BACKGROUND
traditional chinese medicine  is an important part of the current medical system.
it aims to restore the whole-body balance in patients by using herbal formula , which is usually composed of two or more medicinal herbs and has the capacity of systematically treating disease  <cit> .
naturally occurring herbs and herbal ingredients organized into certain formula have been shown to have potential interaction effects.
these include mutual enhancement, mutual assistance, mutual restraint and mutual antagonism  <cit> .
for example, synergistic interactions occur when the efficacy of combinations of herbs  is greater than the summed responses of each individual herb or ingredient.
adams et al.
<cit>  recently reported the synergistic, additive and antagonistic effects exerted by different combinations of six herbal extracts on the viability of prostate cancer cell lines.
wang reported that a realgar-indigo naturalis formula is beneficial for the treatment of promyelocytic leukemia; the synergistic effects exerted by several components of this formula are well documented  <cit> .
ung et al.
<cit>  conducted an analysis of  <dig> tcm herb pairs and  <dig> non-tcm herb pairs using artificial intelligence methods and considering four classes of herbal properties as features including character, taste, meridian, and toxicity level.
their study revealed that herb pairs in tcm contain features distinguishable from those of non-tcm herb pairs.
schmidt et al.
<cit>  believed that mixtures of interacting compounds produced by plants may become a valuable asset and an important resource for drug discovery, especially for the development of combinational therapeutics.
however, there is still a lack of appropriate methods to learn how and why many herbs are grouped in certain formulae, and the combination rule embedding numerous herbal formulae remain unknown.
traditionally herbs have taken different roles in a typical herbal formula; they are usually expressed in the organization order as master, adviser, soldier and guide , each of which is given certain natural properties including cold, cool, neutral, warm or hot.
understanding the combination rule of herbal formulae will not only benefit the modernization of tcm but may also be helpful for the way drugs are studied.
a good example of the potential of tcm involves angiogenesis.
tcm is known to be effective for the treatment of angiogenesis which is the main type of pathological vascular growth associated with various diseases such as cancer and rheumatoid arthritis  <cit> .
we know that more than 60% of the current cancer chemotherapeutic agents are natural products or small molecules based on natural product leads  <cit> .
many pro-angiogenic and anti-angiogenic plant components are potentially useful for curing angiogenic disorders and are well tolerated  <cit> .
especially, herbs originally used for treating “collaterals  diseases” in tcm have been found to be active on angiogenic disorders  <cit> .
as a consequence, combining traditional herbal formulae with existing biological knowledge might allow researchers to rapidly identify combination treatments for angiogenic disorders.
recently, a remarkable development has been the use of systems biology, especially network biology, in drug study.
this methodology has revealed the systematic mechanisms of complex disease and has highlighted the paradigm shift from “one drug, one target” to “multicomponent therapeutics, biological networks”  <cit> .
even though the scientific community has high expectations for systems pharmacology, this field is still in its infancy because of a poor understanding of cell behaviours and drug-protein interactions.
tcm formula is considered to be an empirical system of multicomponent therapeutics which potentially meets the demands of treating a number of complex diseases in an integrated manner  <cit> .
so, in order to find a relationship between groups of drugs and complex diseases, it is important to introduce a powerful approach to bridge the tradition and the modern, and pursue a priori knowledge about the combination rules embedded in tcm.
in this work, we developed a distance-based mutual information model  to extract the herb relationships from plentiful herbal formulae.
this method was then used to construct the “herb network” from  <dig> collaterals-related herbal formulae, following by in vitro experiments designed to evaluate the angiogenic effects and synergistic properties of strongly connected herbs and herb pairs.
a new concept of “co-module” was further proposed and network biology analyses were conducted to explore the potential combination mechanism of the networked herbal formulae.
methods
data sources of herbal formulae
candidate herbal formulae selection
tcm values the “collaterals” theory and therapy.
using “collaterals ” as the keyword, we searched the sirc-tcm herbal formula database  which contains  <dig>  million herbal formulae.
then we collected  <dig> herbal formulae with formula names and functions, or herb’s meridian tropism , or targeted syndromes and diseases containing the keyword.
we standardized the herbal formulae by substituting all the polysemes, synonyms and acronyms of the herbs in the dataset using the standardized herb name list.
the standardized herb name list consists of  <dig> herbs.
the  <dig> collaterals-related herbal formulae, as examples, will be subject to the following dmim analysis.
traditionally-defined herb pairs
the herb pair is the basic unit of a herbal formula.
to evaluate the reliability and utility of the dmim-extracted herb network,  <dig> traditionally-defined herb pairs recorded in  <cit>  and  <dig> herb pairs from  <cit>  were collected.
this resulted in  <dig> non-redundant traditionally-defined herb pairs made up of  <dig> separate herbs in the collaterals-related herbal formulae.
establishment of dmim scoring system
numerical representation for herbal formulae
in the dmim, we turn the normalized formula data into a numeral matrix to indicate the relative position of the herbs in a formula.
assuming there are a total of n herbs and m formulae, we assign serial numbers to all the herbs from  <dig> to n. as illustrated in table  <dig>  we use a m×n matrix a = m*n to indicate the formula where the ith row vector denotes the components of the ith formula, and aij is the number of the position of the jth herb in ith formula .
to eliminate the impact of the total number of herbs in one formula, we define the matrix b= as
where k denotes the total number of herbs in a formula.
*assume there are a total of  <dig> herbs denoted by herb <dig>  herb2…herb <dig> , and three herbal formulae containing the following herbs in sequence : formula 1: herb <dig>  herb <dig>  herb <dig> and herb <dig> ; formula 2: herb <dig>  herb <dig>  herb <dig>  herb <dig>  herb <dig>  herb <dig>  herb <dig> and herb <dig> ; and formula 3: herb <dig> and herb <dig> .
for herb <dig> in formula  <dig>  we calculated that a <dig> = <dig> and b12=2/4= <dig> .
the matrix representation for this artificial data set is shown in the table.
from this we had matrix b , where bij indicates the relative position of herb j in the formula i. finally, the real data set is represented by a 3865× <dig> matrix.
then, for given two herbs, x and y, we deduce that the tendency of x and y to form a herb pair is dependent on two factors: mutual information entropy characteristics and the average distance between herbs.
mutual information entropy
to begin with, we calculate the traditional mutual information entropy  <cit>  for x and y as:
.
here
is the frequency that herb x and herb y occurred, and i is the indicator function of x and y, showing whether herb x and y coexist in the formula i.
is the frequency of herb x. it is the same with p. a large value of mi indicates a strong correlation between herb x and herb y .
between-herb-distance
considering a later order indicates a less importance in the organization of master, adviser, soldier or guide herbs in a herbal formula, we assume that the further the distance between two herbs in a formula, the less likely they are to be relevant to one another.
the distance between herb x and herb y in the ith formula, called the “between-herb-distance”, is defined as: d = |b - b|.
the average distance of herb x and herb y in the dataset is
.
dmim scoring system
the dmim combines the mutual information  entropy characteristics and the average distance between herbs  to form a scoring system,
, which describes the tendency of herb x and herb y to form a herb pair.
so when two herb pairs share the same information entropy, the one with the smaller average distance shows a stronger connection.
when two herb pairs have the same average distance, the one with the larger information entropy shows a greater interaction.
evaluation of the dmim-extracted herb network
in vitro assays for evaluating angiogenic activities of dmim-extracted herbs
we selected major herbal ingredients from dmim outputs to evaluate angiogenic activities.
two kinds of endothelial cell proliferation assays, namely with or without vascular endothelial growth factor  stimulation, were used to evaluate respectively the anti-angiogenic or the pro-angiogenic activity of herbal ingredients.
only the positive results were reported.
human umbilical vein endothelial cells  from cascade biologics  were cultured in endothelial cell medium  together with 10% fetal bovine serum and endothelial cell growth supplement.
this mixture was sub-cultured using a 1: <dig> ratio with trypsin/edta solution provided by the manufacturer.
herbal ingredients were purchased from the national institute for the control of pharmaceutical and biological products, china.
huvecs  in a 96-well plate were starved with  <dig> % fbs medium and then treated with or without vegf  along with different concentrations of herbal ingredients for  <dig> hours.
cell viability was determined by cell counting kit  following the measurement of optical density values using mrx revelation absorbance reader.
herb interaction measurement of dmim-extracted herb pairs
we investigated whether combination effects were produced by dmim-extracted herb pairs and whether there was a role for the natural properties of the herbs.
the highest single compound model  <cit>  was used as the reference model for measuring additivity to identify herbal interactions such as synergism or antagonism.
the combination effects were determined by selecting the greatest effect produced by each of the combination’s individual compounds using similar concentrations as in the combination.
positive or negative deviations from this predicted additivity demonstrated synergistic or antagonistic interactions.
co-module analysis for the dmim-extracted herbal formula
co-module concept, herbal formula selection and biological data preparation
to further explore the combination mechanism of dmim-extracted herbal formulae, we propose a new concept of “co-module” based on the assumption that there may exist certain consistent and common biological patterns, which act as “co-modules”, underlying networked herbs and their targeted diseases simultaneously.
we took a famous formula, “liu-wei-di-huang” , as an example, since we found that all six herbs of this formula are connected closely in the dmim-extracted herb network including shan-zhu-yu , ze-xie , dan-pi , di-huang , fu-ling  and shan-yao .
then, we collected the biological entities  affected by individual herbs  of lwdh from pubmed and china national knowledge infrastructure .
this resulted in a total of  <dig> manually collected genes or gene products, called lwdh genes, contributed respectively to the actions of the lwdh constituent six herbs.
<dig> lwdh genes were nodes of the protein-protein interaction  network .
next, we collected the documented diseases for which the lwdh formula may serve as a potential treatment.
this resulted in  <dig> diseases containing  <dig> types of cancer ,  <dig> diseases with dysfunction of the neuro-endocrine-immune-metabolism system , and  <dig> cardiovascular disorders  .
by mapping these  <dig> diseases into the omim database, we identified  <dig> exclusive phenotypes with omim ids and obtained  <dig> disease genes called lwdh-disease genes,  <dig> of which were networked in hprd.
performing co-module analysis for lwdh and lwdh-treated diseases
we conducted the co-module analysis from the following three aspects.
we analyzed the enriched kegg pathways for either lwdh genes or lwdh-disease genes with a false discovery rate less than  <dig>  by fisher exact test in david  <cit> .
we evaluated the “closeness” between lwdh genes and lwdh-disease genes in the ppi network and used the permutation test to calculate the statistical significance of the average shortest path.
here we kept the original  <dig> lwdh genes and randomly selected other  <dig> disease genes from  <dig> networked genes in all  <dig> non-redundant disease genes stored in the omim moridmap.txt ; this was repeated independently  <dig> times.
we calculated the average phenotype similarity score determined by the cosine of vector angle  <cit>  of  <dig> phenotypes of lwdh-diseases, and evaluated the statistical significance by comparison with randomly selected  <dig> omim phenotypes for  <dig> times.
statistical analysis
the mutual information statistics were transformed to equivalent odds ratios using monotonic transform and then subjected to standard χ <dig> test.
in doing so, we used χ <dig> test to test whether the occurrence of the two herbs in the formulae is correlated with each other by generating a contingency table.
experimental data from the in vitro assay were presented as mean±sd  of four independent experiments with six repeat wells for each experiment.
the statistical difference between treatments was determined by the t test.
RESULTS
dmim-extracted herb network from collaterals-related formulae
dmim was used for extracting the combination rule of  <dig> collaterals-related formulae.
in all  <dig> formulae, we found that eight of the top  <dig> most frequently occurring herbs  are reported to pro-angiogenesis or anti-angiogenesis activity  <cit> .
this provides evidence that the collaterals-related formulae may have a possible relationship with angiogenic disorders.
each of the top  <dig> dmim-extracted herb pairs had statistical significance .
table  <dig> summarized the top  <dig> dmim-extracted herb pairs with the highest rankings; six of these herb pairs are novel when compared with traditionally-defined herb pairs  <cit> .
interestingly, we found that gan-cao , a commonly-used supplementary herb , ranked 2nd with a frequency of  <dig> % in all  <dig> herbal formulae.
however, the position of herb pairs containing gan-cao fell to  <dig> , suggesting that the dmim method was able to balance the frequency, independence, and relative distance in the herbal formulae.
figure
<dig> shows that we constructed a herb network by using the interactions of the top  <dig> herb pairs extracted by dmim, in which we found that full or part of six classical herbal formulae are nicely recovered.
the distinct modular feature is also observed from the dmim-extracted herb network.
*: herb pairs extracted by dmim but not recorded in traditionally-defined herb pairs.
measurement of angiogenic activities for dmim-extracted modular herbs
as shown in figure  <dig>  the hub module or the interconnected sub-network in the dmim-extracted herb network is centered on the most frequently occurring herbs, chuan-xiong  and dang-gui .
we extended this hub module to all herb pairs with statistical significance   and assumed that herbs presented in this module could have potential angiogenic activities.
by selecting the major herbal ingredients in these herbs and taking their natural properties into consideration, the following in vitro experimental results support our hypothesis.
as shown in figure 2b, in the hub module, vitexicarpin  and timosaponin a-iii  as major ingredients taken from two herbs with cold properties were very active on inhibiting endothelial cell proliferation .
also, hydroxysafflor yellow a  and astragaloside  from herbs with hot properties had partial pro-angiogenesis activities when compared with the vegf treatment group.
another trend  was that berberine from huang-bai  and tetramethylpyrazine  from chuan-xiong had a biphasic effect on endothelial cells proliferation.
lower doses caused an increase in cell proliferation whereas higher doses resulted in an anti-angiogenic response.
overall, the experimental results validated the potential angiogenic activities of the modular herbs.
measurement of dmim-extracted modular herb interactions
we evaluated whether modular herbs with different properties had potential combination effects.
figure  <dig> shows that huvecs were treated with different compound combinations in a 6× <dig> dose matrix using the same conditions as the cell growth assay.
by using the highest single compound model  <cit>  we found that tmp  in combination with hya  caused moderate synergistic pro-angiogenic activity, whereas antagonistic effects were observed when tmp was combined with ast .
noticeably, tmp and tsa  produced obvious antagonism at higher concentrations .
we also observed that the traditional herb pairs chuan-xiong and huang-qi, and the novel herb pairs chuan-xiong and hong-hua identified by dmim exhibited clear combination effects on endothelial cell proliferation.
these results suggest that the different interaction patterns of herb pairs may be associated with their different herb properties, although this association remains unclear.
co-module underlying dmim-extracted herbal formula in treating different diseases
dmim can recover and connect all six herbs of the liu-wei-di-huang formula.
this formula is reported to potentially treat  <dig> types of diseases .
thus, we performed a co-module analysis to explore the potential combination mechanism of dmim-extracted herbal formula.
table  <dig> shows that lwdh genes as well as lwdh-disease genes are mainly enriched in cancer pathways and neuro-endocrine-immune pathways .
moreover, based on the ppi network, it is noted that the average shortest path length is significantly smaller between lwdh genes and lwdh-disease genes than between lwdh genes and randomly selected disease genes .
this highlights the specificity of the lwdh for treating these  <dig> different diseases.
in addition to this, the average phenotype similarity scores for these  <dig> lwdh diseases are higher than the scores of random controls , suggesting that it might be possible to group together lwdh-treated diseases through a common molecular basis.
these findings evidenced that lwdh might act on a common network target underlying these diseases, and we can capture the “one formula, different diseases” relationship from a co-module viewpoint based on multilayer networks of herb-biomolecule-disease .
discussion
in this work, we proposed a distance-based mutual information model, dmim, to uncover the combination rule embedded in herbal formulae, which not only uses mutual information entropy but also introduces a new factor, “between-herb-distance”, into measuring the tendency of two herbs to form an herb pair.
this makes dmim suitable for deciphering herbal formulae and distinguishes it from other analytical methods such as clustering.
for example, herb <dig> and herb <dig> are often used together to reduce toxicity and side-effects, while herb <dig> and herb <dig> may be clustered into a single category because of their co-location in similar organs or meridians.
according to the principles of clustering, herb <dig>  herb <dig> and herb <dig> may be clustered into one category, but in reality, herb <dig> and herb <dig> have no inherent relationship.
moreover, the results of clustering are qualitative rather than quantitative and clustering does not show which herbs have a tendency to form herb pairs.
dmim avoids these pitfalls by calculating the mutual information entropy for each of the herbs and their “between-herb-distance”.
we demonstrated the reliability and usefulness of dmim by using  <dig> collaterals-related herbal formulae.
firstly, we showed that the dmim method retains the traditional combination rule of tcm.
dmim identified many herbal pairs which have already been defined .
we also found that the dmim-extracted herb network identified six classical herbal formulae from the paired herbs , which are expressed as connected sub-networks.
on the other hand, dmim-extracted herb network can eliminate the disturbance from herbs such as gan-cao , a widely used “guide” herb that coordinates the actions of other herbs in formulae, though it ranks at top  <dig> in  <dig> herbal formulae.
next, we showed that dmim has the potential to discover angiogenic herbs and non-addictive herb pairs from tcm.
this study found that the  <dig> most common herbs in the  <dig> formulae had potential angiogenic effects   <cit> .
we also conducted in vitro assay to evaluate the extended hub module for chuan-xiong  and dang-gui  in the dmim-extracted herb network .
as the ingredients of herbs are very complicated and the quality of herbs is still unstable, for simplify, this work used major ingredients of herbs to perform experiments.
results showed that the herbs or herb pairs in the hub modules produced anti-angiogenic or pro-angiogenic activities, suggesting that the modular herbs may have functional dependence.
in particular, we detected the novel bioactivity of two herb ingredients which inhibited angiogenesis, including vitexicarpin  and timosaponin a-iii  .
we also validated the synergistic effects produced by dmim-extracted novel herb pairs such as chuan-xiong and hong-hua .
additionally, in this study, we observed that the active compounds from the herbs with different natural properties might account for their different angiogenic responses .
for instance, major ingredients from cool/cold herbs tend to produce anti-angiogenic activities whereas major ingredients from warm/hot herbs tend to exert pro-angiogenic activities  <cit> .
the dose-response relationship is another way to understand the characteristics of the herb’s natural properties.
we found that berberine and tetramethylpyrazine can cause a pro-angiogenic effect at low dose and anti-angiogenic effects at high dose , suggesting that some herbs may cause biphasic regulation if different dosing regimens are used.
for herb interaction effects we assumed that herb pairs in a formula with the same properties were more likely to lead to synergistic interactions, whereas combinations with different properties were inclined to cause antagonism.
as shown in figure  <dig>  combination effects from herb pairs with the same properties  and different properties  support our assumption, but the combination of chuan-xiong and huang-qi is not the case, making it an open question whether or not herbal properties are related to herb combination behaviours.
last but not least, we demonstrated that the dmim-extracted herbal formula, liu-wei-di-huang, may have its molecular basis for treating different diseases in a co-module manner .
lwdh is one of the most famous tcm formulae developed during the song dynasty in china.
results show that the six herbs in lwdh not only have high dmim scores, but also connected closely with common responsive genes enriched in cancer pathways and neuro-endocrine-immune pathways .
interestingly, lwdh genes show a significantly close relationship with lwdh-disease genes in the ppi network , forming a co-module underlying herbal formula as well as different diseases.
moreover, the  <dig> lwdh-treated diseases mainly including cancer, neuro-endocrine-immune-metabolism, and cardiovascular disorders show high phenotype similarity scores  and might share a overlapped molecular basis associated with the angiogenic processes as well as the imbalance of the human body  <cit> .
such phenomena of “one formula, different diseases” reinforce the idea that different diseases with similar phenotypes might possess internal coherence  <cit> , and a group of diseases with similar mechanisms might be able to be treated by intervening their common network target  <cit> , which in turn illustrates the rationality of multicomponent therapies such as herbal formulae .
the novel concept of co-module throughout the multilayer networks of herb-biomolecule-diseases may promote our awareness of herbal formulae as well as multicomponent therapies.
dmim is currently the first step towards building herb network from tcm herbal formula.
for future work, dmim could be generalized to mine synergistic combinations made up of more than two herbs by replacing the “between-herb-distance” with a properly defined index of the distance among multiple herbs in a formula or by introducing multivariate mutual information.
as this work treats formula independently, we will take the redundancies and correlations between formulae into consideration for calculating the herb distance.
the dose information and natural properties of herbs  are also the next step to create a multi-weight herb network.
moreover, we believe that the combination mechanism of herbal formulae will be more deeply identified in a “co-module” manner and contribute to the progression of the modern tcm as well as network pharmacological studies  <cit> .
CONCLUSIONS
dmim yields a systematic framework for scoring herb pairs and the resulted herb network can uncover some combination rules of tcm.
we also provide preliminary clues that the “co-module” across multilayer networks of herb-biomolecule-disease may be responsible for the combination mechanism underlying herbal formulae.
this study is the first step forward in exploring the unique theories of tcm herbal formula by network biology approaches and may also benefit the coming network pharmacology as well.
competing interests
the authors declare that they have no competing interests.
authors' contributions
sl conceived and designed the experiments, analyzed the data and wrote manuscript.
bz participated in the cell experiments and writing manuscript.
yw, dj and nz participated in the computational works and writing manuscript.

 traditional chinese medicine is an important part of the current medical system. it aims to restore the whole-body balance in patients by using herbal formula, which is usually composed of two or more medicinal herbs and has the capacity of systematically treating disease. naturally occurring herbs and herbal ingredients organized into certain formula have been shown to have potential interaction effects. these include mutual enhancement, mutual assistance, mutual restraint and mutual antagonism. for example, synergistic interactions occur when the efficacy of combinations of herbs is greater than the summed responses of each individual herb or ingredient. adams et al. recently reported the synergistic, additive and antagonistic effects exerted by different combinations of six herbal extracts on the viability of prostate cancer cell lines. wang reported that a realgar-indigo naturalis formula is beneficial for the treatment of promyelocytic leukemia; the synergistic effects exerted by several components of this formula are well documented. ung et al. conducted an analysis of tcm herb pairs and non-tcm herb pairs using artificial intelligence methods and considering four classes of herbal properties as features including character, taste, meridian, and toxicity level. their study revealed that herb pairs in tcm contain features distinguishable from those of non-tcm herb pairs. schmidt et al. believed that mixtures of interacting compounds produced by plants may become a valuable asset and an important resource for drug discovery, especially for the development of combinational therapeutics. however, there is still a lack of appropriate methods to learn how and why many herbs are grouped in certain formulae, and the combination rule embedding numerous herbal formulae remain unknown. traditionally herbs have taken different roles in a typical herbal formula; they are usually expressed in the organization order as master, adviser, soldier and guide, each of which is given certain natural properties including cold, cool, neutral, warm or hot. understanding the combination rule of herbal formulae will not only benefit the modernization of tcm but may also be helpful for the way drugs are studied. a good example of the potential of tcm involves angiogenesis. tcm is known to be effective for the treatment of angiogenesis which is the main type of pathological vascular growth associated with various diseases such as cancer and rheumatoid arthritis. we know that more than 60% of the current cancer chemotherapeutic agents are natural products or small molecules based on natural product leads. many pro-angiogenic and anti-angiogenic plant components are potentially useful for curing angiogenic disorders and are well tolerated. especially, herbs originally used for treating “collaterals diseases” in tcm have been found to be active on angiogenic disorders. as a consequence, combining traditional herbal formulae with existing biological knowledge might allow researchers to rapidly identify combination treatments for angiogenic disorders. recently, a remarkable development has been the use of systems biology, especially network biology, in drug study. this methodology has revealed the systematic mechanisms of complex disease and has highlighted the paradigm shift from “one drug, one target” to “multicomponent therapeutics, biological networks”. even though the scientific community has high expectations for systems pharmacology, this field is still in its infancy because of a poor understanding of cell behaviours and drug-protein interactions. tcm formula is considered to be an empirical system of multicomponent therapeutics which potentially meets the demands of treating a number of complex diseases in an integrated manner. so, in order to find a relationship between groups of drugs and complex diseases, it is important to introduce a powerful approach to bridge the tradition and the modern, and pursue a priori knowledge about the combination rules embedded in tcm. in this work, we developed a distance-based mutual information model to extract the herb relationships from plentiful herbal formulae. this method was then used to construct the “herb network” from collaterals-related herbal formulae, following by in vitro experiments designed to evaluate the angiogenic effects and synergistic properties of strongly connected herbs and herb pairs. a new concept of “co-module” was further proposed and network biology analyses were conducted to explore the potential combination mechanism of the networked herbal formulae. methods data sources of herbal formulae candidate herbal formulae selection tcm values the “collaterals” theory and therapy. using “collaterals ” as the keyword, we searched the sirc-tcm herbal formula database which contains million herbal formulae. then we collected herbal formulae with formula names and functions, or herb’s meridian tropism, or targeted syndromes and diseases containing the keyword. we standardized the herbal formulae by substituting all the polysemes, synonyms and acronyms of the herbs in the dataset using the standardized herb name list. the standardized herb name list consists of herbs. the collaterals-related herbal formulae, as examples, will be subject to the following dmim analysis. traditionally-defined herb pairs the herb pair is the basic unit of a herbal formula. to evaluate the reliability and utility of the dmim-extracted herb network, traditionally-defined herb pairs recorded in and herb pairs from were collected. this resulted in non-redundant traditionally-defined herb pairs made up of separate herbs in the collaterals-related herbal formulae. establishment of dmim scoring system numerical representation for herbal formulae in the dmim, we turn the normalized formula data into a numeral matrix to indicate the relative position of the herbs in a formula. assuming there are a total of n herbs and m formulae, we assign serial numbers to all the herbs from to n. as illustrated in table we use a m×n matrix a = m*n to indicate the formula where the ith row vector denotes the components of the ith formula, and aij is the number of the position of the jth herb in ith formula. to eliminate the impact of the total number of herbs in one formula, we define the matrix b= as where k denotes the total number of herbs in a formula. *assume there are a total of herbs denoted by herb herb2…herb, and three herbal formulae containing the following herbs in sequence: formula 1: herb herb herb and herb; formula 2: herb herb herb herb herb herb herb and herb; and formula 3: herb and herb. for herb in formula we calculated that a = and b12=2/4=. the matrix representation for this artificial data set is shown in the table. from this we had matrix b, where bij indicates the relative position of herb j in the formula i. finally, the real data set is represented by a 3865× matrix. then, for given two herbs, x and y, we deduce that the tendency of x and y to form a herb pair is dependent on two factors: mutual information entropy characteristics and the average distance between herbs. mutual information entropy to begin with, we calculate the traditional mutual information entropy for x and y as:. here is the frequency that herb x and herb y occurred, and i is the indicator function of x and y, showing whether herb x and y coexist in the formula i. is the frequency of herb x. it is the same with p. a large value of mi indicates a strong correlation between herb x and herb y. between-herb-distance considering a later order indicates a less importance in the organization of master, adviser, soldier or guide herbs in a herbal formula, we assume that the further the distance between two herbs in a formula, the less likely they are to be relevant to one another. the distance between herb x and herb y in the ith formula, called the “between-herb-distance”, is defined as: d = |b - b|. the average distance of herb x and herb y in the dataset is. dmim scoring system the dmim combines the mutual information entropy characteristics and the average distance between herbs to form a scoring system,, which describes the tendency of herb x and herb y to form a herb pair. so when two herb pairs share the same information entropy, the one with the smaller average distance shows a stronger connection. when two herb pairs have the same average distance, the one with the larger information entropy shows a greater interaction. evaluation of the dmim-extracted herb network in vitro assays for evaluating angiogenic activities of dmim-extracted herbs we selected major herbal ingredients from dmim outputs to evaluate angiogenic activities. two kinds of endothelial cell proliferation assays, namely with or without vascular endothelial growth factor stimulation, were used to evaluate respectively the anti-angiogenic or the pro-angiogenic activity of herbal ingredients. only the positive results were reported. human umbilical vein endothelial cells from cascade biologics were cultured in endothelial cell medium together with 10% fetal bovine serum and endothelial cell growth supplement. this mixture was sub-cultured using a 1: ratio with trypsin/edta solution provided by the manufacturer. herbal ingredients were purchased from the national institute for the control of pharmaceutical and biological products, china. huvecs in a 96-well plate were starved with % fbs medium and then treated with or without vegf along with different concentrations of herbal ingredients for hours. cell viability was determined by cell counting kit following the measurement of optical density values using mrx revelation absorbance reader. herb interaction measurement of dmim-extracted herb pairs we investigated whether combination effects were produced by dmim-extracted herb pairs and whether there was a role for the natural properties of the herbs. the highest single compound model was used as the reference model for measuring additivity to identify herbal interactions such as synergism or antagonism. the combination effects were determined by selecting the greatest effect produced by each of the combination’s individual compounds using similar concentrations as in the combination. positive or negative deviations from this predicted additivity demonstrated synergistic or antagonistic interactions. co-module analysis for the dmim-extracted herbal formula co-module concept, herbal formula selection and biological data preparation to further explore the combination mechanism of dmim-extracted herbal formulae, we propose a new concept of “co-module” based on the assumption that there may exist certain consistent and common biological patterns, which act as “co-modules”, underlying networked herbs and their targeted diseases simultaneously. we took a famous formula, “liu-wei-di-huang”, as an example, since we found that all six herbs of this formula are connected closely in the dmim-extracted herb network including shan-zhu-yu, ze-xie, dan-pi, di-huang, fu-ling and shan-yao. then, we collected the biological entities affected by individual herbs of lwdh from pubmed and china national knowledge infrastructure. this resulted in a total of manually collected genes or gene products, called lwdh genes, contributed respectively to the actions of the lwdh constituent six herbs. lwdh genes were nodes of the protein-protein interaction network. next, we collected the documented diseases for which the lwdh formula may serve as a potential treatment. this resulted in diseases containing types of cancer, diseases with dysfunction of the neuro-endocrine-immune-metabolism system, and cardiovascular disorders. by mapping these diseases into the omim database, we identified exclusive phenotypes with omim ids and obtained disease genes called lwdh-disease genes, of which were networked in hprd. performing co-module analysis for lwdh and lwdh-treated diseases we conducted the co-module analysis from the following three aspects. we analyzed the enriched kegg pathways for either lwdh genes or lwdh-disease genes with a false discovery rate less than by fisher exact test in david. we evaluated the “closeness” between lwdh genes and lwdh-disease genes in the ppi network and used the permutation test to calculate the statistical significance of the average shortest path. here we kept the original lwdh genes and randomly selected other disease genes from networked genes in all non-redundant disease genes stored in the omim moridmap.txt; this was repeated independently times. we calculated the average phenotype similarity score determined by the cosine of vector angle of phenotypes of lwdh-diseases, and evaluated the statistical significance by comparison with randomly selected omim phenotypes for times. statistical analysis the mutual information statistics were transformed to equivalent odds ratios using monotonic transform and then subjected to standard χ test. in doing so, we used χ test to test whether the occurrence of the two herbs in the formulae is correlated with each other by generating a contingency table. experimental data from the in vitro assay were presented as mean±sd of four independent experiments with six repeat wells for each experiment. the statistical difference between treatments was determined by the t test.  dmim-extracted herb network from collaterals-related formulae dmim was used for extracting the combination rule of collaterals-related formulae. in all formulae, we found that eight of the top most frequently occurring herbs are reported to pro-angiogenesis or anti-angiogenesis activity. this provides evidence that the collaterals-related formulae may have a possible relationship with angiogenic disorders. each of the top dmim-extracted herb pairs had statistical significance. table summarized the top dmim-extracted herb pairs with the highest rankings; six of these herb pairs are novel when compared with traditionally-defined herb pairs. interestingly, we found that gan-cao, a commonly-used supplementary herb, ranked 2nd with a frequency of % in all herbal formulae. however, the position of herb pairs containing gan-cao fell to, suggesting that the dmim method was able to balance the frequency, independence, and relative distance in the herbal formulae. figure shows that we constructed a herb network by using the interactions of the top herb pairs extracted by dmim, in which we found that full or part of six classical herbal formulae are nicely recovered. the distinct modular feature is also observed from the dmim-extracted herb network. *: herb pairs extracted by dmim but not recorded in traditionally-defined herb pairs. measurement of angiogenic activities for dmim-extracted modular herbs as shown in figure the hub module or the interconnected sub-network in the dmim-extracted herb network is centered on the most frequently occurring herbs, chuan-xiong and dang-gui. we extended this hub module to all herb pairs with statistical significance and assumed that herbs presented in this module could have potential angiogenic activities. by selecting the major herbal ingredients in these herbs and taking their natural properties into consideration, the following in vitro experimental results support our hypothesis. as shown in figure 2b, in the hub module, vitexicarpin and timosaponin a-iii as major ingredients taken from two herbs with cold properties were very active on inhibiting endothelial cell proliferation. also, hydroxysafflor yellow a and astragaloside from herbs with hot properties had partial pro-angiogenesis activities when compared with the vegf treatment group. another trend was that berberine from huang-bai and tetramethylpyrazine from chuan-xiong had a biphasic effect on endothelial cells proliferation. lower doses caused an increase in cell proliferation whereas higher doses resulted in an anti-angiogenic response. overall, the experimental results validated the potential angiogenic activities of the modular herbs. measurement of dmim-extracted modular herb interactions we evaluated whether modular herbs with different properties had potential combination effects. figure shows that huvecs were treated with different compound combinations in a 6× dose matrix using the same conditions as the cell growth assay. by using the highest single compound model we found that tmp in combination with hya caused moderate synergistic pro-angiogenic activity, whereas antagonistic effects were observed when tmp was combined with ast. noticeably, tmp and tsa produced obvious antagonism at higher concentrations. we also observed that the traditional herb pairs chuan-xiong and huang-qi, and the novel herb pairs chuan-xiong and hong-hua identified by dmim exhibited clear combination effects on endothelial cell proliferation. these results suggest that the different interaction patterns of herb pairs may be associated with their different herb properties, although this association remains unclear. co-module underlying dmim-extracted herbal formula in treating different diseases dmim can recover and connect all six herbs of the liu-wei-di-huang formula. this formula is reported to potentially treat types of diseases. thus, we performed a co-module analysis to explore the potential combination mechanism of dmim-extracted herbal formula. table shows that lwdh genes as well as lwdh-disease genes are mainly enriched in cancer pathways and neuro-endocrine-immune pathways. moreover, based on the ppi network, it is noted that the average shortest path length is significantly smaller between lwdh genes and lwdh-disease genes than between lwdh genes and randomly selected disease genes. this highlights the specificity of the lwdh for treating these different diseases. in addition to this, the average phenotype similarity scores for these lwdh diseases are higher than the scores of random controls, suggesting that it might be possible to group together lwdh-treated diseases through a common molecular basis. these findings evidenced that lwdh might act on a common network target underlying these diseases, and we can capture the “one formula, different diseases” relationship from a co-module viewpoint based on multilayer networks of herb-biomolecule-disease. discussion in this work, we proposed a distance-based mutual information model, dmim, to uncover the combination rule embedded in herbal formulae, which not only uses mutual information entropy but also introduces a new factor, “between-herb-distance”, into measuring the tendency of two herbs to form an herb pair. this makes dmim suitable for deciphering herbal formulae and distinguishes it from other analytical methods such as clustering. for example, herb and herb are often used together to reduce toxicity and side-effects, while herb and herb may be clustered into a single category because of their co-location in similar organs or meridians. according to the principles of clustering, herb herb and herb may be clustered into one category, but in reality, herb and herb have no inherent relationship. moreover, the results of clustering are qualitative rather than quantitative and clustering does not show which herbs have a tendency to form herb pairs. dmim avoids these pitfalls by calculating the mutual information entropy for each of the herbs and their “between-herb-distance”. we demonstrated the reliability and usefulness of dmim by using collaterals-related herbal formulae. firstly, we showed that the dmim method retains the traditional combination rule of tcm. dmim identified many herbal pairs which have already been defined. we also found that the dmim-extracted herb network identified six classical herbal formulae from the paired herbs, which are expressed as connected sub-networks. on the other hand, dmim-extracted herb network can eliminate the disturbance from herbs such as gan-cao, a widely used “guide” herb that coordinates the actions of other herbs in formulae, though it ranks at top in herbal formulae. next, we showed that dmim has the potential to discover angiogenic herbs and non-addictive herb pairs from tcm. this study found that the most common herbs in the formulae had potential angiogenic effects. we also conducted in vitro assay to evaluate the extended hub module for chuan-xiong and dang-gui in the dmim-extracted herb network. as the ingredients of herbs are very complicated and the quality of herbs is still unstable, for simplify, this work used major ingredients of herbs to perform experiments. results showed that the herbs or herb pairs in the hub modules produced anti-angiogenic or pro-angiogenic activities, suggesting that the modular herbs may have functional dependence. in particular, we detected the novel bioactivity of two herb ingredients which inhibited angiogenesis, including vitexicarpin and timosaponin a-iii. we also validated the synergistic effects produced by dmim-extracted novel herb pairs such as chuan-xiong and hong-hua. additionally, in this study, we observed that the active compounds from the herbs with different natural properties might account for their different angiogenic responses. for instance, major ingredients from cool/cold herbs tend to produce anti-angiogenic activities whereas major ingredients from warm/hot herbs tend to exert pro-angiogenic activities. the dose-response relationship is another way to understand the characteristics of the herb’s natural properties. we found that berberine and tetramethylpyrazine can cause a pro-angiogenic effect at low dose and anti-angiogenic effects at high dose, suggesting that some herbs may cause biphasic regulation if different dosing regimens are used. for herb interaction effects we assumed that herb pairs in a formula with the same properties were more likely to lead to synergistic interactions, whereas combinations with different properties were inclined to cause antagonism. as shown in figure combination effects from herb pairs with the same properties and different properties support our assumption, but the combination of chuan-xiong and huang-qi is not the case, making it an open question whether or not herbal properties are related to herb combination behaviours. last but not least, we demonstrated that the dmim-extracted herbal formula, liu-wei-di-huang, may have its molecular basis for treating different diseases in a co-module manner. lwdh is one of the most famous tcm formulae developed during the song dynasty in china. results show that the six herbs in lwdh not only have high dmim scores, but also connected closely with common responsive genes enriched in cancer pathways and neuro-endocrine-immune pathways. interestingly, lwdh genes show a significantly close relationship with lwdh-disease genes in the ppi network, forming a co-module underlying herbal formula as well as different diseases. moreover, the lwdh-treated diseases mainly including cancer, neuro-endocrine-immune-metabolism, and cardiovascular disorders show high phenotype similarity scores and might share a overlapped molecular basis associated with the angiogenic processes as well as the imbalance of the human body. such phenomena of “one formula, different diseases” reinforce the idea that different diseases with similar phenotypes might possess internal coherence, and a group of diseases with similar mechanisms might be able to be treated by intervening their common network target, which in turn illustrates the rationality of multicomponent therapies such as herbal formulae. the novel concept of co-module throughout the multilayer networks of herb-biomolecule-diseases may promote our awareness of herbal formulae as well as multicomponent therapies. dmim is currently the first step towards building herb network from tcm herbal formula. for future work, dmim could be generalized to mine synergistic combinations made up of more than two herbs by replacing the “between-herb-distance” with a properly defined index of the distance among multiple herbs in a formula or by introducing multivariate mutual information. as this work treats formula independently, we will take the redundancies and correlations between formulae into consideration for calculating the herb distance. the dose information and natural properties of herbs are also the next step to create a multi-weight herb network. moreover, we believe that the combination mechanism of herbal formulae will be more deeply identified in a “co-module” manner and contribute to the progression of the modern tcm as well as network pharmacological studies.  dmim yields a systematic framework for scoring herb pairs and the resulted herb network can uncover some combination rules of tcm. we also provide preliminary clues that the “co-module” across multilayer networks of herb-biomolecule-disease may be responsible for the combination mechanism underlying herbal formulae. this study is the first step forward in exploring the unique theories of tcm herbal formula by network biology approaches and may also benefit the coming network pharmacology as well. competing interests the authors declare that they have no competing interests. authors' contributions sl conceived and designed the experiments, analyzed the data and wrote manuscript. bz participated in the cell experiments and writing manuscript. yw, dj and nz participated in the computational works and writing manuscript. 
from a network perspective, we established a method called distance-based mutual information model to identify useful relationships among herbs in numerous herbal formulae. we also provide the first evidence that the co-module across multilayer networks may underlie the combination mechanism of herbal formulae and demonstrate the potential of network biology approaches in the studies of tcm. to evaluate the efficacy of the dmim-extracted herb network, we conducted in vitro assays to measure the activities of strongly connected herbs and herb pairs. dmim, when used for retrieving herb pairs, achieves a good balance among the herb’s frequency, independence, and distance in herbal formulae. a herb network constructed by dmim from collaterals-related herbal formulae can not only nicely recover traditionally-defined herb pairs and formulae, but also generate novel anti-angiogenic herb ingredients as well as herb pairs with synergistic or antagonistic effects. traditional chinese medicine is characterized by the wide use of herbal formulae, which are capable of systematically treating diseases determined by interactions among various herbs. however, the combination rule of tcm herbal formulae remains a mystery due to the lack of appropriate methods. moreover, using the networked liu-wei-di-huang formula as an example, we proposed a novel concept of “co-module” across herb-biomolecule-disease multilayer networks to explore the potential combination mechanism of herbal formulae. dmim is a powerful method to identify the combination rule of herbal formulae and lead to new discoveries. dmim combines mutual information entropy and “between-herb-distance” to score herb interactions and construct herb network. based on gene and phenotype information associated with both lwdh herbs and lwdh-treated diseases, we found that lwdh-treated diseases show high phenotype similarity and identified certain “co-modules” enriched in cancer pathways and neuro-endocrine-immune pathways, which may be responsible for the action of treating different diseases by the same lwdh formula.
 traditional chinese medicine is characterized by the wide use of herbal formulae, which are capable of systematically treating diseases determined by interactions among various herbs. however, the combination rule of tcm herbal formulae remains a mystery due to the lack of appropriate methods. methods from a network perspective, we established a method called distance-based mutual information model to identify useful relationships among herbs in numerous herbal formulae. dmim combines mutual information entropy and “between-herb-distance” to score herb interactions and construct herb network. to evaluate the efficacy of the dmim-extracted herb network, we conducted in vitro assays to measure the activities of strongly connected herbs and herb pairs. moreover, using the networked liu-wei-di-huang formula as an example, we proposed a novel concept of “co-module” across herb-biomolecule-disease multilayer networks to explore the potential combination mechanism of herbal formulae.  dmim, when used for retrieving herb pairs, achieves a good balance among the herb’s frequency, independence, and distance in herbal formulae. a herb network constructed by dmim from collaterals-related herbal formulae can not only nicely recover traditionally-defined herb pairs and formulae, but also generate novel anti-angiogenic herb ingredients as well as herb pairs with synergistic or antagonistic effects. based on gene and phenotype information associated with both lwdh herbs and lwdh-treated diseases, we found that lwdh-treated diseases show high phenotype similarity and identified certain “co-modules” enriched in cancer pathways and neuro-endocrine-immune pathways, which may be responsible for the action of treating different diseases by the same lwdh formula.  dmim is a powerful method to identify the combination rule of herbal formulae and lead to new discoveries. we also provide the first evidence that the co-module across multilayer networks may underlie the combination mechanism of herbal formulae and demonstrate the potential of network biology approaches in the studies of tcm. 16– december the 21st international conference on genome informatics hangzhou, people’s republic of china 