BioModels Database (Caltech mirror)

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.

Reactions (84)

→ [Tau03R];

Math:

(Details: $View Math$ )

Annotations:

Notes:

Tau synthesis

[Tau03R] + [ATP] → [TauN3R] + [ADP]; {Tau03R} , {ATP}

Math:

(Details: $View Math$ )

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Notes:

Phosphorylation of newly synthesized tau

[TauN3R] → [Tau03R]; {TauN3R}

Math:

(Details: $View Math$ )

Annotations:

Notes:

dephosphosrylation of normally phosphorylated tau

[TauN3R] + [ATP] → [TauH3R] + [ADP]; {TauN3R} , {ATP}

Math:

(Details: $View Math$ )

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Notes:

Phosphorylation of normally phosphorylated tau

[TauH3R] → [TauN3R]; {TauH3R}

Math:

(Details: $View Math$ )

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Notes:

Dephosphorylation of abnormal/misfolded tau

[Tau03R] → [Tau0*3R]; {Tau03R}

Math:

(Details: $View Math$ )

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Conformation change favoring MT binding

[Tau0*3R] → [Tau03R]; {Tau0*3R}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Conformational change back to original

[Tau0*3R] + [MT] → [Tau03RMT]; {Tau0*3R} , {MT}

Math:

(Details: $View Math$ )

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Binding of newly synthesized tau to MT

[Tau03RMT] → [Tau0*3R] + [MT]; {Tau03RMT}

Math:

(Details: $View Math$ )

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Release of newly synthesized au from MT

r10

[TauN3R] → [TauN*3R]; {TauN3R}

Math:

(Details: $View Math$ )

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Conformation chang favoring MT binding

r11

[TauN*3R] → [TauN3R]; {TauN*3R}

Math:

(Details: $View Math$ )

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Notes:

Conformational change back to original

r12

[TauN*3R] + [MT] → [TauN3RMT]; {TauN*3R} , {MT}

Math:

(Details: $View Math$ )

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Binding of normally phosphorylated tau to MT

r13

[TauN3RMT] → [TauN*3R] + [MT]; {TauN3RMT}

Math:

(Details: $View Math$ )

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Release of normally phosphorylated tau from MT

r14

[TauH3R] → [TauH*3R]; {TauH3R}

Math:

(Details: $View Math$ )

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Conformational change favoring MT binding

r15

[TauH*3R] → [TauH3R]; {TauH*3R}

Math:

(Details: $View Math$ )

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Notes:

Conformational change backt to original

r16

[TauH*3R] + [MT] → [TauH3RMT]; {TauH*3R} , {MT}

Math:

(Details: $View Math$ )

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Binding of misfolded tau to MT

r17

[TauH3RMT] → [TauH*3R] + [MT]; {TauH3RMT}

Math:

(Details: $View Math$ )

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Release of misfolded tau from microtubules

r18

[Tau03R] + [20S] + [ATP] → [ADP] + [20S]; {Tau03R} , {20S} , {ATP}

Math:

(Details: $View Math$ )

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Degradation of newly synthesized tau

r19

[TauN3R] + [20S] + [ATP] → [ADP] + [20S]; {TauN3R} , {20S} , {ATP}

Math:

(Details: $View Math$ )

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Degradation of phosphorlated tau

r20

[TauH3R] + [20S] + [ATP] → [20S] + [ADP]; {TauH3R} , {20S} , {ATP}

Math:

(Details: $View Math$ )

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Degradation of misfolded tau

r21

[Tau03RMT] + [ATP] → [TauN3RMT] + [ADP]; {Tau03RMT} , {ATP}

Math:

(Details: $View Math$ )

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Phosphorylation of MT-bound newly synthesized tau

r22

[TauN3RMT] → [Tau03RMT]; {TauN3RMT}

Math:

(Details: $View Math$ )

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Dephosphorylation of MT-bound normally phosphorylated tau

r23

[TauN3RMT] + [ATP] → [TauH3RMT] + [ADP]; {TauN3RMT} , {ATP}

Math:

(Details: $View Math$ )

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Phosphorylation of MT-bound normally phosphorylated tau

r24

[TauH3RMT] → [TauN3RMT]; {TauH3RMT}

Math:

(Details: $View Math$ )

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Dephosphorylation of MT-bound abnormal/midfolded tau

r25

[TauH3R] + [Hsc70] → [TauH3R-Hsc70]; {TauH3R} , {Hsc70}

Math:

(Details: $View Math$ )

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Association of misfolded tau with Hsp70

r26

[TauH3R-Hsc70] → [TauH3R] + [Hsc70]; {TauH3R-Hsc70}

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(Details: $View Math$ )

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Hsc70 release

r27

[TauH3R-Hsc70] + [Hsp90] → [TauH3R-Hsp90] + [Hsc70]; {TauH3R-Hsc70} , {Hsp90}

Math:

(Details: $View Math$ )

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Exchange of Hsc70 for Hsp90

r28

[TauH3R-Hsp90] → [Tau03R-Hsp90]; {TauH3R-Hsp90}

Math:

(Details: $View Math$ )

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Restoration of TauH to Tau0 via Hsp90

r29

[Tau03R-Hsp90] → [Hsp90] + [Tau03R]; {Tau03R-Hsp90}

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(Details: $View Math$ )

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Release of Tau0 from Hsp90

r30

[TauH3R-Hsc70] + [CHIP] → [TauH3R-CHIP-Hsc70]; {TauH3R-Hsc70} , {CHIP}

Math:

(Details: $View Math$ )

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Exchange of Hsc70 for CHIP

r31

[TauH3R-CHIP-Hsc70] → [TauH3RUb] + [Hsc70] + [CHIP]; {TauH3R-CHIP-Hsc70}

Math:

(Details: $View Math$ )

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Ubiquitination of tau

r32

[TauH3R-CHIP-Hsc70] + [Bag2] → [TauH3R-CHIP-Hsc70-Bag2]; {TauH3R-CHIP-Hsc70} , {Bag2}

Math:

(Details: $View Math$ )

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Binding of Bag-2 to the degradation complex

r33

[TauH3R-CHIP-Hsc70-Bag2] → [TauH3R-Hsc70] + [CHIP] + [Bag2]; {TauH3R-CHIP-Hsc70-Bag2}

Math:

(Details: $View Math$ )

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Rescue for degradation by Bag2

r34

[TauH3RUb] + [26S] + [ATP] → [ADP] + [26S]; {TauH3RUb} , {26S} , {ATP}

Math:

(Details: $View Math$ )

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Degradation of ubiquitinated tau

r35

→ [Tau04R];

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(Details: $View Math$ )

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Synthesis of 4R tau

r36

[Tau04R] + [ATP] → [TauN4R] + [ADP]; {Tau04R} , {ATP}

Math:

(Details: $View Math$ )

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Phosphorylation of newly synthesized tau

r37

[TauN4R] → [Tau04R]; {TauN4R}

Math:

(Details: $View Math$ )

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Dephosphorylation of normally phosphorylated tau

r38

[TauN4R] + [ATP] → [TauH4R] + [ADP]; {TauN4R} , {ATP}

Math:

(Details: $View Math$ )

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Phosphorylation of normally phosphorylated tau

r39

[TauH4R] → [TauN4R]; {TauH4R}

Math:

(Details: $View Math$ )

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Dephosphorylation of abnormal/misfolded tau

r40

[Tau04R] → [Tau0*4R]; {Tau04R}

Math:

(Details: $View Math$ )

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Conformation change favoring MT binding

r41

[Tau0*4R] → [Tau04R]; {Tau0*4R}

Math:

(Details: $View Math$ )

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Notes:

Conformational change back to original

r42

[Tau0*4R] + [MT] → [Tau04RMT]; {Tau0*4R} , {MT}

Math:

(Details: $View Math$ )

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Binding of newly shynthesized tau to MT

r43

[Tau04RMT] → [Tau0*4R] + [MT]; {Tau04RMT}

Math:

(Details: $View Math$ )

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Release of newly shyntesized tau from MT

r44

[TauN4R] → [TauN*4R]; {TauN4R}

Math:

(Details: $View Math$ )

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Notes:

Conformation change favoring MT binding

r45

[TauN*4R] → [TauN4R]; {TauN*4R}

Math:

(Details: $View Math$ )

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Conformational change back to original

r46

[TauN*4R] + [MT] → [TauN4RMT]; {TauN*4R} , {MT}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Binding of normally phosphorylated tau to MT

r47

[TauN4RMT] → [TauN*4R] + [MT]; {TauN4RMT}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Release of normally phosphorylated tau from MT

r48

[TauH4R] → [TauH*4R]; {TauH4R}

Math:

(Details: $View Math$ )

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Notes:

Conformation change favoring MT binding

r49

[TauH*4R] → [TauH4R]; {TauH*4R}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Conformational change back to original

r50

[TauH*4R] + [MT] → [TauH4RMT]; {TauH*4R} , {MT}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Binding of misfolded tau to MT

r51

[TauH4RMT] → [TauH*4R] + [MT]; {TauH4RMT}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Release of misfolded tau from microtubules

r52

[Tau04R] + [20S] + [ATP] → [ADP] + [20S]; {Tau04R} , {20S} , {ATP}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Degradation of newly shynthesized tau

r53

[TauN4R] + [20S] + [ATP] → [ADP] + [20S]; {TauN4R} , {20S} , {ATP}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Degradation of phosphorylated tau

r54

[TauH4R] + [20S] + [ATP] → [ADP] + [20S]; {TauH4R} , {20S} , {ATP}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Degradation of misfolded tau

r55

[Tau04RMT] + [ATP] → [TauN4RMT] + [ADP]; {Tau04RMT} , {ATP}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Phosphorylation of MT-bound newly synthesized tau

r56

[TauN4RMT] → [Tau04RMT]; {TauN4RMT}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Dephosphorylation of MT-bound normally phosphorylated tau

r57

[TauN4RMT] + [ATP] → [TauH4RMT] + [ADP]; {TauN4RMT} , {ATP}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Phosphorylation of MT-bound normally phosphorylated tau

r58

[TauH4RMT] → [TauN4RMT]; {TauH4RMT}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Dephosphorylation of MT-bound abnormal/misfolded tau

r59

[TauH4R] + [Hsc70] → [TauH4R-Hsc70]; {TauH4R} , {Hsc70}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Association of misfolded tau with Hsp70

r60

[TauH4R-Hsc70] → [TauH4R] + [Hsc70]; {TauH4R-Hsc70}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Hsc70 release

r61

[TauH4R-Hsc70] + [Hsp90] → [TauH4R-Hsp90] + [Hsc70]; {TauH4R-Hsc70} , {Hsp90}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Exchange of Hsc70 for Hsp90

r62

[TauH4R-Hsp90] → [Tau04R-Hsp90]; {TauH4R-Hsp90}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Restoration of TauH to Tau0 via Hsp90

r63

[Tau04R-Hsp90] → [Hsp90] + [Tau04R]; {Tau04R-Hsp90}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Release of Tau0 from Hsp90

r64

[TauH4R-Hsc70] + [CHIP] → [TauH4R-CHIP-Hsc70]; {TauH4R-Hsc70} , {CHIP}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Exchange of Hsc70 for CHIP

r65

[TauH4R-CHIP-Hsc70] → [TauH4RUb] + [Hsc70] + [CHIP]; {TauH4R-CHIP-Hsc70}

Math:

(Details: $View Math$ )

Annotations:

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Ubiquitination of tau

r66

[TauH4R-CHIP-Hsc70] + [Bag2] → [TauH4R-CHIP-Hsc70-Bag2]; {TauH4R-CHIP-Hsc70} , {Bag2}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Binding of Bag-2 to the degradation complex

r67

[TauH4R-CHIP-Hsc70-Bag2] → [TauH4R-Hsc70] + [CHIP] + [Bag2]; {TauH4R-CHIP-Hsc70-Bag2}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Rescue from degradation by Bag2

r68

[TauH4RUb] + [26S] + [ATP] → [ADP] + [26S]; {TauH4RUb} , {26S} , {ATP}

Math:

(Details: $View Math$ )

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Notes:

Degradation of ubiquitinated tau

r69

[ADP] → [ATP]; {ADP}

Math:

(Details: $View Math$ )

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Generation of ATP

r70

[ATP] → [ADP]; {ATP}

Math:

(Details: $View Math$ )

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Use of ATP by other processes

r71

2.0 × [TauH3RUb] → [Nucleus3]; {TauH3RUb}

Math:

(Details: $View Math$ )

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Nucleation of Tau3

r72

[Nucleus3] → 2.0 × [TauH3RUb]; {Nucleus3}

Math:

(Details: $View Math$ )

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Dissociation of Tau3 Nucleus

r73

2.0 × [TauH4RUb] → [Nucleus4]; {TauH4RUb}

Math:

(Details: $View Math$ )

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Nucleation of Tau4

r74

[Nucleus4] → 2.0 × [TauH4RUb]; {Nucleus4}

Math:

(Details: $View Math$ )

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Notes:

Dissociation of Tau4 Nucleus

r75

[Nucleus3] + [TauH3RUb] → [Agg33]; {Nucleus3} , {TauH3RUb}

Math:

(Details: $View Math$ )

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Formation of Tau3, length 3

r76

[Agg33] → [Nucleus3] + [TauH3RUb]; {Agg33}

Math:

(Details: $View Math$ )

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Dissociation

r77

[TauH3RUb] + [Agg33] → [Ap]; {TauH3RUb} , {Agg33}

Math:

(Details: $View Math$ )

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Notes:

Formation of Tau3, 1 > 3 from Tau3 aggregate of length 3

r78

[TauH3RUb] + [Ap] → [Ap]; {TauH3RUb} , {Ap}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Formation of Agg of 1 > 3 from aggregaties of 1 > 3

r79

[Ap] → [TauH3RUb] + [Ap]; {Ap}

Math:

(Details: $View Math$ )

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Notes:

Dissociation of aggregates 1 > 3

r80

[Nucleus4] + [TauH4RUb] → [Agg43]; {Nucleus4} , {TauH4RUb}

Math:

(Details: $View Math$ )

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Formation of Tau4, length 3

r81

[Agg43] → [Nucleus4] + [TauH4RUb]; {Agg43}

Math:

(Details: $View Math$ )

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Dissociation

r82

[TauH4RUb] + [Agg43] → [Bp]; {TauH4RUb} , {Agg43}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Formation of Tau4, 1 > 3 from Tau3 aggreate of length 3

r83

[TauH4RUb] + [Bp] → [Bp]; {TauH4RUb} , {Bp}

Math:

(Details: $View Math$ )

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Formation of Agg of 1 > 3 from aggregates of 1 >3

r84

[Bp] → [TauH4RUb] + [Bp]; {Bp}

Math:

(Details: $View Math$ )

Annotations:

Notes:

Dissociation of aggregates 1 > 3

Rules (4)

Rate Rule (name: _20S)

d [ 20S] / d t= 0

Math:

(Details: $View Math$ )

Rate Rule (name: _26S)

d [ 26S] / d t= 0

Math:

(Details: $View Math$ )

Rate Rule (name: Ap)

d [ Ap] / d t= r77

Math:

(Details: $View Math$ )

Rate Rule (name: Bp)

d [ Bp] / d t= r82

Math:

(Details: $View Math$ )

Functions (6)

Constant flux (irreversible)

lambda(v, v)

Math:

Henri-Michaelis-Menten (irreversible)

lambda(substrate, Km, V, V*substrate/(Km+substrate))

Math:

Mass Action*

lambda(k1, x1, x2, k1*x1*x2)

Math:

Michaelis-Menten*

lambda(k1, x1, x2, k2, k1*x1*x2/(k2+x1))

Math:

Mass Action**

lambda(K1, x1, x2, x3, K1*x1*x2*x3)

Math:

Nucleation

lambda(k1, x1, k1*x1^2)

Math:

Brain

Spatial dimensions: 3.0 Compartment size: 1.0

ADP

Compartment: Brain

Initial concentration: 1.0

ATP

Compartment: Brain

Initial concentration: 0.0

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

Compartment: Brain

Initial concentration: 0.0

Agg43

Compartment: Brain

Initial concentration: 0.0

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

BioModels Database

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