BACKGROUND
the barabási and albert scale free network model is a mathematical precept that describes the innate connectivity and distribution within complex networks.
these scale free networks defy the traditional random graph model of erdös and renyi and display a connectivity distribution where the occurrence of highly interacting components of the network, defined as nodes decay as a power law, p ~ k-γ  <cit> .
in turn, growth of a scale free network is characterized by a preferential attachment scheme in which new nodes attach to older more connected nodes with a higher probability  <cit> .
this model facilitates a rich-get-richer schema and allows for the existence of a very important class of highly connected hubs  <cit> .
these hubs are largely responsible for the non-gaussian connectivity distribution of scale free networks and are commonly orders of magnitude more connected than the average node.
the existence of the hubs also provide a robust environment that is tolerant of random attack and failure but is very sensitive to hub perturbation  <cit> .
this scale free topology has been demonstrated in a variety of man-made networks such as the world wide web and the actor collaboration network  <cit> .
scale free principles have also been noted in biologic systems such as the yeast protein-protein interaction dataset and the metabolic protein network  <cit> .
nevertheless, the suitability of the static scale free construct across diverse biologic systems has been challenged as a universal principle.
for example, the yeast protein interaction network has been described as a date and party hub scale free network, in which these hubs are defined by variable or consistent interactions, respectively  <cit> .
more critically, mathematical models of network growth have shown that preferential attachment may follow a random geometric topology rather than a scale free distribution  <cit> .
another study uses a learning algorithm to infer duplication-mutation-complementation as the central topology mechanism in the drosophila melanogaster protein interaction network  <cit> .
indeed, it has been reported that the essential proteins within the larger yeast protein interaction network form an exponential connectivity distribution rather than a scale free distribution  <cit> .
these observations raise intriguing possibilities, one of which suggests that broader scale free systems may evolve from a compilation of sub networks of different topology.
alternatively, this non-scale free structure may be an anomaly that originates from examining essential hubs versus non-essential hubs in the framework of an already established network.
within this context, phosphorylation dependent signal transduction pathways provide an interesting venue to examine network behavior.
in eukaryotic organisms, kinase directed phosphorylation is one of the most common forms of post-translational modification and as such this protein class is noted as a vital regulator of cellular function  <cit> .
in addition, kinase families are well conserved across diverse phyla, suggesting that network organization may be similarly conserved.
however, phosphorylation pathways are commonly studied as linear events connecting stimulus to response through a simple ladder of molecular interactions, a concept that is based largely on experimental perturbation and observation of directly connected proteins.
as such, identification of the select kinase hubs and interaction profiling should offer an insight into the functional complexities of cellular signaling in yeast and higher eukaryotes.
here, we examined the subset of the s. cerevisiae interaction data, which include protein kinases and their direct protein interactions.
in all cases, analysis was performed on filtered datasets available in public databases to identify likely hub kinases and their interactivity.
we confirmed scale free behaviour of this dataset using connectivity analysis and observed parameters as applied to a novel computer program/visualization tool we termed hubview  <cit> .
interactions between the  <dig> most connected kinases, which we identified as super-hubs, were mapped along with less connected hub kinases.
from this map we were able to discern three distinct clusters of kinase proteins, with each cluster retaining a common biologic function, i.e.
cell cycle control, dna repair/recombination and the pheromone/mating response.
together these observations suggest that scale free topology of the yeast kinome co-evolved with the emergence of distinct biologic domains.
RESULTS
to study the topological properties of kinase mediated phosphorylation it was necessary to isolate the signaling component of the s. cerevisiae proteome which we refer to as the kinase-partner interaction set .
the kpi node set was assembled from the concatenation of kinases from the database of interacting proteins  kinase search, the yeast kinases identified by hunter and plowman  <cit>  and their non-kinase interaction partners.
the interactions of the kpi nodes were considered bidirectional, as no directionality can be consistently inferred in most experimental conditions, and consisted of kinase-kinase and kinase-non-kinase interactions only .
the core and complete kpi consisted of  <dig> nodes with  <dig> interactions and  <dig> nodes and  <dig> interactions respectively.
analysis using maximum likelihood estimation  of the degree distributions  resulted in derived γ values of γ =  <dig>  in the core kpi and γ =  <dig>  in the complete kpi which is in the biologically robust range of  <dig> < γ <  <dig>  <cit> .
the kolmogorov-smirnov test for power law distribution  <cit>  of both mles  support the hypothesis that the kpi networks are indeed both power-law distributions and hence scale free in topology.
the γ-values found for the kpis are very consistent with reports from complete protein interaction data analysis and the deterministic scale free model  <cit>  which confirms that the selection criteria for the kpi is not biased to any connectivity class.
a study of metabolic networks has shown that the largest most connected part of a network  tends to dominate the parameters found through topological analysis  <cit> .
here the degree distribution is challenged as a global property and treated as a local property of the network.
it is worth noting that while the kpi does contain a limited number of segregated modules, the size of the largest component accounts for roughly 95% of the network and the degree distribution does represent a global property of the network.
the kpi interaction data was analyzed by our visualization tool, hubview.
the hub-star-satellite view separates nodes with degrees higher than a user defined cut-off and their substrates of unary degree, groups the rest of the nodes within a sphere, and places the hub-stars around the sphere as satellites.
the core and complete kpi were viewed with a cut-off of  <dig> and  <dig> respectively  and in both cases resulted in  <dig> satellites responsible for about 69% and 71% of the interactions respectively.
the average node degree for both the core and complete kpi was found to be <k> ≅  <dig> .
the putative hubs identified by hubview were compiled into a list of  <dig> distinct nodes and ranked by average degree where the degree found in the core kpi was given twice the weight .
defining the actual cut-off degree for a hub is a subjective task, here we defined  <dig>  as the cut-off for high confidence in super-hub status.
this cut-off retains  <dig> proteins as high confidence hubs that still maintain ~64% of kpi interactions which suggests that less understood signaling systems in higher eukaryotes may be studied with higher efficiency by identifying likely hub kinases  and mapping the complete set of their immediate interaction partners.
the  <dig> members of the protein kinase superfamily list  <cit>  were cross referenced with the list of essential yeast proteins  <cit>  to identify the yeast kinases with known knockout lethal phenotypes.
of the  <dig> kinases only  <dig> were deemed to be lethal deleterious mutants yielding a 13% chance of lethality in an instance of random single kinase deletion.
in contrast,  <dig> of the  <dig> hubs named as high confidence in table  <dig> are listed as essential resulting in a 32% chance of lethality attributed to random deletion of one of the  <dig> high confidence hubs.
this marked increase in lethality associated with directed hub attack is consistent with existing studies of scale free networks  <cit>  and indicates a likely tendency for hub kinases to be preserved in an evolutionary perspective.
<dig> of the  <dig> hubs listed in table  <dig> were found to interact with one another.
the interplay between these  <dig> connected hubs forms a kinase signaling backbone  through which  <dig> distinct groups of interacting hubs  can be identified.
presumably, the hub clusters would provide vital functions as whole as in most cases the constituent hubs are not directly essential themselves.
the structure of this backbone may offer some insight in identifying synthetic lethality strategies, i.e.
cka <dig> and cka <dig> knockouts are both viable but double deletion mutant has a lethal phenotype  <cit> .
backbone hubs have been ordered by degree to illustrate a possible correlation between degree and phylogenetic age where, by direct consequence of the growth and preferential attachment conditions in scale free systems, more connected hubs are likely to be older than less connected hubs  <cit> .
a cross genome study of four organisms from different regions of the phylogenetic tree has been used to identify connectivity and emergence time of yeast proteins  <cit> .
the results of this study support the preferential attachment and growth criteria as outlined by the scale free theory.
older proteins appear to be more connected than younger proteins.
another explanation of the degree arrangement is that the average size or degree of a cluster is associated with the evolutionary age of the clusters functional class  <cit> .
this perspective is based on a similar study using a more rigorous phylogenetic profiling technique.
the results suggest a modified form of scale free preferential attachment whereby proteins bind preferentially within their own functional class and not globally or promiscuously.
by this model a younger protein may be more connected than an older one simply because it is part of an older and more connected functional grouping which emerged during an earlier phylogenetic period.
here the average connectivity of the functional group is proportional to the age of that group i.e.
older eukaryotic proteins are shown to be more connected than yeast specific proteins.
this perspective is very plausible as it suggests that proteins of similar function will interact within the same pool.
in response to the latter interpretation we examined the basic purpose of the individual hubs and observed a common functional theme concomitant with each cluster.
the largest cluster, containing cdc <dig>  is functionally associated with cell cycle propagation through the various phases.
the second cluster, with cka <dig> as a peak, is generally associated with kinase proteins that manipulate response to dna damage and the final kss/mapk cluster is involved with the regulation of the pheromone response.
these results seem to offer a reasonable order to the emergence of specialized functions central to all eukaryotes i.e., the cell division cycle predates the dna verification mechanisms, which in turn predates the youngest reproductive module, the mating response.
the entire core and complete kinomes were clustered using the probabilistic method described by samanta and liang  <cit> .
this method identifies functional relationships between proteins through redundancy of interaction partners.
a number of the associations in the backbone clusters were confirmed using this algorithm .
interestingly the proteins in the cell cycle propagation cluster did not appear as functionally redundant in the clustering.
presumably the three clusters converge downstream to some extent but at the hub level this indicates that these components offer highly specialized non redundant services to the cell cycle cluster likely due to the ancient nature of their function.
this method can also be used to identify likely synthetic lethality as many viable knockouts are rescued through redundant interactions.
the full results of the clustering is available as supporting information  or can be generated using hubview.
in addition to the scale free topology, modeling of the yeast kinome using the hubview cascade crawler function revealed other notable characteristics.
specifically, individual clusters containing hub kinases also include kinases that interact both inside and outside the scope of the immediate functional cluster.
this characteristic was generally not observed with non-hub clusters.
for example, the cluster of kinases involved in the mapk cascade  retain interactions with a number of non-mapk kinases i.e.
single points that interact both within and outside of the mapk class.
this is a feature we refer to as an open loop signal .
identifying open points within a cluster provides the user with probable targets for regulation of that functional cluster or even likely paths for signaling crosstalk.
open loop kinase cascades appear to reflect robust cellular responses that require multiple alterations and as such would require direct communication and signal propagation between numerous key regulatory factors/kinases themselves.
however, non hub kinase clusters such as the tor kinase cascade do not retain direct interactions between unclustered kinases and as such conform to a closed loop structure .
closed loop structures are likely to be kinase directed cascades that perform a very discrete cellular function in response to a limited or very specific initiating event.
the network of essential yeast proteins has been compiled and identified as an exponential distribution  <cit> .
this distribution is normally associated with more stochastic evolutionary mechanisms.
it has been argued that this network may represent an ancestral core about which the rest of the yeast interactome has formed  <cit> .
the existence of an exponential core does not directly contradict the scale free topology observed in the protein interaction network but may simply exist as a scaffold for scale free mechanisms to adhere to.
this possibility is interesting as it may also suggest that different parts of the interactome may have evolved by different evolutionary pressures causing unequal distribution of topological properties within the same interactome.
a recent investigation concerning the effects of sampling on topology adds a small shard of doubt to studies of protein network topology.
in this study the effects of various large scale experiments were simulated by first generating different networks of known topology and then sampling interactions in a scale mimicking yeast two hybrid and co-affinity purification  <cit> .
they found that under some conditions that non-scale free topologies , when sampled, can generate sub-networks with scale free properties.
here the kinome benefits from the fact that it is a widely studied mechanistic class and many of the interactions, especially in the core kinome, have been identified in smaller scale experiments and not exclusively large scale experiments.
this suggests that the much smaller kinome network may not suffer as much as networks derived solely from large scale experiments.
the results of this study certainly insist on the caveat that the results of our kpi network cannot be extrapolated to the complete yeast protein interaction network with any amount of confidence.
CONCLUSIONS
our analysis suggests that the yeast kinome is an evolved scale free system.
moreover, these observations suggest the intriguing possibility that the scale free topology of the global protein-protein interaction network or any larger biologic network may be the composite of smaller evolving topologies , all of which are subject to their own selective pressures.

 the barabási and albert scale free network model is a mathematical precept that describes the innate connectivity and distribution within complex networks. these scale free networks defy the traditional random graph model of erdös and renyi and display a connectivity distribution where the occurrence of highly interacting components of the network, defined as nodes decay as a power law, p ~ k-γ. in turn, growth of a scale free network is characterized by a preferential attachment scheme in which new nodes attach to older more connected nodes with a higher probability. this model facilitates a rich-get-richer schema and allows for the existence of a very important class of highly connected hubs. these hubs are largely responsible for the non-gaussian connectivity distribution of scale free networks and are commonly orders of magnitude more connected than the average node. the existence of the hubs also provide a robust environment that is tolerant of random attack and failure but is very sensitive to hub perturbation. this scale free topology has been demonstrated in a variety of man-made networks such as the world wide web and the actor collaboration network. scale free principles have also been noted in biologic systems such as the yeast protein-protein interaction dataset and the metabolic protein network. nevertheless, the suitability of the static scale free construct across diverse biologic systems has been challenged as a universal principle. for example, the yeast protein interaction network has been described as a date and party hub scale free network, in which these hubs are defined by variable or consistent interactions, respectively. more critically, mathematical models of network growth have shown that preferential attachment may follow a random geometric topology rather than a scale free distribution. another study uses a learning algorithm to infer duplication-mutation-complementation as the central topology mechanism in the drosophila melanogaster protein interaction network. indeed, it has been reported that the essential proteins within the larger yeast protein interaction network form an exponential connectivity distribution rather than a scale free distribution. these observations raise intriguing possibilities, one of which suggests that broader scale free systems may evolve from a compilation of sub networks of different topology. alternatively, this non-scale free structure may be an anomaly that originates from examining essential hubs versus non-essential hubs in the framework of an already established network. within this context, phosphorylation dependent signal transduction pathways provide an interesting venue to examine network behavior. in eukaryotic organisms, kinase directed phosphorylation is one of the most common forms of post-translational modification and as such this protein class is noted as a vital regulator of cellular function. in addition, kinase families are well conserved across diverse phyla, suggesting that network organization may be similarly conserved. however, phosphorylation pathways are commonly studied as linear events connecting stimulus to response through a simple ladder of molecular interactions, a concept that is based largely on experimental perturbation and observation of directly connected proteins. as such, identification of the select kinase hubs and interaction profiling should offer an insight into the functional complexities of cellular signaling in yeast and higher eukaryotes. here, we examined the subset of the s. cerevisiae interaction data, which include protein kinases and their direct protein interactions. in all cases, analysis was performed on filtered datasets available in public databases to identify likely hub kinases and their interactivity. we confirmed scale free behaviour of this dataset using connectivity analysis and observed parameters as applied to a novel computer program/visualization tool we termed hubview. interactions between the most connected kinases, which we identified as super-hubs, were mapped along with less connected hub kinases. from this map we were able to discern three distinct clusters of kinase proteins, with each cluster retaining a common biologic function, i.e. cell cycle control, dna repair/recombination and the pheromone/mating response. together these observations suggest that scale free topology of the yeast kinome co-evolved with the emergence of distinct biologic domains.  to study the topological properties of kinase mediated phosphorylation it was necessary to isolate the signaling component of the s. cerevisiae proteome which we refer to as the kinase-partner interaction set. the kpi node set was assembled from the concatenation of kinases from the database of interacting proteins kinase search, the yeast kinases identified by hunter and plowman and their non-kinase interaction partners. the interactions of the kpi nodes were considered bidirectional, as no directionality can be consistently inferred in most experimental conditions, and consisted of kinase-kinase and kinase-non-kinase interactions only. the core and complete kpi consisted of nodes with interactions and nodes and interactions respectively. analysis using maximum likelihood estimation of the degree distributions resulted in derived γ values of γ = in the core kpi and γ = in the complete kpi which is in the biologically robust range of < γ <. the kolmogorov-smirnov test for power law distribution of both mles support the hypothesis that the kpi networks are indeed both power-law distributions and hence scale free in topology. the γ-values found for the kpis are very consistent with reports from complete protein interaction data analysis and the deterministic scale free model which confirms that the selection criteria for the kpi is not biased to any connectivity class. a study of metabolic networks has shown that the largest most connected part of a network tends to dominate the parameters found through topological analysis. here the degree distribution is challenged as a global property and treated as a local property of the network. it is worth noting that while the kpi does contain a limited number of segregated modules, the size of the largest component accounts for roughly 95% of the network and the degree distribution does represent a global property of the network. the kpi interaction data was analyzed by our visualization tool, hubview. the hub-star-satellite view separates nodes with degrees higher than a user defined cut-off and their substrates of unary degree, groups the rest of the nodes within a sphere, and places the hub-stars around the sphere as satellites. the core and complete kpi were viewed with a cut-off of and respectively and in both cases resulted in satellites responsible for about 69% and 71% of the interactions respectively. the average node degree for both the core and complete kpi was found to be <k> ≅. the putative hubs identified by hubview were compiled into a list of distinct nodes and ranked by average degree where the degree found in the core kpi was given twice the weight. defining the actual cut-off degree for a hub is a subjective task, here we defined as the cut-off for high confidence in super-hub status. this cut-off retains proteins as high confidence hubs that still maintain ~64% of kpi interactions which suggests that less understood signaling systems in higher eukaryotes may be studied with higher efficiency by identifying likely hub kinases and mapping the complete set of their immediate interaction partners. the members of the protein kinase superfamily list were cross referenced with the list of essential yeast proteins to identify the yeast kinases with known knockout lethal phenotypes. of the kinases only were deemed to be lethal deleterious mutants yielding a 13% chance of lethality in an instance of random single kinase deletion. in contrast, of the hubs named as high confidence in table are listed as essential resulting in a 32% chance of lethality attributed to random deletion of one of the high confidence hubs. this marked increase in lethality associated with directed hub attack is consistent with existing studies of scale free networks and indicates a likely tendency for hub kinases to be preserved in an evolutionary perspective. of the hubs listed in table were found to interact with one another. the interplay between these connected hubs forms a kinase signaling backbone through which distinct groups of interacting hubs can be identified. presumably, the hub clusters would provide vital functions as whole as in most cases the constituent hubs are not directly essential themselves. the structure of this backbone may offer some insight in identifying synthetic lethality strategies, i.e. cka and cka knockouts are both viable but double deletion mutant has a lethal phenotype. backbone hubs have been ordered by degree to illustrate a possible correlation between degree and phylogenetic age where, by direct consequence of the growth and preferential attachment conditions in scale free systems, more connected hubs are likely to be older than less connected hubs. a cross genome study of four organisms from different regions of the phylogenetic tree has been used to identify connectivity and emergence time of yeast proteins. the results of this study support the preferential attachment and growth criteria as outlined by the scale free theory. older proteins appear to be more connected than younger proteins. another explanation of the degree arrangement is that the average size or degree of a cluster is associated with the evolutionary age of the clusters functional class. this perspective is based on a similar study using a more rigorous phylogenetic profiling technique. the results suggest a modified form of scale free preferential attachment whereby proteins bind preferentially within their own functional class and not globally or promiscuously. by this model a younger protein may be more connected than an older one simply because it is part of an older and more connected functional grouping which emerged during an earlier phylogenetic period. here the average connectivity of the functional group is proportional to the age of that group i.e. older eukaryotic proteins are shown to be more connected than yeast specific proteins. this perspective is very plausible as it suggests that proteins of similar function will interact within the same pool. in response to the latter interpretation we examined the basic purpose of the individual hubs and observed a common functional theme concomitant with each cluster. the largest cluster, containing cdc is functionally associated with cell cycle propagation through the various phases. the second cluster, with cka as a peak, is generally associated with kinase proteins that manipulate response to dna damage and the final kss/mapk cluster is involved with the regulation of the pheromone response. these results seem to offer a reasonable order to the emergence of specialized functions central to all eukaryotes i.e., the cell division cycle predates the dna verification mechanisms, which in turn predates the youngest reproductive module, the mating response. the entire core and complete kinomes were clustered using the probabilistic method described by samanta and liang. this method identifies functional relationships between proteins through redundancy of interaction partners. a number of the associations in the backbone clusters were confirmed using this algorithm. interestingly the proteins in the cell cycle propagation cluster did not appear as functionally redundant in the clustering. presumably the three clusters converge downstream to some extent but at the hub level this indicates that these components offer highly specialized non redundant services to the cell cycle cluster likely due to the ancient nature of their function. this method can also be used to identify likely synthetic lethality as many viable knockouts are rescued through redundant interactions. the full results of the clustering is available as supporting information or can be generated using hubview. in addition to the scale free topology, modeling of the yeast kinome using the hubview cascade crawler function revealed other notable characteristics. specifically, individual clusters containing hub kinases also include kinases that interact both inside and outside the scope of the immediate functional cluster. this characteristic was generally not observed with non-hub clusters. for example, the cluster of kinases involved in the mapk cascade retain interactions with a number of non-mapk kinases i.e. single points that interact both within and outside of the mapk class. this is a feature we refer to as an open loop signal. identifying open points within a cluster provides the user with probable targets for regulation of that functional cluster or even likely paths for signaling crosstalk. open loop kinase cascades appear to reflect robust cellular responses that require multiple alterations and as such would require direct communication and signal propagation between numerous key regulatory factors/kinases themselves. however, non hub kinase clusters such as the tor kinase cascade do not retain direct interactions between unclustered kinases and as such conform to a closed loop structure. closed loop structures are likely to be kinase directed cascades that perform a very discrete cellular function in response to a limited or very specific initiating event. the network of essential yeast proteins has been compiled and identified as an exponential distribution. this distribution is normally associated with more stochastic evolutionary mechanisms. it has been argued that this network may represent an ancestral core about which the rest of the yeast interactome has formed. the existence of an exponential core does not directly contradict the scale free topology observed in the protein interaction network but may simply exist as a scaffold for scale free mechanisms to adhere to. this possibility is interesting as it may also suggest that different parts of the interactome may have evolved by different evolutionary pressures causing unequal distribution of topological properties within the same interactome. a recent investigation concerning the effects of sampling on topology adds a small shard of doubt to studies of protein network topology. in this study the effects of various large scale experiments were simulated by first generating different networks of known topology and then sampling interactions in a scale mimicking yeast two hybrid and co-affinity purification. they found that under some conditions that non-scale free topologies, when sampled, can generate sub-networks with scale free properties. here the kinome benefits from the fact that it is a widely studied mechanistic class and many of the interactions, especially in the core kinome, have been identified in smaller scale experiments and not exclusively large scale experiments. this suggests that the much smaller kinome network may not suffer as much as networks derived solely from large scale experiments. the results of this study certainly insist on the caveat that the results of our kpi network cannot be extrapolated to the complete yeast protein interaction network with any amount of confidence.  our analysis suggests that the yeast kinome is an evolved scale free system. moreover, these observations suggest the intriguing possibility that the scale free topology of the global protein-protein interaction network or any larger biologic network may be the composite of smaller evolving topologies, all of which are subject to their own selective pressures. 
analysis of the connectivity distribution has inferred a fat-tailed degree distribution with parameters consistent with those found in other biological networks. we have used publicly available databases and a novel software tool termed hubview to model the interactions of a subset of the yeast interactome, specifically protein kinases and their interaction partners. as such, these results suggest an inherent trend to preserve scale free characteristics at a domain based modular level within large evolvable networks. using connectivity analysis on a functional subset of proteins we have evidence that reinforces the scale free topology as a model for protein network evolution. the complexity and average degree for each of these clusters is indicative of a specialized function and relative age for each cluster.
 the availability of interaction databases provides an opportunity for researchers to utilize immense amounts of data exclusively in silico. recently there has been an emphasis on studying the global properties of biological interactions using network analysis. while this type of analysis offers a wide variety of global insights it has surprisingly not been used to examine more localized interactions based on mechanism. in as such we have particular interest in the role of key topological components in signal transduction cascades as they are vital regulators of healthy and diseased cell states.  we have used publicly available databases and a novel software tool termed hubview to model the interactions of a subset of the yeast interactome, specifically protein kinases and their interaction partners. analysis of the connectivity distribution has inferred a fat-tailed degree distribution with parameters consistent with those found in other biological networks. in addition, hubview identified a functional clustering of a large group of kinases, distributed between three separate groupings. the complexity and average degree for each of these clusters is indicative of a specialized function and relative age for each cluster.  using connectivity analysis on a functional subset of proteins we have evidence that reinforces the scale free topology as a model for protein network evolution. we have identified the hub components of the kinase network and observed a tendency for these kinases to cluster together on a functional basis. as such, these results suggest an inherent trend to preserve scale free characteristics at a domain based modular level within large evolvable networks. 