Analyzing the long-term behaviors (attractors) of dynamic models of biological systems can provide valuable insight into biological phenotypes and their stability. In this paper we identify the allowed long-term behaviors of a multi-level, 70-node dynamic model of the stomatal opening process in plants. We start by reducing the model’s huge state space. We first reduce unregulated nodes and simple mediator nodes, then simplify the regulatory functions of selected nodes while keeping the model consistent with experimental observations. We perform attractor analysis on the resulting 32-node reduced model by two methods: 1. converting it into a Boolean model, then applying two attractor-finding algorithms; 2. theoretical analysis of the regulatory functions. We further demonstrate the robustness of signal propagation by showing that a large percentage of single-node knockouts does not affect the stomatal opening level. Combining both methods with analysis of perturbation scenarios, we conclude that all nodes except two in the reduced model have a single attractor; and only two nodes can admit oscillations. The multistability or oscillations of these four nodes do not affect the stomatal opening level in any situation. This conclusion applies to the original model as well in all the biologically meaningful cases. In addition, the stomatal opening level is resilient against single-node knockouts. Thus, we conclude that the complex structure of this signal transduction network provides multiple information propagation pathways while not allowing extensive multistability or oscillations, resulting in robust signal propagation. Our innovative combination of methods offers a promising way to analyze multi-level models. Crowther Audrey audrey.crowther@huskers.unl.edu University of Nebraska-Lincoln 2016-10-01T13:20:49Z 2018-03-20T10:10:01Z

Blue light

 2018-03-15T14:36:21Z

Abscisic acid

 2018-03-15T13:00:24Z

Red light

 2018-03-15T14:36:21Z

Air with high carbon dioxide concentration

 2018-03-14T11:56:56Z

Air with ambient carbon dioxide concentration

 2018-03-14T11:52:22Z

a serine/threonine protein kinase that directly phosphorylates the plasma membrane H-ATPase

o denote node levels in this model, similar to a multi-level model, the number represents the level of the node, in this case PK.

 2018-02-28T16:17:50Z

Higher levels of cytosolic Ca2+ concentration

 2018-03-14T21:14:31Z

Ca2+-ATPases and Ca2+/H+ antiporters responsible for Ca2+ efflux from the cytosol

 2018-03-14T10:42:32Z

Higher levels of anion efflux channels at the plasma membrane

 2018-03-01T10:04:25Z

Higher levels of phospholipase D

 2018-02-28T17:04:05Z

14-3-3 protein bound H+-ATPase

 2018-03-01T09:19:05Z

Phospholipase D

 2018-03-16T13:22:23Z

The catalytic subunit of type 1 phosphatase located in the cytosol

To denote node levels in this model, similar to a multi-level model, the number represents the level of the node, in this case PP1cc.

 2018-02-28T16:55:44Z

Protein: 14-3-3-like protein GF14 lambda

14-3-3 protein bound phototropin 1

Gene ID: P48349

Gene: GRF6

Protein: Phototropin-1

Gene: PHOT1

Gene ID: 823721

 2018-03-01T09:53:57Z

Higher levels of light-dependent reactions of photosynthesis

 2018-03-14T11:52:22Z

Mesophyll cell photosynthesis

 2018-03-15T14:36:21Z

Phospholipase C

Gene: PLC1/ PLC2

UniProt ID: Q39032/ Q39033

Gene ID: 835981/ 819999

 2016-10-01T16:53:50Z

Stomatal opening

 2016-10-02T08:55:36Z

14-3-3 protein bound H+-ATPase

 2018-03-01T09:19:05Z

Disaccharide made of glucose and fructose, produced by plants

 2017-07-26T13:44:55Z

Ca2+ release from intracellular stores

 2016-10-02T08:45:43Z

Phospholipase A2β

Gene: PLA2-β

UniProt ID: Q8GZB4

Gene ID: ID: 816488

 2018-02-28T13:51:42Z

Intercellular CO2 concentration

 2018-03-15T14:36:21Z

Intercellular CO2 concentration

 2018-03-15T14:36:21Z

Higher levels of mesophyll cell photosynthesis

 2018-02-14T09:20:38Z

cytosolic K+ concentration

 2018-02-22T15:38:15Z

Free Fatty Acids

 2018-03-14T14:27:55Z

a serine/threonine protein kinase that directly phosphorylates the plasma membrane H-ATPase

o denote node levels in this model, similar to a multi-level model, the number represents the level of the node, in this case PK.

 2018-02-28T16:21:42Z

K+ efflux from the vacuole to the cytosol

 2018-03-14T21:14:31Z

Light-dependent reactions of photosynthesis

 2018-03-14T14:27:55Z

Stomatal opening

 2017-07-26T13:44:55Z

Stomatal opening

 2016-10-02T08:53:55Z

K+ outward channels at plasma membrane

 2018-02-22T14:42:50Z

Nitric oxide

 2018-03-15T12:59:57Z

14-3-3 protein bound H+-ATPase

To denote node levels in this model, similar to a multi-level model, the number represents the level of the node, in this case HATPase.

 2018-03-01T09:19:05Z

vacuolar K+ concentration

 2018-03-14T21:14:31Z

Light-independent reactions of photosynthesis

 2018-03-14T11:51:34Z

The catalytic subunit of type 1 phosphatase located in the cytosol

To denote node levels in this model, similar to a multi-level model, the number represents the level of the node, in this case PP1cc.

 2018-02-28T16:44:36Z

Cytosolic Ca2+ concentration

 2016-10-02T08:44:54Z

a serine/threonine protein kinase that directly phosphorylates the plasma membrane H-ATPase

To denote node levels in this model, similar to a multi-level model, the number represents the level of the node, in this case PK.

 2018-02-28T16:44:36Z

Anion efflux channels at the plasma membrane

 2018-03-01T09:48:08Z

Higher levels of light-independent reactions of photosynthesis

 2018-03-14T11:52:22Z

Positive Plasma Membrane Voltage

 2018-03-01T09:17:39Z

Negative Plasma Membrane Voltage

 2018-03-01T09:15:40Z

2C-type protein phosphatase

Gene: ABI1

UniProtID: P49597

Gene ID: 828714

 2018-03-01T09:48:08Z

Inward Ca2+ permeable channels

 2018-03-19T11:35:03Z

K+ inward channels at the plasma

 2018-02-22T15:38:15Z

Reactive oxygen species

 2018-03-15T13:00:24Z

The catalytic subunit of type 1 phosphatase located in the cytosol

To denote node levels in this model, similar to a multi-level model, the number represents the level of the node, in this case PP1cc.

 2018-02-28T17:04:05Z

PP1cc_1 is a positive regulators of PK_1 when specific combinations of each PP1cc are met.

Intercellular carbon dioxide (Ci) indirectly inhbits PK_3.

Type 1 protein phophatase (PP1cc) activates H-ATPase through PK (Vicia faba L.).

Type 1 protein phophatase (PP1cc) activates H-ATPase through PK (Vicia faba L.).

Intercellular carbon dioxide (Ci) indirectly inhbits PK_3.

Type 1 protein phophatase (PP1cc) activates H-ATPase through PK (Vicia faba L.).

 S_38 1 S_49 1 S_20 1 S_9 1 S_21 1 S_21 1 S_9 1 S_20 1 S_49 1 S_20 1 S_9 1 S_49 1 S_21 1

CalC and CaR activate Cac_high when ABA is active. CaATPase inhibits Cac_high and is dominant to CalC and CaR.

Calcium release (CaR) causes an increase in cytosolic calcium ions (Cac) (Arabidopsis thaliana).

Opening of calcium-permeable channels (Calc) allows for the increase in cytosolic calcium ions (Cac) (Arabidopsis thaliana).

ABA indirectly activates Cac (Commelina communis L.).

CaATPase directly inhibits Cac. CaATPase removes calcium ions (Cac) from the cell.

 S_46 1 S_15 1 S_3 1 S_18 1 S_15 1 S_3 1

Cac activates CaATPase.

Cytosolic Ca2+ (Cac) is removed from the cell by plasma membrane Ca2+ ATPase (CaATPase). Thus activation of CaATPase is dependent on Cac.

 S_39 1

ABA and Cac_high activates AnionCh_high. Ci activates AnionCh_high when Ci_sup is active. ABI1 inhibits AnionCh_high and is dominant to ABA and Cac_high.

CO2 (represented as Ci) indirectly stimulates anion channels (represented as AnionCh_high) (Vicia faba L).

CO2 (represented as Ci_sup) indirectly stimulates anion channels (represented as AnionCh_high) (Vicia faba L).

ABI1 indirectly inhibits plant response to ABA, possibly through the inactivation of MAPKKK18 (Arabidopsis thaliana).

ABA indirectly activates AnionCh_high (Arabidopsis thaliana, Vicia faba L).

ABA triggers the increase in cytosolic Ca2+ (represented as Cac_high), which activates AnionCh_high (Arabidopsis thaliana, Vicia faba L).

 S_15 1 S_45 1 S_2 1 S_45 1 S_20 1 S_21 1

ABA activates PLD_high when NO is active.

PLD activity increases in the presence of ABA.

PLD activity is required for NO-induced stomatal closure via the production of phosphatidic acid.

 S_15 1 S_32 1

FFA and PLA2 are positive regulators of HATPase_3. FFA and PLA2 activate HATPase_3 when certain conditions or PK_2, PK_3, PK_1, phph and phph_high are met.

Cac_high inhibits HATPase_3 and is dominant to FFA and PLA2.

Phosphorylation of HATPase creates a binding site for 14-3-3. Thus the PK_3 activates HATPase_3 ( Spinacia oleracea, Vicia faba L.).

FFA indirectly activates HATPase_1.

PLA2 indirectly activates HATPase_1 through production free fatty acids and lysophosphatidylcholine (Arabidopsis thaliana, Avena sativa L.).

Cac_high indirectly inhibits HATPase_3 (Vicia faba L.).

Phosphorylation of HATPase creates a binding site for 14-3-3. Thus the PK_1 activates HATPase_3 ( Spinacia oleracea, Vicia faba L.).

phph_high yields ATP, which is converted from ATP to ADP by HATPase_1.

phph yields ATP, which is converted from ATP to ADP by HATPase_1.

Phosphorylation of HATPase creates a binding site for 14-3-3. Thus the PK_2 activates HATPase_3 ( Spinacia oleracea, Vicia faba L.).

 S_19 1 S_1 1 S_40 1 S_11 1 S_2 1 S_28 1 S_11 1 S_24 1 S_40 1 S_28 1 S_1 1 S_25 1 S_2 1 S_28 1 S_11 1 S_24 1 S_1 1 S_40 1 S_28 1 S_2 1 S_28 1 S_11 1 S_19 1 S_25 1 S_1 1 S_40 1 S_11 1 S_2 1 S_28 1 S_11 1 S_19 1 S_40 1 S_28 1 S_1 1 S_24 1 S_25 1 S_2 1 S_19 1 S_1 1 S_25 1 S_2 1 S_28 1 S_11 1 S_19 1 S_40 1 S_28 1 S_25 1 S_1 1 S_24 1 S_11 1 S_2 1 S_24 1 S_1 1 S_25 1 S_11 1 S_2 1 S_28 1 S_11 1 S_19 1 S_40 1 S_28 1 S_1 1 S_25 1 S_11 1 S_2 1 S_28 1 S_11 1 S_24 1 S_1 1 S_11 1 S_25 1 S_19 1 S_40 1 S_2 1 S_19 1 S_11 1 S_25 1 S_1 1 S_24 1 S_40 1 S_2 1 S_24 1 S_40 1 S_28 1 S_25 1 S_1 1 S_11 1 S_2 1 S_24 1 S_1 1 S_40 1 S_2 1 S_28 1 S_11 1 S_19 1 S_40 1 S_28 1 S_25 1 S_11 1 S_2 1 S_28 1 S_11 1 S_19 1 S_1 1 S_40 1 S_24 1 S_25 1 S_2 1 S_24 1 S_25 1 S_1 1 S_11 1 S_2 1 S_28 1 S_11 1 S_24 1 S_11 1 S_25 1 S_1 1 S_40 1 S_2 1 S_24 1 S_40 1 S_28 1 S_25 1 S_11 1 S_2 1

ABA activates PLD.

NO activates PLD.

PLD activity increases in the presence of ABA.

PLD activity is required for NO-induced stomatal closure via the production of phosphatidic acid.

 S_15 1 S_32 1

PLD_high activates PP1cc_2 when BL and photo1_complex are inactive.

BL and photo1_complex activates PP1cc_2 when PLD is active and PLD_high are inactive.

In order to correctly simulate "OR NOT" relationships (ex, Ci AND Ci_sup OR NOT Cac_high) in Cell Collective, additional positive and negative relationships have been added. The original Boolean equation reads as follows: (not (phot1_complex or BL)and not (PLD and not PLD_high)) or ((phot1_complex or BL) and PLD and not PLD_high).

PLD indirectly activates PP1cc through the production of phosphatidic acid.

BL indirectly activates PP1cc1 through activation of type 1 protein phosphatase regulatory subunit 2-like protein1.

photo1_complex indirectly activates PP1cc1 through activation of type 1 protein phosphatase regulatory subunit 2-like protein1.

PLD indirectly activates PP1cc through the production of phosphatidic acid.

 S_7 1 S_8 1 S_5 1 S_10 1 S_8 1 S_5 1 S_5 1 S_7 1 S_10 1 S_8 1 S_7 1 S_10 1 S_5 1

BL activates phot1_complex.

Phot1 is a receptor for blue light (BL). The presence of blue light activates phot1, which activates phot1_complex (Arabidopsis thaliana, Vicia faba L.).

 S_7 1

Red light activates phph_high when BL is active.

The synergistic relationship between blue light (BL) and red light (RL) in malate formation initiates higher levels of light-dependent reactions of photosynthesis (phph_high).

The synergistic relationship between blue light (BL) and red light (RL) in malate formation initiates higher levels of light-dependent reactions of photosynthesis (phph_high).

 S_26 1 S_7 1

Ci and Ci_sup activate MCPS when either BL or RL is active.

Intercellular CO2 (Ci) is required for mesophyll cell photosynthesis (MCPS).

Blue light (BL) induces stomata opening, which allows for CO2 uptake.

Right light (RL) induces stomata opening, which allows for CO2 uptake.

Intercellular CO2 (Ci_sup) is required for mesophyll cell photosynthesis (MCPS).

 S_21 1 S_7 1 S_26 1 S_20 1 S_7 1 S_26 1

ABA in conjunction with Cac activates PLC.

BL activates PLC.

BL indirectly activates PLC through phot2 stimulation (Arabidopsis thaliana).

ABA in conjunction with Cac indirectly activates PLC (Arabidopsis thaliana).

ABA in conjunction with Cac indirectly activates PLC (Arabidopsis thaliana).

 S_15 1 S_39 1 S_7 1

HATPase_1 activates SO_1 when Kv is active.

Stomatal opening (SO) requires activation of HATPase.

Membrane hyperpolarization by HATPase causes K+ to enter the vacuole (Kv).

 S_6 1 S_35 1

FFA and PLA2 are positive regulators of HATPase_2. FFA and PLA2 activate HATPase_2 when certain conditions or PK_2, PK_3, PK_1, and phph are met.

Cac_high inhibits HATPase_2 and is dominant to FFA and PLA2.

Phosphorylation of HATPase creates a binding site for 14-3-3. Thus the PK_3 activates HATPase_2 ( Spinacia oleracea, Vicia faba L.).

FFA indirectly activates HATPase_1.

PLA2 indirectly activates HATPase_1 through production free fatty acids and lysophosphatidylcholine (Arabidopsis thaliana, Avena sativa L.).

Cac_high indirectly inhibits HATPase_2 (Vicia faba L.).

Phosphorylation of HATPase creates a binding site for 14-3-3. Thus the PK_1 activates HATPase_2 ( Spinacia oleracea, Vicia faba L.).

Phosphorylation of HATPase creates a binding site for 14-3-3. Thus the PK_2 activates HATPase_2 ( Spinacia oleracea, Vicia faba L.).

phph yields ATP, which is converted from ATP to ADP by HATPase_1.

phph_high yields ATP, which is converted from ATP to ADP by HATPase_1.

 S_24 1 S_40 1 S_1 1 S_25 1 S_28 1 S_2 1 S_19 1 S_28 1 S_25 1 S_1 1 S_24 1 S_40 1 S_2 1 S_24 1 S_1 1 S_40 1 S_28 1 S_25 1 S_2 1 S_24 1 S_28 1 S_25 1 S_1 1 S_40 1 S_2 1 S_24 1 S_1 1 S_40 1 S_28 1 S_11 1 S_25 1 S_2 1 S_19 1 S_40 1 S_1 1 S_24 1 S_25 1 S_28 1 S_2 1 S_19 1 S_40 1 S_11 1 S_25 1 S_1 1 S_24 1 S_2 1 S_19 1 S_1 1 S_40 1 S_28 1 S_25 1 S_24 1 S_2 1 S_24 1 S_40 1 S_11 1 S_25 1 S_1 1 S_2 1

PLD activates sucrose. ABA inhibits sucrose and is dominant to PLD.

PLD indirectly activates sucrose.

ABA indirectly inhibits sucrose.

 S_8 1 S_15 1

NO activates CaR.

PLC activates CaR.

PLC indirectly activates CaR (Arabidopsis thaliana).

NO indirectly activates CaR.

 S_32 1 S_13 1

BL, RL, and phot1_complex are positive regulators of PLA2.

BL indirectly activates PLA2.

phot1_complex indirectly activates PLA2.

RL indirectly activates PLA2.

 S_7 1 S_26 1 S_10 1

CO2 activates Ci either when CO2_high is active or when carbfix_high, CO2_high, and MCPS_high is inactive.

Plants are able to absorb atmospheric CO2. This happens when CO2 levels are high (CO2_high).

High levels of carbon fixation (carbfix_high) decrease intercellular CO2 concentration (Ci).

Plants are able to absorb atmospheric CO2. This happens when CO2 levels are high (CO2_high).

High levels of mesophyll cell photosynthesis (MCPS_high) reduces intercellular CO2 concentration (Ci).

 S_37 1 S_34 1 S_34 1 S_42 1 S_22 1

CO2 activates Ci_sup when carbfix_high, CO2_high, or MCPS_high is active.

Plants are able to absorb atmospheric CO2. This happens when CO2 levels are high (CO2_high).

High levels of carbon fixation (carbfix_high) decrease intercellular CO2 concentration (Ci).

Plants are able to absorb atmospheric CO2. This happens when CO2 levels are high (CO2_high).

High levels of mesophyll cell photosynthesis (MCPS_high) reduces intercellular CO2 concentration (Ci).

 S_37 1 S_34 1 S_42 1 S_22 1

Ci and Ci_sup activate MCPS_high when either BL or RL is active.

Intercellular CO2 (Ci) is required for mesophyll cell photosynthesis (MCPS).

Blue light (BL) induces stomata opening, which allows for CO2 uptake.

Right light (RL) induces stomata opening, which allows for CO2 uptake.

Intercellular CO2 (Ci_sup) is required for mesophyll cell photosynthesis (MCPS).

 S_20 1 S_7 1 S_26 1 S_21 1 S_7 1 S_26 1

HATPase_1, HATPase_2, and HATPase_3 activate Kc when Kin or Kv and KEV are active. HATPase also activates Kc when AnionCh, HATPase_2, and KEV are active or when AnionCh and HATPase_2 and Kin is active.

Kout inhibits Kc and is dominant to HATPase_1, HATPase_2, and HATPase_3.

AnionCh_high inhibits Kc and is dominant to HATPase_2 and HATPase_3.

AnionCh can either inhibit or activate Kc depending on certain conditions.

HATPase_1 indirectly activates Kc.

Movement of K+ from the vacuole to the cytosol (KEV) increases cytosolic K+ concentration (Kc).

AnionCh indirectly inhibits Kc.

The majority of K+ released into the cytosol originates from guard cell vacuoles (Kv).

HATPase_1 indirectly activates Kc.

AnionCh indirectly inhibits Kc.

Opening of outward K+ channels (Kout) decreases the cytosolic K+ concentration (Kc).

Opening of inward K+ channels (Kin) increases the cytosolic K+ concentration (Kc).

HATPase_1 indirectly activates Kc.

 S_16 1 S_27 1 S_35 1 S_47 1 S_31 1 S_4 1 S_41 1 S_6 1 S_41 1 S_47 1 S_16 1 S_27 1 S_35 1 S_41 1 S_16 1 S_31 1 S_4 1 S_6 1 S_47 1 S_27 1 S_35 1 S_31 1 S_4 1 S_41 1 S_33 1 S_47 1 S_35 1 S_27 1 S_31 1

PLA2 activates FFA.

FFA is one of the hyprolytic products of PLA2 activity.

 S_19 1

PP1cc_1 and PP1cc_2 are positive regulators of PK_1 when specific combinations of each PP1cc are met. Ci and Ci_sup can activate PK_1 when specific conditions of PP1cc are met.

Ci and Ci_sup are negative regulators of PK_1 and are dominant to The PP1cc's.

Intercellular carbon dioxide (Ci) indirectly inhbits PK_2.

Type 1 protein phophatase (PP1cc) activates H-ATPase through PK (Vicia faba L.).

Type 1 protein phophatase (PP1cc) activates H-ATPase through PK (Vicia faba L.).

Intercellular carbon dioxide (Ci) indirectly inhbits PK_2.

Type 1 protein phophatase (PP1cc) activates H-ATPase through PK (Vicia faba L.).

 S_21 1 S_38 1 S_49 1 S_9 1 S_49 1 S_38 1 S_9 1 S_49 1 S_9 1 S_38 1 S_20 1 S_38 1 S_20 1 S_49 1 S_21 1 S_9 1 S_49 1 S_38 1 S_20 1 S_21 1 S_49 1 S_38 1 S_9 1 S_9 1 S_38 1 S_9 1 S_38 1 S_20 1 S_21 1 S_20 1 S_49 1 S_9 1 S_21 1 S_38 1

Cac_high in conjunction with Kv activates KEV.

High levels of cytosolic Ca2+ (Cac_high) trigger the release of vacuolar K+ (Kv), causing the movement of K+ from the vacuole to the cytosol (KEV).

High levels of cytosolic Ca2+ (Cac_high) trigger the release of vacuolar K+ (Kv), causing the movement of K+ from the vacuole to the cytosol (KEV).

 S_2 1 S_35 1

BL and RL activate phph.

Blue light (BL) indirectly activates the light-dependent reactions of photosynthesis (phph).

Red light (RL) indirectly activates the light-dependent reactions of photosynthesis (phph).

 S_26 1 S_7 1

HATPase_1 activates SO_1 when Kv is active.

Membrane hyperpolarization by HATPase causes K+ to enter the vacuole (Kv).

Sucrose indirectly activates SO_2.

Stomatal opening (SO) requires activation of HATPase.

 S_16 1 S_35 1 S_17 1 S_35 1

HATPase_1 activates SO_1 when Kv is active.

Stomatal opening (SO) requires activation of HATPase.

Membrane hyperpolarization by HATPase causes K+ to enter the vacuole (Kv).

 S_33 1 S_35 1

PMV_pos activates Kout when one of the following conditions is met: ci and Ci_sup are active, ABA is active, ROS is inactive, NO is inactive, or FFA is inactive.

Elevated intercellular CO2 (Ci) causes stomatal closure and thus indirectly activates K+ outward channels (Kout) (Vicia faba L.).

A holding potential more positive than -40mV (PMV_pos) induces K+ outward flow (Kout) (Vicia faba L.).

The FFA linolenic acid and arachidonic acid activates inward K+ currents, thus inhibiting K+ outward current (Kout) (Arabidopsis thaliana).

Elevated intercellular CO2 (Ci_sup) causes stomatal closure and thus indirectly activates K+ outward channels (Kout) (Vicia faba L.).

ABA indirectly stimulates outward K+ current (Kout) (Vicia faba L.).

The addition of ROS, specifically H2O2, depressed K+ outward flow (Kout) (Vicia faba L.).

Exposure to nitric oxide (NO) reduces K+ outward flow (Kout) (Vicia faba L.).

 S_43 1 S_20 1 S_21 1 S_24 1 S_48 1 S_32 1 S_15 1

phph in conjunction with ROS activates NO.

ROS indirectly activates NO (Arabidopsis thaliana).

Photophosphorylation (phph) indirectly activates NO through NADH.

 S_28 1 S_48 1

FFA and PLA2 are positive regulators of HATPase_1. FFA and PLA2 activate HATPase_1 when certain conditions of PK_2, PK_3, PK_1, and phph are met.

Cac_high inhibits HATPase_1 and is dominant to FFA and PLA2.

Phosphorylation of HATPase creates a binding site for 14-3-3. Thus the PK_3 activates HATPase_1 ( Spinacia oleracea, Vicia faba L.).

FFA indirectly activates HATPase_1.

Cac_high indirectly inhibits HATPase_1 (Vicia faba L.).

PLA2 indirectly activates HATPase_1 through aactivation of free fatty acids and lysophosphatidylcholine (Avena sativa L.).

Phosphorylation of HATPase creates a binding site for 14-3-3. Thus the PK_1 activates HATPase_1 ( Spinacia oleracea, Vicia faba L.).

Phosphorylation of HATPase creates a binding site for 14-3-3. Thus the PK_2 activates HATPase_1 ( Spinacia oleracea, Vicia faba L.).

phph yields ATP, which is converted from ATP to ADP by HATPase_1.

 S_24 1 S_40 1 S_25 1 S_1 1 S_1 1 S_40 1 S_25 1 S_1 1 S_40 1 S_25 1 S_1 1 S_28 1 S_25 1 S_40 1 S_40 1 S_28 1 S_25 1 S_2 1 S_19 1 S_1 1 S_28 1 S_25 1 S_24 1 S_40 1 S_1 1 S_40 1 S_24 1 S_25 1 S_40 1 S_28 1 S_1 1 S_24 1 S_25 1 S_1 1 S_40 1 S_28 1 S_25 1 S_24 1 S_40 1 S_25 1 S_24 1 S_2 1

Kc activates Kv.

Cytosolic K+ (Kc) is taken into the vacuole (Kv).

 S_23 1

CO2 and Ci actvate carbfix when phph is active.

Carbon dioxide is required for carbon fixation (carbfix). This can come from the environment (CO2) or from the intercellularenvironment (Ci).

Carbon dioxide is required for carbon fixation. This can come from the environment (CO2) or from the intercellularenvironment (Ci).

Photophosphorylation (phph) generates metabolites required for carbon fixation (ATP and NADPH).

 S_37 1 S_28 1 S_20 1 S_28 1

BL or photo1_complex activates PP1cc1.

BL indirectly activates PP1cc1 through activation of type 1 protein phosphatase regulatory subunit 2-like protein1.

photo1_complex indirectly activates PP1cc1 through activation of type 1 protein phosphatase regulatory subunit 2-like protein1.

 S_7 1 S_10 1

ABA activates Cac.

CaATPase inhibits Cac and is dominant to CalC and CaR.

Calc activates Cac.

CaR activates Cac.

Calcium release (CaR) causes an increase in cytosolic calcium ions (Cac) (Arabidopsis thaliana).

Opening of calcium-permeable channels (Calc) allows for the increase in cytosolic calcium ions (Cac) (Arabidopsis thaliana).

ABA indirectly activates Cac (Commelina communis L.).

CaATPase directly inhibits Cac. CaATPase removes calcium ions (Cac) from the cell.

 S_46 1 S_3 1 S_18 1 S_3 1 S_15 1

Ci and Ci_sup are negative regulators of PK_1 and are dominant to The PP1cc's.

PP1cc_1 and PP1cc_2 are positive regulators of PK_1 when specific combinations of each PP1cc are met. Ci and Ci_sup can activate PK_1 when specific conditions of PP1cc are met.

Intercellular carbon dioxide (Ci) indirectly inhbits PK_1.

Type 1 protein phophatase (PP1cc) activates H-ATPase through PK (Vicia faba L.).

Intercellular carbon dioxide (Ci_sup) indirectly inhbits PK_1.

Type 1 protein phophatase (PP1cc) activates H-ATPase through PK (Vicia faba L.).

Type 1 protein phophatase (PP1cc) activates H-ATPase through PK (Vicia faba L.).

 S_21 1 S_9 1 S_38 1 S_49 1 S_49 1 S_38 1 S_9 1 S_20 1 S_49 1 S_9 1 S_38 1 S_20 1 S_21 1 S_38 1 S_49 1 S_49 1 S_9 1 S_20 1 S_21 1 S_20 1 S_49 1 S_38 1 S_9 1 S_21 1

Cac-high, Ci, Ci_sup, and ABA are positive regulators of AnionCh. ABI1 and BL is a negative regulator of AnionCh.

In order to correctly simulate "OR NOT" relationships (ex, Ci AND Ci_sup OR NOT Cac_high) in Cell Collective, additional positive and negative relationships have been added. The original Boolean equation reads as follows: ((((Cac_high ∨ ABA) ∧ ¬ABI1) ∨ (Ci ∧ Ci_sup)) ∨ (¬(((Cac_high ∨ ABA) ∧ ¬ABI1) ∨ (Ci ∧ Ci_sup)) ∧ ¬(phot1_complex ∨ BL)))

CO2 (represented as Ci) indirectly stimulates anion channels (represented as AnionCh) (Vicia faba L).

Blue light (BL) induces a response at the plasma membrane. The addition of blue light induces K+ inward channels.

Phototropins (represented as phot1_complex) inhibit the slow anion current (AnionCh). This has been shown to happen through activation of phosphatidylinositol 4,5-bisphosphate at the plasma membrane (Arabidopsis thaliana, Commelina communis L, Vicia faba L).

CO2 (represented as Ci_sup) indirectly stimulates anion channels (represented as AnionCh) (Vicia faba L).

ABI1 indirectly inhibits plant response to ABA, possibly through the inactivation of MAPKKK18 (Arabidopsis thaliana).

ABA triggers the increase in cytosolic Ca2+ (represented as Cac_high), which activates AnionCh (Arabidopsis thaliana, Vicia faba L).

ABA indirectly activates AnionCh (Arabidopsis thaliana, Vicia faba L).

 S_20 1 S_21 1 S_2 1 S_45 1 S_15 1 S_45 1 S_7 1 S_10 1 S_7 1 S_10 1 S_2 1 S_15 1 S_20 1 S_45 1 S_21 1 S_2 1 S_45 1 S_20 1 S_21 1 S_45 1 S_7 1 S_10 1 S_45 1 S_20 1 S_10 1 S_7 1 S_2 1 S_45 1 S_20 1 S_7 1 S_10 1 S_45 1 S_21 1 S_15 1 S_2 1 S_20 1 S_7 1 S_10 1 S_21 1 S_2 1 S_45 1 S_15 1 S_45 1 S_7 1 S_10 1 S_15 1 S_21 1 S_7 1 S_10 1 S_45 1 S_15 1 S_2 1 S_20 1 S_7 1 S_10 1 S_21 1 S_45 1 S_2 1 S_15 1

Ci and CO2 activate carbfix_high when phph_high is active.

Carbon dioxide is required for carbon fixation. This can come from the environment (CO2) or from the intercellularenvironment (Ci).

Carbon dioxide is required for carbon fixation. This can come from the environment (CO2) or from the intercellularenvironment (Ci).

Photophosphorylation (phph_high) generates metabolites required for carbon fixation (ATP and NADPH).

 S_37 1 S_11 1 S_20 1 S_11 1

In order to correctly simulate "OR NOT" relationships (ex, PMV_neg or not PMV_pos) in Cell Collective, additional positive and negative relationships have been added. The original Boolean equation reads as follows:( not (HATPase_1 or HATPase_2 or HATPase_3) and (((AnionCh and PMV_neg) and (Cac_high or KEV)) or (not (AnionCh and PMV_neg) and not PMV_neg and PMV_pos) or (not (AnionCh and PMV_neg) and (not PMV_pos and not PMV_neg) and (Cac_high or KEV)))) or ((HATPase_1 or HATPase_2 or HATPase_3) and (not (AnionCh and PMV_neg)) and not PMV_neg and PMV_pos and (Cac_high or KEV)).

Hyperpolarization of the membrane is caused by the activation of HATPase.

KEV indirectly activates PMV_pos.

Hyperpolarization of the membrane is caused by the activation of HATPase.

PMV_pos is required for PMV_pos activation.

Activation of anion channels (AnionCh) causes membrane depolarization.

Increaes in cytosolic Ca2+ levels indirectly causes membrane depolarization.

Hyperpolarization of the membrane is caused by the activation of HATPase.

The membrane cannot be simultaneously be hyperpolarized (PMV_neg) and depolarized (PMV_pos).

 S_43 1 S_27 1 S_6 1 S_33 1 S_16 1 S_2 1 S_6 1 S_33 1 S_16 1 S_27 1 S_6 1 S_33 1 S_2 1 S_16 1 S_44 1 S_41 1 S_2 1 S_6 1 S_33 1 S_16 1 S_44 1 S_41 1 S_41 1 S_43 1 S_6 1 S_33 1 S_2 1 S_16 1 S_44 1 S_27 1 S_6 1 S_33 1 S_2 1 S_16 1 S_6 1 S_33 1 S_16 1 S_2 1 S_43 1 S_41 1 S_2 1 S_6 1 S_33 1 S_16 1 S_27 1 S_41 1 S_6 1 S_33 1 S_16 1 S_44 1 S_27 1 S_6 1 S_33 1 S_16 1 S_44 1 S_41 1

In order to correctly simulate "OR NOT" relationships (ex, PMV_neg or not PMV_pos) in Cell Collective, additional positive and negative relationships have been added. The original Boolean equation reads as follows: ((HATPase_1 or HATPase_2 or HATPase_3) and (((AnionCh and PMV_neg) and not (Cac_high or KEV)) or (not (AnionCh and PMV_neg) and ((PMV_neg) or ((not PMV_pos and not PMV_neg) and not (Cac_high or KEV)))))) or (not (HATPase_1 or HATPase_2 or HATPase_3) and (not (AnionCh and PMV_neg))and PMV_neg and not (Cac_high or KEV))

KEV indirectly inhibits PMV_neg.

Hyperpolarization of the membrane is caused by the activation of HATPase.

The membrane cannot be simultaneously be hyperpolarized (PMV_neg) and depolarized (PMV_pos).

Hyperpolarization of the membrane is caused by the activation of HATPase.

Activation of anion channels (AnionCh) causes membrane depolarization.

Increaes in cytosolic Ca2+ levels indirectly causes membrane depolarization.

Hyperpolarization of the membrane is caused by the activation of HATPase.

PMV_neg is required for PMV_neg activation.

 S_44 1 S_43 1 S_27 1 S_6 1 S_33 1 S_41 1 S_2 1 S_16 1 S_27 1 S_6 1 S_43 1 S_33 1 S_41 1 S_2 1 S_16 1 S_2 1 S_6 1 S_33 1 S_16 1 S_2 1 S_6 1 S_33 1 S_16 1 S_41 1 S_33 1 S_41 1 S_44 1 S_43 1 S_2 1 S_27 1 S_16 1 S_43 1 S_41 1 S_44 1 S_2 1 S_27 1 S_6 1 S_41 1 S_44 1 S_43 1 S_2 1 S_27 1

ABA inhibits ABl1.

The PYL family of ABA-receptors inhibit phosphatase activity of ABI1 (Arabidopsis thaliana).

 S_15 1

ROS activates Calc.

PMV-neg activates Calc.

ROS indirectly activates CaIc.

Hyperpolarization of the plasma membrane (PMV-neg) activates CaIc (Vicia faba L., Commelina communis L.).

 S_48 1 S_44 1

FFA, ABA, PMV_neg activate Kin when certain conditions with Ci, Ci_sup, Cac_high, ABA, and PMV_neg are met.

In order to correctly simulate "OR NOT" relationships (ex, FFA or not Cac_high) in Cell Collective, additional positive and negative relationships have been added. The original Boolean equation reads as follows: (FFA or not Cac_high or ABA) and (not (Ci and Ci_sup))and PMV_neg.

Elevated intercellular CO2 (Ci) causes stomatal closure and thus indirectly inhibits K+ inward channels (Kin) (Vicia faba L.).

The FFA linolenic acid and arachidonic acid activates inward K+ currents (represented here as activating K+ inward channels [Kin]) and inhibits outward K+ currents (Arabidopsis thaliana).

Elevated intercellular CO2 (Ci_sup) causes stomatal closure and thus indirectly inhibits K+ inward channels (Kin) (Vicia faba L.).

K+ inward channels (Kin) are inhibited upon the addition of ABA. This inhibition is driven by the increase in Ca2+ (Cac_high) levels in guard cells (Vicia faba L.).

K+ inward channels (Kin) are inhibited upon the addition of ABA. This inhibition is driven by the increase in Ca2+ (Cac_high) levels in guard cells (Vicia faba L.).

Hyperpolarized membranes (PMV_neg) activates the inward flux of K+ through K+ inward channels (Kin) (Vicia faba L.).

 S_15 1 S_20 1 S_21 1 S_44 1 S_24 1 S_20 1 S_21 1 S_44 1 S_44 1 S_24 1 S_21 1 S_15 1 S_2 1 S_44 1 S_21 1 S_20 1 S_24 1 S_2 1 S_15 1

phph in conjunction with PDL, when ABl1 is inactive, activates ROS.

PLD indirectly activates ROS through production of phosphatidic acid.

ABI1 inhibits OST1, an indirect activator for ROS.

phph indirectly activates ROS through the production of NADH.

 S_28 1 S_8 1 S_45 1

BL and photo1_complex activates PP1cc_2 when PLD is inactive.

PLD_high inhibits PP1cc_2 and is dominant to BL, photo1_complex, and PLD.

PLD_high activates PP1cc_2 when BL or photo1_complex are inactive.

In order to correctly simulate "OR NOT" relationships (ex, Ci AND Ci_sup OR NOT Cac_high) in Cell Collective, additional positive and negative relationships have been added. The original Boolean equation reads as follows: ((phot1_complex or BL)and not PLD and not PLD_high) or (not (phot1_complex or BL)and not PLD_high).

PLD indirectly activates PP1cc through the production of phosphatidic acid.

BL indirectly activates PP1cc1 through activation of type 1 protein phosphatase regulatory subunit 2-like protein1.

photo1_complex indirectly activates PP1cc1 through activation of type 1 protein phosphatase regulatory subunit 2-like protein1.

PLD indirectly activates PP1cc through the production of phosphatidic acid.

 S_8 1 S_7 1 S_10 1 S_5 1 S_7 1 S_8 1 S_5 1 S_10 1 S_8 1 S_5 1 S_8 1 S_7 1 S_10 1 S_5 1