:

>>> plt.figure()
>>> plt.imshow(PSD)
>>> plt.colorbar()

Calculate probability Matrices and update the PSD Matrix:

>>> Mbu=sm.kBUcoop(kBU, NN, PSD, ID_basal)*dt
>>> Mub=sm.kUBcoop(kUB*U, NN, PSD)*dt
>>> Mbu_notBleached=sm.kBUcoop(kBU, NN, PSD, ID_notBleached)*dt
>>> Mub_notBleached=sm.kUBcoop(kUB*U_notBleached, NN, PSD)*dt
>>>
>>> PSD,dBoff,dBon,dBoff_notBleached,dBon_notBleached=sm.probabilityEval(Mub,Mbu,PSD,ID_basal,Mub_notBleached,Mbu_notBleached,ID_notBleached)

Plot PSD:

>>> plt.figure()
>>> plt.imshow(PSD)
>>> plt.colorbar()

Output: (left: before, right: after)

ampartrafficking.stochastic_model.update_mobilePool(U, pin, pout, dBoff, dBon, U_notBleached=None, pin_notBleached=None, pout_notBleached=None, dBoff_notBleached=None, dBon_notBleached=None)

Updates the value for the mobile receptor pool. When simulating FRAP, a second type “not bleached” is considered.

Parameters

Ufloat

Mobile AMPAR pool.

pinfloat

Probability of a receptor to enter the spine’s mobile pool.

poutfloat

Probability of a receptor to leave the spine’s mobile pool.

dBofffloat

Number of receptors that got unbound from the PSD grid.

dBonfloat

Number of receptors that got bound to the PSD grid.

U_notBleachedfloat, optional

Mobile AMPAR pool (bleached).

pin_notBleachedfloat, optional

Probability of a not bleached receptor to enter the spine’s mobile pool.

pout_notBleachedfloat, optional

Probability of a not bleached receptor to enter the spine’s mobile pool.

dBoff_notBleachedfloat, optional

Number of not bleached receptors that got unbound from the PSD grid.

dBon_notBleachedfloat, optional

Number of not bleached receptors that got bound to the PSD grid.

Returns

out: float, float

U, U_notBleached.

ampartrafficking.stochastic_model.calcTimeStep(UFP_0, A_spine, kUB, alpha, kBU, kout, kin)

Returns integration time step dt. By default simulations are carried out at dt=0.5s. If parameter choices require a smaller time step, dt is set to 0.25s. If dt is still too large, the simulation is cancelled and an error message is displayed. In this case dt needs to be set manually.

Parameters

UFP_0float

Mobile receptor pool fixed points. Sets the influx of receptors into spine.

A_spinefloat

Spine surface area.

kUBfloat

bidning rate

alphafloat

cooperativity factor for the binding

kBUfloat

unbidning rate

koutfloat

Total rate at which receptors exit the spine membrane (e.g. kout+kendo).

kinfloat

Total rate at which receptors enter the spine membrane (e.g. kexo*Sexo+kin).

Returns

float

Integration time step dt.

frap

Created on Thu Nov 5 15:35:31 2020

@author: Moritz

ampartrafficking.frap.FRAP(N_List, Conc_List, beta, alpha, kUB, kBU, duration, Nr_Trials)

Returns evolution over time of photobleached and not photobleached mobile and bound receptors (FRAP simulation).

Parameters

N_Listarray_like

List of PSD sizes P

Conc_Listarray_like

List of target fixed points for the mobile receptor concentration. Sets the influx of receptors into spine.

betafloat

cooperativity factor for the unbinding. (Should be set to 1 or 0)

alphafloat

cooperativity factor for the binding

kUBfloat

bidning rate

kBUfloat

unbidning rate

durationfloat

Duration of the simulation

Nr_Trialsinteger

Number of trials.

Returns

B_Narray_like

Time evolution of bound receptors for different conditions and number of Trials; shape(len(N_List), len(Conc_List), Trials, duration/0.5+1)

U_Narray_like

Time evolution of mobile receptors for different conditions and number of Trials; shape(len(N_List), len(Conc_List), Trials, duration/0.5+1)

B_notBleached_N

Time evolution of bound receptors not photobleached for different conditions and number of Trials; shape(len(N_List), len(Conc_List), Trials, duration/0.5+1)

U_notBleached_N

Time evolution of mobile receptors not photobleached for different conditions and number of Trials; shape(len(N_List), len(Conc_List), Trials, duration/0.5+1)

PSDarray_like

Matrix representing the PSD grid and its receptors at the end of the simulation (bleached, not bleached).

Timearrayl_like

Time; shape(duration/0.5+1,)