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Efficient metabolic evolution of engineered Yarrowia lipolytica for succinic acid production using a glucose-based medium in an in situ fibrous bioreactor under low-pH condition
Chong Li1,2,
Shi Gao1,
Xiaotong Li1,
Xiaofeng Yang3 &
Carol Sze Ki Lin ORCID: orcid.org/0000-0002-8493-43071
Alkali used for pH control during fermentation and acidification for downstream recovery of succinic acid (SA) are the two largest cost contributors for bio-based SA production. To promote the commercialization process of fermentative SA, the development of industrially important microorganisms that can tolerate low pH has emerged as a crucial issue.
In this study, an in situ fibrous bed bioreactor (isFBB) was employed for the metabolic evolution for selection of Y. lipolytica strain that can produce SA at low pH using glucose-based medium. An evolved strain named Y. lipolytica PSA3.0 that could produce SA with a titer of 19.3 g/L, productivity of 0.52 g/L/h, and yield of 0.29 g/g at pH 3.0 from YPD was achieved. The enzyme activity analysis demonstrated that the pathway from pyruvate to acetate was partially blocked in Y. lipolytica PSA3.0 after the evolution, which is beneficial to cell growth and SA production at low pH. When free-cell batch fermentations were performed using the parent and evolved strains separately, the evolved strain PSA3.0 produced 18.4 g/L SA with a yield of 0.23 g/g at pH 3.0. Although these values were lower than that obtained by the parent strain PSA02004 at its optimal pH 6.0, which were 25.2 g/L and 0.31 g/g, respectively, they were 4.8 and 4.6 times higher than that achieved by PSA02004 at pH 3.0. By fed-batch fermentation, the resultant SA titer of 76.8 g/L was obtained, which is the highest value that ever achieved from glucose-based medium at low pH, to date. When using mixed food waste (MFW) hydrolysate as substrate, 18.9 g/L SA was produced with an SA yield of 0.38 g/g, which demonstrates the feasibility of using low-cost glucose-based hydrolysate for SA production by Y. lipolytica in a low-pH environment.
This study presents an effective and efficient strategy for the evolution of Y. lipolytica for SA production under low-pH condition for the first time. The isFBB was demonstrated to improve the metabolic evolution efficiency of Y. lipolytica to the acidic condition. Moreover, the acetate accumulation was found to be the major reason for the inhibition of SA production at low pH by Y. lipolytica, which suggested the direction for further metabolic modification of the strain for improved SA production. Furthermore, the evolved strain Y. lipolytica PSA3.0 was demonstrated to utilize glucose-rich hydrolysate from MFW for fermentative SA production at low pH. Similarly, Y. lipolytica PSA3.0 is expected to utilize the glucose-rich hydrolysate generated from other carbohydrate-rich waste streams for SA production. This study paves the way for the commercialization of bio-based SA and contributes to the sustainable development of a green economy.
Green technology is becoming a driving force in most industrial sectors because of the current demand to decrease the pollution caused by chemical processing, and the future needs to replace the environmental unsustainable hydrocarbon economy with a renewable and environmentally sound carbohydrate economy. As a building block compound which is currently produced by petroleum-based processes, bio-based succinic acid has attracted increasing interest due to its industrial potential for cleaner production and extensive applications in the food and pharmaceutical industries [1], which leads to rapid expansion of market size in recent years. By 2015, the production of bio-based products was around 150 kilotons, and it is predicted to reach 710.0 kilotons by 2020, growing at a compound annual growth rate of 45.6% [2]. Despite the great demand for SA, the current status of microbiological production is still not economically competitive as compared to the traditional petro-chemical synthesis.
Downstream processing is the most expensive step which affects the final cost of bio-based SA and accounts for 60–70% of the overall production cost. Among all unit operation within the process, the acidification of succinate salt from fermentation broth for separation of succinic acid crystals is one of the most costly steps [3]. To date, the bacterial strains such as Actinobacillus succinogenes and Escherichia coli are considered to be feasible succinate producers. However, they are still unable to grow effectively in a low-pH environment [3, 4], as the excess requirement of energy production for effective retention of intracellular pH and transmembrane gradient of acid is still a question for anaerobic processes due to insufficient ATP generation [5]. In contrast, eukaryotic microorganisms which are known to maintain intracellular pH efficiently could be preferable for such conditions [5]. As an unconventional yeast that is regarded as Generally Recognized As Safe (GRAS) [6], Yarrowia lipolytica has been demonstrated to be suitable for SA fermentation with high yield and productivity under neutral condition [7,8,9,10,11,12,13,14]. More importantly, engineered Y. lipolytica that can produce SA at low pH has been successfully constructed [5, 15], which demonstrated the feasibility of using Y. lipolytica for SA production under low-pH condition. This also led to subsequent reduction in production cost which would bridge the gap between research and commercialization of bio-based SA production.
Nevertheless, owing to the inactivation of the succinate dehydrogenase subunit (SDH), the genetically modified Y. lipolytica reported in the literature mainly uses glycerol as the carbon source for SA production [5, 7, 8, 10], and it was regarded as unable to grow well in glucose-based medium which results from the loss of the FAD/FADH2 recycling pathway [9, 16, 17]. As a feedstock that was commonly used for fermentative SA production [18,19,20,21], glucose is more accessible and could even be obtained from waste streams [22,23,24,25]. Very recently, Bondarenko et al. reported a glucose-consuming Y. lipolytica VKPM Y3753 that can produce SA at pH 3.65 was achieved using an engineered Y. lipolytica VKPM Y3314 which was genetically modified by multistage mutagenesis [26]. Although with lower SA production and higher fermentation pH than that reported by Cui et al. [15] and Yuzbashev et al. [5], the study demonstrated the feasibility of using engineered Y. lipolytica for SA production using glucose-based medium [26]. Recently, a Y. lipolytica strain PSA02004 that is able to grow and produce SA in glucose-based medium under neutral conditions has been developed in our group [17]. Therefore, it would be greatly beneficial if fermentative SA production using glucose-based medium by Y. lipolytica can be achieved in low-pH environment.
Metabolic evolution is an approach to strain improvement for metabolic engineering applications that utilizes a microorganism's natural ability to grow and evolve [27]. Different from the genetic modification applied in Yuzbashev's study [5], the evolutionary phenotype changes and selection via metabolic evolution based on cell growth behavior was identified as a suitable approach for generating an improved strain with the desired metabolic pathways [27,28,29,30]. As an efficient way to gain advantageous mutations through positive selection, it has been successfully used to improve the production of many fermentation products [31,32,33,34,35]. In our previous study, it was successfully used for restoration of glucose metabolism in Y. lipolytica for SA production [17]. On the other hand, as a newly developed fermentation mode which consists of a normal 2.5-L fermenter embedded with immobilized matrix, the in situ fibrous bed (isFBB) fermentation has been demonstrated not only to enhance product production and prevent contamination, but also improve the efficiency of metabolic evolution [7, 8, 17, 36,37,38]. In this case, it is expected that the combination of isFBB fermentation and metabolic evolution would provide new avenues for screening and selection of Y. lipolytica with the desired phenotypic trait and characteristic.
The objective of this study was to obtain an evolved Y. lipolytica strain that can produce SA from glucose-based substrate at low pH via metabolic evolution. First, metabolic evolution of the parent strain Y. lipolytica PSA02004 was carried out via repeated isFBB fermentation with YPD as the cultivation medium for strain selection with a unique character for producing SA steadily under low-pH conditions. Then, the evolved strain PSA3.0 was cultivated in YPD with various initial glucose concentrations. Afterwards, fed-batch fermentation was employed to achieve a high SA production by the evolved PSA3.0 at low pH. Finally, the feasibility of using glucose-rich hydrolysate from food waste for SA production by PSA3.0 at low pH was investigated. Upon successful implementation of metabolic evolution, an improved strain that could produce SA from glucose-based medium at low pH was screened and selected.
Metabolic evolution of Y. lipolytica for SA production at low pH
Metabolic evolution of Y. lipolytica by repeated batch fermentation
Repeated batch fermentation in isFBB was applied to perform metabolic evolution of Y. lipolytica to obtain an evolved strain that can produce SA at low pH using glucose-based medium. Y. lipolytica PSA02004 that can consume glucose for SA production under the neutral condition (pH 6.0) was used as the parent strain in this study [17]. The Additional file 1: Table S1 shows the number of repeated batch fermentation, their corresponding pH, and the name of evolved strains.
First, the Y. lipolytica PSA02004 was cultivated in repeated batch fermentation at its optimal pH 6.0 for eight batches. As shown in Fig. 1a, the cell growth and SA production of PSA02004 varied in the first three batches. Afterwards, cell growth and SA production of PSA02004 became stable during the 4th–8th batches. As shown in Fig. 1a, glucose was completely consumed in about 45 h, and their corresponding glucose consumption rates were around 1.5 g/L/h (Fig. 1f). By setting the specific growth rate of the first batch (0.18 h−1) as 100% (Fig. 1g), the relative specific growth rates fluctuated between 125 and 175%, and the average DCW around 20 g/L were obtained (Fig. 1a) in these batches. On the other hand, the SA production in titer, productivity, and yield were stabilized at around 20.0 g/L, 0.43 g/L/h, and 0.28 g/g, respectively. Since that stable cell growth and SA production were obtained at this pH 6.0, pH of the fermentations was decreased to 5.0 from the 9th batch. As shown in Table 1, high acetate concentration (15.7 g/L) was obtained at pH 6.0.
Metabolic evolution of Y. lipolytica PSA02004 for SA production at low pH. a Cell growth and SA production at pH 6.0. b Cell growth and SA production at pH 5.0. c Cell growth and SA production at pH 4.0. d Cell growth and SA production at pH 3.0. e Cell growth and SA production at pH without control. W.C refers to without pH control. f Glucose consumption rate at different pH. g Relative specific growth rate at different pH, in which the specific growth rate of the first generation was set as 100%. Relative specific growth rate (%) = (specific growth rate in any generation)/(specific growth rate in the first generation) × 100. h, i SA productivity and SA yield at different pH (filled triangles represent glucose concentration; filled circles represent SA concentration; open squares represent DCW; shaded areas represent the corresponding pH; open triangles represent glucose consumption rate; filled square represents the relative specific growth rate; open circles represent SA productivity; open stars represent SA yield)
Table 1 Summary of SA fermentation at different pH via metabolic evolution
When pH was decreased to 5.0 from the 9th batch, inadaptability of the strain was observed. To be more specific, the fermentation time increased from about 45 h at pH 6.0 to over 140 h at pH 5.0 in the 9th batch, in which around half of the glucose (31.5 g/L) in broth was still remained unconsumed (Fig. 1b). Correspondingly, SA productivity decreased by 83.3% to 0.07 g/L/h as compared to the 8th batch at pH 6.0 (Fig. 1h). In addition, a very low relative specific growth rate of 17.5% was recorded in this batch (Fig. 1g). The negative influence of the acidic condition to the strain lasted for three batches (Fig. 1b, g–i) before the cell growth and SA production recovered (Fig. 1b). It should be pointed out that no obvious decline in SA yield was recorded when the pH decreased to pH 5.0 in the 9th batch (Fig. 1i), this indicated that the strain was not damaged. From the 12th batch, cell growth and SA production were fully recovered (i.e., glucose was completely depleted in around 45 h again, as shown in Fig. 1b), while SA production became stable at around 18.0–20.0 g/L in titer and 0.35–0.40 g/L/h in productivity (Fig. 1h). Moreover, the relative specific growth rate increased to 100% in the 14th batch and even higher in the last two batches (i.e., 15th and 16th batches) at pH 5.0 (Fig. 1g). These indicated that the stable cell growth and SA production at pH 5.0 were obtained, and the evolved strain was named as 'PSA5.0' (Additional file 1: Table S1).
On the other hand, when the fermentation pH was decreased from 6.0 to 5.0, acetate production dropped sharply to 3.2 g/L, while pyruvate production increased from 2.5 to 6.7 g/L (Table 1). According to the metabolic pathways of succinate production in Y. lipolytica [15, 17], it may be anticipated that the conversion from pyruvate to acetate was partially blocked in PSA5.0 due to reduced enzyme activities by lowering the environmental pH condition (Fig. 2). It should be pointed out that the relatively high SA conversion rates in the 9th–11th batches should be partially contributed by water evaporation during the extended fermentation period at pH 5.
Metabolic pathways for succinate production in Y. lipolytica
After the progressive selection of the evolved PSA5.0 strain with phenotype improvement for stable SA production at pH 5.0, the fermentation pH was decreased stepwise to 4.0 in the 17th–21st batches. Figure 1c depicts no significant inhibition on cell growth or SA production was observed. In contrast, a significant increase in cell growth (31.5–35.1 g/L DCW, Fig. 1a–c), glucose consumption rate (2.18–2.60 g/L/h, Fig. 1f), and SA productivity (0.62–0.76 g/L/h, Fig. 1h) were observed as compared to that obtained at pH 5.0. This evolved strain that could grow and produce SA stably at pH 4.0 was designated as 'PSA4.0' (Additional file 1: Table S1). Another interesting phenomenon observed in Table 1 was no acetate was detected, but the pyruvate concentration remained at a high level of 5.9 g/L at pH 4, which suggested that the pathway from pyruvate to acetate remained blocked. This may indicate that the inhibition of microbial growth and SA production under low-pH condition was attributed to the presence of acetate (i.e., carboxyl group) instead of the acidic condition (i.e., hydronium ion) [5, 15].
After generating the evolved strain PSA4.0 via incremental reduction in pH to progressively improve the pH tolerance of Y. lipolytica strain, the fermentation pH was further declined to 3.0 in the 22nd–28th batches. As shown in Fig. 1d, h, i, the decrease of pH from 4.0 to 3.0 resulted in no significant change to SA production, and the corresponding SA production in titer, productivity, and yield were around 19.3 g/L, 0.52 g/L/h, and 0.29 g/g, respectively. However, a significant increase in biomass accumulation was resulted, which might be the coupled response of this strain to the acidic condition. Meanwhile, pyruvate production decreased to a level below 1.0 g/L at pH 3.0. These indicate that more carbon source was distributed to biomass accumulation instead of going through the TCA cycle for SA production. The evolved strain selected at pH 3.0 was titled 'PSA3.0' (Additional file 1: Table S1).
Finally, the fermentation pH was decreased to the range of 2.1–2.5 (without pH control) in the 29th–31st batches. As shown in Fig. 1e, SA titer decreased by 60.2% to around 7.4 g/L as compared to that obtained at pH 3.0. Accordingly, SA productivity decreased by over 50% to around 0.20 g/L/h (Fig. 1h). As shown in Fig. 1I, SA yield decreased to below 0.10 g/g in this pH range. In contrast, DCW and the relative specific growth rate remained at high levels (Fig. 1e, g), which demonstrated that most substrate was used for biomass formation instead of SA production in this pH range. This result agrees well with the former studies in bacteria, in which the metabolic evolution is beneficial to ATP generation and thus contributes to microbial growth [28, 29]. However, it is controversial to the study which reported that cells spend more energy on catabolism (i.e., to favor succinate production) at low pH [5]. Due to poor SA production which was resulted at this pH range, metabolic evolution was stopped at this stage and the evolved strain was titled 'PSA 2.5' in Additional file 1: Table S1.
After the metabolic evolution, the evolved strain PSA 3.0 that could steadily grow and produce SA at pH 3.0 was selected for the following experiments for the balance between cell growth and SA production.
Evaluation of the metabolic evolved strain
To evaluate the evolved strain PSA3.0, comparisons in cell growth and SA production between PSA3.0 and the parent strain PSA02004 were conducted by free-cell batch fermentation at pH 3.0 and pH 6.0 (i.e., at the optimal pH of 6.0 for PSA02004 and pH 3.0 for both strains). As shown in Table 2, the evolved strain PSA3.0 grew well at pH 3.0. After 34.5 h, glucose was completely depleted by PSA3.0 and the DCW was 1.5 times higher than that obtained by PSA02004, even at its optimal pH of 6.0. At pH 3.0, poor cell growth of PSA02004 was observed and the DCW only reached at 1.5 g/L after 50 h, which was much lower than that achieved by PSA3.0 at pH 3.0, and thus, it indicates the improved pH tolerance of the evolved strain PSA3.0 in cell growth at low-pH environment.
Table 2 Cell growth and SA production of Y. lipolytica PSA02004 and PSA3.0 at different pH
When comparing SA production of the strains, 18.4 g/L SA with a yield of 0.23 g/g was produced by PSA3.0 at pH 3.0, which were 27.0% and 25.8% lower than that achieved by PSA02004 at its optimal pH of 6.0, respectively. Nevertheless, the SA production by PSA3.0 at pH 3.0 was 4.8, 4.6, and 6.6 times of those obtained by PSA02004 at pH 3.0 in terms of SA titer, yield, and productivity, respectively. Moreover, there was essentially no acetate which was produced by PSA3.0, the downstream process for SA recovery from fermentation broth of PSA3.0 would be simpler than that using fermentation broth of PSA02004 [15, 39]. The results demonstrate the stronger ability of PSA3.0 than the parent strain PSA02004 in SA production at low pH, and it also indicates the success of metabolic evolution.
Comparison of enzyme activities in the initial and evolved strains
To assure the reason for the disappearance of acetate production in PSA3.0, the activities of two enzymes including pyruvate decarboxylase (PDC) and aldehyde dehydrogenase (ALDH), those are responsible for the conversion of pyruvate to acetate in Y. lipolytica were determined and analyzed in the parent and evolved strains, respectively [15]. As shown in Table 3, although PDC activity was present in both strains, the value was 39.2% higher in PSA02004 than that in PSA3.0, which indicated that the activity of PDC may be reduced with the decrease of pH during metabolic evolution. On the other hand, no ALDH activity was detected from PSA3.0, suggesting that its activity also declined with the decrease of pH during the evolution.
Table 3 Enzyme activity measurement of Y. lipolytica PSA02004 and PSA3.0
According to the acetate and pyruvate production summarized in Table 1, it can be inferred that when the pH decreased from 6.0 to 5.0, inadaptability appeared in the strain, and it reorganized the oxidative metabolism to first meet the anabolic requisition for cell growth [40]. Therefore, the activities of PDC and ALDH declined (Table 3), and the formation of acetate decreased sharply from 15.7 to 3.2 g/L. The increased accumulation of pyruvate may result from the impairment of the pathway to acetate. Further decreasing the pH to 4.0 resulted in disappearance of acetate. When the pH decreased to 3.0 (i.e., under an adverse condition), the strain distributed more resource to the anabolic constituents to support cell growth, so the concentrations of metabolites including succinate and pyruvate were even lower than that at pH 6.0, while the DCW doubled.
Effect of the initial glucose concentration on Y. lipolytica PSA3.0
It was reported that a significant amount of byproducts including mannitol, erythritol, and arabitol would be produced from high concentrations of glycerol at low pH by Y. lipolytica [15]. As a result, the effect of the initial glucose concentrations on cell growth and SA production of Y. lipolytica PSA3.0 was investigated.
According to Table 4, SA titer increased from 6.9 to 18.9 g/L with the rise of the initial glucose concentration from 25 to 75 g/L. Similarly, SA productivity doubled and reached the highest at 0.55 g/L/h when the initial glucose concentration was 75 g/L. Continuously increasing the glucose concentration to 150 g/L led to the decline of both SA titer and productivity to only 13.9 g/L and 0.26 g/L/h, respectively. In contrast, with the rise of glucose concentration from 25 to 150 g/L, SA yield decreased constantly from 0.3 g/g to 0.09 g/g, while DCW increased from 19.9 to 49.5 g/L at the same time. This indicates that although a higher glucose concentration is beneficial to the accumulation of cell mass, a glucose concentration range of 50–75 g/L is preferred for the balance between microbial growth and SA production.
Table 4 Effect of initial glucose concentrations on cell growth and SA production of Y. lipolytica PSA3.0
On the other hand, apart from pyruvate and acetate that were produced by Y. lipolytica PSA02004 at pH 6.0, no additional by-product was detected in SA fermentation by Y. lipolytica PSA3.0.
Fed-batch fermentation at low pH for high SA production
Currently, the highest fermentative SA production in titer, either from glucose [41] or glycerol [7], was obtained by the fed-batch fermentation strategy. To achieve a high SA titer at low pH by Y. lipolytica PSA3.0, fed-batch fermentation was employed.
As shown in Fig. 3, the pH of the fermentation broth decreased rapidly from 6.8 to the set point of 3.0 before the depletion of glucose in 28 h, and remained at this value till the end of fermentation. With the decrease of pH, DCW increased exponentially from 0.2 to 31.4 g/L, and reached 50 g/L after two feedings of glucose in 70 h. Afterwards, the DCW remained in the range of 45.3–53.1 g/L till the end of fermentation.
Fed-batch fermentation for SA production by evolved strain PSA 3.0 at low pH. (dotted line represents pH value; filled triangles represent glucose concentration; filled circles represent SA concentration; open squares represent DCW)
SA titer increased gradually with the feeding of glucose. After seven times of feeding, a SA titer of 76.8 g/L resulted in 324 h. This is the highest fermentative SA was titer achieved using glucose-based medium by Y. lipolytica at low pH ever reported to date. However, owing to the relatively long fermentation time, the average SA productivity was relatively low (i.e., 0.24 g/L/h). Moreover, resulting from the shift of the metabolic ratio to anabolic requisition for biomass accumulation, a relatively low SA yield of 0.20 g/g was obtained [28, 29, 40]. Nevertheless, the study demonstrated the successful implementation of metabolic evolution of Y. lipolytica in the fermentative SA production using glucose-based medium at low pH.
SA production from glucose-rich hydrolysate at low pH
The high cost of raw materials is one of the major obstacles to the commercialization of bio-SA [9, 23, 42]. In this study, the feasibility of using MFW hydrolysate as substrate for SA production by Y. lipolytica at low pH was investigated.
As shown in Table 5, the hydrolysate contains a relatively high initial concentration of glucose of 100.8 g/L. Moreover, free amino nitrogen (FAN) concentration in hydrolysate was 1.7 g/L. The high glucose content combined with the existence of FAN indicated that the hydrolysate would be an ideal cultivation medium and nutrient source in the fermentative production of SA [9]. Apart from glucose, other free sugars such as fructose (1.5 g/L) were also obtained from the hydrolysate, and it might be also used as the carbon source by Y. lipolytica in other studies [43, 44].
Table 5 Composition of the mixed food waste hydrolysate
The results for fermentative SA production using the hydrolysate as feedstock by Y. lipolytica PSA3.0 at low pH are depicted in Fig. 4. Glucose in the hydrolysate was completely depleted in 76 h, and SA was produced simultaneously with a titer of 18.9 g/L and a yield of 0.38 g/g. This value is similar to that obtained by Y. lipolytica PGC01003 using crude glycerol as the carbon source [10], but 46.2% higher than that by Y. lipolytica PSA3.0 from the defined medium at pH 3.0 (Table 4). Moreover, when considering the higher resultant DCW (33.8 g/L) of fermentation broth from defined medium at pH 3.0 (Table 4) than that resulting from hydrolysate (i.e., DCW = 12.3 g/L), this indicated that the utilization of hydrolysate as nutrient source would favor SA production instead of cell growth by Y. lipolytica PSA3.0. Based on the fermentation results from hydrolysate, it is inferred that Y. lipolytica PSA3.0 has a good substrate adaptability for SA production at low pH. It is anticipated that the glucose-rich hydrolysate from other carbohydrate-rich waste streams [45,46,47] may also be suitable in the fermentative SA production by Y. lipolytica PSA3.0 at low pH.
Cell growth and SA production of evolved PSA 3.0 under low-pH condition with mixed food waste hydrolysate as feedstock (dotted line represents pH value; filled triangles represent glucose concentration; filled circles represent SA concentration; open squares represent DCW)
This is the first investigation using metabolic evolution of Y. lipolytica in microbial biosynthesis of SA at low pH. The isFBB was demonstrated to improve the metabolic evolution efficiency of Y. lipolytica. The evolved strain PSA3.0 was able to produce 19.3 g/L SA with a productivity of 0.52 g/L/h and a yield of 0.29 g/g from glucose at pH 3.0. Moreover, acetate accumulation was found to be the major reason for inhibition of Y. lipolytica in cell growth and SA production at low pH, which suggested the direction for further metabolic modification of the strain for improved SA production. Furthermore, the evolved strain Y. lipolytica PSA3.0 was demonstrated to utilize glucose-rich hydrolysate from MFW for fermentative SA production at low pH, which indicated the extensive substrate adaptability of the strain. In summary, this study paves the way for the commercialization of bio-based SA, which would contribute to the sustainable development of a green and circular bio-economy.
Strains and medium
The Y. lipolytica PSA02004 used as the starting parent strain in this study was obtained in our former study [17]. The seed culture was prepared by incubating the strain from a cryopreservation vial in a 250-mL shake flask containing 50 mL of YPD medium that was comprised of (w/v) 1% yeast extract, 2% tryptone, and 3% glucose at 28 °C and 250 rpm. The fermentation media used in this study were mainly YPD with various initial concentrations of glucose (25–150 g/L) and pH (2.5–6.0). Carbon and nitrogen sources were prepared separately and sterilized at 121 °C for 15 min.
Chemicals were mainly purchased from Oxoid (Basingstoke, UK) or Sigma-Aldrich (MO, USA). The enzymes used in this study were kindly provided by Novozymes® (China). Enzyme assay kits were bought from Beijing Solarbio Science & Technology Co., Ltd. (China). Mixed food waste (MFW) consisting of rice, noodles, meat, and vegetables were collected from Asia Pacific Catering at Hong Kong Science Park.
Preparation of food waste hydrolysate
Mixed food waste was blended immediately after collection and stored at 4 °C until use. Enzymatic hydrolysis of the MFW and composition determination of the hydrolysate were conducted based on the methods described in our previous study [17, 48]. The MFW was hydrolyzed at a solid-to-liquid ratio of 30% (w/v) in a 2.5-L bioreactor (New Brunswick Scientific, USA) at 50 °C. Enzymes including glucoamylase (1%, v/w), cellulase (1%, v/w), and protease (1%, v/w) were added to the bioreactor when the temperature reached 50 °C. After 24 h when the hydrolysis was completed, hydrolysate samples were taken for composition analysis.
The hydrolysate was sterilized by membrane filtration (0.22 μm, Sartorius, Germany) and stored at − 20 °C until use. The hydrolysate was diluted to obtain glucose at a suitable concentration and supplemented with corn steep liquor (2%, w/v) when necessary [17].
Construction of an in situ fibrous bed bioreactor
The in situ fibrous bed bioreactor was constructed in a 2.5-L bench-top fermenter (Sartorius Biostat B, Germany). After the pretreatment steps of washing, sterilization by steam, drying, crushing, and sieving, 20 g sugarcane bagasse with a suitable size range of 1.0–1.5 mm was put into silk stockings and stitched onto a piece of stainless steel wire mesh. The mesh was then fixed to the baffle of the fermenter to complete the construction [8].
Metabolic evolution of Y. lipolytica PSA02004 for SA production at low pH by repeated isFBB fermentation
isFBB fermentation is a two-stage process, which consists of immobilization and fermentation stages [8]. When the immobilization stage finished, the fermentation broth was replaced by fresh YPD medium. Once the glucose is nearly depleted (< 5 g/L), the fermentation broth was replaced by fresh YPD medium. The process was repeated to start the repeated isFBB fermentation and metabolic evolution.
For the first several batches, the pH of the YPD for replacement was adjusted to 6.0 in advance. The repeated fermentation was carried out at pH 6.0 several times until stable cell growth and SA production were achieved. Then, the pH of the YPD for replacement was adjusted to 5.0 and repeated fermentation was performed at pH 5.0 until stable cell growth and SA production again. Afterwards, the pH of the YPD for replacement was adjusted to 4.0 or 3.0 for the repeated isFBB fermentation. The repeated fermentation without pH control followed with the fermentations at pH 3.0, and the pH of the YPD for replacement was also adjusted to 3.0. However, the pH was not controlled during the fermentation, so the final pH eventually decreased to the range of 2.1–2.5.
Stable cell growth and SA production refer to the DCW and resultant SA of the last several repeated batches at any specific pH (e.g., pH 6.0 or 5.0) were similar. Glucose concentrations in YPD for replacement were around 80 g/L, and the pH of the fermentation was automatically controlled by adding 5-M sodium hydroxide when necessary.
Enzyme activity assay
The parent strain Y. lipolytica PSA02004 was cultured in a 250-mL shake flask at pH 6.0, and the evolved strain Y. lipolytica PSA3.0 was grown at pH 3.0. When they reached the stationary phase, about 10 mL of the culture broth for two strains were harvested and separately suspended in 1-mL extraction buffer consisting of 50-mM Tris–HCl and 20% glycerol at pH 8.0. The cells were broken using 0.4–0.6-mm glass beads (Sigma-Aldrich, St. Louis, MO) at low temperature for 10 min prior to centrifugation. The supernatant was obtained and put on ice for further analysis [15].
The activities of pyruvate decarboxylase (PDC) and aldehyde dehydrogenase (ALDH) were determined by Assay Kits (Cat Number: BC1070 and BC0750, respectively; Solarbio Science & Technology Co., Ltd., Beijing, China). The principle of these methods was based on spectrophotometry, and detailed description is provided in the specifications. In general, the crude enzyme solutions were obtained and they were mixed with special reagents that provided in the kits, and then, OD340 was measured per minute. The difference in OD340 at various time intervals was used for enzyme activities calculation based on the corresponding equations provided in the specifications. The same procedures were conducted for the control group, except that the crude enzyme solution was replaced by DI water.
Free-cell batch fermentation
To evaluate the results of the metabolic evolution, free-cell batch fermentation was carried out for SA production using YPD with an initial glucose concentration of 80 g/L at pH 3.0 by the evolved strain Y. lipolytica PSA3.0. Fermentations with the initial strain of Y. lipolytica PSA02004 at pH 3.0 and 6.0 were set as the control. The free-cell batch fermentations were performed in 2.5-L bench-top fermenters with a working volume of 1.0 L at 28 °C, with an agitation speed of 600 rpm and aeration rate of 2 L/min.
To investigate the influence of the glucose concentration on cell growth and SA production of the evolved strain PSA3.0, fermentations were carried out with various glucose concentrations from 25 to 150 g/L. The initial pH of the YPD media was between 6.0 and 7.0 after autoclaving, and decreased naturally until pH 3.0 where it was controlled.
To test the feasibility of using cheap substrates for SA production at low pH, hydrolysate containing an initial glucose concentration of 50 g/L from mixed food waste was used as feedstock for fermentative SA production by Y. lipolytica PSA3.0. Corn steep liquor (2%, w/v) was supplemented as the nitrogen source.
Fed-batch fermentation for SA production
Fed-batch fermentation was carried out in a 2.5-L bench-top bioreactor at 28 °C, with an agitation speed of 600 rpm and aeration rate of 2 L/min. The initial glucose concentration of YPD medium was 50 g/L, and about 80–100 mL of 500 g/L glucose was fed to supplement the carbon source when the glucose concentration was below 10 g/L.
Microbial growth was determined by OD600 and DCW [8]. The specific growth rate (μ) was calculated by the following equation:
$$ \mu = \frac{1}{X} \times \frac{{{\text{d}}X}}{{{\text{d}}t}}, $$
where X is DCW and t is fermentation time.
Concentrations of glucose, SA, and other organic acids were determined by HPLC (Waters, MA, USA) [8]. Unless specifically stated, all the concentrations of substrate and products in isFBB fermentation were calculated after subtracting the residues from the previous batches. The content of the free amino nitrogen (FAN) was measured using the ninhydrin reaction method as described in Lie's study [49]. SA yield in this study refers to the amount of succinic acid (g) produced from the initial amount of glucose (g).
Apart from fermentations for metabolic evolution at any specific pH value (i.e., from 6.0 to 3.0 or even without control) were repeated more than three times until stable cell growth and SA production obtained, and the fed-batch fermentations were performed in duplicate; all other experiments were performed in triplicate. It should be pointed out that data in all tables of this study are shown as mean ± standard deviation.
isFBB:
in-situ fibrous bed bioreactor
free amino nitrogen
pyruvate decarboxylase
ALDH:
DCW:
dry cell weight
N.D:
W.C:
pH without control
TCA cycle:
tricarboxylic acid cycle
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Lie S. The EBC-ninhydrin method for determination of free alpha amino nitrogen. J Inst Brew. 1973;79(1):37–41.
CL designed and wrote the manuscript. CL and SG carried out the major parts of the experiment, and XL carried out the enzyme activity assay. XY participated in the data analysis and manuscript revision. CSKL participated in design of the study, revision of the manuscript, and coordination of the work. All authors read and approved the final manuscript.
The authors acknowledge the Strategic Research Grant from City University of Hong Kong [Project No. 7004922]. Dr. Xiaofeng Yang acknowledges the support by the Fundamental Research Funds for the Central Universities [2017BQ025].
Data supporting the results of the article are included within this manuscript.
All authors have approved the manuscript for publication.
The work described in this paper was supported by the Strategic Research Grant from City University of Hong Kong [Project No. 7004922], and the Fundamental Research Funds for the Central Universities [2017BQ025].
School of Energy and Environment, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong
Chong Li
, Shi Gao
, Xiaotong Li
& Carol Sze Ki Lin
Agricultural Genomic Institute at Shenzhen, Chinese Academy of Agricultural Sciences, Shenzhen, 518120, Guangdong, People's Republic of China
School of Biology and Biological Engineering, South China University of Technology, Guangzhou, 510006, People's Republic of China
Xiaofeng Yang
Search for Chong Li in:
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Correspondence to Carol Sze Ki Lin.
13068_2018_1233_MOESM1_ESM.docx
Additional file 1: Table S1. Number of repeated batch fermentation, their corresponding pH and the names of evolved strains.
Li, C., Gao, S., Li, X. et al. Efficient metabolic evolution of engineered Yarrowia lipolytica for succinic acid production using a glucose-based medium in an in situ fibrous bioreactor under low-pH condition. Biotechnol Biofuels 11, 236 (2018) doi:10.1186/s13068-018-1233-6
Metabolic evolution
Yarrowia lipolytica


text:
Seeing Red, Alice, Sean Rosen, Better Nate Than Ever, and first award prediction of the year
Another round-up of good recent reads:
Seeing Red, by Katherine Erskine. I'm surprised I haven't heard more about this one, out in October. Katherine Erskine's writing process seems to involve putting a character in a tough situation, finding several ways to make the situation tougher, and then challenging the character to do the right thing. In this case, Red, who lives in 1972 Virginia, has just lost his father and is desperately against his mother's plan to take the family back to her home state of Ohio. That desperation makes him willing to do anything (he thinks) to prevent the sale of their land, but that "anything" turns out to include using race. Red gets caught up in things he doesn't believe in, and ends up a reluctant participant in a scene that amounts to kids playing at KKK-type activities. There's no permanent physical damage, but the images are frightening nonetheless, and I admire Erskine's willingness to show how a generally sympathetic character can be driven to do something evil, and then to stick with that character through the fallout. This is upper-middle-grade, and I think I would've been ready for it around 11 or 12.
On a very different note, several omnibuses of Phyllis Reynolds Naylor's Alice books have recently come my way, so I've been catching up on my Alice in preparation for upcoming series finale. I'm sure I'll have more to say once I've finished the series, but oh, Alice, I'm glad you're there in all your sometimes ridiculous and didactic glory.
I Represent Sean Rosen is a fun and silly middle-grade novel about a kid who has a cool idea for Hollywood, but no idea how Hollywood works. Think of him as a slightly more successful Timmy Failure, and though it's not quite semi-graphic, parts of it are written in screenplay form, which breaks up the text. Between that, the humor, and the Hollywood connection, this could be a great light read for readers on the reluctant side. I'll very likely recommend it the next time a parent begs me for "something that isn't Wimpy Kid" (while I praise Wimpy Kid as a gateway series).
Better Nate Than Ever is another story about a kid with grand showbiz dreams, one who sneaks off to New York to try out for a Broadway musical. I did a lot of you're thirteen and innocent and practically penniless and alone in New York, you brave idiot panicking for the poor kid, but I also did a lot of nodding. Because this is a middle-grade novel about a boy who's getting teased about maybe being gay, and who isn't quite sure whether he is or not, but who is reassured to see same-sex couples walking around openly in New York. With the exception of the graphic novel Drama, I haven't seen this topic covered at length for an audience younger than YA. (Books showing gay parents and other adults are a valuable thing, but they're a different thing from this.) I have thoughts, lots of them, about how children's lit as a whole portrays boys with nontraditionally male interests, but that's a topic for another post (probably in the near future). For now, I'll just say that this is one of the types, though not the only type, of book I'd like to see more of.
The Thing About Luck by Cynthia Kadohata shows a family of Japanese-American migrant workers. Summer, age 12, has a lot to put up with, beginning with a prickly grandmother whom I kept wanting to shake. There's a lot of humor and a lot of originality in this one - how many novels have main characters obsessed with bug spray because they've just recovered from malaria? A great glimpse into the modern migrant working culture, which I hadn't known much about, and also a great story.
Finally, if Neil Gaiman's The Ocean at the End of the Lane doesn't win an Alex Award, I'll eat a bug. (There are, like, chocolate grasshoppers or something to get me out of this if I need it, right?)
Fasten your Backseatbelts...
NPR released its "Ultimate Backseat Bookshelf" this week - its recommendations of "books that every 9- to 14-year-old should read," in the words of the call for listener suggestions. That phrasing sticks in my craw; I'm sure the intent was to highlight the awesomeness of the books, but it comes off as prescriptive, and if there's one thing I'd love all whatever-to-whatever-year-olds to learn, it's that they can make reading into whatever kind of experience they want by choosing their own reading material.
And once you get rid of that "should" business, it's a great list that sends exactly that message. Like the extensive summer reading list from our local schools, this list is broken into categories that practically scream, "You get to spend your reading life on whatever kinds of books you want!" You like magic? The NPR list has a "Fantasy Worlds" category. Prefer a cozier read? Try something from the "Family Life" list. Graphic novels count. So does nonfiction, with or without lots of pictures (or adolescent snark from a certain young diarist). You can read about kids whose backgrounds are like your own or different from your own, whoever you are. You can read a book that says "ages 9 to 12" when you're 8 or 13, and you can skip a book that doesn't look interesting and, if you want, come back to it when you're 29 or 92.
"Must-read" in the sense that we might call a summer blockbuster a "must-see?" Heck yes. I just hope no one's looking at that list as "must-read" in the homework sense.
Labels: If I used tags all of them would be "reader choice"
Preview time!
Is it just me, or are there a lot of cool projects on the horizon?
Here's one: Laurie Halse Anderson and artist Emily Carroll are adapting Speak into a graphic novel. There's so much that's visual about this story, and I imagine the new format will highlight the contrast between Melinda's silence and everyone else's chatter. Just look at that piece of sample art in the article linked above. I really think this has the potential to be something special. Tentatively Fall 2016 (which makes me think they're putting a lot into it.)
So does the Hallmark Channel's upcoming film of The Watsons Go to Birmingham -1963 (film title simply The Watsons Go to Birmingham). What I love about Christopher Paul Curtis, especially in this book, is his power to create absolutely hilarious characters who are loveable in completely three-dimensional ways. When history happens in his books, we care that it's happening because we care about the people it's impacting. My sense from this featurette is that the movie remembers to emphasize all that; I see loving family scenes, I see Byron's tongue frozen to a car window, and I see the serious aspects of the book, too. (September 20) (Fear not, fellow lackers of cable - it looks like there will be a DVD.)
And then there's Dear Mr. Watterson. The first person who says anything in the trailer talks about how Calvin and Hobbes got him to read. Sounds like a movie after my own heart. (November 15)
I'm not saying the summer should end any faster. I'm just saying good stuff is coming afterwards.
And what would *you" steal from a children's book?
This week, I've been getting my background noise from the Kidlit Red Carpet. Interviewers Jim Averbeck, Betsy Bird, and Kristin Clark spend blessedly little time grilling Newbery-Caldecott-Wilder Banquet attendees about their outfits, instead getting actual interesting information out of them. Many of the authors and illustrators revealed their upcoming projects, some of which were new to me. For instance, did you know Brian Selznick is working on another book in the style of The Invention of Hugo Cabret and Wonderstruck? The word "trilogy" came up (in terms of "structure" and "theme"), and if this one has another one-eyed spine, the S-shelf is going to look a little creepy... but seriously, I can't wait. (And yes, that's what face-outs are for.)
Daisy of Chris Raschka's A Ball for Daisy is getting another book, and Patricia Polacco has a new companion coming out to the 25-year-old The Keeping Quilt. Katherine Paterson and her Brother Son, Sister Moon collaborator Pamela Dalton have a beautiful-sounding new book about how people give thanks around the world. Sheila Turnage says her protagonist keeps giving her sequels; we'll see Three Times Lucky heroine Mo LoBeau at least three times. And Leonard Marcus has a new biography of Randolph Caldecott, who sounds like he was quite a character himself.
In honor of the high-profile theft in current winner This Is Not My Hat, the interviewers asked the passing luminaries what object they would most like to steal from a Caldecott winner/any picture book/any work of children's literature; the parameters changed a few times. If the answer is limited just to Caldecott winners, I think I'd have to go for Sylvester's magic pebble and just use it very, very carefully. If the pilfered item can come from anywhere in kidlt (and not necessarily American kidlit), then the real question is which magical gadget I would steal from Harry Potter and friends. Hermione's time-turner, I think. Of course, there are other magical worlds full of goodies, and Lyra does have an alethiometer, though I might first have to steal Will's knife to get to it... Maybe I should just keep it simple and, in the tradition of a Klassen character, steal a snazzy hat.
If you need me, I'll be sneaking through the pages of Go, Dog, Go.
Posted by Shoshana at 11:53 AM No comments:
Seeing Red, Alice, Sean Rosen, Better Nate Than Ev...

redpajama_set_name: RedPajamaCommonCrawl


This track's about when you're with someone you really care about and it all sort of falls apart. You replay those last moments over and over again in your head. It consumes you. Although at the same time it's kind of liberating and inspiring. I really love the instrumentation for this song as well as the way it builds. Its another one of my favourites from the EP.


text:
SAVE THIS | EMAIL THIS | Close
Amazon announces e-book loans for the Kindle
(CNN) -- Want to check out e-books from the library and read them on your Kindle? That will be possible later this year as Amazon announced Wednesday that it would join a library loan program for electronic books.
More than 11,000 libraries in the United States participate in this electronic-book-loaning program, managed by a company called OverDrive.
Amazon, whose Kindle is the top-selling e-reader, is the last big e-book company to make this technology available. The Barnes & Noble Nook and Sony Reader already allow users to check out digital books from their local libraries using the service, according to OverDrive.
The company offers more than 400,000 digital books and has had a library loan program for e-books since 2003, said David Burleigh, an OverDrive spokesman.
The electronic-book checkout process is similar to that for real-world books. Libraries purchase licenses to offer certain titles to their patrons. Books are checked out for a certain period of time -- two weeks in many cases -- after which they become locked and inaccessible on a person's e-reading device.
"Most of the books in the collection are one copy, one user, which is similar to the print model," Burleigh said. "So when it's checked out it's unavailable for anyone else until it's returned."
Amazon said the library books will be available on the Kindle "later this year," but the company did not specify a launch date. The free e-books will be available though Kindle apps on smartphones and on the Kindle e-reader device, which can download books over Wi-Fi or 3G internet connections.
The service will work only in the United States.
"We're excited that millions of Kindle customers will be able to borrow Kindle books from their local libraries," Jay Marine, Amazon's director for the Kindle, said in a press release.
The library books will sync with many of the Kindle's existing features.
"Normally, making margin notes in library books is a big no-no. But we're extending our Whispersync technology so that you can highlight and add margin notes to Kindle books you check out from your local library. Your notes will not show up when the next patron checks out the book. But if you check out the book again, or subsequently buy it, your notes will be there just as you left them, perfectly Whispersynced," the Amazon release said.
Kindle users will have to check out books through their local libraries, so they will need a library account to use the service. To see if your library has a contract with OverDrive, and therefore will be able to loan you Kindle books, go to overdrivesearch.com and type in your ZIP code.
OverDrive's Burleigh said this service helps make library services available to new groups of people, who may not be inclined to go to a physical library to check out hard copies of books.
"Libraries have always been at the forefront of making new forms of reading available," he said. "It's helping them do that and to reach more people in their communities."
http://www.cnn.com/2011/TECH/mobile/04/20/amazon.kindle.library.loan
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© 2008 Cable News Network


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Dodgers Briefing: New batter's eye, injury updates, Chico mania
Max Muncy, Los Angeles Dodgers. (Photo by Ralph Freso/Getty Images) /
GLENDALE, ARIZONA – FEBRUARY 20: Pitcher Edwin Uceta #92 of the Los Angeles Dodgers (Photo by Christian Petersen/Getty Images) /
2. Three players added to the injured list
As the Dodgers still wait for six players from their 40-man roster to report to summer camp (Tony Gonsolin had been missing, but reported yesterday), the team announced three players have been added to the 10-day Injured List – Edwin Uceta, Cody Thomas, and Zach Reks – without providing reason as to why.
Player pool: While none of Uceta, Thomas, or Reks are on the 40-man roster, all three were included on the Dodgers' initial player pool. Players must be included on the player pool to be eligible to play this season. They cannot be removed without being released, traded, suspended, or suffer serious injury (including Covid-19 exceptions).
Cody Thomas: The 25-year-old left-handed hitter was hitting the cover off the baseball in the Cactus League before play was suspended. He hit 5 home runs in 12 games, batting .318/.333/1.091 along the way. He is coming off a strong season in Double-A Tulsa where he hit 23 home runs and drove in 76 RBIs.
Edwin Uceta: The 22-year-old right hander is coming off a strong season at Tulsa (AA) and Rancho Cucamonga (A+) where he made 24 combined starts and went 11-2 with a 2.77 ERA.
Zach Reks: After quitting baseball in 2014, Reks found his way back to the sport and arrived at his first big league camp this past spring. Playing for both Tulsa (AA) and Oklahoma City (AAA) last season, he batted .291/.385/.536.


Oxbo International develops, manufactures, supplies and services specialized agricultural equipment worldwide. Oxbo International offers equipment for pesticide, nutrient, and waste application, berries, coffee, commercial corn, fresh market vegetables, forage, jatropha, olives, processed vegetables, seed corn and vineyards. Strong values such as integrity, innovation and superb commitment to customer service are at the root of Oxbo's business approach.


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Q: UINavigationItem titleView "ignored if leftBarButtonItem is set"? The documentation for UINavigationItem's titleView property says:

"This property is ignored if leftBarButtonItem is not nil."

However, I've set both the titleView and leftBarButtonItem properties in my testing and they both appear to show up fine. I've tested on all the simulators in my Xcode: 4.3, 5.0, and 5.1. Does anyone know if the documentation is just wrong, or is it correct on some older versions (e.g. 4.2, 3.x) that I haven't been able to test?

A: Check the documentation for property leftBarButtonItems, it says:

If there is not enough room to display all of the items in the array,
  those that would overlap the title view (if present) or the buttons
  on the right side of the bar are not displayed.

So, what's said for titleView is probably incorrect.

A: I think the documentation is wrong, and you should file a bug report.

A: I tested this on iOS6.1 and iOS7. My UINavigationItem had a non-nil titleView and leftBarButtonItem, and both the titleView and leftBarButtonItem were visible. I filed a radar.

A: I've run into this as well. In My specific problem both the titleview and leftbar item would appear. However If I had a Back Button then my titleview would disappear on Push and use the default title. If I have a custom uibuttonitem set for the left it works fine. So It seems to be related to back button. I ended up solving by setting title attributes and no doing a custom view.

A: I just ran into this and found the same thing you did. I also noted that the documentation for UINavigationItem was last updated in 2011, while UINavigationBar got updates in both iOS 5 and 6, so it's possible this behavior changed since the last time the UINavigationItem doc was updated.
Very confusing though.
Noticed this as well in UINavigationController's reference:

"The navigation controller updates the middle of the navigation bar as follows:
...
If the new top-level view controller has a custom title view, the navigation bar displays that view in place of the default title view. To specify a custom title view, set the titleView property of the view controller's navigation item."

Since there's a leftBarByButton (the back button) by definition anytime you're at the non-root view, it sure seems like a mistake in the UINavigationItem's documentation

redpajama_set_name: RedPajamaStackExchange


Day and night runners for the stable on Friday as Bianco Nuovo heads to Geelong and Touch A Cloud is under lights at Cranbourne.
Bianco Nuovo runs in the first race, the Maiden Plate over 2200m where he will be ridden by Rhys McLeod and jump from barrier two.
The son of Artie Schiller has improved as he has stepped up in trip and last start finished a close second at Warrnambool over 1700m.
Mike Moroney is expecting the extra distance of his race on Friday to suit even further.
"We've always had a decent opinion of him and he's improving with racing," Moroney said.
"His last start was excellent - he just got left in front a bit too soon and was left a sitting target for the winner.
Touch A Cloud (pictured) is in race three at Cranbourne, the 3YO Fillies Maiden Plate over 1400m with Jordan Childs to ride and jump from barrier four after scratchings.
The daughter of Glass Harmonium pleased with third on debut over 1300m at Cranbourne last month.
"She's come out of her first run really well and continues to progress," Moroney said.
"I've always thought she will be better over a bit further so it will be interesting to see how she copes tonight.


text:
Q: Finding the slopes of the sides of a triangle, when only given the slopes of internal angle bisectors Finding the slopes of internal or external angle bisectors, when given the slopes of the sides of a triangle, it's a simple question, the one you can easily find in any textbook of analytic geometry.
But  the reverse problem : finding the slopes of the sides of a triangle, when only given the slopes of internal angle bisectors. Is it possible? Is there a straightforward formula for that?

A: Yes. The slopes of the internal bisectors intersect at the incentre I. You will thus know the angles AIB, BIC and CIA.
180 = AIB + IAB + IBA
180 = ACB + 2*IAB + 2*IBA
ACB = 2*AIB - 180
From this you can figure out the side slopes.

A: Thanks, Paul Childs, finally the solution dawned on me!
First step: Knowing the slopes of the bisectors you calculate tan(A/2), tan(B/2), tan(C/2).
Second step: you calculate the slopes of straight lines from the vertices making these angles to the bisectors.
Case closed.


Located on the corner opposite the National Gallery of Victoria and Melbourne Theatre Company's Southbank Theatre, Buxton Contemporary is the home of Melbourne property developer and collector Michael Buxton's art collection. He's got a great eye for contemporary Australasian art, and his first exhibition included work by Patricia Piccinini, Mikala Dwyer, Emily Floyd, Marco Fusinato and Shaun Gladwell. He's also collected work by luminaries like Howard Arkley, Mike Parr, Tracey Moffatt and Bill Henson.
The 2,200 square metre gallery, which opened in March 2018, is designed by leading Australian architects Fender Katsalidis, the team behind Hobart's MONA. It features five large galleries and a teaching space, which is rather appropriate as the building is part of the University of Melbourne's Victorian College of the Arts.