Open Access RESEARCH Hepatic zonation of carbon and nitrogen fluxes derived from glutamine and ammonia transformations
2010

Jurandir F Comar
Fumie Suzuki-Kemmelmeier
Jorgete Constantin
Adelar Bracht
Open Access RESEARCH Hepatic zonation of carbon and nitrogen fluxes derived from glutamine and ammonia transformations

Journal of Biomedical Science
1712010The cost of publication in Journal of Biomedical Science is bourne by the National Science Council, Taiwan. Research
Background: Glutaminase predominates in periportal hepatocytes and it has been proposed that it determines the glutamine-derived nitrogen flow through the urea cycle. Glutamine-derived urea production should, thus, be considerably faster in periportal hepatocytes. This postulate, based on indirect observations, has not yet been unequivocally demonstrated, making a direct investigation of ureogenesis from glutamine highly desirable.Methods: Zonation of glutamine metabolism was investigated in the bivascularly perfused rat liver with [U-14 C]glutamine infusion (0.6 mM) into the portal vein (antegrade perfusion) or into the hepatic vein (retrograde perfusion).Results: Ammonia infusion into the hepatic artery in retrograde and antegrade perfusion allowed to promote glutamine metabolism in the periportal region and in the whole liver parenchyma, respectively. The results revealed that the space-normalized glutamine uptake, indicated by 14 CO 2 production, gluconeogenesis, lactate production and the associated oxygen uptake, predominates in the periportal region. Periportal predominance was especially pronounced for gluconeogenesis. Ureogenesis, however, tended to be uniformly distributed over the whole liver parenchyma at low ammonia concentrations (up to 1.0 mM); periportal predominance was found only at ammonia concentrations above 1 mM. The proportions between the carbon and nitrogen fluxes in periportal cells are not the same along the liver acinus.Conclusions:In conclusion, the results of the present work indicate that the glutaminase activity in periportal hepatocytes is not the rate-controlling step of the glutamine-derived nitrogen flow through the urea cycle. The findings corroborate recent work indicating that ureogenesis is also an important ammonia-detoxifying mechanism in cells situated downstream to the periportal region.

Background

Glutamine is one of the most abundant amino acids in the organism of mammals and it is involved in more metabolic processes than any other amino acid [1]. Also for the liver the role of glutamine is very important. It is known that the metabolism of glutamine presents zonation [2], i.e., the different regions along the hepatic acini respond in a different way to the amino acid [3][4][5]. The underlying mechanisms of the zonation of enzymes involved in glutamine metabolism are controversial. Recent work has suggested a role for lev-els of substrate, autocrine soluble factor or cytoskeleton interactions putatively associated with the beta-catenin signaling pathway [6]. Knowledge about zonation of the metabolism of L-glutamine is centered mainly on nitrogen metabolism. The dominant idea is that, along the hepatic acinus, the pathways of urea production and glutamine synthesis are arranged in sequence in order to optimize ammonia detoxification. The urea synthesis in the periportal region represents the system of low affinity for ammonia detoxification. Glutamine synthesis in the perivenous zone represents the system of high affinity for ammonia detoxification. The periportal glutaminase [7], located in the mitochondria, is stimulated by ammonia and influenced by pH and hormones [8,9]. The activity of this enzyme is believed to determine, partly at least, the flow of nitrogen derived from glutamine through the urea cycle [10]. The glutamine synthetase, restricted to a limited number of perivenous hepatocytes, is believed to act as a kind of scavenger for the ammonia that escapes from the periportal urea synthesis [3].

If the activity of glutaminase determines the nitrogen flow derived from glutamine through the urea cycle, urea production from glutamine should be considerably faster in periportal hepatocytes [5,10]. This postulate is based on the measurement of enzymatic activities under artificial conditions and has not yet been unequivocally demonstrated by flux measurements in intact cell systems. Such measurements are important, however, because discrepancies between enzyme activity or gene expression evaluations and the actual metabolic fluxes in the living cell are common. Recent studies have shown, for example, that urea production from alanine, lactate + ammonia and pyruvate + ammonia is faster in cells situated downstream to the periportal zone at most substrate concentrations [11,12] in spite of the observation that the expression of key enzymes from the urea cycle predominates in these cells [13]. Periportal predominance of urea production was found only at high ammonia concentrations in the presence of pyruvate [12]. Absence of correlation between enzyme activity or enzyme expression and metabolic fluxes in the cell are actually quite common and direct measurements of the latter are, thus, desirable. Moreover, glutamine is also a gluconeogenic substrate and it has been found that periportal and perivenous cells present different glucose to urea production ratios from alanine [11]. This is an important observation if one takes into account the reciprocal regulation of both ureogenesis and gluconeogenesis [14,15], which seems to be different in periportal and perivenous cells, and raises the question about the relative proportions between ureogenesis and glutamine transformation. These and other questions prompted us to undertake a detailed investigation of the zonation of glutamine transformation with the simultaneous measurement of nitrogen and carbon fluxes. The methodology to be utilized is the bivascularly perfused rat liver, which allows to reach selectively periportal hepatocytes via the hepatic artery in retrograde perfusion [16] and which has been successfully used for investigating hepatic zonation without significant alterations of the liver structure [11,12,17].

Methods

Materials

The liver perfusion apparatus was built in the workshops of the University of Maringá. Enzymes and coenzymes used in the metabolite assays were purchased from Sigma Chemical Co. (St Louis, USA). [U-14 C]Glutamine (258 mCi/mol) was purchased from Amersham Bioscience (Buckimghamshire, UK). All standard chemicals were from the best available grade (>99.5% purity) and were purchased from Merck (Darmstadt, FRG), Carlo Erba (São Paulo, Brasil) and Reagen (Rio de Janeiro, Brazil).

Animals and bivascular liver perfusion

Male albino rats (Wistar), weighing 180-220 g, were fed ad libitum with a standard laboratory diet (Purina ® ). Food was withdrawn 18 hours prior to the liver perfusion experiments. For the surgical procedure of liver isolation, the rats were anesthetized by intraperitoneal injection of sodium pentobarbital (50 mg/kg). All experiments were done in accordance with the world-wide accepted ethical guidelines for animal experimentation. The authors were duly authorized by the Coordination of the PhD Program in Biological Sciences of the University of Maringá to conduct this animal study.

Hemoglobin-free, non-recirculating bivascular liver perfusion was performed either in the antegrade mode (entry via the portal vein plus hepatic artery and exit via the hepatic vein) or in the retrograde mode (entry via the hepatic vein plus hepatic artery and exit via the portal vein; Fig. 1). The surgical procedure was described previously [17]. In situ perfusion was carried out, the flow being provided by two peristaltic pumps. The perfusion fluid was Krebs/Henseleit-bicarbonate buffer (pH 7.4) containing 25 mg% bovine-serum albumin, saturated with a mixture of oxygen and carbon dioxide (95:5) by means of a membrane oxygenator with simultaneous temperature adjustment (37°C). The portal flow was adjusted between 28 and 32 ml/min and the arterial flow between 2 and 3 ml/min. All perfusion experiments were initiated in the antegrade mode. Retrograde perfusion was established by changing the direction of flow at 15-20 minutes before initiating sampling of the effluent perfusate. In all perfusion experiments, livers from fasted rats were used so that glycogenolysis and glycolysis from endogenous sources was minimal [18].

Analytical

Samples of the effluent perfusion fluid were collected according to the experimental protocol and analyzed for their metabolite contents. The following compounds were measured by means of standard enzymatic procedures: glucose, lactate, urea and ammonia [19]. The oxygen concentration in the outflowing perfusate was monitored continuously, employing a teflon-shielded platinum electrode adequately positioned in a plexiglass chamber at the exit of the perfusate [20].

The carbon dioxide production from L-[U-14 C]glutamine was measured by trapping 14 CO 2 in phenylethylamine [21]. Radioactivity was measured by liquid scintillation spectroscopy. The following scintillation solution was used: toluene/ethanol (2/1) containing 5 g/liter 2,5-diphenyloxazole and 0.15 g/liter 2,2-p-phenylene-bis(5-phenyloxazole).

Experimental protocol and data analysis

The experimental protocol that was adopted in the present work takes advantage of some particularities of the hepatic microcirculation of the rat. In bivascular perfusion of the rat liver (Fig. 1), a portion of the periportal hepatic parenchyma can be reached selectively with substances that are infused into the hepatic artery in retrograde perfusion [11,12,16]. In the present work glutamine was infused at the physiological concentration of 0.6 mM into the portal vein in antegrade perfusion and into the hepatic vein in retrograde perfusion so that all hepatocytes were supplied with this substrate. At the concentration of 0.6 mM, however, metabolic transformation of glutamine only occurs when ammonia is present in the perfusion fluid [8]. In the present work the latter was infused into the hepatic artery. By virtue of the existence of two arterio-sinusoidal confluences, if ammonia is infused into the hepatic artery in retrograde perfusion only periportal hepatocytes will be supplied with this compound (Fig. 1B) [11,12,16]. Consequently, only periportal cells will be stimulated to metabolize glutamine. If ammonia is infused into the hepatic artery in antegrade perfusion, however, all hepatocytes will be supplied ( Fig. 1A) and also all hepatocytes will transform glutamine [11,12,16]. Comparison of the metabolic fluxes in antegrade (J ant ) and retrograde (J ret ) perfusion requires normalization by dividing them through the corresponding accessible cell spaces, as determined by previous work [22,23]. Analysis also requires to take into account the different concentrations of ammonia in the regions that are accessible during antegrade and retrograde perfusion, which depend on the distribution of the arterial flow between the pre-and intrasinusoidal confluences (Fig. 1). A simple mathematical description of the flux responses that can be expected when substrates and effectors are infused into the hepatic artery in antegrade or retrograde perfusion has been proposed in previous work [11,12,24]. The same

Antegrade perfusion

Hepatic artery ramifications
Sinusoid A A B Glutamine

Ammonia infusion

Periportal zone Perivenous zone

Retrograde perfusion

Hepatic artery ramifications
Sinusoid B A B
treatment can be extended to the situation in which a metabolic effector such as ammonia is infused. If J ret and J ant are the cell space-normalized metabolic responses of glutamine metabolism due to the ammonia infusion into the hepatic artery in retrograde and antegrade perfusion ( Fig. 1), respectively, the following relations are valid: [11,12,24]:

In equation (1) v 1R is the metabolic flux in region 1 in retrograde perfusion (Fig. 1B), function (f) of the ammonia concentration (c 1R ) in this region during retrograde perfusion, whereas v 1A is the metabolic flux in region 1 in antegrade perfusion, function of the ammonia concentration (c 1A ) in this region in antegrade perfusion. The values of c 1R and c 1A are not the same even though the difference is not very pronounced [12]. They are different for a given ammonia infusion rate because the arterial flow that reaches the intrasinusoidal confluence (F AIS ) corresponds to 58% of the total arterial flow (F A ), i.e., F AIS = 0.58F A [12]. The symbol v 2A represents the metabolic flux in region 2, also function of the ammonia concentration (c 2A ) during antegrade perfusion (Fig. 1A). The parameter r is the fraction of the cellular space that can be reached via the hepatic artery in retrograde perfusion; this parameter has been measured previously as being equal to 0.38 in the hemoblogin-free perfused rat liver [22,23].

Comparison of the v 1R versus c 1R and v 2A versus c 2A relationships should provide an immediate answer about a possible different sensitivity of glutamine metabolism to ammonia in regions 1 and 2, v 1R = v 2A meaning absence of zonation, v 1R > v 2A periportal predominance and v 1R < v 2A perivenous predominance. It should be noted, however, that when J ret > J ant is observed for a given infusion rate, this can be immediately interpreted as periportal predominance in all cases where a positive correlation exists between fluxes and concentrations, because c 2A is always greater than c 1R for identical infusion rates [12].

The value of v 1R corresponds to J ret as given by equation (1). Values of c 1R were calculated using the relation [24] where is the rate of ammonia infusion (μmol min -1 g liver -1 ), F T the total flow through the liver (ml min -1 ), F A the arterial flow (ml min -1 ) and F AIS the arterial flow that reaches the intrasinusoidal confluence (F AIS = 0.58F A ) [12]. Following c 1R calculation, v 1A can be obtained by interpolating within the v 1R versus c 1R curve. Using these v 1A values, v 2A can be calculated using the relation derived from Eq. (2). The c 2A values, finally can be determined simply as [24] Treatment of data Statistical analysis of the data was done by means of the Statistica™ program (Statsoft ® , 1998). The Scientist software from Micro Math Scientific Software (Salt Lake City, UT) was used for the numerical interpolations (using Stineman's interpolation formula).

Results

Time courses of the reponses to glutamine and ammonia infusions

All perfusion experiments were done with livers from 18 hours fasted rats in order to minimize interference by glycogen catabolism. Control experiments (Fig. 2) confirmed the earlier observations that the infusion of glutamine at physiological concentrations (0.6 mM) does not produce significant increases in glucose, urea and ammonia productions and oxygen uptake even if the infusion time is as long as 90 minutes [8]. Ammonia infusion into the hepatic artery, however, increased glutamine metabolism in both antegrade and retrograde perfusion (Figs. 3 and 4). Five parameters were measured: urea, lactate, glucose and 14 CO 2 productions and oxygen consumption. Pyruvate production, which is significant at high glutamine concentrations (2.5 mM; [25]), was not significantly increased at the low physiological glutamine concentrations employed in the present work. Both glucose and urea productions increased significantly after initiation of ammonia infusion either in antegrade or retrograde perfusion (Fig. 3). At 70 minutes perfusion time new steady-state levels were reached. Notably, glucose production in antegrade perfusion experienced a transient decline just after initiation of ammonia infusion before elevating to a new steady-state. Also notable is the observation that glucose production in retrograde perfusion was higher than that in antegrade perfusion in spite of the fact that a considerably smaller cell space is reached by arterially infused ammonia in retrograde perfusion when compared to antegrade perfusion (Fig. 1). Oxygen uptake and 14 CO 2 production during portal or venous [U-14 C]glutamine infusion were also increased by arterially infused ammonia in both antegrade and retrograde perfusion (Fig.   J c
v ret R R = = f ( ) 1 1 (1) J c r c r r v r v ant R A A A = ⋅ + ⋅ − = − f f ( ) ( ) ( ) ( ) 1 2 1 2 1 1 (2) c F NH F T F AIS F A R 1 3 = ⋅ (3) F NH v J ant rv A r A 2 1 1 = − − (4) c F NH F T A 2 3 =(5)
4). They had a similar tendency of reaching state-state levels at the end of the experiment. Note that there are relatively small, though significant, 14 CO 2 productions even in the absence of ammonia, a phenomenon that was also observed in earlier work [8]. They are equal in antegrade and retrograde perfusion, however, reflecting the fact that glutamine infused into either the portal or hepatic veins has access to the same cell masses. As expected, basal oxygen uptake rates in antegrade and retrograde perfusion were also nearly the same.

Cell space corrected fluxes of glutamine metabolism

So far the metabolic fluxes were expressed as μmol min -1 g -1 (Figs. 3 and 4). This is valid for comparing basal rates or rates before ammonia infusion because glutamine, when infused into the portal or hepatic veins, has access to the whole liver parenchyma. In order to compare the ammoniadependent glutamine metabolism, however, the metabolic fluxes must be normalized with reference to the cell spaces that are accessible via the hepatic artery in antegrade and retrograde perfusion. These spaces are equal to 0.684 and 0.266 ml/g, respectively, for antegrade and retrograde perfusion [22,23]. For the normalization process the rates before ammonia infusion were subtracted from the rates at the end of the ammonia infusion period (70 minutes perfusion time in Figs. 3 and 4); this difference was than divided by the corresponding accessible cell space. Implicit in this procedure is the assumption that the increments caused by ammonia reflect solely the contribution of the cell spaces that are accessible via the hepatic artery in antegrade and Ammonia Oxygen Urea Glucose retrograde perfusion, whereas the basal rates represent the contribution of the whole liver parenchyma (Fig. 1). The normalized fluxes calculated in this way correspond to the variables J ret and J ant as defined by equations (1) and (2), respectively. It is apparent ( Table 1) that the ammonia-dependent fluxes were faster in retrograde perfusion (i.e., J ret > J ant ) for all ammonia infusion rates with the exception of urea production. The most accentuated difference was found for glucose production, but the difference was also significant for 14 CO 2 production and oxygen uptake. As mentioned and justified in the Materials and Methods section the observation J ret > J ant always means an enrichment of the metabolic activity in the periportal space accessible via the intrasinu-soidal confluence in comparison to the mean metabolic activity of the liver.

Fine analysis of the zonation of glutamine metabolism

The near equality of J ant and J ret for urea production from glutamine (Table 1), needs a more accurate analysis if one wishes to conclude about the distribution along the hepatic acinus. The analysis can be done using equations (1), (3), (4) and (5) for calculating the metabolic fluxes in the different spaces that are accessible via the hepatic artery in antegrade and retrograde perfusion, namely v 1R , v 2A , c 1R and c 2A . The v 1R versus c 1R and v 2A versus c 2A plots (Fig. 5A) reveal that urea production in region 1 (v 1R ; periportal cells) was not superior to that in region 2 (v 2A ; mainly perivenous cells) at low ammonia concentrations. Only for concentrations above 1 mM periportal predominance of ureogenesis can be expected. In region 2 urea production was apparently near to saturation in the range between 1 and 2 mM. In the periportal region, however, no saturation was evident in the range up to 1.5 mM. When the same analysis that was done for urea production was repeated for glucose production, the results fully confirmed the conclusion that gluconeogenesis from glutamine amply predominates in periportal cells (Fig. 5B), as revealed by the great difference in gluconeogenesis from glutamine in regions 1 and 2. Actually, for low ammonia concentrations there was almost no glucose production in the liver cells situated downstream to the intrasinusoidal confluence of the arterial and portal beds (Fig. 5B).

Discussion

The main question of the present study was related to the accepted notion that the ammonia-dependent glutaminase in periportal hepatocytes determines the glutamine-derived nitrogen flow through the urea cycle. This would imply in a clear predominance of ureogenesis in periportal cells because this enzyme is much more concentrated in these cells [7]. Our results did not confirm this hypothesis for low and physiologic ammonia concentrations. Actually, for low ammonia concentrations there was a clear tendency toward lower rates of urea production in periportal cells. Periportal predominance was found only at high ammonia concentrations. In this respect it is noteworthy to mention that in previous experiments, conducted with lactate + ammonia and pyruvate + ammonia as precursors of glucose and urea, predominance of urea production in cells localized down- stream to the periportal region was found for most conditions [12]. The exception was the condition pyruvate + high ammonia concentrations, for which periportal predominance of ureogenesis was found. All these observations are somewhat surprising because periportal predominance of the activity and expression of key enzymes of the urea cycle has been found in several studies [13,26]. It is also true, however, that the enzymes of the urea cycle are present in 93 to 95% of the parenchymal cells.

The key-enzyme carbamoyl-phosphate synthase, for example, seems to be absent only from those hepatocytes immediately surrounding the hepatic venules [26]. The hepatocytes not containing carbamoyl-phosphate synthase are precisely those ones containing glutamine synthetase, which have been estimated as comprising only 5 to 7% [27]. Most hepatocytes, thus, are perfectly able to synthesize urea and the final ureogenic activity will depend not only on the maximal activity (which is that one detected when "enzyme activities" are measured) but also on the real cellular conditions in terms of the concentrations of substrates and allosteric regulators. A question that can be raised at this point is about the factors that limit ureogenesis in the periportal region in spite of the potentially higher enzyme activities [26,27]. With the available data only hypothetical possibilities can be discussed. The production of N-acetyl-glutamate, the key activator of carbamoylphosphate synthase [28] should not be restrained by the periportal availability of glutamate, which is the immediate product of glutamine deamination. It should be remembered, however, that the N-acetyl-glutamate synthase is itself a regulatory enzyme, dependent on regulatory mechanisms with participation of arginine [29] and ornithine [30] whose concentrations are not necessarily equal along the hepatic acinus. Aspartate is an essential amine group donnor for the urea cycle and it is produced by the aspartate transaminase reaction. This enzyme is said to be more active in periportal cells [31,32], but its activity depends on the availability of oxaloacetate and glutamate. The availability of the latter, as already mentioned, should not be a limiting factor. Oxaloacetate, however, could be a limiting factor in periportal cells. This could happen, for example, when a high gluconeogenic activity combines with a rela- Table 1: Changes in glucose, 14  tively reduced state of the malate dehydrogenase reaction, which is detrimental to the oxaloacetate concentration.

Although the glutamine-derived ureogenic flux did not predominate in periportal cells at low ammonia concentrations, this was not determined by the rate of glutamine transformation, which was more elevated in the periportal region for all ammonia concentrations. The latter is indicated by four parameters, 14 CO 2 production from labeled glutamine, gluconeogenesis, lactate production and the corresponding oxygen uptake increments which, when normalized with reference to the corresponding cell spaces that are accessible to ammonia via the hepatic artery, were all more pronounced in periportal cells. The relative distribution between periportal and perivenous cells, however, was not the same for all parameters. The periportal predominance of gluconeogenesis, for example, was more pronounced than that of 14 CO 2 production. This particular observation has at least two causes. The first one is that the difference in 14 CO 2 production reflects solely the unequal distribution of the ammonia-dependent glutaminase along the hepatic acinus [7], whereas the difference in gluconeogenesis reflects both the unequal distributions of glutaminase and of several enzymes of the gluconeogenic pathway which also predominate in the periportal region [2]. The second cause could be  Table 1 were used to calculate v 1R and v 2A using equations (3) to (5) and the numerical procedures described in the text; c 1R and c 2A were calculated from the rates of ammonia infusion, the total flow and the arterial flow as described in the text. related to the inhibitory effect of ammonia on gluconeogenesis. Ammonia is indispensable for glutamine transformation when the latter compound is present at low concentrations, but it also inhibits gluconeogenesis [12,14,15]. Consequently, the final rates of gluconeogenesis in the presence of glutamine plus ammonia are the result of two opposing effects of ammonia: stimulation of glutamine transformation and inhibition of gluconeogenesis. The inhibitory effect of ammonia on gluconeogenesis is not the same in periportal and perivenous hepatocytes [12]. In the present work, indication that it can be more pronounced in perivenous cells is the observation that ammonia infusion into the hepatic artery in antegrade perfusion was always followed by a short period of inhibition of glucose production before stimulation took place (Fig. 3), a phenomenon that was not observed in retrograde perfusion.

Conclusions

It can be concluded that, at least under the conditions of the present work, the glutaminase activity in periportal hepatocytes is not the rate-controlling step of the glutaminederived nitrogen flow through the urea cycle [10]. The current view of the hepatic ammonia-detoxifying system proposes that the small perivenous fraction of glutamine synthesizing perivenous cells removes a minor fraction of ammonia that escapes from ureogenesis in periportal cells [3]. It certainly continues to be a valid assumption that the perivenous cells immediately surrounding the hepatic venules, which contain glutamine synthetase and do not contain carbamoyl-phosphate synthase, are able to remove ammonia solely by glutamine synthesis [26,27]. However, ureogenesis can be very active in cells situated downstream to the periportal zone. Under some conditions it can even be more active in these cells than in the periportal cells [12]. This set of observations indicates that ureogenesis is also an important ammonia-detoxifying mechanism in the perivenous region excepting only the small fraction of cells deprived from carbamoyl-phosphate synthase.

Figure 1
1Schematic representation of some characteristics of the hepatic microcirculation and the experimental protocols. The arrows indicate the direction of flow. Legends: A the presinusoidal confluence of the arterial and portal bed; B the intrasinusoidal confluence of the arterial and portal bed.

Figure 2
2Time courses of ammonia, urea and glucose productions and oxygen uptake during portal infusion of 0.6 mM glutamine. Livers from fasted rats were perfused as described in Materials and Methods. Glutamine was infused as indicated. Data are from 4 liver perfusion experiments and error bars are mean standard errors.

Figure 3
3Time courses of the actions of arterially infused ammonia on urea and glucose productions from [U-14 C]glutamine in antegrade and retrograde perfusion. Livers from fasted rats were perfused as described in Materials and Methods. [U-14 C]Glutamine and ammonia were infused as indicated. Data are from 5 liver perfusion experiments and error bars are mean standard errors.

Figure 4
4Time courses of the actions of arterially infused ammonia on 14 CO 2 production from [U-14 C]glutamine and the corresponding oxygen uptake increments in antegrade and retrograde perfusion. Livers from fasted rats were perfused as described in Materials and Methods. [U-14 C]Glutamine and ammonia were infused as indicated. Data are from 5 liver perfusion experiments and error bars are mean standard errors.

CO 2 and urea productions and oxygen uptake due to glutamine + ammonia as a function of the arterial ammonia infusion in antegrade and retrograde perfusion. data were obtained from experiments of the type illustrated by Figures 3 and 4. The glutamine concentration was the same for all experiments, namely 0.6 mM. The changes correspond to the final metabolic fluxes in the presence of both glutamine and ammonia (70 minutes perfusion time inFigures 3 and 4), subtracted from the fluxes in the sole presence of glutamine. All values were expressed as μmol per minute per ml cell space that is accessible via the hepatic artery in each perfusion mode. The data were analyzed by variance analysis. The p values were obtained by applying the Student-Newman-Keuls test.

Figure 5
5Urea and glucose productions from glutamine and ammonia in 2 different zones along the hepatic parenchyma as a function of the extracellular ammonia concentrations. The corresponding experimental data J ant and J ret in
AcknowledgementsThis work was supported by grants from the Programa Nacional de Núcleos de Excelência (PRONEX; CNPq-Fundação Araucária) and from the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq).Author DetailsLaboratory of Liver Metabolism, Biochemistry Department, University of Maringá, Maringá, BrazilCompeting interestsThe authors declare that they have no competing interests.Authors' contributionsJFC designed and performed the experiments, analysed the data, and drafted the manuscript. FSK co-designed and co-performed the experiments and participated in the discussion of the experimental results. JC co-performed the experiments and participated in the discussion of the experimental results. AB conceived the study, coordinated the implementation of the study and revised the final manuscript.
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Tracing dynamic biological processes during phase transition
2011. September 2011

Tao Zeng
Luonan Chen
Tracing dynamic biological processes during phase transition

From The 5th IEEE International Conference on Computational Systems Biology
Zhuhai, China2011. September 2011R E S E A R C H Open Access
Background: Phase transition widely exists in the biological world, such as transformation of cell cycle phases, cell differentiation stages, disease development, and so on. Such a nonlinear phenomenon is considered as the conversion of a biological system from one phenotype/state to another. Studies on the molecular mechanisms of biological phase transition have attracted much attention, in particular, on different genotypes (or expression variations) in a specific phase, but with less of focus on cascade changes of genes' functions (or system state) during the phase shift or transition process. However, it is a fundamental but important mission to trace the temporal characteristics of a biological system during a specific phase transition process, which can offer clues for understanding dynamic behaviors of living organisms.Results: By overcoming the hurdles of traditional time segmentation and temporal biclustering methods, a causal process model (CPM) in the present work is proposed to study the biological phase transition in a systematic manner, i.e. first, we make gene-specific segmentation on time-course expression data by developing a new boundary gene estimation scheme, and then infer functional cascade dynamics by constructing a temporal block network. After the computational validation on synthetic data, CPM was used to analyze the well-known Yeast cell cycle data. It was found that the dynamics of the boundary genes are periodic and consistent with the phases of the cell cycle, and the temporal block network indeed demonstrates a meaningful cascade structure of the enriched biological functions. In addition, we further studied protein modules based on the temporal block network, which reflect temporal features in different cycles. Conclusions: All of these results demonstrate that CPM is effective and efficient comparing to traditional methods, and is able to elucidate essential regulatory mechanism of a biological system even with complicated nonlinear phase transitions.

Introduction

In the biological world, a phase transition can be defined as the transformation of a biological system from one phenotype or state to another, where different phenotypes can be mapped to distinct states. For example, cell cycle is known to have four distinct phases: G1, S, G2 and M phases; cell differentiation contains different stages like cell proliferation, growth arrest and mature differentiation; and cancer development mainly involves three steps as mutation, promotion and invasion. Obviously, analysing those biological phase transitions will offer valuable clues for understanding life and its dynamics. Therefore, a fundamental but important question is how to trace the temporal characteristics or dynamics of a biological system during a particular phase transition process.

The study on molecular mechanism of biological phase transition has attracted much attention [1][2][3][4]. For instance, by modulating the intracellular redox state and measuring cell cycle progression, the redox cycle within the (mammalian) mouse embryonic fibroblast cell cycle was found to maintain the metabolic processes early in G1 and activate G1-regulatory proteins ahead of entry into S phase [1]. For a well known agricultural pest as migratory locust with a phase transition from the solitary to the gregarious, many down-regulated and some up-regulated genes were found in various organs when arriving to gregarious phase [2], which provides molecular indicators and recovers genetic mechanisms of phase transition in locusts. To determine the dormancy status of raspberry buds whose developmental regulation is helpful to promote the economic values of fruit and horticultural industries, a few significant dormancyrelated candidate genes for raspberry buds had been identified by principal component analysis on clones' expressions [5]. Generally speaking, these research works are mainly on the different genotypes or expression variations at the level of individual genes under specific phases. Despite of those progresses, however, there is much less of focus on studying cascade changes or sequential dynamics of genes' or modules' functions at the level of networks during phase transition process.

As well known to us, one gene generally has multiple roles in biological processes but what role at a specific time is still unclear. Thus, identifying a gene functional group or module, which is composed of cooperative genes in biological processes or pathways, can reveal the functional specificity of individual genes or network modules. On the other hand, nowadays, there is rich information on biological processes [6,7], but the information on biological processes generally lacks dynamic features even compared with pathways [8,9]. Hence, in this paper we intend to identify the sequential structure or cascade dynamics of biological processes during phase transitions by developing a general framework for gene-specific segmentation and temporal block network (or network module), in particular on when and what a biological process or function will be cooperatively facilitated by network modules (or gene modules) during a phase transition. Note that, in the previous studies, the term "dynamic biological process" was usually used to refer to the dynamics of some general biological functional work-flow rather than sequential dynamics of biological processes or pathways [10][11][12]. In contrast, our work focuses on studying conditional and time-dependent behaviours or sequential dynamics of network modules, which are functionally enriched on specific biological processes [13].

The rapid accumulation of temporal gene expression data provides us the opportunity to unveil mechanisms of dynamic processes behind phenotype changes. In particular, a recent work shows that temporal dynamical model has ability to detect the presence and absence of stage/phase specific biological processes in Yeast cell cycle and metabolic cycle [13]. But, this model is limited to the analysis on the time segmentation for all genes, by simply using the replicated observations to infer biological processes' temporal coordination. To overcome this problem, a new bicluster-based temporal segmentation method in this paper is developed to build a causal process model (CPM) for identifying the temporal features of biological processes during genotype or system reorganizations. In addition to biological processes and pathways, network modules or protein complexes [14] are used to further illustrate the sequential dynamics of biological systems as the molecular basis of those functional temporal features. Actually, protein modules or protein complexes have been found to play many important roles in biological phase changes, such as, indicator of genetic effect during mammary gland oncogenesis [15], marker of cancer diagnosis and prognosis [16], predictor of genotype-phenotype associations [17,18], and responser of dynamic cues from the environment [19].

In summary, the construction of our causal process model (CPM) includes three steps. First, we identify specific biclusters with linear patterns, and assemble them into temporal blocks representing a group of genes and their time segmentations. Then, each temporal block is refined by conducting functional enrichment analysis. Finally, we infer the sequential or cascade (causal) relations between temporal blocks by a graphical model (e. g., partial correlation) among two groups of genes. Through various experiments, we demonstrate the effect of our method on gene-specific temporal segmentation. In particular, on Yeast cell cycle data, we show that the phase division based on CPM is more efficient and effective than the segmentation based on traditional CCC-biclustering method [20]; and in the analysis of phase/cell cycle related biological processes, we found that the group of genes actually displays conditional functional enrichment and protein interaction network rewiring. All those results show that CPM is indeed able to unveil the biological mechanism behind complicated phase transitions.

Method

Causal process model: temporal block based on biclusters' assembler Unlike traditional time segmentation methods requiring the same division on a time period for all genes [13] (see Figure 1 (A)), the gene-specific time segmentation is considered in the present work. That means, for different genes or gene groups, they can have different corresponding time segmentations based on their expressions, which can be considered as a general framework without the uniform division constraint. This is why the biclustering methodology [21,22] (see Figure 1 (B)), which can group genes and conditions simultaneously, is adopted. However, as discussed in the study of temporal dynamic model [13], state-of-the-art CCC-biclustering method [20] has the limitation that it usually cannot cover all/most genes and time points. To overcome this problem, an in-house biclustering method (noted as EBB: Error-Bounded Biclustering) is used to enumerate so-called error-bounded linear patterns, e.g. traditional shifting pattern and scaling pattern [22], which can model a group of genes having similar expression change tendency, and further assemble them into the proposed temporal blocks by estimating the following boundary genes.

The brief framework of EBB includes three main steps: (1) discretizing the raw data matrix to a 0-1 matrix by a referred element in data matrix and a given error bound; (2) building a suffix tree based on 0-1 sequences encoded by rows in the above 0-1 matrix where '0' represents left child node and '1' represents right child node; (3) identifying the deepest right-only node in the suffix tree as a potential bicluster with error-bounded linear pattern. In fact, CCC-biclustering is also an exhaustive method [20], but it adopts a significant trend filtering to handle with the data pre-processing and thereby cannot guarantee to find all potential scaling patterns/linear patterns. This problem leads to loss of most low-signal patterns and some important expression patterns (e.g. linear patterns), which prohibit method itself to explore whole information of data. On the other hand, EBB method seeks linear patterns covering traditional shifting/scaling patterns [22] so that it can identify all interesting expression patterns in theory. Besides, EBB can also keep low-varying signals as many as possible because it uses the error bound but not the tendency bound to discrete the raw data.

As well known to us, biclusters represent similar expression behaviors of a group of genes at the same time points. However, our temporal block gathers those genes with the cooperative expression change during a specific time period, i.e. find those genes which simultaneously obtain or lose similar expression with their partner genes. Qualitatively, a temporal block is a sub-matrix in the original data to cover the complete biclusters as many as possible but split the known biclusters as few as possible. According to the following concepts and definitions, the genes on so-called temporal boundary are used to divide the whole data matrix into different matrices named as temporal blocks (see Figure 1 (C)).

Definition 1 (Boundary gene and set) Given a data matrix D = {d m,n } m I,n J , let a set of gene expression patterns as biclusters
{P i = {(G i , T i )|G i ⊆ I, T i ⊆ J}} K i=1 .
Then, a gene g in I is on the temporal boundary at time point t in J only when its R value is larger than a given threshold θ with default value as one, where R is calculated as formula (1). And all boundary genes at every time point consist of a boundary set {BG(t) = {g|R(g, t) >θ, g I}} t J .
R(g, t) = {T i |g ∈ G i , t = min τ ∈Ti τ } max(1, |{τ |τ ∈ J, τ < t}|) {T i |g ∈ G i , t ∈ T i , t = min τ ∈Ti τ }(1)
Definition 2 (Temporal block) Given a matrix data D = {d m,n } m I,n J and its boundary set BG, the temporal block
B i = {(G i , T i )|G i ⊆ I, T i ⊆ J} should satisfy following conditions: (a) ∀g ∈ G i , g ∈ BG(min τ ∈T i τ ) (b) ∀g ∈ G i , g ∈ I − BG(min τ ∈T i τ − 1) or min τ ∈T i τ = min τ ∈J τ (c) ∀g ∈ G i , g ∈ I − BG(max τ ∈T i τ ) or max τ ∈T i τ = max τ ∈J τ (d) ∀g ∈ G i , g ∈ BG(max τ ∈T i τ + 1)or max τ ∈T i τ = max τ ∈J τ (e) ∀G ⊆ G i , T ⊂ T i , (G, T) does not satisfy conditions (a)-(d); (f) ∀G ⊆ I -G i , T = T i , (G, T) does not satisfy condi- tions (a)-(d).
For convenience, min τ ∈T i τ points the starting point or left-end of temporal block and max τ ∈T i τ points the ending point or right-end of temporal block, which are similar for temporal bicluster. Some additional differences between the proposed temporal block and traditional bicluster will be discussed in the next section. Zeng and Chen BMC Systems Biology 2012, 6(Suppl 1):S12 http://www.biomedcentral.com/1752-0509/6/S1/S12

Causal process model: expansion of temporal block for functional enrichment analysis

Like temporal segmentation, CPM gives a non-overlapping division on the whole data. It means that one gene within one time point at most belongs to one temporal block although this gene can belong to a different temporal block but at a different time, i.e. one temporal block cannot cover any other one in CPM. Taking Figure 2 as an example, six genes {(g 1 , g 2 , g 3 , g 4 , g 5 , g 6 )} might have coherent expression on time points {(t 3 , t 4 , t 5 , t 6 )}. In order to reflect the different gene reorganization events happening on time points t 2 and t 3 , these genes are divided into two temporal blocks during the co-expression period. This is just the over-division phenomenon in biclustering study which can supply a multi-granularity model for overlapping patterns [23]. When analyzing functional enrichment on temporal blocks, the over-divided genes should be gathered again. This can be easily achieved by the expansion of temporal blocks.

Definition 3 (Expanded temporal block) Given a data matrix D = {d m,n } m I,n J and its temporal block
B i = {G i , T i |G i ⊆ I, T i ⊆ J}, the corresponding expanded temporal block B i = {G i , T i |G i ⊆ I, T i ⊆ J} satisfies: B * i = {G * i , T * i |G * i ⊆ I, G * i ⊇ G i , T * i = T i }.
Where, C x,y represents the Pearson coefficient correlation between expression profiles of two genes during the time period T * i , and p is a threshold with a default value as 0.8.

Therefore, the temporal blocks are useful to give a global scheme of the data division, and the expanded temporal blocks are suitable to reflect the local property of large data.

Causal process model: temporal block network construction based on partial correlation

In order to extract the cascade dynamics of temporal blocks representing the sequential order of biological processes, there is a need to build a directed network among different temporal blocks whose qualitative connections are evaluated by the partial correlation [24]. It should be emphasized that, at present, our model concerns the linear relationship (i.e., linear pattern in temporal bicluster) so that the correlation but not mutual information is considered in relationship measurement. And to infer direct but not indirect correlation among genes, we adopted the partial correlation to measure association between two genes by removing the effect of their controlling genes.

Definition 4 (Partial correlation) Given three gene expression profiles or vectors X,Y and Z, the partial correlation between X and Y under condition Z is calculated as:
PR(X, Y|Z) = C X,Y − C X,Z C Y,Z 1 − C 2 X,2 1 − C 2 Y,Z(2)
where C.,. represents the Pearson coefficient correlation. Definition 5 (Link strength between temporal blocks) Given two temporal blocks B 1 = (G 1 ,
T 1 ) and B 2 = (G 2 , T 2 ), if min τ ∈T 1 τ ≤ min τ ∈T 2 τ ≤ max τ ∈T 1 τ + 1, these two blocks have a link with direction from B 1 to B 2 . The link strength between their referred gene expres- sion profiles in the time period [min τ ∈T 1 τ , min(max τ ∈T 1 τ , max τ ∈T 2 τ )]
can be calculated as:
LS(B 1 , B 2 ) = X∈G1 max Y∈G2 (min Z∈G2,Z =X,Y PR(X, Y|Z) ) |G 1 |(3)
This strength measurement indicates the potential partial relation from genes in a source block B 1 to genes in a target block B 2 . It requires that the gene X in a source can directly interact with gene Y in a target (the correlation between X and Y is maximal as shown in the above definition), or be indirectly related to Y without the conduction from other target genes (the minimal partial correlation between X and Y under the Zeng and Chen BMC Systems Biology 2012, 6(Suppl 1):S12 http://www.biomedcentral.com/1752-0509/6/S1/S12 control of any Z is maximal as shown in above definition). When the link strength is larger than a threshold with default value as 0.9, the connected temporal blocks are thought to have significant causal relation.

Based on the links (edges) with strengths (weights) among temporal blocks (nodes), the temporal block network (TBN) is constructed for deep analysis on dynamic biological processes. And the execution program (CPM) for temporal blocks can be accessed from http://www. sysbio.ac.cn/cb/chenlab/software.htm.

Result and discussion

There are different characteristics between the proposed temporal blocks and traditional biclusters. Due to the module-in-focus property of biclustering, biclusters always have overlap with each other and have less size (i.e., in terms of clusters) than the original data [20]. The redundancy elimination of those overlapped biclusters is still a relevant and open question in the study of biclustering. On the other hand, in the present work, CPM suffers from few effects of potential bicluster redundancy according to the principles of temporal block construction. In order to divide original time course data, the temporal blocks instead of biclusters are used to build the dynamic model constructed by boundary gene estimation so that any temporal block is not a traditional bicluster pattern but a bicluster assembler. In other words, a temporal block does not represent the coherent expression solely as a bicluster but represents the similar expression pattern change events (condition (a) in Definition 2) as the concept of gene reorganization across the neighbouring time windows [13]. With the conditions (b), (c) and (d) in Definition 2, a temporal block can tolerate the so-called disorder period, thereby allowing the boundary genes to present at consecutive time points located at left-end of temporal block. It can also allow the so-called asynchronous ending period, i.e. allow those genes not on temporal boundary when they present at right-end of temporal block or even allow them not belonging to any original bicluster pattern. Besides, temporal blocks also have completeness guaranteed by Conditions (e) and (f) in Definition 2. These advantages of temporal blocks all let them reasonably represent the non-overlapped subregions of the original whole data.

For instance, in the matrix (with synthetic R values) of above Figure 2, an element in red representing its gene (row) is on the temporal boundary at its time point (column); an element in blue means that its gene is not on the temporal boundary but at the starting time point of a few biclusters; an element in orange points that its gene is not at the starting time point of any biclusters yet. Therefore, the temporal block {(g 5 , g 6 ), (t 3 , t 4 , t 5 , t 6 )} is one without either disorder period or asynchronous ending period, while the temporal block {(g 1 , g 2 , g 3 , g 4 ), (t 2 , t 3 , t 4 , t 5 , t 6 )} covers a disorder period because genes (g 1 , g 2 , g 3 ) are at time points (t 2 , t 3 ) and an asynchronous ending period for genes (g 3 , g 4 ) being at time points (t 5 , t 6 ). Furthermore, the time cost of CPM is mainly on the computation of temporal block construction by temporal bicluster mining, which is similar to CCC-biclustering with a polynomial time complexity [20].

Gene-specific temporal segmentation by CPM shown on synthetic data

First of all, we analyzed CPM on a synthetic data in a simple but typical strategy adopted in the previous studies [23]. We produced a random data matrix with 10 rows and 15 columns. Five predefined blocks or patterns with five genes and four consecutive time points were embedded into such a matrix. As the recovering patterns in the above synthetic data are perfect, we used a strict error bound as 0.0001 and minimum bicluster size as 3*3,3*4,4*3,4*4 respectively to run CPM method (hereafter, the annotation x*y means that one bicluster contains at least x genes and y time points). Under different parameter settings, the divisions with temporal blocks on the whole synthetic data are shown in Figure  3, where one temporal block is surrounded by a yellow box. We should emphasize two points on these results. One is, for the effect of minimum bicluster size setting, the biclusters with a shorter time period will lead to more sub-blocks due to over-division (3*3 in Figure 3 (A) and 4*3 in Figure 3 (C)) than those with a longer time period (3*4 in Figure 3 (B) and 4*4 in Figure 3 (D)), but all blocks are still reasonable and acceptable. The other is, according to the proposed design principles, each temporal block can cover all time points of a predefined pattern and some asynchronous ending period (e.g. cases shown in Figure 3), in order to tolerate the noise/error and divide the whole data in a unified way. Totally, CPM can simultaneously group genes and find gene-specific time divisions, which cannot usually be obtained by traditional time segmentation methods, and it can further split the whole data matrix into different sub-matrices, which is disregarded in many previous biclustering studies.

Phase description by CPM comparing with CCCbiclustering based method

Then, we analyzed CPM for the Yeast Cell Cycle of afactor synchronization experiment of Spellman et al. [25]. This dataset comprises two cell cycles, with each cell cycle containing three phases as M/G1, G1&S, and G2&M [13,25]. Every phase crosses three time points in the experiment with a constant time interval as 7 minutes. After using one-way ANOVA [26] to select genes (i.e. setting the number of sample (time point) groups to be six with prior knowledge in six phases of two cell cycles, and the P-value to be based on the F-distribution with significant threshold as 0.05), remaining data denoted as YCC with 730 genes and 18 time points was used for further analysis. Again, we used different error bounds in {0.05, 0.1, 0.15, 0.2, 0.25} and minimum bicluster size as 10*5 (experience values in previous Zeng and Chen BMC Systems Biology 2012, 6(Suppl 1):S12 http://www.biomedcentral.com/1752-0509/6/S1/S12 study) to build CPMs on YCC data for extensive evaluations.

As described before, the boundary genes can be used to trace the role-change events of a group of genes, and their number would increase greatly at a time point around the alternation of phases [13]. Due to the need to cover the possible disorder period, a few boundary genes are not effective on the temporal block construction and others are just the refined boundary genes locating at the left-end (starting time point) of final temporal blocks. According to the statistic of temporal blocks and their depending boundary genes, Figure 4 shows two kinds of distributions of boundary gene numbers under different CPM parameter settings, where the dotted line represents the distribution of the original boundary genes and the solid line represents the distribution of the refined boundary genes. Obviously, the distributions of numbers of the refined boundary genes unveil more convincible phase related characteristics than those of the original boundary genes, thereby confirming the effectiveness of the temporal blocks. Note that boundary genes mean the refined ones in the following discussions. When the error bound is strictly set to 0.05, the peaks of distributions of boundary genes are always located at the middle time of each phase because genes try to keep their status of steady coordination (note that, the strictest parameter setting as 0.01 results in no bicluster output). When error bound is set to 0.1, the peaks of distributions of boundary genes are always located at the time point of a phase transition because genes usually start to cooperatively facilitate functions at this time and temporal block can cover the potential beginning disorder period. On the other hand, when an error bound is set to 0.15 or even a larger value, distributions of boundary genes cannot keep on their correlations with phases because many noises are introduced to mix up the genes on and not on temporal boundaries. Therefore, CPM can directly use the distributions of boundary genes to trace the critical time points of phase transitions, whose dependent parameter setting will be estimated from both experience of data analyzers and pattern quality evaluation of biclustering. Zeng and Chen BMC Systems Biology 2012, 6(Suppl 1):S12 http://www.biomedcentral.com/1752-0509/6/S1/S12

In order to further confirm the efficiency of the proposed (EBB) bicluster-based segmentation method comparing with other bicluster-based methods, we used temporal biclusters produced by CCC-biclustering [20] (under five different parameter settings and with 1.0 as the default value) to assemble temporal blocks again and re-analyzed the relations between developmental stages and distribution of boundary genes. Compared with Figure 4, the results shown in Figure 5 illustrate that CPM is more suitable on phase description than traditional temporal biclustering based segmentation. The further discussion on the differences between bicluster-based segmentation and traditional temporal segmentation is beyond the scope of this paper because they actually belong to two distinct methodology categories like biclustering and clustering.

Temporal trace identification by CPM with functional enrichment analysis

According to the above discussion on parameter setting, we chose the temporal blocks obtained with the most suitable error bound setting as 0.1 to conduct the following functional enrichment analysis [27]. In the temporal block expansion and temporal block network construction, the default thresholds were all used for calculation.

Biological processes during phase transition revealed by CPM and comparison with temporal dynamical model

Due to minimum length requirement of bicluster, the last four time points were not divided in our experiments. That is why we investigated the biological processes enriched in temporal blocks corresponding to the first phase and the latter two phases in each cell cycle, to compare with temporal dynamical model [13]. Similar to the previous studies, the circular presence and absence of some biological processes in two cell cycles are shown in a chart as Figure 6. The obtained biological processes are close to those identified by temporal dynamic model, such as amino acid biosynthetic process, cell wall chitin biosynthetic process, chromosome condensation and nucleosome assembly [13]. Therefore, CPM indeed can reveal biological processes related to phase transitions, by analyzing the phase segmentation and the temporal block network.

It is worth noting that the potential causal relation between temporal blocks in CPM can further strengthen the cascade relation of phases belonging to intra-or inter-cell cycles. Figure 7 displays the whole temporal block network (where the edges between temporal blocks with same starting points were omitted so as to focus on the major asynchronous temporal relation), in which the nodes represent different temporal blocks denoted as {TB k }; the direct edges represent causal relations; the node label shows the id of temporal block k and its time segmentation [f, t] in the form as "k -[f, t]"; and green, blue, yellow and pink nodes mean phase related, cell cycle related, cross-phases related and other kinds of temporal blocks, respectively.

• Obviously, there are direct edges linking temporal block TB 63 to TB 77 , and temporal block TB 21 to TB 41 . They are actually the phases' relations belonging to intra-cell cycle, which further confirm the phase related biological processes shown in the above Figure 6. • In all temporal blocks, only TB 82 directly connects TB 77 and TB 21 , thereby acting as a bridge of (expression) correlation between the last phases of the first cell cycle and the initial phase of the latter cell cycle. This means that CPM can also identify the phases' relations belonging to inter-cell cycle, and has the ability to infer cascade dynamics of biological functions like biological processes across multiple cell cycles. Note that, the previous temporal dynamic model needs multiple datasets to deduce causal relation between biological processes [13], however, our CPM can infer meaningful functional cascade dynamics during biological transitions even on single dataset. At present, it is actually difficult to deeply discuss the biological processes not starting at a "check point" of some phase or cell cycle due to lack of relevant biological data, however, a few processes like protein-DNA complex assembly or nucleosome assembly enriched in temporal block TB 82 suggest that some of those functions will hold before entering the next phase or cell cycle.

• As the temporal dynamical model strongly shows the similarity of two cell cycles after a-factor handling [13], CPM can even be used to elucidate the specificities for cell cycle related temporal blocks TB 39 and TB 20 in Figure 7. These two cell cycle related temporal blocks (note that their functional analysis will be discussed in detail in next subsections) have not direct edges between themselves, but they can also be directly connected by temporal block TB 82 again. This supports the need and importance of novel temporal blocks across neighbouring functional periods which are modelled by the genespecific temporal segmentation integrated in CPM.

Functional enrichment variance during continuous cell cycles after a-factor treatment

The 1 st cell cycle related temporal block TB 39 covers the former three phases with time points 0-8 and has 12 genes expanded to 432 ones. On the other hand, the 2 nd cell cycle related temporal block TB 20 covers the latter three phases with time points 9-17 and has 42 genes expanded to 400 ones. For those two expanded gene sets, the significant phase (cell cycle)-related biological processes and pathways are listed in Table 1 and 2. Obviously, the 1 st cell cycle related genes and 2 nd cell cycle related genes have shown several different biological processes annotated in GO [28], and the 1 st cell cycle related genes are frequently observed in biological pathways annotated in KEGG and Reactome [29,30]. Therefore such two cell cycles after a-factor treatment  Zeng and Chen BMC Systems Biology 2012, 6(Suppl 1):S12 http://www.biomedcentral.com/1752-0509/6/S1/S12 can be just thought as two super-phases with distinct dynamical properties, which is helpful to understand the cascade dynamics of complicated biological procedures across multiple phases or cycles.

In addition, in order to re-validate the cell cycle specificity on gene expression of such two temporal blocks, we used the genes in them to conduct hierarchical clustering with appropriate distance measurements [31] respectively on our analyzed dataset and other three independent Yeast gene expression datasets which also cover two cell cycles after the a-factor handling. They were downloaded from NCBI GEO with id GDS2318 [32] (one contributed dataset is denoted as YCC-gds2318) and GSE4987 [33] (two contributed datasets as dye-swap technical replicates are denoted as YCC-gse4987-53 and YCC-gse4987-35). On these four datasets YCC (Figure 8 (A)), YCC-gds2318 (Figure 8 (B)), YCC-gse4987-53 (Figure 8 (C)) and YCC-gse4987-35 (Figure 8 (D)) respectively, the genes from TB 39 can correctly classify almost all time points into two cell cycles disregarding the effect of potential circular expression profiles in cell cycles. According to Figure 9, genes from TB 20 also have good performance on clustering time points from different cell cycles. Considering the existence of missing expressions (filled with zero) of genes in other independent datasets, we only analyzed the molecular network behind such cell cycle specificity on our main YCC dataset in next subsection.

Relation among modules and complexes in protein interaction network rewiring and temporal trace of biological phase transitions

The co-expression network [34] was also used to reflect the potential cell cycle specificity after a-factor treatment through the rewired structures of the protein interaction network (PIN). Given a cell cycle related temporal block TB(G, T), we had a group of genes G and obtained the interactions of these genes' encoding proteins from STRING database [35]; with the information of Yeast protein subcellular localization [36] denoted as Yeast-eSLDB, we filtered the interaction by requiring that two proteins involved in one interaction must have a same candidate subcellular localization (this is because one protein may move to several subcellular localizations, and we only consider the location as "Nucleus", which has the most known protein members); based on these co-localization proteins' expression profiles in different cell cycles {T i } i=1,2 (for some i, T = T i ), we calculated the Pearson coefficient correlation of two proteins with an interaction; combining the proteins and interactions with weights (or correlations), we extracted a PIN conducted co-expression network (PCCN).

Thus, we used the genes in TB 39 and TB 20 with their expression profiles during two cell cycles to build four PCCNs. They are denoted as {N c i } i∈{1,2},c∈{1,2} , which mean that the genes/proteins in i cell cycle related temporal block have a rewired PCCN in actual c cell cycle. Figure 10 should indeed have specific network characteristic corresponding to cell cycles. Generally, the genes represented by nodes in light blue belong to TB 39 ; the genes represented by nodes in dark blue belong to TB 20 ; while genes represented by nodes in blue belong to the overlap of such two cell cycle related temporal blocks. Each interaction edge becomes from light & thin to dark & thick when its absolute weight (or correlation) increases. By network visualization of Cytoscape [37], we easily observe the approximate network modules C 2 and C 3 in the Figure 10. The largest protein complex Nucleosomal protein complex extracted from the information of Yeast protein complexes [38] denoted as Yeast-CYC is also highlighted as another module C 1 . It is interesting that three different  Amino sugar and nucleotide sugar metabolism ✔ ✔

Steroid biosynthesis ✔

Fructose and mannose metabolism ✔

Regulation of beta-cell development ✔

Regulation of gene expression in beta cells ✔

Zeng and Chen BMC Systems Biology 2012, 6(Suppl 1):S12 http://www.biomedcentral.com/1752-0509/6/S1/S12 changes of network rewired profile correspond to the specificities of proteins in cell cycle related temporal blocks.

• For proteins in TB 39 , they are densely connected to module C 3 in just the first cell cycle but not the second one; while C 3 always has fewer contacts with proteins in TB 20 so that the presence and absence of relation with module C 3 would be a temporal trace for functional specificity in the first cell cycle.

• For proteins in TB 39 or TB 20 , they present strict interactions with module C 2 in the first cell cycle but lose such relation in following cell cycle. This means, in our mathematical model, TB 39 mainly captures the presence of relation with C 2 while TB 20 tends to mine the disappearance of relation with the same module.

• Dissimilar from the above two conditions, protein complex C 1 strengthens its relation with proteins in TB 20 in just the second cell cycle but not the first one. Hence, the varying relation with protein complex C 1 can be a candidate temporal trace for functional specificity in the second cell cycle.

Therefore, attractively, protein interaction modules and their relations with other proteins above can be thought as the dynamical markers (or temporal traces) of cell cycles in phase transitions. The proposed temporal blocks with the causal process model are indeed effective to efficiently uncover such molecular basis of a biological transition.

Conclusion

To overcome the drawbacks of traditional time segmentation and temporal biclustering methods, the causal process model (CPM) was proposed to study the biological phase transitions in a systematic way. The experimental results validated that CPM can effectively identify gene-specific temporal segmentations by developing a boundary gene estimation scheme, and efficiently infer the potential cascade dynamics of biological processes by constructing a temporal block network. CPM not only has identified the phase-specific dynamic biological processes which were found by the traditional dynamic temporal model, but also revealed cell cycle specific rewiring of the protein interaction network which was missed in the previous studies. All in all, along with the improvement of bicluster enumeration and sparse causal network inference, the proposed CPM can both detect unknown phase transitions in real biological systems, and identify the candidate functional cascade dynamics with temporal traces (or dynamical markers) during the transformation of a biological system.

Figure 1
1Different schemes for time segmentation.

Figure 2
2Illustration of temporal blocks based on the estimated boundary genes.

Figure 3
3Temporal blocks on synthetic data according to CPM with different parameter settings.

Figure 4
4Statistic view of boundary genes by CPM with different parameter settings.

Figure 5
5Statistic view of boundary genes by CCC-biclustering based method with different parameter settings.

Figure 6
6Biological processes with potential circular behaviour enriched in phase related temporal blocks.

Figure 7
7Temporal block network on YCC dataset.

Figure 8
8Hierarchical clustering of genes and time points on four independent datasets according to temporal block related to 1 st cell cycle.

Figure 9
9Hierarchical clustering of genes and time points on four independent datasets according to temporal block related to 2 nd cell cycle.

Table 1
1Biological processes enriched in two cell cycles according to genes in TB 39 and TB 20Biological process
cell 1 st
cycle 2 nd

mannose metabolic process
✔

external encapsulating structure organization
✔
✔

cell wall organization or biogenesis
✔
✔

cell wall organization
✔
✔

cellular cell wall organization or biogenesis
✔
✔

cellular cell wall organization
✔
✔

cytokinetic cell separation
✔
✔

cytokinesis, completion of separation
✔
✔

cytokinesis
✔
✔

transition metal ion transport
✔

iron ion transport
✔

chromatin assembly
✔
✔

nucleosome assembly
✔
✔

DNA conformation change
✔

DNA packaging
✔

chromatin assembly or disassembly
✔

Table 2
2Biological pathways enriched in two cell cycles according to genes in TB 39 and TB 20Pathway
cell 1 st cycle 2 nd

Zeng and Chen BMC Systems Biology 2012, 6(Suppl 1):S12 http://www.biomedcentral.com/1752-0509/6/S1/S12
Authors' contributions TZ and LC conceived the research. TZ performed the study. LC supervised the project. TZ drafted a version of the manuscript. All authors wrote and approved the manuscript.Competing interestsThe authors declare that they have no competing interests.Published: 16 July 2012
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Submit your next manuscript to BioMed Central and take full advantage of: • Convenient online submission • Thorough peer review • No space constraints or color figure charges • Immediate publication on acceptance • Inclusion in PubMed, CAS, Scopus and Google Scholar • Research which is freely available for redistribution. Cite this article as: Zeng and Chen: Tracing dynamic biological processes during phase transition. 12Suppl. Submit your manuscript at www.biomedcentral.com/submitCite this article as: Zeng and Chen: Tracing dynamic biological processes during phase transition. BMC Systems Biology 2012 6(Suppl 1): S12. Submit your next manuscript to BioMed Central and take full advantage of: • Convenient online submission • Thorough peer review • No space constraints or color figure charges • Immediate publication on acceptance • Inclusion in PubMed, CAS, Scopus and Google Scholar • Research which is freely available for redistribution Submit your manuscript at www.biomedcentral.com/submit