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BIOMD0000000542 - Yuraszeck2010 - Vulnerabilities in the Tau Network in Tau Pathophysiology

 

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Reference Publication
Publication ID: 21085645
Yuraszeck TM, Neveu P, Rodriguez-Fernandez M, Robinson A, Kosik KS, Doyle FJ 3rd.
Vulnerabilities in the tau network and the role of ultrasensitive points in tau pathophysiology.
PLoS Comput. Biol. 2010; 6(11): e1000997
Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, California, USA.  [more]
Model
Original Model: BIOMD0000000542.origin
Submitter: Audald Lloret i Villas
Submission ID: MODEL1408150000
Submission Date: 15 Aug 2014 10:58:21 UTC
Last Modification Date: 23 Sep 2014 19:41:53 UTC
Creation Date: 15 Aug 2014 12:00:27 UTC
Encoders:  Audald Lloret i Villas
set #1
bqbiol:hasTaxon Taxonomy Homo sapiens
set #2
bqbiol:hasProperty Human Disease Ontology tauopathy
Human Disease Ontology Alzheimer's disease
set #3
bqbiol:isVersionOf Gene Ontology inclusion body assembly
Notes
Yuraszeck2010 - Vulnerabilities in the Tau Network in Tau Pathophysiology

This model is described in the article:

Yuraszeck TM, Neveu P, Rodriguez-Fernandez M, Robinson A, Kosik KS, Doyle FJ 3rd.
PLoS Comput. Biol. 2010; 6(11): e1000997

Abstract:

The multifactorial nature of disease motivates the use of systems-level analyses to understand their pathology. We used a systems biology approach to study tau aggregation, one of the hallmark features of Alzheimer's disease. A mathematical model was constructed to capture the current state of knowledge concerning tau's behavior and interactions in cells. The model was implemented in silico in the form of ordinary differential equations. The identifiability of the model was assessed and parameters were estimated to generate two cellular states: a population of solutions that corresponds to normal tau homeostasis and a population of solutions that displays aggregation-prone behavior. The model of normal tau homeostasis was robust to perturbations, and disturbances in multiple processes were required to achieve an aggregation-prone state. The aggregation-prone state was ultrasensitive to perturbations in diverse subsets of networks. Tau aggregation requires that multiple cellular parameters are set coordinately to a set of values that drive pathological assembly of tau. This model provides a foundation on which to build and increase our understanding of the series of events that lead to tau aggregation and may ultimately be used to identify critical intervention points that can direct the cell away from tau aggregation to aid in the treatment of tau-mediated (or related) aggregation diseases including Alzheimer's.

To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.

Model
Publication ID: 21085645 Submission Date: 15 Aug 2014 10:58:21 UTC Last Modification Date: 23 Sep 2014 19:41:53 UTC Creation Date: 15 Aug 2014 12:00:27 UTC
Mathematical expressions
Reactions
r1 r2 r3 r4
r5 r6 r7 r8
r9 r10 r11 r12
r13 r14 r15 r16
r17 r18 r19 r20
r21 r22 r23 r24
r25 r26 r27 r28
r29 r30 r31 r32
r33 r34 r35 r36
r37 r38 r39 r40
r41 r42 r43 r44
r45 r46 r47 r48
r49 r50 r51 r52
r53 r54 r55 r56
r57 r58 r59 r60
r61 r62 r63 r64
r65 r66 r67 r68
r69 r70 r71 r72
r73 r74 r75 r76
r77 r78 r79 r80
r81 r82 r83 r84
Rules
Rate Rule (variable: 20S) Rate Rule (variable: 26S) Rate Rule (variable: Ap) Rate Rule (variable: Bp)
Physical entities
Compartments Species
Brain ADP ATP MT
20S Hsc70 Hsp90
CHIP Bag2 26S
TauH3RUb TauH4RUb Nucleus3
Nucleus4 Agg33 Ap
Agg43 Bp Tau03R
TauN3R TauH3R Tau0*3R
Tau03RMT TauN*3R TauN3RMT
TauH*3R TauH3RMT TauH3R-Hsc70
TauH3R-Hsp90 Tau03R-Hsp90 TauH3R-CHIP-Hsc70
TauH3R-CHIP-Hsc70-Bag2 Tau04R TauN4R
TauH4R Tau0*4R Tau04RMT
TauN*4R TauN4RMT TauH*4R
TauH4RMT TauH4R-Hsc70 TauH4R-Hsp90
Tau04R-Hsp90 TauH4R-CHIP-Hsc70 TauH4R-CHIP-Hsc70-Bag2
Global parameters
k1 k2 k3 k4
k5 k6 k7 k8
k9 k10 k11 k12
k13 k14 k15 k16
k17 k18 k19 k20
k21 k22 k23 k24
k25 k26 k27 k28
k29 k30 k31 k32
k33 k34 k35 k36
k37 k38 k39 k40
k41 k42 k43 k44
k45 k46 k47 k48
k49 k50 k51 k52
k53 k54 k55 k56
k57 k58 k59 k60
k61 k62 k63 k64
k65 k66 k67 k68
k69 k70 k71 k72
k73 k74 k75 k76
k77 k78 k79 k80
k81 k82 k83 k84
k85 k86 k87 k88
k89 k90 k91 k92
k93      
Reactions (84)
 
 r1  → [Tau03R];  
 
 r2 [Tau03R] + [ATP] → [TauN3R] + [ADP];   {Tau03R} , {ATP}
 
 r3 [TauN3R] → [Tau03R];   {TauN3R}
 
 r4 [TauN3R] + [ATP] → [TauH3R] + [ADP];   {TauN3R} , {ATP}
 
 r5 [TauH3R] → [TauN3R];   {TauH3R}
 
 r6 [Tau03R] → [Tau0*3R];   {Tau03R}
 
 r7 [Tau0*3R] → [Tau03R];   {Tau0*3R}
 
 r8 [Tau0*3R] + [MT] → [Tau03RMT];   {Tau0*3R} , {MT}
 
 r9 [Tau03RMT] → [Tau0*3R] + [MT];   {Tau03RMT}
 
 r10 [TauN3R] → [TauN*3R];   {TauN3R}
 
 r11 [TauN*3R] → [TauN3R];   {TauN*3R}
 
 r12 [TauN*3R] + [MT] → [TauN3RMT];   {TauN*3R} , {MT}
 
 r13 [TauN3RMT] → [TauN*3R] + [MT];   {TauN3RMT}
 
 r14 [TauH3R] → [TauH*3R];   {TauH3R}
 
 r15 [TauH*3R] → [TauH3R];   {TauH*3R}
 
 r16 [TauH*3R] + [MT] → [TauH3RMT];   {TauH*3R} , {MT}
 
 r17 [TauH3RMT] → [TauH*3R] + [MT];   {TauH3RMT}
 
 r18 [Tau03R] + [20S] + [ATP] → [ADP] + [20S];   {Tau03R} , {20S} , {ATP}
 
 r19 [TauN3R] + [20S] + [ATP] → [ADP] + [20S];   {TauN3R} , {20S} , {ATP}
 
 r20 [TauH3R] + [20S] + [ATP] → [20S] + [ADP];   {TauH3R} , {20S} , {ATP}
 
 r21 [Tau03RMT] + [ATP] → [TauN3RMT] + [ADP];   {Tau03RMT} , {ATP}
 
 r22 [TauN3RMT] → [Tau03RMT];   {TauN3RMT}
 
 r23 [TauN3RMT] + [ATP] → [TauH3RMT] + [ADP];   {TauN3RMT} , {ATP}
 
 r24 [TauH3RMT] → [TauN3RMT];   {TauH3RMT}
 
 r25 [TauH3R] + [Hsc70] → [TauH3R-Hsc70];   {TauH3R} , {Hsc70}
 
 r26 [TauH3R-Hsc70] → [TauH3R] + [Hsc70];   {TauH3R-Hsc70}
 
 r27 [TauH3R-Hsc70] + [Hsp90] → [TauH3R-Hsp90] + [Hsc70];   {TauH3R-Hsc70} , {Hsp90}
 
 r28 [TauH3R-Hsp90] → [Tau03R-Hsp90];   {TauH3R-Hsp90}
 
 r29 [Tau03R-Hsp90] → [Hsp90] + [Tau03R];   {Tau03R-Hsp90}
 
 r30 [TauH3R-Hsc70] + [CHIP] → [TauH3R-CHIP-Hsc70];   {TauH3R-Hsc70} , {CHIP}
 
 r31 [TauH3R-CHIP-Hsc70] → [TauH3RUb] + [Hsc70] + [CHIP];   {TauH3R-CHIP-Hsc70}
 
 r32 [TauH3R-CHIP-Hsc70] + [Bag2] → [TauH3R-CHIP-Hsc70-Bag2];   {TauH3R-CHIP-Hsc70} , {Bag2}
 
 r33 [TauH3R-CHIP-Hsc70-Bag2] → [TauH3R-Hsc70] + [CHIP] + [Bag2];   {TauH3R-CHIP-Hsc70-Bag2}
 
 r34 [TauH3RUb] + [26S] + [ATP] → [ADP] + [26S];   {TauH3RUb} , {26S} , {ATP}
 
 r35  → [Tau04R];  
 
 r36 [Tau04R] + [ATP] → [TauN4R] + [ADP];   {Tau04R} , {ATP}
 
 r37 [TauN4R] → [Tau04R];   {TauN4R}
 
 r38 [TauN4R] + [ATP] → [TauH4R] + [ADP];   {TauN4R} , {ATP}
 
 r39 [TauH4R] → [TauN4R];   {TauH4R}
 
 r40 [Tau04R] → [Tau0*4R];   {Tau04R}
 
 r41 [Tau0*4R] → [Tau04R];   {Tau0*4R}
 
 r42 [Tau0*4R] + [MT] → [Tau04RMT];   {Tau0*4R} , {MT}
 
 r43 [Tau04RMT] → [Tau0*4R] + [MT];   {Tau04RMT}
 
 r44 [TauN4R] → [TauN*4R];   {TauN4R}
 
 r45 [TauN*4R] → [TauN4R];   {TauN*4R}
 
 r46 [TauN*4R] + [MT] → [TauN4RMT];   {TauN*4R} , {MT}
 
 r47 [TauN4RMT] → [TauN*4R] + [MT];   {TauN4RMT}
 
 r48 [TauH4R] → [TauH*4R];   {TauH4R}
 
 r49 [TauH*4R] → [TauH4R];   {TauH*4R}
 
 r50 [TauH*4R] + [MT] → [TauH4RMT];   {TauH*4R} , {MT}
 
 r51 [TauH4RMT] → [TauH*4R] + [MT];   {TauH4RMT}
 
 r52 [Tau04R] + [20S] + [ATP] → [ADP] + [20S];   {Tau04R} , {20S} , {ATP}
 
 r53 [TauN4R] + [20S] + [ATP] → [ADP] + [20S];   {TauN4R} , {20S} , {ATP}
 
 r54 [TauH4R] + [20S] + [ATP] → [ADP] + [20S];   {TauH4R} , {20S} , {ATP}
 
 r55 [Tau04RMT] + [ATP] → [TauN4RMT] + [ADP];   {Tau04RMT} , {ATP}
 
 r56 [TauN4RMT] → [Tau04RMT];   {TauN4RMT}
 
 r57 [TauN4RMT] + [ATP] → [TauH4RMT] + [ADP];   {TauN4RMT} , {ATP}
 
 r58 [TauH4RMT] → [TauN4RMT];   {TauH4RMT}
 
 r59 [TauH4R] + [Hsc70] → [TauH4R-Hsc70];   {TauH4R} , {Hsc70}
 
 r60 [TauH4R-Hsc70] → [TauH4R] + [Hsc70];   {TauH4R-Hsc70}
 
 r61 [TauH4R-Hsc70] + [Hsp90] → [TauH4R-Hsp90] + [Hsc70];   {TauH4R-Hsc70} , {Hsp90}
 
 r62 [TauH4R-Hsp90] → [Tau04R-Hsp90];   {TauH4R-Hsp90}
 
 r63 [Tau04R-Hsp90] → [Hsp90] + [Tau04R];   {Tau04R-Hsp90}
 
 r64 [TauH4R-Hsc70] + [CHIP] → [TauH4R-CHIP-Hsc70];   {TauH4R-Hsc70} , {CHIP}
 
 r65 [TauH4R-CHIP-Hsc70] → [TauH4RUb] + [Hsc70] + [CHIP];   {TauH4R-CHIP-Hsc70}
 
 r66 [TauH4R-CHIP-Hsc70] + [Bag2] → [TauH4R-CHIP-Hsc70-Bag2];   {TauH4R-CHIP-Hsc70} , {Bag2}
 
 r67 [TauH4R-CHIP-Hsc70-Bag2] → [TauH4R-Hsc70] + [CHIP] + [Bag2];   {TauH4R-CHIP-Hsc70-Bag2}
 
 r68 [TauH4RUb] + [26S] + [ATP] → [ADP] + [26S];   {TauH4RUb} , {26S} , {ATP}
 
 r69 [ADP] → [ATP];   {ADP}
 
 r70 [ATP] → [ADP];   {ATP}
 
 r71 2.0 × [TauH3RUb] → [Nucleus3];   {TauH3RUb}
 
 r72 [Nucleus3] → 2.0 × [TauH3RUb];   {Nucleus3}
 
 r73 2.0 × [TauH4RUb] → [Nucleus4];   {TauH4RUb}
 
 r74 [Nucleus4] → 2.0 × [TauH4RUb];   {Nucleus4}
 
 r75 [Nucleus3] + [TauH3RUb] → [Agg33];   {Nucleus3} , {TauH3RUb}
 
 r76 [Agg33] → [Nucleus3] + [TauH3RUb];   {Agg33}
 
 r77 [TauH3RUb] + [Agg33] → [Ap];   {TauH3RUb} , {Agg33}
 
 r78 [TauH3RUb] + [Ap] → [Ap];   {TauH3RUb} , {Ap}
 
 r79 [Ap] → [TauH3RUb] + [Ap];   {Ap}
 
 r80 [Nucleus4] + [TauH4RUb] → [Agg43];   {Nucleus4} , {TauH4RUb}
 
 r81 [Agg43] → [Nucleus4] + [TauH4RUb];   {Agg43}
 
 r82 [TauH4RUb] + [Agg43] → [Bp];   {TauH4RUb} , {Agg43}
 
 r83 [TauH4RUb] + [Bp] → [Bp];   {TauH4RUb} , {Bp}
 
 r84 [Bp] → [TauH4RUb] + [Bp];   {Bp}
 
Rules (4)
 
 Rate Rule (name: _20S) d [ 20S] / d t= 0
 
 Rate Rule (name: _26S) d [ 26S] / d t= 0
 
 Rate Rule (name: Ap) d [ Ap] / d t= r77
 
 Rate Rule (name: Bp) d [ Bp] / d t= r82
 
Functions (6)
 
 Constant flux (irreversible) lambda(v, v)
 
 Henri-Michaelis-Menten (irreversible) lambda(substrate, Km, V, V*substrate/(Km+substrate))
 
 Mass Action* lambda(k1, x1, x2, k1*x1*x2)
 
 Michaelis-Menten* lambda(k1, x1, x2, k2, k1*x1*x2/(k2+x1))
 
 Mass Action** lambda(K1, x1, x2, x3, K1*x1*x2*x3)
 
 Nucleation lambda(k1, x1, k1*x1^2)
 
 Brain Spatial dimensions: 3.0  Compartment size: 1.0
 
 ADP
Compartment: Brain
Initial concentration: 1.0
 
 ATP
Compartment: Brain
Initial concentration: 0.0
 
 MT
Compartment: Brain
Initial concentration: 15.0
 
 20S
Compartment: Brain
Initial concentration: 1.0
 
 Hsc70
Compartment: Brain
Initial concentration: 0.1
 
 Hsp90
Compartment: Brain
Initial concentration: 0.1
 
 CHIP
Compartment: Brain
Initial concentration: 0.1
 
 Bag2
Compartment: Brain
Initial concentration: 0.1
 
 26S
Compartment: Brain
Initial concentration: 1.0
 
 TauH3RUb
Compartment: Brain
Initial concentration: 0.0
 
 TauH4RUb
Compartment: Brain
Initial concentration: 0.0
 
 Nucleus3
Compartment: Brain
Initial concentration: 0.0
 
 Nucleus4
Compartment: Brain
Initial concentration: 0.0
 
 Agg33
Compartment: Brain
Initial concentration: 0.0
 
 Ap
Compartment: Brain
Initial concentration: 0.0
 
 Agg43
Compartment: Brain
Initial concentration: 0.0
 
 Bp
Compartment: Brain
Initial concentration: 0.0
 
 Tau03R
Compartment: Brain
Initial concentration: 0.0
 
 TauN3R
Compartment: Brain
Initial concentration: 0.0
 
 TauH3R
Compartment: Brain
Initial concentration: 0.0
 
 Tau0*3R
Compartment: Brain
Initial concentration: 0.0
 
 Tau03RMT
Compartment: Brain
Initial concentration: 0.0
 
 TauN*3R
Compartment: Brain
Initial concentration: 0.0
 
 TauN3RMT
Compartment: Brain
Initial concentration: 0.0
 
 TauH*3R
Compartment: Brain
Initial concentration: 0.0
 
 TauH3RMT
Compartment: Brain
Initial concentration: 0.0
 
 TauH3R-Hsc70
Compartment: Brain
Initial concentration: 0.0
 
 TauH3R-Hsp90
Compartment: Brain
Initial concentration: 0.0
 
 Tau03R-Hsp90
Compartment: Brain
Initial concentration: 0.0
 
 TauH3R-CHIP-Hsc70
Compartment: Brain
Initial concentration: 0.0
 
 TauH3R-CHIP-Hsc70-Bag2
Compartment: Brain
Initial concentration: 0.0
 
 Tau04R
Compartment: Brain
Initial concentration: 0.0
 
 TauN4R
Compartment: Brain
Initial concentration: 0.0
 
 TauH4R
Compartment: Brain
Initial concentration: 0.0
 
 Tau0*4R
Compartment: Brain
Initial concentration: 0.0
 
 Tau04RMT
Compartment: Brain
Initial concentration: 0.0
 
 TauN*4R
Compartment: Brain
Initial concentration: 0.0
 
 TauN4RMT
Compartment: Brain
Initial concentration: 0.0
 
 TauH*4R
Compartment: Brain
Initial concentration: 0.0
 
 TauH4RMT
Compartment: Brain
Initial concentration: 0.0
 
 TauH4R-Hsc70
Compartment: Brain
Initial concentration: 0.0
 
 TauH4R-Hsp90
Compartment: Brain
Initial concentration: 0.0
 
 Tau04R-Hsp90
Compartment: Brain
Initial concentration: 0.0
 
 TauH4R-CHIP-Hsc70
Compartment: Brain
Initial concentration: 0.0
 
 TauH4R-CHIP-Hsc70-Bag2
Compartment: Brain
Initial concentration: 0.0
 
Global Parameters (93)
 
 k1
Value: 0.03725
Constant
 
 k2
Value: 0.391818
Constant
 
 k3
Value: 27.5668
Constant
 
 k4
Value: 6.065997
Constant
 
 k5
Value: 7.99621
Constant
 
 k6
Value: 0.142099
Constant
 
 k7
Value: 21.91138
Constant
 
 k8
Value: 0.608448
Constant
 
 k9
Value: 5.760257
Constant
 
 k10
Value: 7.118684
Constant
 
 k11
Value: 15.0
Constant
 
 k12
Value: 9.633772
Constant
 
 k13
Value: 0.163388
Constant
 
 k14
Value: 1.540886
Constant
 
 k15
Value: 9.220426
Constant
 
 k16
Value: 50.66157
Constant
 
 k17
Value: 0.202066
Constant
 
 k18
Value: 3.940468
Constant
 
 k19
Value: 8.052152
Constant
 
 k20
Value: 19.76984
Constant
 
 k21
Value: 7.248652
Constant
 
 k22
Value: 0.173127
Constant
 
 k23
Value: 0.075176
Constant
 
 k24
Value: 0.039141
Constant
 
 k25
Value: 0.066012
Constant
 
 k26
Value: 0.1452
Constant
 
 k27
Value: 0.473124
Constant
 
 k28
Value: 12.62955
Constant
 
 k29
Value: 0.006017
Constant
 
 k30
Value: 16.56551
Constant
 
 k31
Value: 3.991539
Constant
 
 k32
Value: 7.130081
Constant
 
 k33
Value: 0.009267
Constant
 
 k34
Value: 1.11E-4
Constant
 
 k35
Value: 0.146177
Constant
 
 k36
Value: 0.006298
Constant
 
 k37
Value: 1.07
Constant
 
 k38
Value: 0.029266
Constant
 
 k39
Value: 1.163756
Constant
 
 k40
Value: 0.050949
Constant
 
 k41
Value: 0.279
Constant
 
 k42
Value: 0.025365
Constant
 
 k43
Value: 3.68998
Constant
 
 k44
Value: 27.5668
Constant
 
 k45
Value: 0.216599
Constant
 
 k46
Value: 7.99621
Constant
 
 k47
Value: 2.801964
Constant
 
 k48
Value: 21.91138
Constant
 
 k49
Value: 0.003379
Constant
 
 k50
Value: 5.760257
Constant
 
 k51
Value: 7.118684
Constant
 
 k52
Value: 15.0
Constant
 
 k53
Value: 9.633772
Constant
 
 k54
Value: 0.054463
Constant
 
 k55
Value: 1.540886
Constant
 
 k56
Value: 9.220426
Constant
 
 k57
Value: 50.66157
Constant
 
 k58
Value: 0.067355
Constant
 
 k59
Value: 3.940468
Constant
 
 k60
Value: 8.052152
Constant
 
 k61
Value: 19.76984
Constant
 
 k62
Value: 2.416217
Constant
 
 k63
Value: 0.211664
Constant
 
 k64
Value: 0.074306
Constant
 
 k65
Value: 0.001334
Constant
 
 k66
Value: 0.028914
Constant
 
 k67
Value: 0.1452
Constant
 
 k68
Value: 0.004313
Constant
 
 k69
Value: 12.62955
Constant
 
 k70
Value: 0.073055
Constant
 
 k71
Value: 16.56551
Constant
 
 k72
Value: 0.014352
Constant
 
 k73
Value: 7.130081
Constant
 
 k74
Value: 1.61E-4
Constant
 
 k75
Value: 8.57E-5
Constant
 
 k76
Value: 0.283991
Constant
 
 k77
Value: 1.185806
Constant
 
 k78
Value: 0.004562
Constant
 
 k79
Value: 0.346673
Constant
 
 k80
Value: 0.551509
Constant
 
 k81
Value: 5.59E-5
Constant
 
 k82
Value: 0.644848
Constant
 
 k83
Value: 0.006502
Constant
 
 k84
Value: 0.68
Constant
 
 k85
Value: 0.015317
Constant
 
 k86
Value: 5.0E-6
Constant
 
 k87
Value: 0.0012
Constant
 
 k88
Value: 5.0E-6
Constant
 
 k89
Value: 0.06
Constant
 
 k90
Value: 0.095
Constant
 
 k91
Value: 0.005429
Constant
 
 k92
Value: 0.095
Constant
 
 k93
Value: 0.019
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000542

Curator's comment: (updated: 15 Aug 2014 12:18:53 GMT)

Aggregation-prone simulation from Figure 6 has been reproduced here. Percent change in microtubule bound 4R tau protein with respect to basal concentration during 5000 arbitrary units.

Parameters are took from “Run1” of “Disease Params” sheet, on Dataset S1.
To run this plot, the specie “Tau04MT” from Table S1 using the reactions from Table S2 is divided by the specie “Tau04MT” from Table S1 using the reactions from Table S2 including a 5-fold increase in the parameter associated with the binding of normally phosphorylated tau 3R to microtubules (reaction 12).

The simulation was done using Copasi v4.12 (Build 81) and the plots were generated using Gnuplot. The models with simulation settings can be downloaded from the below links:
- Copasi file of “Tau04MT” basal concentration
- Copasi file of “Tau04MT” concentration when 5-fold increase in reaction 12 is implemented

Additional file(s)
  • Yuraszeck2010 - Vulnerabilities in the Tau Network in Tau Pathophysiology:
    Copasi file of “Tau04MT” concentration when 5-fold increase in reaction 12 is implemented
  • Yuraszeck2010 - Vulnerabilities in the Tau Network in Tau Pathophysiology:
    Copasi file of “Tau04MT” basal concentration
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