Health and Quality of Life Outcomes The OnyCOE-t™ questionnaire: responsiveness and clinical meaningfulness of a patient-reported outcomes questionnaire for toenail onychomycosis

Lori P Potter email@example.com
Ovation Research Group
San FranciscoCAUSA

Susan D Mathias firstname.lastname@example.com
Ovation Research Group
San FranciscoCAUSA

Monika Raut email@example.com
Ortho Biotech Clinical Affairs LLC
BridgewaterNJUSA

Farid Kianifard firstname.lastname@example.com
Novartis Pharmaceuticals Corporation
East HanoverNJUSA

Amir Tavakkol email@example.com
Novartis Pharmaceuticals Corporation
East HanoverNJUSA

Health and Quality of Life Outcomes The OnyCOE-t™ questionnaire: responsiveness and clinical meaningfulness of a patient-reported outcomes questionnaire for toenail onychomycosis
10.1186/1477-7525-4-50BioMed Central Page 1 of 8 (page number not for citation purposes) Research * Corresponding author
Background: This research was conducted to confirm the validity and reliability and to assess the responsiveness and clinical meaningfulness of the OnyCOE-t ™ , a questionnaire specifically designed to measure patient-reported outcomes (PRO) associated with toenail onychomycosis.

Background

Onychomycosis is a common, chronic fungal infection of the keratinized tissue of the nail bed and nail plate that may impact patients' quality of life. Patients often experience pain and discomfort, and normal tactile functions can be impaired or lost. Toenail dystrophy can interfere with walking, standing, exercise, or proper shoe fit. Like other visible dermatologic imperfections, onychomycosis has both psychosocially and physically detrimental effects [1]. Patients report concerns about nail appearance, embarrassment, reduced self-esteem, and social withdrawal. Furthermore, patients may fear injury and spreading the infection to others [2].

To document the effect of onychomycosis on quality of life, Lubeck et al. [3] developed a patient-reported outcomes (PRO) questionnaire consisting of general and disease-specific measures (including symptom frequency and severity), which was used in a telephone study of 916 cases and 673 controls. Persons with toenail and/or fingernail onychomycosis reported statistically significantly lower quality of life scores on almost all measures, including pain, general health, social functioning, mental health, and functional limitation, compared with matched controls.

Subsequent studies have attempted to demonstrate the applicability of PRO results and their value to clinicians [4,5]. Following their initial research, Lubeck et al. conducted a validation study, in which they measured their questionnaire's responsiveness, or sensitivity to change, in a population of patients receiving usual and customary care for onychomycosis [4]. Changes in PRO scores were compared between patients who improved clinically and those who did not improve, based on the physician's subjective determination of clinical status at each visit. While onychomycosis-specific scales were responsive to clinical improvement, while no statistically significant changes were reported in a clinically stable group of patients [4].

Other studies of onychomycosis have had limited success linking PRO results to clinical status in onychomycosis. In a multinational study, Drake et al. [5] divided 532 toenail onychomycosis patients into two groups, based on the extent of nail involvement, and compared their quality of life scores. Patients with whole-nail involvement reported significantly lower quality of life scores than those with half-nail involvement. However, this study could not measure the responsiveness of PRO to changes in clinical status of patients.

In a telephone study of clinical trial participants, Drake et al. [6] attempted to correlate the quality of life scores with a patient-reported global severity rating. However, the study failed to show a clear relationship between quality of life factors (such as pain, discomfort, or psychosocial problems) and the overall severity rating, suggesting that severity and quality of life may be two distinct, non-overlapping measures.

The Drake studies illustrate some of the problems associated with clinical interpretation of PRO measures. Comparing PRO results to objective clinical assessment will provide a context for understanding the impairment in PRO associated with onychomycosis. Responsiveness and clinical meaningfulness are psychometric properties, which depend on clinical information, ideally objective information, such as a laboratory test result or quantifiable improvement. Moreover, there is a lack of prospective trial data in prior studies to demonstrate the impact of PRO on objective clinical measures associated with response to treatment of onychomycosis.

Thus, the objective of this current study was to fully validate the newly developed toenail-specific PRO questionnaire, the OnyCOE-t™, and in particular, to use objective clinical measures to assess its responsiveness and clinical meaningfulness, as part of a prospective trial of patients undergoing treatment for onychomycosis.

Methods

Study design and participants

Data were collected during the Improving Results in Onychomycosis -Concomitant Terbinafine (Lamisil ® ) and Debridement (IRON-CLAD ® ) trial, a prospective, openlabel, randomized, multi-center study designed to evaluate the efficacy and safety of terbinafine. All eligible patients (N = 504) were randomized to one of two treatment groups; both groups received 12 weeks of terbinafine therapy, but only one group received aggressive debridement of the target toenail in addition to oral treatment. A randomization list was produced using a validated system that automates the random assignment of treatment groups to randomization numbers in a 1:1 ratio.

The study protocol was approved by a local institutional review board at each center and was carried out in accordance with Good Clinical Practice guidelines and the Declaration of Helsinki. Written informed consent was obtained from each subject prior to enrollment. Patients were aware of the reason for debridement, and the procedure was explained to them prior to obtaining consent. Debridement was performed at baseline, and weeks 6, 12, and 24 [ Table 1].

The IRON-CLAD ® study was designed to be inclusive (i.e., representative of onychomycosis patients who typically visit a podiatry practice). However, subjects with pre-existing liver disease, gastrointestinal malabsorption, neph-ropathy or blood disorders, liver or kidney dysfunction, and those with HIV or immunocompromized were excluded.

Study medications were provided to participants at no charge. Patient compensation was nominal and included the actual cost of transportation, parking, or other small expenses associated with participating in the study. No other compensation actual or implied was provided.

Patients self-administered the OnyCOE-t™ questionnaire at the time of enrollment (baseline) and at every scheduled visit for the duration of the study (Week 6, Week 12, Week 24, and Week 48), or upon early discontinuation from the study.

Patient-reported outcome measures

The questionnaire was adapted from an existing validated instrument [3,4] that had been used to study onychomycosis of both the toenails and fingernails. It was revised to include only toenail-specific items; the new version of the questionnaire (the OnyCOE-t™ questionnaire) is composed of 33 items, with 6 multi-item scales and 1 singleitem scale:

• A 7-item Toenail Symptom assessment, which comprises both Symptom Frequency (5 response categories: 1 = never, 5 = very often) and Symptom Bothersomeness scales (5 response categories: 1 = not at all bothered, 5 = extremely bothered) For example, patients were asked: "During the past 4 weeks, how much of a problem were the following because of your nail fungal condition: Being embarrassed by the appearance of your nails?" or "Discomfort of pain from wearing shoes?" The response options ranged from 1 ("Very much a problem") to 4 ("Not a problem").

All items in the OnyCOE-t™ questionnaire were transformed to a 0 to 100 scale and scored so higher scores indicated better functioning. Each scale score was calculated as an average of all non-missing items if at least half of the items making up the scale were non-missing. Validation analyses were conducted to confirm that the revised questionnaire is valid and reliable and to assess responsiveness and calculate a minimally clinical important difference.

Clinical outcomes

Clinical outcomes were based on mycology testing performed throughout the study (Culture and KOH results) and on examination of target toenail, specifically percent of the target nail judged clear of infection as well as the amount of new target nail growth observed.

Clinical assessments were performed by a well-trained, qualified person, other than the investigator; that person (nurse/study coordinator) remained blinded to debridement and used an assessment tool to avoid subjective evaluation. For the clinical assessment, the target nail was overlaid with a transparent film. The entire nail plate and the involved nail areas were outlined. The outline was transferred to a template fitted to the approximate size and shape of the nail. The template was divided into eight segments, each representing 12.5% of the nail. At each assessment, the number of segments involved (i.e., infected) was recorded. A segment was counted as infected only if ≥ 50% of the area of the segment was affected. The amount of clearing was determined by multiplying the number of infected segments by 12.5% and subtracting that percentage from 100%. For each patient, this process was performed by the same person at every visit. Cure was designated in three ways. "Complete Cure" was defined as a negative culture and negative KOH, plus 100% clearing of the target nail. "Clinical Cure" was defined as ≥ 87.5% clearing of the target nail. "Mycological Cure" was defined as negative culture plus negative KOH. Cure status was determined at each clinic visit.

Improvement ("Improved") was defined as a positive change in the amount of clearing from baseline to end of study. "Not Improved" was defined as no positive change.

In addition, a three-value categorical outcome of Improvement ("Improved", "Stable", or "Worsened") was used to compute the responsiveness of the questionnaire. Patients in the Stable group showed no change in the amount of clearing, and patients who Worsened showed negative change, or decrease in the amount of clearing.

Clinical assessment also included measuring new, clear nail growth by placing a cut at the proximal nail fold and measuring nail growth from that point onward. "Clinical Success" was determined by = 5 mm of clear new nail growth. Based on the study protocol, nail growth <5 mm at Week 48 was considered a therapeutic failure (i.e., not a Clinical Success).

Confirmation of validity and reliability

Construct validity is assessed by examining the relationship between scales or items. Validity is demonstrated when scales or items that are thought to measure the same construct have high correlation coefficients; conversely, items assumed to measure different, unrelated constructs should have low correlation coefficients.

Known-groups validity evaluates the ability of a questionnaire to discriminate between groups by examining scores from subjects known to be different. In this study, the known-groups validity was evaluated using demographic and clinical criteria.

Internal consistency reliability measures the extent to which items within each scale correlate with each other to form a multi-item scale.

Responsiveness

Responsiveness gauges the ability of a PRO measure to respond appropriately when a patient's clinical state changes. The analysis of responsiveness included patients who completed the OnyCOE-t™ questionnaire at baseline and at the end of the study and who had measures of clinical efficacy (clinical assessment of target nail clearing and re-growth). Change scores were computed for each scale by subtracting baseline scores from scores at the end of study (Week 48). Responsiveness was demonstrated when subjects who showed clinical improvement had greater, positive PRO change scores.

Clinical meaningfulness

Clinical meaningfulness was analyzed by estimating the minimally clinical important difference (MCID) under different assumptions of nail clearing and new nail growth. The MCID was calculated based on differences of 12.5% in the degree of toenail involvement, which corresponded to the measurement method dictated by the protocol to evaluate the percent clearing of mycotic involvement. The MCID was also calculated based on a 25% difference in the degree of toenail involvement; increments of 25% were used in analysis of trial data to categorize severity of mycotic involvement at baseline. In addition to nail clearing, the MCID estimation was performed based on the Clinical Success criteria, i.e., ≥ 5 mm of clear new nail growth of the target nail.

Statistical methods

Variable clustering was performed to evaluate the underlying structure of the theoretical OnyCOE-t™ scales and confirmed the existence of six multi-item scales [7]. Construct validity was limited by having no other scales to compare with the OnyCOE-t™ to establish external (criterion) validity. To test convergent validity, we generated Pearson's correlation coefficients between all items and scales, using pooled data.

Known-groups validity was assessed using a Student's ttest to compare change in patients who were cured (under all three definitions) versus those who were not; known groups was assessed using demographic characteristics as well.

Internal consistency reliability, a measure of the extent to which items within each scale correlate with each other to form a multi-item scale, was examined by computing Cronbach's alpha coefficient. A Cronbach's alpha coefficient of .70 or greater indicates good internal consistency of a multi-item scale [8].

In analyses of responsiveness, change scores were tested against zero using the one-sample t-test. Three groups of patients resulted from the categorical variable for Improvement; group scores were used to calculate Guyatt's statistic, the ratio of the mean change score for each group divided by the standard deviation for the Stable group. A statistic of 1.00 or greater (or -1.00 or less when improvement was denoted by a negative change score) was considered indicative of a measure highly responsive to change [9,10]. In addition, the difference in PRO scores between the Stable group and the Improved group was evaluated using the two-sample t-test.

For the estimation of the MCID, an analysis of variance (ANOVA) model for each OnyCOE-t™ questionnaire scale was fit using target toenail percent clearing or the amount of new growth of the target toenail as the single predictor variable. The least squares means estimate for each Ony-COE-t™ scale score was evaluated for every 12.5% or 25% difference in toenail clearing, and for clinical success as indicated by new toenail growth ≥ 5 mm.

For statistically significant comparisons (based on the pvalues from the ANOVA model), the average difference in mean PRO scores between adjacent categories was used to estimate the MCID for each scale. The MCID calculation based on 12.5% difference included eight categories: 12.5%, 25%, 37.5% 50%, 62.5%, 75%, 87.5%, and 100%; the 25% difference included four categories: 25%, 50%, 75%, and 100%. However, when using the amount of new growth to estimate the MCID for each scale, we used the difference between the two categories (<5 mm, ≥ 5 mm).

All statistical analyses were generated using SAS Software, Version 8.2 or higher of the SAS System for Windows. No imputation (e.g., last-observation-carried-forward) was performed to accommodate missing assessments; analyses included only available data.

Results

Patient demographics

All patients were between 18 and 75 years of age, with a mean age of 48.5 years (terbinafine only) and 49.7 years (terbinafine plus debridement). The majority of patients were Caucasian (63.5%), and approximately two-thirds of patients were male (61.3%). Treatment groups were balanced with respect to patient characteristics [ Table 1].

Validity and reliability

Strong correlations exist between items measuring toenail symptom frequency, and bothersomeness. All the problem scales and items -Physical Activities, Physical Appearance, and Overall Problem -are moderately to highly correlated. Items expected to correlate highly, for instance those measuring constructs of embarrassment about appearance and social stigma, did. For instance, the Stigma scale and individual items correlated highly with both Problems with Activities and Problems with Appear-ance. Treatment Satisfaction correlates most highly with Symptom Frequency and Symptom Bothersomenesss.

We generally confirmed previous findings, demonstrating lower scores for females and for younger patients. Scale scores for cured versus uncured groups were significantly different, based on mycological cure. For instance, in the cured group (terbinafine plus debridement), the mean Symptom Frequency score was 84.2 vs 68.0 in the uncured group (p < 0.001); Overall Problems scores were 83.4 vs 56.4 (p < 0.001).

All scales demonstrated a high degree of internal consistency, as indicated by alpha coefficients > .70 (.84 to .91).

Responsiveness

Patients in both groups (Improved and Not Improved) reported positive PRO change scores, as measured by change from baseline at Week 48 [[ Table 2]. The Improved group demonstrated very good responsiveness, as shown by positive, statistically significant change in all measures. In the Not Improved group, Stigma and Treatment Satisfaction scores demonstrated no statistically significant change; all other PRO scores in the Not Improved group showed significant change, but gains were much smaller than those observed in the Improved group.

Comparison of patients who improved to those who remained stable using Guyatt's statistic indicated that Treatment Satisfaction, Symptom Frequency, Overall Problem and Appearance Problem scales are all highly responsive, while all other scales were moderately responsive to clinical change [ Table 3]. Moreover, results of twosample t-tests showed statistically significant differences (p < .0001 to .0176) between the Improved group and the Stable group on all PRO scores except Symptom Bothersomeness (p = .3384) (data not shown).

Clinical meaningfulness

Using the 12.5% definition, the MCID estimation for individual scales ranged from about 5.5 to 8 points, with the exception of the single item, Overall Problem, which had an MCID of about 11 points. Differences in the Ony- COE-t™ questionnaire scales at adjacent levels of improvement were not significant at all levels. The overall MCID using the 12.5% difference in clearing was 7.30 [ Table 4].

Under the 25% difference scenario, most of the individual MCID estimates were consistent (within a point) of the estimated MCID at 12.5%; the exceptions were Symptom Frequency and Treatment Satisfaction. Using 25% clearing to calculate MCID, all adjacent comparisons were significant. The overall MCID was 8.45 [ Table 4].

The MCID assessment was calculated based on the clinical success criteria, i.e., ≥ 5 mm of clear new nail growth of the target nail [ Table 4]. The Overall MCID for new nail growth was estimated as 16.63.

Discussion

The goal of this study was to confirm the psychometric properties of the OnyCOE-t™ questionnaire as a tool for measuring PRO results specifically related to toenail onychomycosis, and to extend the prior research by evaluating responsiveness against an objective clinical measure and to calculate a measure of clinical meaningfulness [11]. Thus, this study focuses on presenting results of responsiveness and clinical meaningfulness, which interpreted the OnyCOE-t™ scores in clinically relevant terms.  Results of validity and reliability analyses confirmed earlier research [4]. Additional analyses conducted showed the OnyCOE-t™ responded well to significant clinical changes in onychomycosis patients undergoing treatment.

It is important to note that clinical assessments were confined to the target nail, while PRO measures captured the patient's perception of the effects of disease and treatment on all nails affected. In a real-world scenario, this research artifact would not be present, and a clinician would be able to gauge a patient's overall clinical status as well as measure the patient's perception of his or her entire condition and treatment.

This validation study was conducted using data from a clinical trial in which both treatment groups received the same active medication, but only one treatment group received debridement in addition to medication. As expected, both groups improved and, clinically speaking, differences between the groups were small. As a result, the interpretation of results was challenging. Measuring responsiveness requires comparing a group expected to change with a group expected to remain stable [12]. In the absence of a clinical measure, the Minimally Important Difference (MID) can be estimated as some proportion of the standard deviation; a reasonable MID might represent one-quarter to one-third of a standard deviation for the score in question. In the context of baseline PRO scores, which had standard deviations of approximately 22 to 33 points, the overall MCID estimates for nail clearing represented amounts of change that generally fell into that range. The MCID for new nail growth fell outside that range -a MCID of 16.63 points represented one-half to three-quarters of a standard deviation of the baseline PRO scores.

The MCID can help interpret PRO results for the treating provider by translating an objectively understood clinical assessment, such as the percent of nail clearing, into a number of points on a PRO scale. For a clinician, this means that an average gain of about 8 to 9 points in PRO can be expected with a 25% improvement in nail clearing.

Future studies of the responsiveness and clinical meaningfulness of the OnyCOE-t™ questionnaire could address the limitations of the population. Administering this questionnaire to groups of patients expected to have different clinical outcomes (e.g., active versus placebo studies) might allow for sharper distinctions between Improved and Not Improved groups, and for a larger Stable group. Results on both measures of responsiveness would be more robust.

Both responsiveness and clinical meaningfulness provide clinicians with familiar frames of reference for understanding and interpreting PRO scores. In a broader context, the OnyCOE-t™ questionnaire will provide a tool, not only for researchers to assess PRO results from clinical trials, but also for managed care organizations to evaluate PRO measures of patients receiving treatment for onychomycosis. This study fills a gap in the literature by presenting the first validated instrument specific to toenail onychomycosis, and by demonstrating the relationship of the OnyCOE-t™ scales to clinical measures.

Conclusion

The OnyCOE-t™ is a unique, toenail-specific PRO questionnaire that is responsive to clinical change and can be used with confidence in future studies of toenail onychomycosis.

much a problem, 4 = not a problem) • A 7-item Stigma scale (5 response categories: 0 = does not describe me at all, 4 = describes me very well) • A 3-item Treatment Satisfaction scale (5 response categories: 1 = very satisfied, 5 very dissatisfied)

Table 1 :
1Patient CharacteristicsTerbinafine Only
Terbinafine + Debridement
N = 258
N = 246

Table 2 :
2Mean change in scores from baseline to week 48: Responsiveness based on clinical improvement (clearing of the target nail)Clinically improved N = 400
Clinically not improved N = 52

Symptom Frequency
34.5 (<.0001)
21.2 (<.0001)
Symptom Bothersomeness
24.1 (<.0001)
14.5 (.0022)
Physical Activities Problems
30.1 (<.0001)
11.3 (.0100)
Appearance Problems
34.4 (<.0001)
13.6 (.0013)
Overall Problem
44.0 (<.0001)
24.5 (<.0001)
Stigma
15.4 (<.0001)
5.1 (.1416)
Treatment Satisfaction
46.1 (<.0001)
1.7 (.8868)

(p-values are from the one-sample t-test)

Table 4 :
4Minimal Clinically Important DifferenceAverage Difference Between Adjacent PRO Scores

Scale
12.5% Difference in nail clearing*
25% Difference in nail clearing*
≥ 5 mm new nail growth  †

Symptom Frequency
6.48
9.12
17.28
Symptom Bothersomeness
5.95
5.84
11.83
Physical Activities Problems
7.54
8.32
17.69
Appearance Problems
8.04
8.69
18.51
Overall Problem
11.19
11.77
25.32
Stigma
5.44
5.21
9.41
Treatment Satisfaction
7.42
9.11
16.37
Overall
7.30
8.45
16.63

* Based on comparisons that are significant at the .05 level
 † Based on comparisons that are significant at the .0001 level

Table 3 :
3Guyatt's statistic and mean change in scalesScale
Worsened N = 12
Stable N = 37
Improved N = 400

Symptom Frequency
Mean Change
21.6
21.0
34.5
Guyatt's Statistic
.82
.80
1.31
Symptom Bothersomeness
Mean Change
1.5
18.9
24.1
Guyatt's Statistic
.05
.64
.81
Physical Activities Problems
Mean Change
18.3
9.0
30.1
Guyatt's Statistic
.55
.27
.91
Appearance Problems
Mean Change
16.3
12.7
34.4
Guyatt's Statistic
.53
.41
1.11
Overall Problem
Mean Change
22.2
25.2
44.0
Guyatt's Statistic
.57
.65
1.13
Stigma
Mean Change
4.7
5.3
15.4
Guyatt's Statistic
.18
.20
.58
Treatment Satisfaction
Mean Change
16.7
-2.1
46.1
Guyatt's Statistic
.62
-.08
1.72

Clinical meaningfulness is a way of translating a difference in a PRO measure into a difference in a clinical measure. In this study, target nail clearing and new nail growth provided a clinical basis for estimating the MCID for each scale, as well as for generating an overall MCID for the PRO questionnaire.In the estimation of the MCID, the choice of a clinical measure is important, because a measure that captures too large a change in a patient's clinical status can obscure the PRO score's ability to reflect small but measurable changes in status. In this study, two measures of incremental improvement, based on target nail clearing, were evaluated.Results for the smaller level of clinical change (12.5%) corresponded to the smallest average amount of change in the PRO scales (7.30); however, because the clinical differences were probably less discernible to patients (corresponding to one-eighth of a patient's target nail), not all of the adjacent comparisons were statistically significant and therefore not all differences were included in the estimation of the MCID. Estimation using 25% difference in nail clearing was based on statistically significant differences between all adjacent increments of clinical change. Nevertheless, results under both scenarios were consistent with respect to all scores except Symptom Frequency and Treatment Satisfaction.In addition, a Clinical Success measure involving only two categories (Success or Failure, based on new nail growth of 5 mm or more) was used to estimate the MCID. Clinical Success encompassed a large amount of clinical improvement, and corresponded to a much larger MCID than percent clearing (The MCID for Clinical Success was 16.63, almost twice as large as the MCID for a 25% difference in nail clearing). The MCID is a way to quantify how sensitive a measure is to clinical change (i.e., how much does a scale need to change to correspond to a change in clinical status). For instance, based all three estimation methods, Stigma and Symptom Bothersomeness were the most sensitive measures: a 5-to 6-point gain in the scale corresponded to an incremental improvement in nail clearing (based on either 12.5% or 25% nail clearing improvement). Conversely, the Overall Problem measure reflected clinical change only after a gain of over 11 points, indicating a less sensitive scale.How-
ever, based on our definition of improvement, nearly all
patients (91%) improved by the end of the study. Even so,
Treatment Satisfaction and Stigma change scores were sig-
nificantly higher only among patients who demonstrated
clinical improvement by the end of the study.

Even for other PRO measures, where change was signifi-
cant in both the Improved and Not Improved groups,
comparing the groups based on their respective amounts
of change is instructive. For instance, the average change
on the Physical Activities Problems scale in the Improved
group was a 30-point gain, while the average change in the
Not Improved group was only about a third as much, or
11 points.

Interpreting Guyatt's statistic was equally challenging
because the Stable and Worsened groups were so small.
Nevertheless, in the Improved group, most measures were
responsive or highly responsive, while the Stable group
showed no strong responsive measures.

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AcknowledgementsThe authors thank Jennifer Sung, MS, PharmD, Shibani Mahajan, MPH, and Mohamed Omar, PhD of Novartis Pharmaceuticals Corporation and Kimberly Miller, PhD of Ovation Research Group for their help in the preparation of this manuscript.The validation study design, analysis, interpretation of results, the writing of the manuscript represent the joint collaboration of all authors of this study, which was funded solely by Novartis Pharmaceuticals Corporation, East Hanover, NJ, USA. In addition, Amir Tavakkol and Farid Kianifard (Novartis Pharmaceuticals Corporation) and Monika Raut (employed by Novartis Pharmaceuticals Corporation through the time of data analysis) supervised the design and collection of data in the IRON-CLAD trial, conducted under funding by Novartis Pharmaceuticals Corporation. Ovation Research Group provided no additional funding for this study. The decision to submit this manuscript for publication was subject to the approval of Novartis Pharmaceuticals and all authors.Competing interestsFinancial support for this project was provided by Novartis Pharmaceuticals Corporation, East Hanover, NJ, USA. The IRON-CLAD ® trial was conducted, monitored, and data were collected by Novartis Pharmaceuticals Corp. The analysis for this study was conducted by Ovation Research Group.Amir Tavakkol and Farid Kianifard are employees of Novartis Pharmaceuticals Corporation. Monika Raut is an employee of Johnson & Johnson, but was employed by Novartis Pharmaceuticals Corporation when this study was conducted. Lori P. Potter and Susan D. Mathias are employees of Ovation Research Group, a consulting firm, which received financial support for undertaking these analyses.Authors' contributionsLPP supervised the design of the validation study, performed the statistical analysis, and drafted the manuscript. SDM assisted in the design of the validation study, participated in the design of the statistical analysis, and helped to draft the manuscript. MR participated in the design and coordination of the validation study and helped to draft the manuscript. FK participated in the design of the statistical analysis and assisted in interpreting results. He also designed the statistical plan and analysis of IRON-CLAD ® . AT designed the IRON-CLAD ® trial and supervised its analysis, provided advice on the design of the validation analysis, and helped to draft the manuscript. All authors read and approved the final manuscript.
The effect of toenail onychomycosis on patient quality of life. B E Elewski, Int J Dermatol. 3610Elewski BE: The effect of toenail onychomycosis on patient quality of life. Int J Dermatol 1997, 36(10):754-756.

Onychomycosis is more than a cosmetic problem. R K Scher, Br J Dermatol. 13015SupplScher RK: Onychomycosis is more than a cosmetic problem. Br J Dermatol 1994, 130 Suppl 43:15.

Quality of life of persons with onychomycosis. D P Lubeck, D L Patrick, P Mcnulty, S K Fifer, J Birnbaum, Qual Life Res. 25Lubeck DP, Patrick DL, McNulty P, Fifer SK, Birnbaum J: Quality of life of persons with onychomycosis. Qual Life Res 1993, 2(5):341-348.

A healthrelated quality of life measure for use in patients with onychomycosis: a validation study. D P Lubeck, D Gause, J R Schein, L E Prebil, L P Potter, Qual Life Res. 81-2Lubeck DP, Gause D, Schein JR, Prebil LE, Potter LP: A health- related quality of life measure for use in patients with ony- chomycosis: a validation study. Qual Life Res 1999, 8(1- 2):121-129.

The impact of onychomycosis on quality of life: development of an international onychomycosis-specific questionnaire to measure patient quality of life. L A Drake, D L Patrick, P Fleckman, J Andr, R Baran, E Haneke, C Sapede, A Tosti, J Am Acad Dermatol. 412Pt 1Drake LA, Patrick DL, Fleckman P, Andr J, Baran R, Haneke E, Sapede C, Tosti A: The impact of onychomycosis on quality of life: development of an international onychomycosis-specific questionnaire to measure patient quality of life. J Am Acad Der- matol 1999, 41(2 Pt 1):189-196.

Effect of onychomycosis on quality of life. L A Drake, R K Scher, E B Smith, G A Faich, S L Smith, J J Hong, M J Stiller, J Am Acad Dermatol. 385Pt 1Drake LA, Scher RK, Smith EB, Faich GA, Smith SL, Hong JJ, Stiller MJ: Effect of onychomycosis on quality of life. J Am Acad Dermatol 1998, 38(5 Pt 1):702-704.

Exploratory Variable Clustering for Integrating Analyses. D J Pasta, L P Potter, San Francisco, CAPasta DJ, Potter LP: Exploratory Variable Clustering for Inte- grating Analyses: San Francisco, CA. ; 1996:297-301.

Coefficient alpha and the internal structure of tests. L J Cronbach, Psychometrika. 16Cronbach LJ: Coefficient alpha and the internal structure of tests. Volume 16. Psychometrika; 1951:297-334.

Measuring disease-specific quality of life in clinical trials. G H Guyatt, C Bombardier, P X Tugwell, Cmaj. 1348Guyatt GH, Bombardier C, Tugwell PX: Measuring disease-spe- cific quality of life in clinical trials. Cmaj 1986, 134(8):889-895.

Measuring change over time: assessing the usefulness of evaluative instruments. G Guyatt, S Walter, G Norman, J Chronic Dis. 402Guyatt G, Walter S, Norman G: Measuring change over time: assessing the usefulness of evaluative instruments. J Chronic Dis 1987, 40(2):171-178.

The OnyCOE-t Questionnaire: Reliability and Validity of a Patient Reported Outcomes Questionnaire. L P Potter, S D Mathias, Potter LP, Mathias SD: The OnyCOE-t Questionnaire: Reliabil- ity and Validity of a Patient Reported Outcomes Question- naire: October 19-22;

Assessing health status and quality-of-life instruments: attributes and review criteria. Qual Life Res. 113Assessing health status and quality-of-life instruments: attributes and review criteria. Qual Life Res 2002, 11(3):193-205.


On deducing causality in metabolic networks

Chiara Bodei email@example.com
Dipartimento di Informatica
Università di Pisa, I-56127PisaItaly

Andrea Bracciali firstname.lastname@example.com
Dipartimento di Informatica
Università di Pisa, I-56127PisaItaly

Davide Chiarugi firstname.lastname@example.com
Dipartimento di Scienze Matematiche e Informatiche
Università di Siena
I-53100SienaItaly

BMC Bioinformatics

On deducing causality in metabolic networks
10.1186/1471-2105-9-S4-S8BioMed Central Page 1 of 10 (page number not for citation purposes) Research * Corresponding author
Background: Metabolic networks present a complex interconnected structure, whose understanding is in general a non-trivial task. Several formal approaches have been developed to support the investigation of such networks. One of the relevant problems in this context is the comprehension of causality dependencies amongst the molecules involved in the metabolic process.Results:We apply techniques from formal methods and computational logic to develop an abstract qualitative model of metabolic networks in order to determine possible causal dependencies. Keeping in mind both expressiveness and ease of use, we aimed at providing: i) a minimal notation to represent causality in biochemical interactions, and ii) an automated tool allowing human experts to easily vary conditions of in silico experiments. We exploit a reading of chemical reactions in terms of logical implications: starting from a description of a metabolic network in terms of reaction rules and initial conditions, chains of reactions, causally depending one from the another, can be automatically deduced. Both the components of the initial state and the clauses ruling reactions can be easily varied and a new trial of the experiment started, according to a what-if investigation strategy. Our approach aims at exploiting computational logic as a formal modeling framework, amongst the several available, that is naturally close to human reasoning. It directly leads to executable implementations and may support, in perspective, various reasoning schemata. Indeed, our abstractions are supported by a computational counterpart, based on a Prolog implementation, which allows for a representation language closely correspondent to the adopted chemical abstract notation. The proposed approach has been validated by results regarding gene knock-out and essentiality for a model of the metabolic network of Escherichia coli K12, which show a relevant coherence with available wet-lab experimental data.Conclusions:Starting from the presented work, our goal is to provide an effective analysis toolkit, supported by an efficient full-fledged computational counterpart, with the aim of fruitfully driving in vitro experiments by effectively pruning non promising directions.

Background

Understanding the relationships amongst the elements involved in biologic interaction networks, such as the functioning of cellular metabolism, is a relevant problem in Systems Biology. In the words of [1], "diagrams of interconnections represent a sort of static roadmaps, but what we really seek to know are the traffic patterns, why such patterns emerge, and how we can control them". Having a formal description of the interconnections and a methodology to perform software simulation on how these patterns are, should help in orientating in vitro experimentation. Under this regard, causality can play an important role in finding chains of reactions that connect the parts of the system of interest, e.g. for determining causal correlations among molecules that are not apparently correlated. In general, the proposed models of complex systems code a lot of information and determining possible correlations and causal dependencies may be not straightforward or computationally expensive.

We focus here on metabolic networks, i.e. the set of the cellular biochemical pathways involved in energy management and in the synthesis of structural components. Biochemical pathways are typically composed of chains of enzymatically catalyzed chemical reactions and are interconnected in a complex way. Starting from the composition of local, well understood behaviour, the study of the overall emerging behaviour of metabolic networks appears difficult.

We apply techniques from formal methods and from computational logic in order to develop an abstract qualitative model of metabolic networks, focussing on causality. Keeping in mind both expressiveness and ease of use, we aimed at providing: i) a minimal notation to represent causality in biochemical interactions, and ii) an automated tool allowing the human expert to easily vary conditions of the in silico experiment. We introduce a simple and skeletal notation, inspired by biochemical reactions, to emphasize the causality aspects we are concerned with. The choice of relying on computational logic, which "provides a straightforward and intuitive representation of human reasoning" [2], has appeared particularly suitable in the multidisciplinary context of our work. On the one hand, it should be palatable to biologists, since very close to the biochemical intuition. On the other hand, it has a direct computational counterpart, which computer scientists can build upon in order to devise the needed analysis tool.

In our notation, biochemical reactions are given an abstract representation: we only record which are the relations between the source and the target elements of each single reaction, e.g. between two molecules M and N and the molecule P they produce. In turn, P can become a source molecule in another reaction and so on and so forth. In other words, we abstract away from quantities, stoichiometric proportions, kinetical or thermodynamics parameters that are involved in the production of P. Noticeably, we also abstract from the actual dynamics of reactions. Intuitively speaking, we project reactions on a "flat" temporal scale so that the availability of M and N is never spoiled after the production of P, and other metabolites can be caused by M and N. This is also an abstraction over quantities, since "infinite copies" of M and N result always available. Because of the abstraction, the reaction leading to P actually represents the possibility for P to be generated, or caused, in vivo, by the presence of M and N. Indeed, the model gives an over-approximation of the set of the actual pathways, possibly including some pathways that could be actually prevented, for instance, by the lack of a suitable quantity of reactants or by an inadequate temperature. The payoff of the abstraction adopted is in terms of expressiveness of the language and effectiveness of its computational counterpart. Abstracting from quantitative issues may prevent reasoning about some of the dynamical features of (bio)chemical objects. However, it makes possible to take into consideration some aspects of those systems (typically large biochemical networks) whose kinetical and thermodynamical parameters are scarcely known.

Chains of causal reactions can be, step by step, automatically deduced. To this aim, we exploit an analogy between logical implications and chemical reactions, by interpreting the reaction of M and N that produces P as a logical clause stating that M and N imply P. Our method is supported by a computational logic counterpart, based on a Prolog implementation of a bottom-up semantics. This allows us to compute the set of all the metabolites that can be produced as consequences of a given set of rules and starting from a set of initially available metabolites. This is step-wise determined by repeatedly adding the metabolites that can be immediately caused by the application of the rules to the set of the so-far produced metabolites. We then relate the computational construction with the original model and prove convergence properties of the process.

Despite the abstract working hypotheses adopted, our framework has revealed sufficient to provide meaningful approximations of the possible chains of reactions during experiments. Moreover, the approach facilitates thinking and revising the biological model itself, by making easy to vary both the components of the initial state and the clauses that rule reactions.

The proposed approach can serve as a sort of "what-if" analysis, repeatedly exploring different scenarios, each one derived from a different set of working hypotheses.

Our tool allows us to rapidly evaluate the impact of changes in the hypotheses on a particular observable outcome. Thus, we obtain an interactive and effective analysis, that can be used to differentiate the most promising causal relations deduced, which deserve to be tested in vitro, from those that instead can be pruned.

We have validated our approach by studying the robustness of the metabolic network of E. coli K12. Selected genes have been knocked-out by disabling the rules regarding the corresponding encoded enzymes. Results are coherent with the actual biological behaviour, observed in vitro and reported in [3] and in the "Geno Base" (http://ecoli.aist-nara.ac.jp/), a database entirely dedicated to E. coli K-12.

This paper is organized as follows. Next, we will discuss related work and then present our formal framework, illustrating how biochemical processes can be represented inside it. Results about experiments with the metabolic network of the E. coli K-12 metabolic genotype follow. Conclusions are followed by a section Methods, in which we report on the techniques used.

Related work and comparison

Our work can be included in the recent research trend which exploits well established theories and techniques from formal methods in order to support the interpretation of the big amount of the raw biological data now available. By using logic, we slightly diverge from the line of research in which biological modelling is inspired by the use of concurrent models. Concurrency theory offers a wide choice of models naturally expressing causality, that is one of its essential notions. Nevertheless, causality is a natural notion also in the logic framework. Concurrent models are focussed on the description of the dynamic behaviour of whole systems. Considering these aspects can be computationally demanding. This has led us to the choice of an even more abstract model, where -as mentioned above -the notion of time is abstracted away. An abstraction similar to ours can be performed a posteriori on a concurrent model, for instance by resorting to static analysis techniques, which offer static approximations of the dynamic behaviour. Usually, static techniques extract information by systematically inspecting the specification of the dynamic behaviour of systems. In our approach instead, we want to infer information by directly inspecting the set of reactions, modulo the abstractions we discussed above, thus skipping the specification of the chemical dynamics. Resorting to static techniques represents a typical way to drastically reduce the computational cost due to the study of all the possible dynamic evolutions of a system. The price to pay amounts to a loss of precision, since they usually provide over-approximations of the behaviour.

Among the several formalisms developed in concurrency theory and applicable to Systems Biology, we recall below the most relevant for our purposes. Petri Nets [4] offer a way to graphically represent the structure of distributed systems. They have been successfully applied to the modelling of metabolic pathways and simple genetic networks (see e.g. [5,6] to cite only a few). They model pathways and networks in terms of their dynamic evolutions.

Process calculi describe interactions and communications between independent agents or processes. The underlying idea is that a biological system can be seen as concurrent systems. In particular, π-calculus [7] and Ambient Calculus [8] have been transferred from theoretical computer science setting to the biology setting, leading to suitably extended biological versions of them, such as the Biochemical stochastic π-calculus [9,10] and BioAmbients [11]. Also a version of CCS, RCCS [12] has been introduced to address biological issues. Other calculi have been instead specifically defined for biological modelling, such as κ-calculus [13], Brane calculi [14] and Beta Binders [15]. Chemistry has been already invoked explicitly in the process algebraic context many years before the coming of systems biology. In [16], an abstract machine based on the chemical metaphor is introduced: states are chemical solutions where floating molecules can interact according to reaction rules. Rules specify how to produce new molecules from old ones.

Closer to our approach is the work presented in [17], where the authors apply a causal semantics of the π-calculus in order to describe biochemical processes. The process computations that can be obtained quite accurately capture and reflect the behaviour of biological systems and causality has a key role in enhancing precision in such simulations. Our starting point is quite similar, but in our model the description of biological systems is given in terms of molecular entities and reaction rules that implicitly code the causal relationships, and hence the possible pathways. The causal semantics in [17] is based on an enhanced form of transition systems [18], that makes it possible to capture truly concurrent aspects like causality in an interleaving setting, like the process algebraic one. There are also other proposals, introduced with the same aim, see for instance the distributed transition systems in [19].

It is interesting to observe that our results could be comparable with the one obtained by using a quite efficient static technique like Control Flow Analysis (CFA) [20,21], applied to the π-calculus. In these settings, a reaction between M and N that produces P can be abstractly modelled as the synchronization of the process M and N on a shared channel c, with a process P as a continuation. Notice that in this case the full expressiveness of the π-cal-culus and, in particular, name-passing seems not to be needed. In its simplest form, CFA considers as effective all the communications that might occur through given shared channels, disregarding their actual viability, due for instance to synchronization dynamics. In modelling reactions in such a way, also CFA would not consider the possible consumption of reactants. Under this regard, our approach can offer an analogous result, within a more skeletal and abstract setting. Having an over-approximation of the exact behaviour of a system, both in the case of static analysis and in our framework, means that all those events that the prediction does not include will never happen, while when included, the events can happen, i.e. they are only possible.

Another recent proposal that shares some similarities with our approach is the one based on the biochemical abstract machine BIOCHAM [22], which also offers a formal modelling environment for biochemical processes, oriented towards qualitative aspects. It is based on a rule-centered language for specifying biochemical systems. Differently from our approach, BIOCHAM semantics takes into consideration the dynamics of systems and provides tools for querying temporal properties of these systems by using Computation Tree Logic. Refraining from dealing with quantities, BIOCHAM offers explicit controls on reactant consumption during reactions and, by default, all the possibilities are considered. This suggests further developments for our approach, where, currently, only the case of no consumption is admitted. The reason for this choice is effectiveness: in this way, branching semantics is avoided.

Still close to our approach and also to BIOCHAM is Pathway logic (see e.g. [23,24]), where rewriting logic is used for modelling biological processes. Rewrite rules describe local changes and the molecular patterns that cause them. Rules can be concurrently applied and this corresponds to the actual possibility of biological compartments to independently evolve. This offers a basis for in silico experiments and for advanced forms of symbolic analysis. We choose an alternative approach, by not resorting to a concurrent semantics, that is not in accordance with our aims.

Amongst the computational logic tradition, which largely influences our proposal, it is interesting to cite some recent proposals based on Abductive Logic Programming.

Complexity of bio-networks, understood as lack of complete knowledge, has been addressed by means of the capability of making assumptions provided by abduction. This approach has been applied to gene networks in [25], with motivations similar to ours. That proposal is based on a combination of Abduction and Induction: abduction allows inference from observable effects (see also [26]) and therefore it is used to generate hypotheses, while induction has the aim of learning general rules from these abduced hypotheses. The representation language has been ad-hoc devised. The predictive accuracy increases with the number of training examples. This methodology has a richer representation language than ours and aims at addressing a different class of problems in a different experimental setting. Differently, [2], and then [27], are based on a quite general class of languages, extended to deal with the biological context. These language, also known as action or event calculi, are suited to describe the non-monotone evolution of a dynamical environment, and specifically biological networks. Abduction is again used as an expressive means to compute/deduce explanations for missing information due to the dynamical nature of the world. Although perhaps more expressive than our approach, these proposals deal again with an explicit treatment of the dynamics of the systems, differently from our proposal that strives for simplicity in order to address, even approximately, causality in very large metabolic networks.

Finally, it is important to refer to the wide usage of graphs as representation language, traditionally close to biologist experience. Amongst the huge set of papers adopting graphs to model bio-networks, our work is closer to those that use arcs and nodes to directly represent reactions. For instance, an approach quite corresponding to our logical view of reactions -as far as the abstraction level is concerned -is in [28]. There, starting from a chosen qualitative interpretation of biochemistry analogous to ours, the authors focus on the topology of metabolic networks, aiming at defining a representative measure of network activity, the Synthetic Accessibility (the number of chemical reactions needed to transform a set of initial metabolites into a set of output ones). This notion has also been tested for predicting viability of mutant strains with accuracy results comparable to ours, although under a different perspective.

Results and discussion

A constructive formalisation of metabolic causality

We clarify our interpretation of the metabolic causal relations by introducing the notation used to represent biochemical reactions. We consider the assumptions on which such idealised notatation relies, discussing why, according to our aims, these assumptions can be considered viable working hypotheses. Such a notation represents our adopted formalisation of the biochemical reactions. Then, under the chosen hypotheses, we give a formal account of the fact that a metabolite, hereafter also called reactant, is caused by a network. In the section Methods, we will present the computational counterpart of the formalisation and we will relate the computational construction with the adopted model.

From biochemical reactions to causal relations

Let us consider a biochemical reaction written in the classical notation:

M, N, P and Q are the species involved and m, n, p and q the corresponding stoichiometric coefficients. Expression (1) indicates that, when the reaction occurs, a certain amount of M and N becomes a certain amount of P and Q according to the stoichiometric proportions. Besides stoichiometry, in order to exhaustively characterize a chemical reaction, one should take into account a number of factors related to thermodynamics and kinetics that represent the propensity for a reaction to occur and the rate at which reactants eventually become products.

Since we are interested in investigating causality relationships only, we can omit the description of many of the factors cited above. Then, we can give an abstract representation of (1) as follows:

We call such an expression a reaction rule. It simply states that the presence of both M and N represents the possibility for P and Q to be produced or caused. If applicable, i.e. it is known that the premises M and N are producible by a network, then also P and Q are producible. Informally speaking, a standard dynamical reading of (2) would be:

indeed, not considering the evolution of the network, reactants are not consumed at any step.

The description of causal relations within a metabolic network can be made by defining a set of metabolites initially present I and a set of reaction rules R that describe how new metabolites can be produced. Initial metabolites are represented in the form of rules with no premises like → P.

Example 1

Let us consider an experiment about a pathway occurring in an environment providing α-D Glucose, Glycerol and oxygen. By using suitable acronyms like glc, gly and o2, respectively, the initial conditions of such an experiment I will include:
→ glc → gly → o2
Moreover, let us imagine that the overall process to be described includes (some steps of) the upper part of the glycolytic pathway. Then, the set R will contain reaction rules like:

The rules (4), (5), (6), (7) and (8) together, and (9) describe the reaction catalyzed by the enzymes phosphoglucose isomerase, 6-phosphofructo 1-chinase, fructose bisphosphate aldolase, triose phosphate isomerase, glyceraldehyde 3-phosphate dehydrogenase, respectively. Note that a reactant appearing on the right side of the operator → may well appear on the left side in another rule.

We eventually decompose the rules into simpler monadic rules, e.g. (2) will be written as:

This transformation is causality preserving in the sense of the following proposition.

Proposition 1

Let M 1 ❍ … ❍ M m → P 1 ❍ … ❍ P n be an applicable rule, i.e. M 1 , …, M n are producible, and then P 1 , …, P n are producible. Then, also the simplified rules M 1 ❍ … ❍ M m → P i , with i = 1, …, n, are applicable in any order, and their application makes P 1 , …, P n producible, as well.

The above proposition holds because causality behaves in a monotone way, since the application of subsequent rules cannot spoil the fact that any metabolite is producible.

The fact that a reactant is caused by a network is made precise by means of the following definition relating the metabolite to the chain of reactions that have made it exist, starting from an initial state I and according to a set of rules R.

Definition 1

Given a set of rules R, an initial state I, and a reactant a let us consider the following construction:

Then, any E R,I (a) ≠ ⊥ is an explanation for a under R and I.

The construction is non-deterministic (in the choice of the rule and in the choice amongst the first two cases), indeed there may be different ways to cause a metabolite.

False positives and false negatives: a problem of approximation

We here briefly discuss on the precision of our approach. As explained above, our approach is intended to offer an over-approximation of the dynamic behaviour of metabolic pathways. The existence of an explanation gives us indications about the possibility of the production of the metabolite, according to the many relaxing assumptions adopted. This means that we can have false positives, i.e. it is possible to predict in silico the production of metabolites that cannot be produced in vivo. This presence is expected as a consequence of abstraction and of overapproximation. However, the experimental results reported in the final part of the section give accuracy rates, i.e. a measure of approximation, comparable with those obtained by other well-known approaches in the literature.

On the contrary, up to the adequacy of the adopted biological model, we do not expect false negatives, i.e. metabolites that can be produced in vivo but have no explanation in silico, as stated by the following claim.

Claim

If there is no explanation for the production of a certain metabolite a, then a cannot be producible in vivo.

The intuition supporting our claim is based on the following reasoning: if ad absurdum the metabolite a is actually producible in vivo, then there is a certain set of biochemical reactions that can be applied starting from an initial set of metabolites. Starting from the same reactions and applying to them the abstractions illustrated above should lead us to the explanation we are looking for.

Note that experimental evidence of the possible production of a metabolite in vivo but not in silico, should suggest the need of a revision of the adopted biological model.

The set of reactants that can be "motivated", in the sense above illustrated, by an explanation starting from an initial pool of given reactants and a specific set of rules can be automatically determined. Amongst the different and equivalent approaches that could have been used, we follow a logic-deductive interpretation, along the line of the explanatory approach adopted. For further details, see section Methods.

Experiments

We have applied our approach to a biological model based upon the E. coli K-12 metabolic genotype proposed in [29] and [30]. This group of genes represents a subset of the whole genome of E. coli K-12 that includes genes encoding enzymes involved in energetic and biosynthetic metabolism. Using our formalism, we have represented the metabolic network composed by the enzymes encoded by the selected gene set and the metabolites involved in the catalyzed reactions. We have obtained a list of about 600 causal rules. We have performed some in silico "what-if" experiments and compared the obtained results with the correspondent in vitro counterpart, excerpts of which are reported in the following. The experiments have been carried out on a tool (see [31]), briefly presented in section Methods.

Mutually essential genes

In this in silico experimental session we performed a gene knock-out mimicking an homologous in vitro experiment presented in [3]. There, the authors silenced two target genes of E. coli K-12 (sucAB and sucCD) that encode for two enzymes involved in the Krebs cycle (α-ketoglutarate dehydrogenase and succinyl-CoA synthase, respectively). They found those genes "mutually essential" for the production of succinyl-CoA, i.e. sucAB and sucCD could be knocked-out individually, but not simultaneously in order to achieve Succinyl-CoA production. Succinyl-CoA is a critically important metabolite involved in several biochemical pathways leading, e.g., to energy production and peptidoglycan biosynthesis (via Diaminopimelate).

In order to simulate this gene knock-out, we have removed the rules corresponding to the reactions catalysed by α-ketoglutarate dehydrogenase and succinyl-CoA synthase. Then we have set the starting experimental conditions, including in the initial state all the metabolites that the cell is assumed to uptake from the external environment. Checking for the presence of succinyl-CoA at the end of the computation, we found that this metabolite was not produced (i.e. the correspondent fact was not deduced) only when both the target genes (i.e. the rules

In silico gene knock-out

We have performed other in silico gene knock-outs and compared our results with the information contained in the "Geno Base" (http://ecoli.aist-nara.ac.jp/), a database entirely dedicated to E. coli K-12. In this database genes are classified according to various criteria, among which their essentiality, i.e. their capability of causing cell death, when turned off. In our in silico knock-out experiments we tried to test gene essentiality verifying whether or not our in silico knock-out mutants exhibit features typically pertaining to living cells. We assumed that these characteristics should reasonably include the production of ATP (essential for cellular energetic metabolism), the production of reduced coenzymes NADPH and NADH and the production of not dispensable structural components, such as the cell wall (murein Biosynthesis). We have performed our in silico knock-out experiments over a sample of 132 genes of our set, each time removing the rules corresponding to the enzyme encoded by the silenced gene and checking for the presence of the observed elements at the end of each computation. We interpret the results as a prediction on the viability or not viability of the knockout mutant under analysis. In our experimental setting (see Table 1), we slightly extend the notion of false positives and negatives introduced in the first part of the section and we say that a True Positive occurs when a knockout mutant results viable both in silico and in the in vivo counterpart, while a True Negative occurs when a in silico knock-out mutant is not viable both in silico and in vivo, a False Positive occurs when a viable in silico knock-out mutant has an in vivo counterpart which is not, and a False Negative occurs when an in silico knock-out mutants is not viable, while its in vivo counterpart results viable. Note that this assignment has been arbitrarily chosen. To evaluate the performance of our method and compare it with similar approaches we use a performance measure taken by [28], that measures the number of true predictionsboth positive (viability) and negative (non viability) -on the overall ones. Note that our definitions of false positives and false negatives differ from those proposed in [28]. This difference has been taken into account in calculating the accuracy A defined below.

Definition 4

Let TP, TN, FP, FN be the number of true positives, true negatives false positives, and false negatives, respectively. We define accuracy A as . Our experiments give the following results:

As reported in [28], the accuracy of the Synthetic Accessibility approach therein presented ranges from 60% to 74%, while another approach for metabolic networks, i.e. the Flux Balance Analysis [30], has an accuracy that ranges between 62% and 86%. We found 17 false positives, resulting in an accuracy of about 87% over this specific experiment. These differences are probably strongly influenced by the way data sets are interpreted and by which cases are included in the data sets. However, the obtained results make us confident that our approach is reasonably accurate.

To give an intuitive idea of the experiments, we just report in Table 2, some examples of true positive, true negative and false positive cases (reminding that we have no false negatives). The symbols + or − stand for the presence or absence, respectively, of the observed elements in the in silico results.

The presence of false positives (in silico, the mutant is predicted viable, but actually, in vivo, it is not) is expected in our framework, as a consequence of the abstraction and of the over-approximation we used in our model. This corresponds to the fact that something that has influence on viability and that is potentially producible in silico, it is not actually produced in real life. Finally, note that, in the experiments carried out, we have found no false negatives. This makes us confident of the correctness of the adopted biological model.

Conclusions

In metabolic networks, metabolites are produced from a set of initial metabolites, through a set of chemical reactions. These reactions produce intermediate metabolites that can be both products or reactants. We have intro-  duced a simple and skeletal notation to describe these networks in terms of molecular entities and reaction rules that specify their interactions and that implicitly code possible causal dependencies amongst reactions. This notation permits us, on the one hand, to give to chemical reactions an abstract and intuitive representation where quantitative aspects are abstracted away; on the other hand, this representation can be straightforwardly translated into an input for the tool we developed, paving the way for in silico experiments and further tool development. To this aim, we have exploited the analogy between reaction rules and logical implications, that allows us to automatically deduce chains of causally related reactions by means of a logical-based tool. Even though we do not consider the dynamic evolution of metabolic networks, our model is sufficient to give information on which metabolites can be possibly produced and how and, therefore, to give hints on the possible flows of reactions.

Moreover, our methodology makes it possible to reason about the model itself, by allowing us to vary both the initial conditions and the rules. It is easy to program such modifications and evaluating the impact of changes in the hypotheses is quite immediate, because the tool quickly reacts to the queries (typically an answer about a reasonable large network returns almost istantanelously). The what-if approach satisfies the need to simulate and investigate the behaviour of not fully known metabolic networks under different working hypotheses. In particular it allows us to perform perturbative experiments, whose results are not trivial to predict. In fact, if the studied network is complex enough, it results unfeasible to a priori estimate the effects produced by a local perturbation on the overall network. Finally, we have applied our methodology to the metabolic network of the E. coli K-12 metabolic genotype. The in silico experiments presented reflect the in vitro ones. The results obtained up to now show our method not to underperform analogous ones. Noticeably it is ground on a formalism that provides efficient and straightforward implementations.

Our ultimate goal for further investigations is that of supporting a heuristic process of searching causal explanations of metabolic phenomena, with in mind the "emphasis on hypothesis-driven research in biology" advocated in [1].

Methods

To illustrate our methodology, we describe the computational framework that represents the counterpart of the formalisation of metabolic causality, introduced in section Results and Discussion. Finally, we relate the computational construction with the adopted formalisation.

The set of reactants that can be caused -according to our formalisation -by an explanation starting from an initial set of reactants and a set of rules can be automatically determined. Amongst the different and equivalent approaches that we could choose, we eventually follow a logic-deductive interpretation, along the line of the explanatory approach adopted. Technically, what follows consists of a fragment of Horn-based Logic Programming (having only a finite set of ground predicates) equipped with bottom-up semantics (see, e.g. [32]). However, for the sake of accessibility, the theory is recast in terms of rules (i.e., clauses) and reactants (i.e., predicates). In the following, reactants are directly represented, while causal rules of the model, a ❍ c → b say, are straightforwardly translated into Horn-rules, like a, c → b, according to the following definition.

Definition 2

Let A a finite set of reactants such that a 1 ,…, a n , a ∈ A, then with n ≥ 0 is a rule.

Notice that we can have rules with empty premises. These rules are used for representing the elements present in the initial state I.

The set of consequences of a given set of rules (respectively, the semantics of a logic program) can be defined according to a step-wise bottom-up process. The application of a rule to a set of reactants causes a new reactant when all the premises of the rule can be verified in the set. Starting from the set of the initially available reactants, the set of all the reactants that can be caused can be obtained by repeatedly adding the reactants that can be immediately caused by the application of all the rules.

Definition 3

Let R be a set of rules and A a set of reactants, then the immediate consequence operator T R (A) : 2 A → 2 A is defined as a a a n 1 , , instead of as (A)).
… → T A a a a a R a a A A R n n ( ) → ∈ ∈ { } ∪ … … | , ,, , 1 1 and

Proposition 2

Let R be a set of rules, A a set of reactants, and m the number of all the reactants in the model under consideration. Then, n <m exists such that

Example 2

Let us consider a network with reactants I = { → b} initially available and consisting of the following simple rules R:
Applying T R ({b}) we have

Coherence of computational and metabolic causality

As standard, one would like to relate the computational construction provided with the original model, i.e. our adopted formalisation of biochemical reactions, introduced in section Results and Discussion. Let us start to observe that keeping track of the rule used when applying T R (_) would allow us to reconstruct explanations (which indeed recall SLD-trees of the top-down semantics of Logic Programming). Considering again the example above, the reactant c is caused in by the application of rule (12), that in turn depends on rule (13), for the production of a that does not belong to the initial set I = {→ b}. Consequently, one would have the explanation c[a[b],b] for c. However, it is important to have considered convergence over reactants rather than over explanations. It is easy to observe that at the fourth step we would have the explanation a[b[a [b]]] due to the cycle between a and b. This amounts to say that -in the presence of cyclesexplanations can growth indefinitely, i.e. convergence occurs at infinity. Hence, we have restricted ourselves to compute the reactants that can be produced, which is a finite process. However, the following correspondence between computational results and the potentially infinite model of explanations can be drawn.

Theorem 1

Let R be a set of rules, a a reactant, I a set of reactants and the minimum natural number such that . Then the following holds Proof (Outline).

(⇒) By induction on the number of steps needed to firstly cause a in the bottom-up process (the rule that has motivated the inclusion of a can also be used as the top-most rule in the definition of an explanation for a. All the reactants in the premises of the rule must have been caused in less steps, and then, by inductive hypothesis, explanations for them exist, and these can be used to construct the explanation for a). To address the problem of causality in metabolic networks, as seen above, we developed a software tool based on an implementation of a standard bottom-up semantics, running on top of SICTUS Prolog Interpreter (see [31]).

T A T T A T A A

b a → (13) a b → (14) c d →

(
⇐) By induction on structural complexity of E I,R (a). (By inductive hypothesis, all the reactants in the premises of the top-most rule in the explanation belong to , then either a is in or is not a fix point, since the rule is clearly applicable and would cause a).

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corresponding to the action of the encoded enzymes) were simultaneously turned off. This reflects what actually happens in vitro.E a

a

a E a
E a

a I
a
a
a R
E

R I
R I
R I
n
n
R
,
,
,

, ,

( ) =

( )
( )

⎡ ⎣
⎤ ⎦

⊥

→ ∈
→ ∈

1
1

…
…

if
if
and , ,
..

I
i

a
i
n

( )≠⊥ ∀ ∈[ ]

⎧

⎨
⎪

⎩
⎪

1
otherwise

Table 1 :
1True and false positives and negatives according to our
definition, depending on the viability of knock-out mutants in
silico and in vivo

CASE
IN SILICO
IN VIVO

True Positive
viable
viable
True Negative
not viable
not viable
False Positive
viable
not viable
False Negative
not viable
viable

Table 2 :
2Gene knock-out experimental resultsThe convergence of the outlined process is guaranteed by the following result, which is based on the observationthat, trivially, is a (finite) complete partial order(c.p.o.) and T(_) is continuous over it (keeping the original A guarantees monotonicity). Moreover, being the set of reactants finite -i.e. the number of all the reactants occurring in rules R and in the initial state I -the bottomup construction is also guaranteed to converge in a finite number of steps (then the fix point is indicated as (A)Gene
ATP
NADPH
NADH
cellwall
outcome

acpS
−
−
−
−
true negative
lpxA
+
+
+
−
true negative
glk
+
+
+
+
true positive
aceA
+
+
+
+
true positive
prsA
+
+
+
+
false positive
pfk
+
+
+
+
false positive

(page number not for citation purposes)
AcknowledgementsThis article has been published as part of BMC Bioinformatics Volume 9 Supplement 4, 2008: A Semantic Web for Bioinformatics: Goals, Tools, Systems, Applications. The full contents of the supplement are available online at http://www.biomedcentral.com/1471-2105/9?issue=S4.Competing interestsThe authors declare that they have no competing interests.Authors' contributionsAll the authors equally contributed to the present work and wrote the paper. More precisely, CB and AB taken care of the computational framework and DC carried out the in silico experiments, while they jointly develop the formalisation of the metabolic causality and the analysis of the experimental results.
H Kitano, Systems Biology: a brief overview. 295Kitano H: Systems Biology: a brief overview. Science 2002, 295(5560):1662-1664.

Knowledge-based framework for hypothesis formation in biochemical networks. N Tran, C Baral, V J Nagaraj, L Joshi, Bioinformatics. 212SupplTran N, Baral C, Nagaraj VJ, Joshi L: Knowledge-based frame- work for hypothesis formation in biochemical networks. Bio- informatics 2005, 21(Suppl 2):ii213-ii219.

sucAB and sucCD are mutually essential genes in Escherichia coli. B Yu, B Sung, J Lee, S Son, M Kim, S Kim, FEMS Microbiology Letters. 2542Yu B, Sung B, Lee J, Son S, Kim M, Kim S: sucAB and sucCD are mutually essential genes in Escherichia coli. FEMS Microbiology Letters 2006, 254(2):245-250.

Petri Nets: an introduction Springer-Verlag. W Reisig, Reisig W: Petri Nets: an introduction Springer-Verlag; 1985.

Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri Nets. Proceedings of the National Academy of Sciences USA. P Goss, J Peccaud, 12Goss P, Peccaud J: Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri Nets. Proceed- ings of the National Academy of Sciences USA 1998, 12:6750-6754.

Modeling biological processes using Workflow and Petri Nets models. M Peleg, I Yeh, R Altman, Bioinformatics. 18Peleg M, Yeh I, Altman R: Modeling biological processes using Workflow and Petri Nets models. Bioinformatics 2002, 18:825-837.

Communicating and mobile systems: the π-calculus. R Milner, Cambridge University PressMilner R: Communicating and mobile systems: the π-calculus Cambridge University Press; 1999.

. L Cardelli, A Gordon, Mobile Ambients. Theoretical Computer Science. 240Cardelli L, Gordon A: Mobile Ambients. Theoretical Computer Sci- ence 2000, 240:177-213.

Application of a stochastic name-passing calculus to representation and simulation of molecular processes. C Priami, A Regev, E Shapiro, W Silvermann, Theoretical Computer Science. 325Priami C, Regev A, Shapiro E, Silvermann W: Application of a sto- chastic name-passing calculus to representation and simula- tion of molecular processes. Theoretical Computer Science 2004, 325:141-167.

Representation and Simulation of Biochemical Processes Using the pi-Calculus Process Algebra. A Regev, W Silvermann, E Shapiro, Proceedings of Pacific Symposium on Biocomputing World Scientific. Pacific Symposium on Biocomputing World ScientificRegev A, Silvermann W, Shapiro E: Representation and Simula- tion of Biochemical Processes Using the pi-Calculus Process Algebra. In Proceedings of Pacific Symposium on Biocomputing World Scientific; 2001:459-470.

Bioambients: An abstraction for biological compartements. A Regev, E Panina, W Silverman, L Cardelli, E Shapiro, Theoretical Computer Science. 325Regev A, Panina E, Silverman W, Cardelli L, Shapiro E: Bioambients: An abstraction for biological compartements. Theoretical Com- puter Science 2004, 325:141-167.

Transactions in RCCS. V Danos, J Krivine, Proceedings of Conference on Concurrency Theory (CONCUR'05). Conference on Concurrency Theory (CONCUR'05)San Francisco, CA, USASpringer3653Danos V, Krivine J: Transactions in RCCS. In Proceedings of Con- ference on Concurrency Theory (CONCUR'05), Lecture Notes in Computer Science 3653 San Francisco, CA, USA: Springer; 2005:398-412.

Graphs for Core Molecular Biology. V Danos, C Laneve, Proceedings of Computational Methods in Systems Biology (CMSB'03). Computational Methods in Systems Biology (CMSB'03)Rovereto, ItalySpringer2602Danos V, Laneve C: Graphs for Core Molecular Biology. In Pro- ceedings of Computational Methods in Systems Biology (CMSB'03), Lecture Notes in Computer Science 2602 Rovereto, Italy: Springer; 2003:34-46.

Brane calculi-interactions of biological membranes. L Cardelli, Proceedings of Computational Methods in Systems Biology (CMSB'04. Computational Methods in Systems Biology (CMSB'04Paris, FranceSpringer3082Cardelli L: Brane calculi-interactions of biological mem- branes. In Proceedings of Computational Methods in Systems Biology (CMSB'04) Lecture Notes in Computer Science 3082 Paris, France: Springer; 2005:257-280.

Beta Binders for Biological Interactions. C Priami, P Quaglia, Proceedings of Computational Methods in Systems Biology (CMSB'04). Computational Methods in Systems Biology (CMSB'04)Paris, FranceSpringer3082Priami C, Quaglia P: Beta Binders for Biological Interactions. In Proceedings of Computational Methods in Systems Biology (CMSB'04), Lec- ture Notes in Computer Science 3082 Paris, France: Springer; 2005:20-33.

The Chemical Abstract Machine. G Berry, G Boudol, Proceeding of Symposium on Principles of Programming Languages (POPL). eeding of Symposium on Principles of Programming Languages (POPL)San Francisco, CaliforniaBerry G, Boudol G: The Chemical Abstract Machine. In Proceed- ing of Symposium on Principles of Programming Languages (POPL) San Francisco, California; 1990:81-94.

Modeling biochemical pathways through enhanced pi-calculus. M Curti, P Degano, C Priami, C Baldari, Theoretical Computer Science. 325Curti M, Degano P, Priami C, Baldari C: Modeling biochemical pathways through enhanced pi-calculus. Theoretical Computer Science 2004, 325:111-140.

Non-Interleaving Semantics for Mobile Processes. P Degano, C Priami, Theoretical Computer Science. 2161-2Degano P, Priami C: Non-Interleaving Semantics for Mobile Processes. Theoretical Computer Science 1999, 216(1-2):237-270.

Concurrent Histories: A Basis for Observing Distributed Systems. P Degano, U Montanari, Journal of Computer and System Sciences. 342/3Degano P, Montanari U: Concurrent Histories: A Basis for Observing Distributed Systems. Journal of Computer and System Sciences 1987, 34(2/3):422-461.

Static analysis for the π-calculus with their application to security. Information and Computation. C Bodei, P Degano, F Nielson, H Riis-Nielson, 165Bodei C, Degano P, Nielson F, Riis-Nielson H: Static analysis for the π-calculus with their application to security. Information and Computation 2001, 165:68-92.

Static analysis for systems biology. F Nielson, H Riis-Nielson, D Schuch-Da-Rosa, C Priami, Proceedings of workshop on Systeomatics -dynamic biological systems informatics. workshop on Systeomatics -dynamic biological systems informaticsTrinity College DublinComputer Science PressNielson F, Riis-Nielson H, Schuch-Da-Rosa D, Priami C: Static anal- ysis for systems biology. In Proceedings of workshop on Systeomatics -dynamic biological systems informatics Computer Science Press, Trinity College Dublin; 2004:1-6.

The Biochemical abstract machine BIOCHAM. N Chabrier, F Fages, S Soliman, Proceedings of Computational Methods in Systems Biology (CMSB'04). Computational Methods in Systems Biology (CMSB'04)3082Chabrier N, Fages F, Soliman S: The Biochemical abstract machine BIOCHAM. In Proceedings of Computational Methods in Systems Biology (CMSB'04), Lecture Notes in Computer Science 3082

Pathway Logic: Executable Models of Biological Network. S Eker, M Knapp, P Lincoln, K Laderoute, C Talcott, Proceedings of the Fourth International Workshop on Rewriting Logic and Its Applications (WRLA '02). the Fourth International Workshop on Rewriting Logic and Its Applications (WRLA '02)Elsevier71Eker S, Knapp M, Lincoln P, Laderoute K, Talcott C: Pathway Logic: Executable Models of Biological Network. In Proceedings of the Fourth International Workshop on Rewriting Logic and Its Applications (WRLA '02), Electronic Notes in Theoretical Computer Science 71 Elsevier; 2002:144-161.

Pathway Logic Modeling of Protein Functional Domains in Signal Transduction. C Talcott, S Eker, M Knapp, P Lincoln, K Laderoute, Proceedings of Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing9Talcott C, Eker S, Knapp M, Lincoln P, Laderoute K: Pathway Logic Modeling of Protein Functional Domains in Signal Transduc- tion. Proceedings of Pacific Symposium on Biocomputing 2004, 9:568-580.

Application of abductive ILP to learning metabolic network inhibition from temporal data. A Tamaddoni-Nezhad, R Chaleil, A Kakas, S Muggleton, Machine Learning. 641-3Tamaddoni-Nezhad A, Chaleil R, Kakas A, Muggleton S: Application of abductive ILP to learning metabolic network inhibition from temporal data. Machine Learning 2006, 64(1-3):209-230.

Inference of Gene Relations from Microarray Data by Abduction. I Papatheodorou, A C Kakas, M Sergot, Proceedings of Logic Programming and Nonmonotonic Reasoning (LPNMR'05). Logic Programming and Nonmonotonic Reasoning (LPNMR'05)Diamante, Italy3662Papatheodorou I, Kakas AC, Sergot M: Inference of Gene Rela- tions from Microarray Data by Abduction. In Proceedings of Logic Programming and Nonmonotonic Reasoning (LPNMR'05), Lecture Notes in Computer Science 3662 Diamante, Italy; 2005:389-393.

Modelling Biological Networks by Action Languages Via Answer Set Programming. S Grell, T Schaub, J Selbig, Proceedings of International Conference on Logic Programming (ICLP'06. International Conference on Logic Programming (ICLP'06Seattle, WA, USASpringer4079Grell S, Schaub T, Selbig J: Modelling Biological Networks by Action Languages Via Answer Set Programming. In Proceed- ings of International Conference on Logic Programming (ICLP'06) Lecture Notes in Computer Science 4079 Seattle, WA, USA: Springer; 2006:285-299.

Using the topology of metabolic networks to predict viability of mutant strains. Z Wunderlich, L Mirny, Biophysical Journal. 91Wunderlich Z, Mirny L: Using the topology of metabolic net- works to predict viability of mutant strains. Biophysical Journal 2006, 91:2304-2311.

Metabolic flux analysis of Escherichia coli in glucose-limited continuous culture. A Kayser, J Weber, V Henkt, U Rinas, Transactions on Computational System Biology VII. 151Kayser A, Weber J, Henkt V, Rinas U: Metabolic flux analysis of Escherichia coli in glucose-limited continuous culture. Trans- actions on Computational System Biology VII 2005, 151:693-706.

Metabolic flux balance analysis and in silico analisis of Escherichia Coli K-12 gene deletion. J Edwards, B Palsson, BMC Bioinformatics. 11Edwards J, Palsson B: Metabolic flux balance analysis and in sil- ico analisis of Escherichia Coli K-12 gene deletion. BMC Bioin- formatics 2000, 1(1):1-10.

A Toolkit Supporting Formal Reasoning about Causality in Metabolic Networks. A Toolkit Supporting Formal Reasoning about Causality in Metabolic Networks. . [http://www.di.unipi.it/~braccia/Tool Code].

J Lloyd, Foundations of Logic Programming. SpringerSecond edition editionLloyd J: Foundations of Logic Programming Second edition edition. Springer; 1987.