NIHMS266526-supplement-Supplemental_Online_Materials.pdf

8/9/2019 NIHMS266526-supplement-Supplemental_Online_Materials.pdf

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Supplementary Online Materials for:

Formation of regulatory patterns during signal propagation in a mammalian cellular network

Avi Ma’ayan, Sherry L. Jenkins, Susana Neves, Anthony Hasseldine, Elizabeth Grace, Benjamin

Dubin-Thaler, Narat J. Eungdamrong, Gehzi Weng, Prahlad Ram, J. Jeremy Rice,

Aaron Kershenbaum, Gustavo A. Stolovitzky, Robert D. Blitzer, and Ravi Iyengar

Contents

Methods

Supporting text

Supporting Figures S1- S11

Supporting Table S1

Supporting references

Author contributions

Table of supporting external files: text files, source code segments, movies and spreadsheets

Methods

Constructing the network:We used published research literature to identify the key components of signaling pathways

and cellular machines, and their binary interactions. Most components (~80%) have been described

in hippocampal neurons or related neuronal cells. Other components are from other cells, but areincluded because they are key components in processes known to occur in hippocampal neurons,

such as translation. We then established that these interactions were both direct and functionally

relevant. All of the connections were individually verified by at least one of the authors of this paper by reading the relevant primary paper(s). We developed a system made of 545 components (nodes)

and 1259 links (connections). We used arbitrary but consistent rules to sort components into various

groups. For instance, transcription factors are considered a as part of the transcriptional machinery,although it may also be equally valid to consider them as the most downstream component of thecentral signaling network. Similarly the AMPA receptor-channel (AMPAR) is considered part of the

ion channels in the electrical response system since its activity is essential to defining the

postsynaptic response, although it binds to and is activated by glutamate, and hence can be alsoconsidered a ligand gated receptor-channel in the plasma membrane.

The links were specified by two criteria: function and biochemical mechanism. Three types

of functional links were specified. This follows the rules used for representation of pathways in


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Science’s STKE (S1). Links may be activating, inhibitory or neutral. Neutral links do not specify

directionality between components, and are mostly used to represent scaffolding and anchoring

undirected or bidirectional interactions. The biochemical specification includes defining the

reactions as non-covalent binding interactions or enzymatic reactions. Within the enzymaticcategory, reactions were further specified as phosphorylation, dephosphorylation, hydrolysis, etc.

These two criteria for specification are independent and were defined for all interactions. For the

analyses in this study we only used the functional criteria: activating, inhibitory or neutralspecifications.

We chose papers that demonstrated direct interactions that were supported by either

biochemical or physiological effects of the interactions. From these papers we identified thecomponents and interactions that make up the system we analyzed. During this specification process

we did not consider whether these interactions would come together to form higher order

organizational units. Each component and interaction was validated by a reference from the primaryliterature (1202 papers were used). A list of authors who read the papers to validate the components

and interactions is provided under authors contributions.

Storage of the network data:The data describing the components (nodes) and their interactions (links) that compose the

network are stored in a text file, see Text file S1, using the flat file *sig format described below.

The *sig flat text file format:

Source Name: cellular component that is affecting a target componentSource Human Accession: Swiss-Prot accession if available

Source Mouse Accession: Swiss-Prot accession if available

Source Type: the type of molecule classification this componentSource Location: cellular localization of the component

Target Name: generalized cellular component that is affected by the source componentTarget Human Accession: Swiss-Prot accession if available

Target Mouse Accession: Swiss-Prot accession if availableTarget Type: the type of molecule classification for this component

Target Location: generalized cellular localization of the componentEffect: activation (+), inhibition (-), or neutral (0)

Type of Interaction: type of chemical interaction directly linking the two components

PubMed ID: PubMed database accession number

Sorting cellular components (nodes) into cellular machines:Components (nodes) were separated into functional machines based on their molecule type and

location attributes using Code segment S7.

Visualization of the entire network:The diagram of the network in figure S1 was created with Code segment S8 that creates Text file

S2. This text file can be loaded into the Pajek software for visualization (S2).

Subnetworks obtained by signal propagation from ligands:

To generate these subnetworks we used a depth-first search algorithm expanding the search solely in

the downstream direction, to confirm with biologically specified directional transfer of information.


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For example, when a Gs protein is activated by an upstream ligand-receptor interaction it connects

only to the downstream component adenylyl cyclase. The subnetworks do not include another Gs

coupled receptor unless that receptor also interacts with the specific ligand.

The recursive algorithm (using depth-first search) is listed as Code segment S9. It was used tocreate 15 subnetworks for each node of the type “Ligand” by changing the number of steps from the

ligand. This concept is termed breadth-first search and is illustrated in Movie S20. The subnetworks

were then analyzed by computing the number of nodes, links, clustering, average path length andmotifs.

Visualization of the resulting data for connections per step for all ligands, Spreadsheet S23, was

created with MatlabTM

, Natick, MA (S3).Three sets of subnetworks induced by the nodes: GLUTAMATE, NE and BDNF were analyzed for

number of nodes and links, clustering, average path-length and motifs with Code segment S10.

These results, Spreadsheet S24, were visualized with ExcelTM

(S4).

Overall statistics of the network:

The connectivity distribution data, Spreadsheet S25, was plotted with MatlabTM

, Natick, MA (S3).

Characteristic path-length measure was implemented by using Floyd’s algorithm (S5), with Code

segment S11.

Clustering Coefficient was implemented with custom code based on the concept developed by Wattsand Strogatz (S6), using Code segment S12.

Grid Coefficient was implemented with custom code based on the concept developed by Caldarelliet al. (S7), using Code segment S13.

The results, Spreadsheet S26, were compared to the same parameters computed for 100 shufflednetworks of one island that maintain the same connectivity distribution using an algorithm

developed by Milo et al. (S8), using Code segment S14.

Network Motifs:Counting motifs in the network was accomplished by using the MFinder program developed by

Kashtan et al. (S9). Motifs of size 3, 4, 5 and 6 were visualized using VisioTM

(S10).See Table S29 of the complete results for the motifs of sizes 3 and 4.

Output files in text format from the MFinder program:

Motifs size 3: Text file S3.Motifs size 4: Text file S4.

Motifs size 5: Text file S5.

Motifs size 6: Text file S6.

Our method for motif search:

In our detailed analysis of subnetworks, we only considered closed loop circular motifs. Wesearched for these motifs using a depth-first search algorithm (Code segments S17 through S19).An example of counting motifs in a toy network is given below:


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A

C D

B

The above toy network contain: 1 positive feedback loop of size 3, 1 negative feedback loop of size3 and 1 negative feed-forward motif of size 4. Nodes C and D contribute to 3 motifs whereas nodes

B and C contribute to 2 motifs. This is slightly different from the method used by Kashtan et al. (S9) because, with their method, A, B, C, and D will not be considered a feedforward loop due to the link

between A and D.

Positive vs. negative feedback and feedforward loops:

Positive feedback loops motifs are defined as loops where all the links in the loop are positive(activating), or there are an even number of negative (inhibitory) links. Negative feedback loops are

loops where there is an odd number of negative links. Feedforward loops have two “arms”, each

starting at a source node and merging into a target (sink) node. To determine if a feedforward loop is positive or negative, each “arm” was evaluated separately. Both “arms” must be positive for the

feedforward motifs to be positive. An “arm” that has all links positive or even number of negative

links is considered positive; whereas, an arm with an odd number of negative links is considerednegative.

Subnetworks from source to target nodes:

Series of subnetworks from specific source nodes (generally ligands) to specific targets

(components within machines such as channels or transcription factors), with limited path lengths,

were created using the following code: Code segment S15. The concept is illustrated in Movie S21. Shuffled networks, where only links that do not involved the source nodes and target nodes, were

created for statistical control. In the control subnetworks, we preserved the biologically specified

connectivity and directionality between ligands and their receptors and from the immediateupstream components to the AMPA channel and CREB. For all other connections we randomly

swapped the direction of the connection while preserving the overall connectivity structure of thenetwork. Curve fitting of the data, Spreadsheet S27, was done with ExcelTM

(S4).

Subnets based on nodal connectivity:

Series of sub-networks created based on nodal connectivity were created using Code segment S16.

The concept is illustrated in Movie S22. Search for feedback loops was implemented with Codesegment S17, feed-forward loops with Code segment S18, bi-fan motifs with Code segment S19.

The results are summarized in Spreadsheet S28 and were visualized with ExcelTM

(S4). The

number of islands does not consider highly connected nodes as single islands when they are notincluded. For example, PKA, a highly connected node (k=49) is not included in the subnetworks

with lower connectivity threshold and is not considered an island by itself.

Computing the Density of Information Processing (DIP):

DIP is a measure of the local density of motifs and their interconnectedness within the interaction

space of the network. DIP is defined as:

i

ii

ii

i GC L L

M M DIP ⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛

−

−=

−

−

1

1 (1)

Whereiiiiii

BIFAN FFLFFLFBLFBL M ++++= 4343


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M i is the total number of feedback loops, feedforward loops and bifan motifs. Li is the total links and

i represent the step. FBL3 and FBL4 are feedback loops of size 3 and 4, FFL3 and FFL4 are

feedforward loops of size 3 and 4 and BIFAN are bi-fan motifs of size 4. GC is the grid coefficient

representing interconnectedness for the motifs, computed for the subnetwork at step i.

Computing the Motif Location Index (MLI):

MLI measure the concentration of specified motifs and various locations within thenetwork. MLI can vary from 0 to 1 depending on its relative distance from the extracellular ligands

to cellular machine, where 0 indicates location at the level of machines. MLI was calculated as

follows:

MLI =n

CPLLCPLM

CPLM n

i ii

i∑=

⎟⎟ ⎠

⎞⎜⎜⎝

⎛

+1 (2)

where n is the size of the motif, CPLM is the characteristic path length from a node within the motif

to all other nodes in the cellular machine and CPLL is the characteristic path length from a node to

all extracellular ligands. If a node is an extracellular ligand then CPLL = 0; if the node is in the plasma membrane CPLL= 1. If a node belongs to a cellular machine, CPLM = 0. The average

shortest path length was computed using Floyd’s algorithm (S5).

Supporting text

Functional Organization: From Components to Information Processing Motifs

Components within mammalian cells interact with one another to form local networks thattogether form a single large network. This organization is essential for cellular components to

coordinate their individual activities and achieve the cohesiveness needed for cellular functions.

Information needs to flow between components in a continuous and organized manner. Determininghow this flow of information occurs is a crucial step in understanding the functional organization of

mammalian cells. This system of interacting cellular components based on phenotypic behavior

allows us to analyze the flow of information between the components to identify the emergence ofregulatory motifs that are capable of processing information as it flows through the network.

Regulatory motifs such as feedback loops and feedforward motifs allow the cell to process

information from extracellular signals, and decide when such information persists and when it is

transient. The presence of positive feedback loops arising from coupled biochemical reactions leadsto switching behavior that can enable state changes (S11). State change triggered by biochemical

switches has been demonstrated in developmental systems (S12).

The overall profile of motifs may be an initial indicator of the cell’s information processingcapability, when the quantitative and temporal characteristics of the interactions and consequent

motif formation are taken into account. Such quantitative specification may lead to comparative

profiles different from that observed here. Nevertheless, the identification and characterization of

motifs allows us to move from components and interactions to the next level of organization withinthe cell.

Distinct regulatory motifs are active in response to signals from different ligands. The balanceof the emergent positive and negative motifs may define the capability of the ligand to induce

plasticity or maintain homeostasis. Comparison between motifs assumes that the motifs can be

formed and function concurrently. The relationship between the interaction steps in this

pseudodynamic analysis which considers propagation of functional connectivity over chemicalspace and time steps needs to be specified at the level of individual interactions. This is discussed in


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greater detail below. The relationship between distances in chemical space in such a functional

organization scheme and subcellular localization in terms of organelles and identified physical

compartments require further analysis to identify where the two types of organization overlap and

where they diverge.At the functional level, each network configuration is likely to have its own distinct pattern of

regulatory motifs, and thus define capability of the cell for either maintaining homeostasis or

promoting state change such as that seen in synaptic plasticity. Would a large ensemble of suchstates make the system intractably complex, such that we would not be able to either understand or

predict its behavior? This is unlikely because many of the states may have profiles of regulatory

motifs that produce convergent effects on cellular machines. Such convergence would provide amolecular basis for redundancy of cellular function and endow the cellular system with robustness.

Functionally, cellular network states may fall into two broad categories: those that preserve

homeostasis during system perturbation and those that promote reorganization of the parts of thecellular network. Such reorganization may include the synthesis of new components such as

transcription factors as well as other components that are required for expression of phenotypic

behavior. The notion that multiple network states may converge to yield a limited set of phenotypic

responses is supported by recent studies of networks of neurons where similar network behavior, asdefined by firing patterns, can arise from multiple network configurations based on individual

parameters that are quite different (S13). Perhaps such convergence represents a higher order oforganized redundancy arising from the many feedforward motifs. Thus, it is likely that cellularsystems are robust at varying levels of organization.

From Qualitative Representation to Quantitative Behavior of MotifsQualitative representations of cellular interaction such as those analyzed here do not take

into account individual reaction rates that define individual links. This simplifying assumption leads

to questions such as whether the identity and function of regulatory motifs would be preserved if thereaction reactions for the links that make up the motifs vary over many orders of magnitude.

Experimental studies have shown that some of the links are relevant only at specific times, atdifferent perturbation, and at different locations within the cell. Such conditionality can be

manifested in many formats. Positive (also termed coherent) feedforward loops (FFL) can functionin several ways. For example, they can be coincidence detectors (AND gates), provide redundant

pathways to the same effectors (OR gates); they can lead to long sustained activity if one arm is fastand the other arm is slower (S14, S15). These functions depend on the reaction rates of the two

arms. To obtain a preliminary idea of the potential validity of the motifs we have identified in this

study, we gathered a set of representative reactions from various classes (i.e., ligand-protein, protein-protein, and enzymatic reactions) and evaluated their rates by comparing on and off rates

and K cat values. The maximum observable difference was about 1000 fold (Table S2). We then

constructed a toy ODE model for motif 44 (Fig. S3). A schematic of the model is shown (Fig.S11A). We varied the difference in rates between the two arms by a factor of up to 1000. Although

there are temporal differences in the output, the overall output profiles are quite similar within the

same time scale (Fig. S11B). These initial simulations suggest that the integrity of the motif is persevered even with widely varying rates.

Although this toy ODE model has few components, it should be noted that this is likely to be

a limiting case since with multiple components in each arm, reactions rates are also likely to vary

and thus reducing the difference between the two arms. This is especially true for situations at two-three steps from the ligand, the location where the motifs become more prevalent. Thus, it is likely

that many of the motifs identified by qualitative analysis will be operative even when interaction

rates vary and the concentrations of components change in a regulated manner. Definitive proof that


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each of these motifs is functional will only come when each reaction within a motif is parameterized

and input/output relationships are determined, and the existence of the motifs will be experimentally

verified.

Configuration of Motifs and choosing between homeostasis and plasticity:

The conversion of short term biochemical changes into long-term physiological changes including

state changes is often driven prolonged activation of key protein kinases and/or the activation orinduction of transcription factors. The extent and duration of activity of these downstream

components is regulated by the upstream signaling network. Since the network contains various

types of regulatory motifs, the balance between these motifs will determine the extent and durationof the signal reaching these key components. Abundance of positive feed-forward or feedback loops

would evoke the extended activation of these components, while the presence of negative feedback

loops and gates could limit the duration of activation of the downstream components. Hence, theratio of the positive to negative feedback and feed-forward loops can determine whether or not

downstream components are activated for extended periods at sufficient levels. This extent and

duration of activation of the downstream components like the protein kinases or transcription factor

may in turn determine if the cell can maintain homeostatic behavior or undergo long-term physiological changes. Thus, the ratio of positive to negative feedback and feed-forward motifs

could be a key indicator of whether, in the presence of external signals, the cell is configured tomaintain homeostatic balance or undergo state change. Since the propagation of connectivity bydifferent ligands involves different components and pathways, the ratio of the positive and negative

motifs is a function of the types of signals the cell receives and hence is conditional. Comparison of

the ratio of these motifs recruited per step for different ligands, glutamate, NE and BDNF clearlydemonstrates that the regulatory configuration is defined by the ligand that initiates the signal

propagation. Thus, by balancing the positive to negative motifs for different extracellular signals the

cell may be able to tune itself to either respond or not respond to extracellular signals by undergoinglong-term physiological changes. It is noteworthy that for both glutamate and BDNF in the

pathways to CREB the positive and negative loops are evenly balanced through nine steps. Such balance of regulatory loops provides an explanation of how homeostasis within the cell can be

achieved even when a perturbing signal propagates through the system. The relative abundance ofthe positive feedback and feedforward loops as compared to the negative loops in the sub-network

for NE to AMPA channels and to CREB is also noteworthy. These ratios may indicate that this sub-network can hold and transfer information across time-scales leading to persistent changes. This

configuration of motifs might provide a systems level explanation of why the cAMP pathway is

associated with the late phase of long-term potentiation in the CA1 neuron (S16). It is alsonoteworthy that propagation of connectivity from BDNF to AMPA channels and CREB results in

equal numbers of positive and negative feedback loops suggesting that BDNF would not play an

important role in changing the state of this cell. This is in agreement with experimental observationthat BDNF induces plasticity by affecting the functions of the presynaptic CA3 neuron (S17)

although acute effects of BDNF are observed in the postsynaptic CA1 neuron (S18). Thus some of

the characteristic responses evoked by important neurotransmitters may be understood byidentifying the configurations of the regulatory motifs they evoke within the cell.


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Supporting figures

Fig. S1

Fig. S1 Visualization of the mammalian neuronal cellular network using the Pajek software

The network is visualized by placing nodes as triangles based in their functional compartments.Size of triangles demonstrates the level of connectivity for the node. Green arrows represent

activation links, red arrows inhibition links, and blue arrows neutral links. The network data was

stored in the .net file format using custom code (Code segment S8). The output was then loaded intothe Pajek program (S2) for visualization.


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Fig. S2

A C

BStatistical characteristics of the fully connected network: Average links per node: 4.62 Characteristic Path Length: 4.21 (3.81 ± 0.026)*Grid Coefficient: 0.026 (0.005 ± 0.0005)*Clustering Coefficient: 0.11 (0.03 ± 0.004)** Mean ± SD computed for 100 shuffled networks

Fig. S2 Statistics of the fully connected network

A) Distribution of interactions (links) into various categories. Interactions (links) in the cellular

network were sorted using two different criteria: the biochemical reaction and the effect of the link.

Upper pie chart shows sorting by biochemical reaction mechanism and the lower pie chart shows the

distribution of connections that activate or inhibit downstream components. Neutral links indicateinteractions where the directionality is unspecified. B) Overall network characteristics: In

parentheses are the mean and standard deviation of the characteristic path-lengths, clustering-

coefficients and grid-coefficients computed for 100 shuffled “null” networks with the sameconnectivity distribution as the cellular network. These shuffled networks were created using an

approach based on Milo et al (S8). C) Log-log plot of the connectivity distribution. The number of

links per node (k ) is plotted against the number of nodes with the same level of connectivity.


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Fig. S3

Fig. S3 Schematic representation of the motifs identified within the cellular network

Network Motifs identified using the MFinder program. The figure visually represents the text based

output, produced by the MFinder program. These motifs are the most statistically significant

identified network motifs within the network. The MFinder program searches for motifs in directed

networks, it does not distinguish between positive and negative links. Thus, for this analysis weconsidered positive and negative links as unidirectional and neutral links as bi-directional. The

MFinder program was developed by Alon and coworkers (S9). The network motifs of size 5 and 6were identified using the sampling methods. The various types of motifs are identified by numbers.

The counts of the various types of motifs in the fully connected network are given in Table S1.


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Table S1

Motifs counts

Moti f # CN* SN** Z-score

31 16 4.8 ± 2.8 3.98

32 22 9.3 ± 3.3 3.84

33 14 8.1 ± 2.6 2.30

34 36 12.5 ± 3.7 6.38

35 32 12.2 ± 3.8 5.16

36 25 9.8 ± 3.7 4.12

41 1011 186.6 ± 32.6 25.31

42 108 68.2 ± 14.8 2.69

43 26 7.2 ± 4.8 3.91

44 303 104.0 ± 15.5 12.88

45 57 17.8 ± 7.3 5.39

46 105 40.0 ± 10.9 5.97

47 49 31.5 ± 8.3 2.12

* CN- Cellular Network.

** SN- Shuffled networks.Mean ± SD computed for 100 shuffled networks.

Using the sampling method (S8):

Motifs counts

Moti f # CN* SN** Z-score

51 0.254 0.023 ± 0.025 9.27

52 0.065 0.002 ± 0.003 11.42

53 0.662 0.005 ± 0.011 60.05

54 0.048 0.000 ± 0.002 26.57

55 0.100 0.003 ± 0.007 13.92

56 0.020 0.0 ± 0.0 NA57 0.016 0.0 ± 0.0 NA

61 0.395 0.001 ± 0.011 36.01

62 0.189 0.0 ± 0.0 NA

63 0.050 0.0 ± 0.0 NA

64 0.096 0.0 ± 0.0 NA

65 0.070 0.0 ± 0.0 NA

66 0.059 0.0 ± 0.0 NA

67 0.049 0.0 ± 0.0 NA

Table S1 Counts of the various types of motifs found in the cellular network Motifs were counted using the MFinder program (S9). Counts for the motifs in the cellular network

(CN) are compared to the mean for 100 control (shuffled) networks. Z-score indicates the statistical

significance for the number found in the real network as compared to the mean of the controlnetworks. Motifs of size 5 and 6 were estimated using the sampling method described by Kashtan et

al. (S9). Estimated values are given as fractions (count of the specified motifs / the total number of

motifs of the same size).


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Fig. S4

A B

C D E

Fig. S4 Analysis of subnetworks from glutamate, NE and BDNF

The number of links (A) and nodes (B) added per step, downstream from three ligands known to

regulate plasticity in hippocampal neurons. C) Characteristic Path Length (CPL), D) ClusteringCoefficient (CC) and E) Grid Coefficient (GC) computed for subnetworks emanating from

glutamate, nor-epinephrine and BDNF.

Fig. S5

A B C

Fig. S5 Comparison of positive vs. negative feed-forward loop motifs in subnetworks

emanating in steps from the three ligands: glutamate, nor-epinephrine and BDNFCounts were obtained using the source code described under Methods. Positive feed-forward loop

motifs are feed-forward loops where both “arms” to the target node are positive. If at least one arm

is negative the feed-forward is considered negative. Positive “arm” is defined as an “arm” with

either no negative links or even number of negative links.


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Fig. S6

Fig. S6 Regulatory motifs identified in subnetworks emanating in steps from glutamate (Glu),

norepinephrine (NE) and BDNF

The motifs identified using our algorithms (see custom codes S17-S19) can classify motifs based on

the different types of links and nodes. This is an enhancement to the MFinder program that onlyidentifies more abstract motifs based on directionality only.

A) The scaffold motif is made of three nodes connected solely by neutral links.

A-I: A schematic illustration of a scaffold motif.A-II: The counts of scaffold motifs found in subnetworks generated from the three ligands

A-III: Representative examples of the scaffold motifs.B) The bi-fan motifB-I: Schematic representation of the bifan motif.

B-II: The counts of bi-fan motifs found in subnetworks generated from the three ligands.

B-III: Representative examples of bifan motifs.

C) The feedforward loop motifs are composed of three or four nodes connected with directed linksonly where a source node feeds into a target node through two alternative routes.

C-I: Schematic representations of the feedforward loops


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C-II: The counts of feed-forward loop motifs found in the subnetworks generated from the three

ligands

C-III: Representative examples of feed-forward motifs.

Positive feed-forward loop motifs are feed-forward loops where both “arms” to the target node are positive. Positive “arm” is defined as an “arm” with either no negative links or even number of

negative links. If at least one arm is negative the feed-forward is considered negative.

Abbreviations: PKA: protein kinase A, PKC: protein kinase C, CaM: calmodulin, CaN: calcineurin,

GlyR: glycine receptor, NMDAR: NMDA receptor, AC2: adenylyl cyclase 2, PLCβ: phospholipaseC beta, CREB: cyclic-AMP response element binding protein. CREM: cyclic-AMP response

element modulator. β-ARK: beta adrenergic receptor kinase.

Fig. S7 A

B

Fig. S7 Size of subnetworks from extracellular ligands to specified effectors

A) Schematic representation of the source and target nodes for the subnetworks starting from the

three extracellular ligands: glutamate, nor-epinephrine (NE) and brain-drived neurotrophic factor(BDNF), (source nodes) to reach the effectors AMPA receptor-channels (AMPAR) or the

transcription factor cyclic-AMP response element binding protein (CREB) (target nodes). B) The

changes in the number of nodes as more steps are allowed to reach the target nodes (effectors) from

the source ligands for six sets of subnetworks.


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Fig. S9

A

B C D

E F G

Fig. S9 Subnetworks characteristics from extracellular ligands to AMPAR

A) Schematic of the source and target nodes for the subnetworks starting from the three extracellularligands: glutamate, nor-epinephrine (NE) and brain-derived neurotrophic factor (BDNF), (source

nodes) to reach the effector AMPA channel/receptor (AMPAR) (target node). B-D) Changes in the

number of links as more steps are allowed to reach the effectors from each ligand are compared to

the same analysis with shuffled networks. Only the directionality of the links that do not involve theligands or the effectors was randomly swapped while preserving the connectivity. The resultant

graphs for both the cellular network and shuffled networks were curve fitted. For all cellular

subnetworks the best fit function was linear (R 2 =0.99-0.96). Individual values are given as lin R

2.

For all of the shuffled networks the best fit was obtained for either exponential or power law

functions (lin and pow respectively). E-G) Counts of the number of total three and four component positive and negative feedback and feedforward loops, in subnetworks where more steps aregradually allowed between the source and target nodes.


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Fig. S11

A

input

Act ivated A Act ivated B

output

Negative

Regulator

B

0 500 1000 15000.00

0.05

0.10

0.15 kcat A/kcat B = 1/1

kcat A/kcat B = 10/1

kcat A/kcat B = 10/0.1

kcat A/kcat B = 10/0.01

t

O u t p u t

0 500 1000 15000.00

0.05

0.10

0.15

Km A/Km B = 1/1

Km A/Km B = 10/1

Km A/Km B = 10/0.1

Km A/Km B = 10/0.01

t

O u t p u t

Fig. S11 Quantitative evaluation of a simple feedforward motif (motif 44 in Fig. S3).

A) A feedforward motif (Motif 44, Fig S3) was constructed and simulated using a system of coupledODEs. In this model, a simulated square pulse of input activates enzymes A and B. After 300seconds, the input was “washed out,” and the behavior of the output, which is activated by both A

and B, was studied. To balance the activities of the activator, a negative regulator was included.

The initial concentration of all components was 1 µM. B) To study the motif behavior, sensitivityanalyses were performed on k cat and K m. The ratio between the kinetics parameters of the two arms

were varied from 10 (k catA = 10 s-1

, k catB = 1 s-1

), to 1000 (k catA = 10 s-1

, k catB = 0.01 s-1

). Similaranalysis was performed on K m. The activity of the output component is plotted as a function of

time. The analysis shows that the motif behavior is robust. Changing the kinetics parameters over 3

orders of magnitude had little effect on the qualitative behavior of the motif. As assessed by input-output relationships. These initial results suggests that components with widely varying reactions

rates can come together to form functional units.


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Table S2

Molec#1/Catalyst Molec#2/Substrate/Product Reaction typek f

(/µM/s)kr (/s)

KD/KM (µM)

kcat (/s) Ref. Notes

Rap1GAPII Rap1 GAP 1.4 80.5 65 11 (1)

cAMP PKA site1 Binding 1.67 0.0167 0.010 (2)

cAMP PKA site2 Binding 0.0093 0.00028 0.030 (2)

β ARK β -AR Phosphorylation 0.2 0.2 (3)

Csk Src Phosphorylation 1.8 40 22 0.4 (4)2-fold adjustment for T;KD & kr are lower limits

calcium N-term calmodulin Binding 6 500 (5)

calcium C-term calmodulin High Aff-Binding 6 10 (5)

calcium C-term calmodulin Low Aff-Binding 6 100 (5)

high and low-affinitybinding @ C-term reflects

CaM complexing;dissociation but not

association rate constantswere modified by CaM's

interactions

MKP3 ERK2 Dephosphorylation 0.022 0.2 (6)

CDK1-cyclin Clb2 unidentified substrate/s35

(ATP)2.2 (7)

Used crude cell lysate assubstrate. i.e. no single

target, but perhaps morephysiological

PIP2 PKB (PH dom) Binding 0.5 (8)

RasGAP Ras GAP 4.8 9.12 (9)

Caspase 9 Caspase3 Cleavage 0.089 0.0168 (10)

Caspase 3 PARP Cleavage 5.6 0.213 (10)

Sos Ras GEF 0.50505 0.02 (11)

PKA Representative substrate Phosphorylation 2.4 2.7 (12)

PKA Representative substrate Phosphorylation 7.5 9 (13)

CDK5 (p35isoform)

Tau Phosphorylation 33 0.0433 (14)

CDK5 (p25isoform)

Tau Phosphorylation 27 0.217 (14)

CalcineurinG-substrate, a substrate for

PKGDephosphorylation 3.8 0.41 (15)

Calcineurin DARPP-32, a substrate forPKA Dephosphorylation 1.6 0.2 (15)

Calcineurin synapsin I (site 1) Dephosphorylation 7 0.053 (15)

Calcineurin synapsin I (site 2) Dephosphorylation 4.4 0.04 (15)

Grb2 Sos Binding 0.025 0.0168 (16)

PKC (Ca bound) DAG Binding 0.008 8.6348 (16)

calmodulin MLCK (non phosphorylated) Binding 28 0.031 (17)

calmodulin MLCK (non phosphorylated) Binding 8 0.186 (17)

MEK MAPK Phosphorylation 0.476 0.113(18,19)

Km = 0.476 uM for 1stphosphorylation, 0.046

uM for secondphosphorylation

Raf MEK1 Phosphorylation 0.8 0.105 (20)

GSK3β β-CATENINPhosphorylation 0.1276 3.5

(21,

22)1.7 6.13 (23)

STEP MAPK Dephosphorylation 38 12(24,25)

AC 1

AC cAMP Synthesis 1.4 7.9(26,27)

PDE4D cAMP Cleavage

NWASP Arp2/3 Binding 0.003 (28)

Grb2 NWASP Binding 0.005 (28)


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20

References for Table S2:1. Kraemer, A., Brinkmann, T., Plettner, I., Goody, R. & Wittinghofer, A. (2002) J Mol Biol 324, 763-74.2. Zorn, M., Fladmark, K. E., Ogreid, D., Jastorff, B., Doskeland, S. O. & Dostmann, W. R. (1995) FEBS Lett 362, 291-4.3. Kim, C. M., Dion, S. B. & Benovic, J. L. (1993) J Biol Chem 268, 15412-8.4. Lieser, S. A., Shindler, C., Aubol, B. E., Lee, S., Sun, G. & Adams, J. A. (2005) J Biol Chem 280, 7769-76.5. Gaertner, T. R., Putkey, J. A. & Waxham, M. N. (2004) J Biol Chem 279, 39374-82.6. Zhou, B., Wang, Z. X., Zhao, Y., Brautigan, D. L. & Zhang, Z. Y. (2002) J Biol Chem 277, 31818-25.7. Ubersax, J. A., Woodbury, E. L., Quang, P. N., Paraz, M., Blethrow, J. D., Shah, K., Shokat, K. M. & Morgan, D. O. (2003)

Nature 425, 859-64.8. Frech, M., Andjelkovic, M., Ingley, E., Reddy, K. K., Falck, J. R. & Hemmings, B. A. (1997) J Biol Chem 272, 8474-81.

9. Gideon, P., John, J., Frech, M., Lautwein, A., Clark, R., Scheffler, J. E. & Wittinghofer, A. (1992) Mol Cell Biol 12, 2050-6.10. Bentele, M., Lavrik, I., Ulrich, M., Stosser, S., Heermann, D. W., Kalthoff, H., Krammer, P. H. & Eils, R. (2004) J Cell Biol 166,

839-51.11. Orita, S., Kaibuchi, K., Kuroda, S., Shimizu, K., Nakanishi, H. & Takai, Y. (1993) J Biol Chem 268, 25542-6.12. Hemmings, H. C., Jr., Nairn, A. C. & Greengard, P. (1984) J Biol Chem 259, 14491-7.13. Bhalla, U. S. (2002) Biophys J 83, 740-52.14. Hashiguchi, M., Saito, T., Hisanaga, S. & Hashiguchi, T. (2002) J Biol Chem 277, 44525-30.15. King, M. M., Huang, C. Y., Chock, P. B., Nairn, A. C., Hemmings, H. C., Jr., Chan, K. F. & Greengard, P. (1984) J Biol Chem

259, 8080-3.16. Bhalla, U. S., Ram, P. T. & Iyengar, R. (2002) Science 297, 1018-23.17. Kasturi, R., Vasulka, C. & Johnson, J. D. (1993) J Biol Chem 268, 7958-64.18. Seger, R., Ahn, N. G., Posada, J., Munar, E. S., Jensen, A. M., Cooper, J. A., Cobb, M. H. & Krebs, E. G. (1992) J Biol Chem

267, 14373-81.19. Haystead, T. A., Dent, P., Wu, J., Haystead, C. M. & Sturgill, T. W. (1992) FEBS Lett 306, 17-22.20. Force, T., Bonventre, J. V., Heidecker, G., Rapp, U., Avruch, J. & Kyriakis, J. M. (1994) Proc Natl Acad Sci U S A 91, 1270-4.21. Ikeda, S., Kishida, S., Yamamoto, H., Murai, H., Koyama, S. & Kikuchi, A. (1998) Embo J 17, 1371-84.

22. Lee, E., Salic, A., Kruger, R., Heinrich, R. & Kirschner, M. W. (2003) PLoS Biol 1, E10.23. Paul, S., Snyder, G. L., Yokakura, H., Picciotto, M. R., Nairn, A. C. & Lombroso, P. J. (2000) J Neurosci 20, 5630-8.24. Tang, W. J., Stanzel, M. & Gilman, A. G. (1995) Biochemistry 34, 14563-72.25. Taussig, R., Tang, W. J., Hepler, J. R. & Gilman, A. G. (1994) J Biol Chem 269, 6093-100.26. Lim, J., Pahlke, G. & Conti, M. (1999) J Biol Chem 274, 19677-85.27. Bolger, G. B., Erdogan, S., Jones, R. E., Loughney, K., Scotland, G., Hoffmann, R., Wilkinson, I., Farrell, C. & Houslay, M. D.

(1997) Biochem J 328 ( Pt 2), 539-48.28. Carlier, M. F., Nioche, P., Broutin-L'Hermite, I., Boujemaa, R., Le Clainche, C., Egile, C., Garbay, C., Ducruix, A., Sansonetti,

P. & Pantaloni, D. (2000) J Biol Chem 275, 21946-52.

Table S2 Reaction rates for representative reactions underlying interactions in the network

and a listing of the primary references from which these rates were obtained

Rates for several classes of the reactions underlying the links in the network were collected from

published studies. The reactions for which rates are shown include: non-covalent binding includingligand-protein and protein-protein interactions, enzymatic reactions such as cAMP synthesis,

phosphorylation, dephosphorylation, proteolytic cleavage, and changes in catalytic activity resulting

from protein-protein interactions such as the GEF and GAP activity for GTPases. These types ofreactions account for a large portion of the interactions within the cellular network.


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21

Table S3

Table 3 Supporting external files

The network database is provided in Text file S1 as a flat file where the field separator is a blank

space. Each line in the file describes an interaction extracted from a specific journal. The tokensdescription is provided in the methods section under “Storage of the network data”. The Pajek

software can be used to visualize the network with Text file S2 (S2). Text files S3-S6 are the raw

output files from the MFinder program. Code segments S7-S19 contain algorithms written in C/C++used to generate, analyze and visualize the subnetworks in the study. Movies S20-S23 illustrate the

concept we termed pseudodynamics used to create the three different types of subnetworks.

Spreadsheets S23-S28 contain the raw data from the analysis. These tables were used to create most

of the graphs in the study. The supporting external files can be found also athttp://amp.pharm.mssm.edu/network/sm/SM.htm and at http://www.mssm.edu/labs/iyengar .

Other supporting online materials are available at: http://amp.pharm.mssm.edu/network/index.htm

File name Description

Text file S1 Network data in flat file format.

Text file S2 Pajek format text file describing the network data and assigns 2D location for nodes on the map.

Text file S3 Raw output from the MFinder program searching for motifs of size 3.



Text file S6 Raw output from the MFinder program searching for motifs of size 6.Code segment S7 Rules for sorting components into functional machines.

Code segment S8 Converts the network into a Pajek format text file.

Code segment S9 Creates sub-network where connectivity is propagated from ligands.

Code segment S10 Analysis for nodes, interactions, motifs, clustering and path-lengths of sub-networks starting at

ligands.

Code segment S11 Implementation of the Floyd algorithm to compute the characteristic path-length.

Code segment S12 Implementation of the clustering coefficient algorithm.

Code segment S13 Implementation of the grid coefficient algorithm.

Code segment S14 Algorithm used to create 100 shuffled networks with the same connectivity distribution and oneisland.

Code segment S15 Code segment used to create sub-network from specified source node to specified target node.

Code segment S16 Code used to create sub-networks with gradual allowable nodal connectivity.

Code segment S17 Algorithm used to search for feedback loops.Code segment S18 Algorithm used to search for feed-forward loops.

Code segment S19 Algorithm used to search for bi-fan motifs.

Movie S20 Illustration of the breadth-first concept.

Movie S21 Illustration of the sub-networks where the source and target are specified.

Movie S22 Illustration of the concept of gradual inclusion of nodes based on connectivity.

Spreadsheet S23 Connectivity propagation per step from all ligands.

Spreadsheet S24 Number of nodes, interactions, motifs, computed clustering and path-lengths for sub-networks

starting at ligands.

Spreadsheet S25 Connectivity distribution table.

Spreadsheet S26 Characteristic path-lengths, clustering coefficients and grid coefficients for the real network andfor 100 shuffled networks with the same connectivity distribution.

Spreadsheet S27 Results of the analysis of sub-networks from source to target.

Spreadsheet S28 Analysis of sub-networks based on nodal connectivity.


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Supporting References:

S1. N. R. Gough, L. B. Ray, Science STKE. 135, EG8 (2002)

S2. http://vlado.fmf.uni-lj.si/pub/networks/pajek/ (2004)S3. http://www.mathworks.com/products/matlab/ (2004)

S4. http://office.microsoft.com/excel/ (2004)

S5. T. H. Cormen, et al. 2002, Introduction to Algorithms, MIT Press Cambridge, MA.S6. D. J. Watts, S. H. Strogatz, Nature. 393, 440 (1998)

S7. G. R. Caldarelli, Pastor-Satorras et al. European Physical Journal B. 38, 183 (2004)

S8. R. Milo, S. Shen-Orr, S. Itzkovitz, et al., Science. 298, 824 (2002)S9. N. Kashtan, S. Itzkovitz, R. Milo, Bioinformatics. 20, 1746 (2004)

S10. http://office.microsoft.com/visio (2004)

S11. U.S. Bhalla, R. Iyengar, Science. 283, 381 (1999)S12. W. Xiong , J. E, Ferrell Jr. Nature. 426, 460 (2003)

S13. A.A. Prinz AA, D. Bucher, E. Marder, Nature Neuroscience 7, 1345 (2004)

S14. S. Mangan, U. Alon, Proc Natl Acad Sci U S A. 100, 11980 (2003)

S15. S. Mangan, A. Zaslaver, U. Alon, J Mol Biol. 334, 197 (2003)S16 P. V. Nguyen, T. Abel, E. R. Kandel, Science. 265, 1104 (1994).

S17. S. S. Zakharenko, S. L. Patterson, I. Dragatsis, et al., Neuron. 39, 975 (2003).S18. Y. Kovalchuk, E. Hanse, K. W. Kafitz, et al., Science. 295, 1729 (2002).

Author Contributions

AM assembled the large-scale network, wrote all of the custom-code and conducted all of

the analysis described in this study. SLJ developed the database to manage and maintain the

components links and references programs; AM, SN, AH, EG, BD-T, NJE, SLJ, RDB and RI foundand read the original papers cited as references to verify the components and interactions. GW and

PTR developed the original connections map of nearly 200 components on which the network usedin this study was based upon. JJR, AK and GAS provided approaches to analyze and statistically

validate several of the key findings. NJE performed the quantitative analysis of the feedforwardmotif. AH assembled the table of rate constants. RDB provided supervision of the development of

interactions maps and its anchoring to the hippocampal neuron. RI was responsible for overallsupervision of the project including analysis of the data and writing of the manuscript and is

responsible for the final version of the submitted paper.

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