Metabolic flux analysis for recombinant protein production by Pichia pastoris using dual carbon sources: Effects of methanol feeding rate

The intracellular metabolic fluxes through the central carbon pathways in the bioprocess for recombinant human erythropoietin (rHuEPO) production by Pichia pastoris (Mut⁺) were calculated to investigate the metabolic effects of dual carbon sources (methanol/sorbitol) and the methanol feed rate, and to obtain a deeper understanding of the regulatory circuitry of P. pastoris, using the established stoichiometry‐based model containing 102 metabolites and 141 reaction fluxes. Four fed‐batch operations with (MS‐) and without (M‐) sorbitol were performed at three different constant specific growth rates (h^?1), and denoted as M‐0.03, MS‐0.02, MS‐0.03, and MS‐0.04. Considering the methanol consumption pathway, the M‐0.03 and MS‐0.02 conditions produced similar effects and had >85% of formaldehyde flux towards the assimilatory pathway. In contrast, the use of the dual carbon source condition generated a shift in metabolism towards the dissimilatory pathway that corresponded to the shift in dilution rate from MS‐0.03 to MS‐0.04, indicating that the methanol feed exceeded the metabolic requirements at the higher µ₀. Comparing M‐0.03 and MS‐0.03 conditions, which had the same methanol feeding rates, sorbitol addition increased the rHuEPO synthetic flux 4.4‐fold. The glycolysis, gluconeogenesis, and PPP pathways worked uninterruptedly only at MS‐0.02 condition. PPP and TCA cycles worked with the highest disturbances at MS‐0.04 condition, which shows the stress of increased feeding rates of methanol on cell metabolism. Biotechnol. Bioeng. 2010; 105: 317–329. © 2009 Wiley Periodicals, Inc.     

甘油及甲醇补料策略对毕赤酵母表达猪α-干扰素的影响

本文研究了甘油及甲醇补料策略对重组毕赤酵母细胞生长及猪α-干扰素(p IFN-α)表达的影响。结果表明,甘油采取不同的补料策略,以及甲醇浓度控制于不同水平时,细胞生长速度不同,p IFN-α抗病毒活性水平也明显不同。高密度发酵阶段,甘油采用指数方式流加控制时,相较于40 g/L/h、10 g/L/h,恒速流加组的细胞浓度最先达最高水平132 g/L,后一直保持稳定,且发酵液中几乎无残留甘油;与之相应的p IFN-α抗病毒活性水平最高。诱导表达阶段,甲醇浓度须控制并恒定于12 g/L时,p IFN-α抗病毒活性最高水平能达到5.95×106IU/m L,而当甲醇浓度稳定于3.5 g/L、16.0 g/L、或者浓度波动较大(10.2~13.8 g/L)时,p IFN-α抗病毒活性均远低于最高水平。     

A rational approach to improving productivity in recombinant Pichia pastoris fermentation

A Mut(S) Pichia pastoris strain that had been genetically modified to produce and secrete sea raven antifreeze protein was used as a model system to demonstrate the implementation of a rational, model-based approach to improve process productivity. A set of glycerol/methanol mixed-feed continuous stirred-tank reactor (CSTR) experiments was performed at the 5-L scale to characterize the relationship between the specific growth rate and the cell yield on methanol, the specific methanol consumption rate, the specific recombinant protein formation rate, and the productivity based on secreted protein levels. The range of dilution rates studied was 0. 01 to 0.10 h(-1), and the residual methanol concentration was kept constant at approximately 2 g/L (below the inhibitory level). With the assumption that the cell yield on glycerol was constant, the cell yield on methanol increased from approximately 0.5 to 1.5 over the range studied. A maximum specific methanol consumption rate of 20 mg/g. h was achieved at a dilution rate of 0.06 h(-1). The specific product formation rate and the volumetric productivity based on product continued to increase over the range of dilution rates studied, and the maximum values were 0.06 mg/g. h and 1.7 mg/L. h, respectively. Therefore, no evidence of repression by glycerol was observed over this range, and operating at the highest dilution rate studied maximized productivity. Fed-batch mass balance equations, based on Monod-type kinetics and parameters derived from data collected during the CSTR work, were then used to predict cell growth and recombinant protein production and to develop an exponential feeding strategy using two carbon sources. Two exponential fed-batch fermentations were conducted according to the predicted feeding strategy at specific growth rates of 0.03 h(-1) and 0.07 h(-1) to verify the accuracy of the model. Cell growth was accurately predicted in both fed-batch runs; however, the model underestimated recombinant product concentration. The overall volumetric productivity of both runs was approximately 2.2 mg/L. h, representing a tenfold increase in the productivity compared with a heuristic feeding strategy.     

Effect of methanol feeding strategies on production and yield of recombinant mouse endostatin from Pichia pastoris

Pichia pastoris, a methylotrophic yeast, is an efficient producer of recombinant proteins in which the heterologous gene is under the control of the methanol-induced AOX1 promoter. Hence, the accepted production procedure has two phases: In the first phase, the yeast utilizes glycerol and biomass is accumulated; in the second phase, the yeast utilizes methanol which is used both as an inducer for the expression of the recombinant protein and as a carbon source. Since the yeast is sensitive to methanol concentration, the methanol is supplied gradually to the growing culture. Three methanol addition strategies were evaluated for the purpose of optimizing recombinant endostatin production. Two strategies were based on the yeast metabolism; one responding to the methanol consumption using a methanol sensor, and the other responding to the oxygen consumption. In these two strategies, the methanol supply is unlimited. The third strategy was based on a predetermined exponential feeding rate, controling the growth rate at 0.02 h(-1), in this strategy the methanol supply is limited. Throughout the induction phase glycerol, in addition to methanol, was continuously added at a rate of 1 g L h(-1). Total endostatin production was similar in all three strategies, (400 mg was obtained from 3 L initial volume), but the amount of methanol added and the biomass produced were lower in the predetermined rate method. This caused the specific production of endostatin per biomass and per methanol to be 2 times higher in the predetermined rate than in the other two methods, making the growth control strategy not only more efficient but also more convenient for downstream processing.     

甲醇抑制时重组毕赤酵母发酵的特性研究

本文对毕赤酵母进行了恒化培养研究。以甲醇为唯一碳源时,在稀释率较低时(D<0.048 h^-1),连续培养系统操作很稳定。但在稀释率高时(D>0.048h^-1),连续培养系统的定态点不止一个,实验不能维持,故采用比生长速率恒定的分批流加培养进行研究。结果表明,毕赤酵母的生长符合Andrew普遍化底物抑制模型。综合考虑水蛭素的生成、底物的消耗,在生产中维持甲醇浓度为限制性浓度(0.5 g/L),且维持比生长速率为0.02 h^-1时,水蛭素Hir65的比生成速率达到最大值0.2 mg/(g·h)且甲醇的比消耗速率为0.04 g/(g·h)。     

混合碳源流加对重组毕赤酵母生产碱性果胶酶的影响

为提高重组毕赤酵母生产碱性果胶酶(PGL)的产量和生产强度,在诱导期采用多种碳源与甲醇混合添加的模式。实验结果发现:甘油、山梨醇、乳酸与甲醇的混合添加均可以提高PGL的产量,其中山梨醇与甲醇的混合流加效果最为显著。研究表明,通过双碳源混合流加可以提高细胞活力,增强醇氧化酶活力,提高毕赤酵母表达外源蛋白效率。当山梨醇的流速为3.6g/(h·L)时,PGL酶活可达1593U/mL,生产强度为16.7U/(mL·h),比对照分别提高了84.6%和45.2%,实现了碱性果胶酶的高效生产。     

Production of lipase by high cell density fed-batch culture of Candida cylindracea

Candida cylindracea NRRL Y-17506 was grown to produce extracellular lipase from oleic acid as a carbon source. Through flask cultures, it was found that the optimum initial oleic acid concentration for cell growth was 20 g l⁻¹. However, high initial concentrations of oleic acid up to 50 g l⁻¹ were not inhibitory. The highest extracellular lipase activity obtained in flask culture was 3.0 U ml⁻¹ after 48 h with 5 g l⁻¹ of initial oleic acid concentration. Fed-batch cultures (intermittent and stepwise feeding) were carried out to improve cell concentration and lipase activity. For the intermittent feeding fed-batch culture, the final cell concentration was 52 g l⁻¹ and the extracellular lipase activity was 6.3 U ml⁻¹ at 138.5 h. Stepwise feeding fed-batch cultures were carried out to simulate an exponential feeding and to investigate the effects of specific growth rate (0.02, 0.04 and 0.08 h⁻¹) on cell growth and lipase production. The highest final cell concentration obtained was 90 g l⁻¹ when the set point of specific growth rate (μ_set) was 0.02 h⁻¹. High specific growth rate (0.04 and 0.08 h⁻¹) decreased extracellular lipase production in the later part of fed-batch cultures due to build-up of the oleic acid oversupplied. The highest extracellular lipase activity was 23.7 U ml⁻¹ when μ_set was 0.02 h⁻¹, while the highest lipase productivity was 0.31 U ml⁻¹ h⁻¹ at μ_set of 0.08 h⁻¹.     

Effect of dilution rate and methanol‐glycerol mixed feeding on heterologous Rhizopus oryzae lipase production with Pichia pastoris Mut+ phenotype in continuous culture

The induction using substrate mixtures is an operational strategy for improving the productivity of heterologous protein production with Pichia pastoris. Glycerol as a cosubstrate allows for growth at a higher specific growth rate, but also has been reported to be repressor of the expression from the AOX1 promoter. Thus, further insights about the effects of glycerol are required for designing the induction stage with mixed substrates. The production of Rhizopus oryzae lipase (ROL) was used as a model system to investigate the application of methanol‐glycerol feeding mixtures in fast metabolizing methanol phenotype. Cultures were performed in a simple chemostat system and the response surface methodology was used for the evaluation of both dilution rate and methanol‐glycerol feeding composition as experimental factors. Our results indicate that productivity and yield of ROL are strongly affected by dilution rate, with no interaction effect between the involved factors. Productivity showed the highest value around 0.04–0.06 h^?1, while ROL yield decreased along the whole dilution rate range evaluated (0.03–0.1 h^?1). Compared to production level achieved with methanol‐only feeding, the highest specific productivity was similar in mixed feeding (0.9 UA g‐biomass^?1 h^?1), but volumetric productivity was 70% higher. Kinetic analysis showed that these results are explained by the effects of dilution rate on specific methanol uptake rate, instead of a repressor effect caused by glycerol feeding. It is concluded that despite the effect of dilution rate on ROL yield, mixed feeding strategy is a proper process option to be applied to P. pastoris Mut⁺ phenotype for heterologous protein production. © 2015 American Institute of Chemical Engineers Biotechnol. Prog., 31:707–714, 2015     

Influence of methanol/sorbitol co-feeding rate on pAOX1 induction in a <Emphasis Type="Italic">Pichia pastoris</Emphasis> Mut+ strain in bioreactor with limited oxygen transfer rate

High Pichia pastoris biomass density could be obtained using high co-feeding rate of methanol and sorbitol in a fed-batch or continuous culture, while further higher feeding rate finally leads to oxygen limitation in bioreactor. In the literature, there is lack of report about AOX1 promoter regulation with regard to dissolved oxygen level (DO). Therefore, in this work, chemostat cultures were performed to investigate the cell growth, metabolism and regulation of the AOX1 promoter (pAOX1) regarding co-feeding rate of optimized methanol/sorbitol mixture (methanol fraction 0.60 C-mol/C-mol) using a P. pastoris Mut+/pAOX1-lacZ strain. The oxygen transfer rates (OTR) in bioreactor were kept in the range of typical values of large bioreactor, i.e., 4–8 g/(L h) if DO equals 30 % saturation or 5–10 g/(L h) if DO nears zero. For DO >0, an increase of the carbon fed led to an increase of pAOX1 induction. By contrast, when dissolved oxygen was completely depleted, methanol accumulated, causing a 30 % decrease of pAOX1 induction. However, this decrease is more likely to be lined to methanol accumulation than to low level of dissolved oxygen (<4 % DO). Methanol/sorbitol co-feeding allowed cells to adapt to oxygen transient limitations that often occur at industrial scale with reduced effect on pAOX1 induction. The optimal feeding rate tested here was 6.6 mmol C (DCW h)^?1 at an OTR of 8.28 g O₂(L h)^?1 with over fivefold pAOX1 induction (probably directly associated with target protein productivity) compared with previous work.     

Patterns of growth and beta-galactosidase production by bifidobacteria

We investigated the patterns of growth and beta-galactosidase formation in the strains Bifidobacterium adolescentis GO-13, MS-42, 91-BIM, and 94-BIM, and B. bifidum No. 1, LVA-3, 791 on media with various carbon sources. The synthesis of beta-galactosidase was shown to be associated with exponential growth of the cultures involved. The maximum specific rate of beta-galactosidase synthesis of 0.20 U mg(-1) h(-1) was observed in B. bifidum LVA-3 after 3-6 h of cultivation. This value for B. adolescentis 91-BIM and 94-BIM was lower and amounted to 0.03-0.08 U mg(-1) h(-1). On the medium with lactose, the highest specific growth rates for B. bifidum LVA-3 and B. bifidum No.1 were 0.38 and 0.60 h(-1), respectively, after 3-6 h of cultivation. For B. adolescentis 91-BIM and 94-BIM, this parameter peaked at 12-15 h of cultivation at 0.13 and 0.22 h(-1), respectively. The hydrolytic activity of beta-galactosidase in the growth medium decreased during the stationary growth phase of the tested cultures.     

Properties of cytochrome c and methanol dehydrogenase produced by wild type and mutant strains of Methylomonas sp. in continuous culture

The cytochrome c production of the wild type strain and a mutant strain, YK 56, of Methylomonas sp. grown with excess methanol was higher than wild with limited methanol. The wild type strain grown under both conditions contained two soluble cytochromes c (c-I and c-II), though the mutant strain contained three (c-I, c-II, and c-III). The proportions of cytochromes c-II and c-III of the mutant strain damage changed according to the culture conditions.The methanol dehydrogenase of the wild type and mutant strains was purified and characterized. The enzymes were similar; they consisted of two subunits and their molecular weight was 120,000. The reactivity of cytochromes c with methanol dehydrogenase was investigated.     

表达血管生长抑制素的重组毕赤酵母在诱导阶段混合碳源的流加

为进行高密度发酵并实现外源基因的高表达,在表型为Mut^S的重组毕赤酵母（Pichia pastoris）表达人血管生长抑制素的诱导阶段,采用了甘油甲醇混合补料的培养方式。以溶氧水平作为甘油代谢指针来控制甘油限制性流加既可维持一定菌体生长,又不会发生发酵液中残余甘油及有害代谢产物（乙醇）阻遏蛋白表达。当表达阶段的菌体平均比生长速率控制于0.012h^-1,菌体浓度达150 g/L,血管生长抑制素浓度最高达到108 mg/L,血管生长抑制素的平均比生产速率为0.02 mg/(g·h),菌体关于甘油的表观得率为0.69 g/g,菌体关于甲醇的表观得率为0.93g/g,较没有采用甘油限制性流加时都有所提高。     

Enhancement of alkaline polygalacturonate lyase production in recombinant Pichia pastoris according to the ratio of methanol to cell concentration

Polygalacturonate lyase (PGL) production by Pichia pastoris GS115 was used as a model to study the mechanism and strategy for enhancing heterologous protein production. It was found that the ratio of methanol to cell concentration had a significant influence on PGL production. In this study, an advanced glycerol exponential feeding strategy was developed for biomass accumulation in cell growth phase, by which cell concentration reached 140 g L(-1) after 19 h glycerol feeding. In subsequent production phase, a methanol feeding profile was proposed according to the optimal ratio of methanol to cell concentration at a range of 0.163-0.171 g g(-1), and PGL activity and productivity reached 430 U mL(-1) and 4.34 U mL(-1)h(-1), respectively. The strategy for enhancing PGL production by controlling the optimal ratio may provide an alternative approach to enhance heterologous protein production with P. pastoris.     

Sorbitol co-feeding reduces metabolic burden caused by the overexpression of a Rhizopus oryzae lipase in Pichia pastoris

To improve the specific production rate of Rhizopus oryzae lipase (ROL) in Pichia pastoris, a protein that triggers the unfolded protein response in P. pastoris, the effect of sorbitol/methanol mixed substrates was tested in batch and fed-batch cultures. Remarkably, a different substrate consumption behaviour was observed depending on the host's phenotype (Mut(+) or Mut(s)) in batch cultures: when the methanol assimilation capacity is genetically reduced (Mut(s) phenotype), both substrates were consumed simultaneously, allowing not only a higher specific growth rate but also higher lipase levels (8.7-fold) compared to those obtained by cells growing on methanol as a sole carbon source in batch culture. This effect was not observed in Mut(+) phenotype, where the two substrates were consumed sequentially and the levels of heterologous product were only slightly higher (1.7-fold). A mixed substrate strategy was also applied to a Mut(s) fed-batch culture at a low methanol concentration set-point (0.5 gl(-1)). This resulted in a 2.2-fold increase in the heterologous protein level achieved, compared with the methanol-only feeding strategy. In addition, sorbitol co-feeding permitted the achievement of higher specific growth rates, and avoided the drastic decrease of the specific production rate observed after the start of the induction phase when methanol was used as sole carbon source This resulted in a significant increase in the overall bioprocess volumetric productivity (2.2-fold) and specific productivity (1.7-fold). Moreover, whereas increased ROL gene dosage in Mut(s) strains have been previously reported to be deleterious for P. pastoris cells growing on methanol, sorbitol co-feeding allowed for sustained cell growth and lipase production.     

氧化低密度脂蛋白经AMPK/mTOR信号通路诱导HUVECs自噬

氧化低密度脂蛋白（oxygenized low density lipoprotein, ox-LDL）诱导人脐静脉内皮细胞（human umbilical vein endothelial cells, HUVECs）损伤有助于动脉粥样硬化（atherosclerosis, AS）的发展。但ox-LDL对HUVECs自噬的影响及机制尚不清楚。为探究其机制,采用体外培养HUVECs,建立ox-LDL损伤模型。透射电子显微镜观察HUVECs中自噬体的变化;Western印迹法检测p-AMPK、AMPK、p-mTOR、mTOR及Beclin1、LC3-II、P62的表达。结果显示,与对照组比较,透射电子显微镜下观察到ox-LDL组的自噬体明显增多。Western印迹结果显示,与对照组比较,ox-LDL组Beclin1(0.81±0.04 vs. 1.83±0.11,P＜0.01)、LC3-II(0.80±0.06 vs. 1.61±0.06, P＜0.01)和P62(0.65±0.10 vs. 1.64±0.17, P＜0.01)表达显著增高。ox-LDL和BafilomycinA1共同干预组Beclin-1(3.15±0.15 vs. 3.17±0.13, P>0.05)、LC3-II(2.95±0.12 vs. 2.96±0.12, P >0.05)和P62(3.26±0.15 vs. 3.19±0.15, P>0.05)表达与BafilomycinA1组无显著差异,ox-LDL未使自噬起始增加,可能是降解受损导致自噬体的积累。与对照组比较,ox-LDL增加p-AMPK (0.47±0.03 vs. 0.96±0.03, P＜0.01)表达,并降低p-mTOR(0.86±0.04 vs. 0.25±0.05, P＜0.01)表达。单独阻断mTOR时, Beclin-1(0.81±0.05 vs. 2.19±0.17, P＜0.01)、LC3-II(0.76±0.13 vs 2.00±0.05, P＜0.01)和P62(0.74±0.12 vs. 1.94±0.11, P＜0.01)表达显著增加。亮氨酸（Leucine）可增加p-mTOR(0.87±0.11 vs. 1.67±0.07, P＜0.01)表达,并降低Beclin-1(0.81±0.05 vs. 0.37±0.03, P＜0.01)、LC3-II（0.76±0.13 vs. 0.41±0.02, P＜0.01）和P62（0.76±0.10 vs. 0.44±0.04, P＜0.01）表达,但ox-LDL可使Leucine预处理后的p-mTOR（1.67±0.11 vs. 0.82±0.02, P＜0.01）表达显著降低,并且Beclin-1（0.37±0.03 vs. 0.78±0.04, P＜0.01）、LC3-II（0.41±0.02 vs. 0.78±0.02, P＜0.01）和P62（0.44±0.04 vs. 0.74±0.04, P＜0.01）表达显著增加。说明mTOR参与ox-LDL诱导的自噬。与ox-LDL组相比,ox-LDL和Si-AMPK共同处理组p-mTOR(0.25±0.05 vs. 0.46±0.03, P＜0.01)表达增加以及Beclin-1(1.97±0.04 vs. 1.26±0.12, P＜0.01)、LC3-II(1.42±0.10 vs. 0.95±0.05, P＜0.01)和P62(1.58±0.09 vs. 0.98±0.11, P＜0.01)表达降低。以上结果表明,ox-LDL通过AMPK/mTOR途径诱导HUVECs发生自噬,并且导致自噬体的积累。     

Use of different carbon sources in cultivation of recombinant Pichia pastoris for angiostatin production

To improve the growth of recombinant Pichia pastoris with a phenotype of Mut^S and expression of angiostatin, the effects of glycerol, sorbitol, acetate and lactic acid which were, respectively, added together with methanol in the expression phase, were studied in a 5-l fermentor. Methanol concentration was automatically controlled at 5 g/l by a methanol monitor and control system, while the feeding of the other carbon source was manually adjusted. The angiostatin production level was 108 mg/l when glycerol was added at an initial rate of 2.3 g/h and gradually increased to 9.9 g/h within an induction period of 96 h. The angiostatin concentration was 141 mg/l as sorbitol was used, while only 52 mg/l were obtained on acetate. The highest angiostatin production of 191 mg/l was achieved as lactic acid was used; whose feeding rate was gradually increased from 2.6 to 11.3 g/h. Lactic acid accumulated during the induction phase and reached 6.3 g/l at the end of fermentation. However, the accumulation of lactic acid did not interfere with angiostatin production, indicating that lactic acid to be a non-repressive carbon source. The average productivity and specific productivity of angiostatin obtained on lactic acid and methanol were, respectively, 2.96 and 0.044 mg/(g h), 1.7- and 2.5-fold of those obtained in the fermentation fed with glycerol and methanol.     

甲醇／山梨醇共混诱导改善重组毕赤酵母表达猪a干扰素发酵过程和NADH再生效率

在10L发酵罐中利用重组毕赤酵母诱导表达猪a干扰素（pIFN-a）,考察甲醇／山梨醇共混诱导策略对pIFN-a表达水平提高和能量（NADH）再生效率的影响。结果表明：在诱导稳定期,甲醇／山梨醇共混诱导可弱化细胞的甲醇代谢,有利于缓解毒副中间产物（过氧化氢、甲醛等）的生成积累;以0．785g／（L·h）的速率缓慢共混流加山梨醇时,pIFN-a抗病毒活性最大,最高活性可达1．8×107IU／mL,与30℃常温甲醇单独诱导（最高活性1．0X10。IU／mL）和20℃低温甲醇单独诱导（最高活性1．4×lO6IU／mL）相比,活性均大幅提高,且胞外pIFN-a的降解减缓;发酵体系的抗高甲醇浓度冲击能力有效提高,发酵生产的稳定性增强;能量利用效率大幅提高,NADH的再生利用效率提高了29％-84％。     

Continuous culture of Candida boidinii variant 60 growing on methanol

Summary A new variant, Candida boidinii variant 60, which is less sensitive to methanol and formaldehyde shocks was grown in continuous cultures with methanol as sole carbon source. The substrate concentration in the feeding medium was either 1% methanol or 3% methanol. Biomass production, methanol consumption, the formation of formaldehyde and gas exchange were measured at different dilution rates. With low methanol feeding (10 g/l) maximal productivity of 0.44 g biomass/l·h is obtained at a dilution rate of 0.14 h^–1. Maximal specific growth rate is 0.18 h^–1. A yield of 0.32 g biomass/g methanol was obtained and the respiration quotient was determined as 0.55. Independently of initial substrate concentration, biomass decreases if methanol and formaldehyde are accumulating in the culture broth.In the culture with high methanol feeding (30 g/l) cell concentratioon increases up to 9 g/l at D=0.04 h^–1. At higher dilution rates methanol and form-aldehyde appear in the medium. Formaldehyde is then preferably oxidized without energy advantages for the cells. It seems that this enables the cells to overcome toxic effects caused by methanol and formaldehyde.     

Mixed-feed exponential feeding for fed-batch culture of recombinant methylotrophic yeast

A simple, accurate model capable of predicting cell growth and methanol utilization during the mixed substrate fed-batch fermentation of Mut^S recombinant Pichia pastoris was developed and was used to design an exponential feeding strategy for mixed substrate fed-batch fermentation at a constant specific growth rate. Mixed substrate feeding has been shown to boost productivity in recombinant fed-batch culture of P. pastoris, while fixed growth rate exponential feeding during fed-batch culture is a useful tool in process optimization and control.