- Email: [email protected]
Simulating the dynamics of lipid droplets in adipocyte differentiation
computer methods and programs in biomedicine 138 (2017) 65–71
j o u r n a l h o m e p a g e : w w w. i n t l . e l s e v i e r h e a l t h . c o m / j o u r n a l s / c m p b
Simulating the dynamics of lipid droplets in adipocyte differentiation Federico Boschi a,*, Vanni Rizzatti b, Mauro Zamboni b, Andrea Sbarbati c a
Department of Computer Science, University of Verona, Strada Le Grazie 15, 37134 Verona, Italy Department of Medicine, Geriatric Section, University of Verona, Piazzale Stefani 1, 37126 Verona, Italy c Department of Neurological and Movement Sciences, University of Verona, Strada Le Grazie 8, 37134 Verona, Italy b
A R T I C L E
I N F O
A B S T R A C T
Article history:
Background: Lipid droplets are cellular organelles that regulate the storage and hydrolysis
Received 20 June 2016
of neutral lipids. The dynamic of lipid droplets (LDs), during the differentiation process from
Received in revised form
fibroblast-like cells into adipocyte, is strictly related to the lipid storage in cells. The number
3 October 2016
and size of the LDs depends on the lipidic or lipolytic stimulations to which the cells are
Accepted 18 October 2016
exposed. Method: Here, we propose a computational approach to study the processes regulating the
Keywords:
LDs’ number and growth/reduction in size using Monte Carlo simulations. The number and
Lipid droplet
size of LDs are measured before and after experimental treatment in 3T3-L1 cell cultures.
3T3-L1
The algorithms simulating the evolution from basal to differentiate (lipidic or lipolytic) con-
Adipocyte
ditions are here detailed step by step. The algorithms can mimic thousand interacting events
Fat
between LDs or squeezing/enlargement events of a single LD in a very brief computational
Triglycerides accumulation
time, from seconds up to few minutes.
Monte Carlo simulation
Results: The main processes regulating the interactions between LDs are here presented, and for each of them, all the needed information to re-write the computational routine are provided. More specifically, the results obtained, analyzing the fusion process between LDs, are here presented. Conclusions: Here, we would like to supply the basis to explore the dynamics of lipid storage in cells with a computational approach and to encourage the applications of numerical simulation to cell studies. © 2016 Elsevier Ireland Ltd. All rights reserved.
1.
Introduction
Lipid droplets (LDs) are cellular dynamic structures spanning in size from few to 100 µm in white adipocytes [1]. Their number and size is related to the cellular requests [2–4]. Their size dis-
tribution is a powerful tool useful to describe the differentiation of LDs in mature adipocyte and fibroblast like cells [5]. LDs can experience different processes: growth through additional neutral lipids deposition in existing droplets, de novo formation of LDs, fusion (interaction with other LDs), fission, decrease through neutral lipids exit from pre-existing LDs, and
* Corresponding author. Department of Computer Science, University of Verona, Strada Le Grazie 15, 37134 Verona, Italy. E-mail address: [email protected] (F. Boschi). http://dx.doi.org/10.1016/j.cmpb.2016.10.013 0169-2607/© 2016 Elsevier Ireland Ltd. All rights reserved.
66
computer methods and programs in biomedicine 138 (2017) 65–71
interaction with other organelles. In particular they can interact with endoplasmic reticulum, endosomes, mitochondria and peroxisomes [6]. The homotypic (LD-LD) fusion is a very rare process in which two smaller droplets fuse in only one droplet with volume equal to the sum of the original volumes. LDs can also grow in size through the addition of neutral lipids to the pre-existing LDs [7–9] or by transfer of neutral lipids from a smaller (donor) to a larger (acceptor) LD. Instead the inverse process, the fission process, is characterized by the fragmentation of LDs in many smaller LDs and it is observed in adipocytes after lipolytic stimulation [10]. The knowledge of the processes regulating the LDs growth and reduction is crucial for the comprehension of all the pathologies related to the lipid accumulation and to design new strategies to fight obesity. Stochastic modeling of adipogenesis was developed by Gefen and co-workers [11,12] in order to determine the probabilities of events in the cell’s life cycle. The researchers simulated the growth of LDs in cell culture with different insulin concentration in the medium. They reproduced the mean size of the LDs, the mean number of LDs for cell and the mean area of adipocytes. They simulated also the images representing the LDs in the adipocytes mimicking real micrographs. The aim of this paper is to highlight the potentialities of Monte Carlo (MC) simulations mimicking the processes responsible for the number and size of the LDs and to supply the basis to reproduce and extend their applications in this field. In particular here we explain step by step how an algorithm studying the behavior of the LDs can be written, as the algorithms used in our previous works simulate the fusion and other processes [13,14]. We focused our attention not on the mean value of the LDs’ size but on the shape of the LDs size distribution, which is well represented by the kernel distribution, and we monitored the similarities between computational and experimental data. We report here some noteworthy hypothesis used to simulate the processes. a. Two LDs can merge together (fusion process) or, alternatively, a LD can be split (fission process) in two or more LDs. Only one event occurs at each time. b. No new LDs are synthesized and no LDs can disappear apart for the simulated process (i.e. LDs do not interact with other organelles). c. The new formed LD has a volume corresponding to the sum of the volumes of the two initial LDs (fusion process) or, alternatively, the LDs’ daughters have the total volume of the progenitor (fission process). d. In case of simulations of more than a single process, the processes act in sequence, not simultaneously. This is suggested by the experimental observations regarding the growth of the LDs which are in agreement with the hypothesis that their formation occurs in steps [15]: first increasing the number of small droplets and then increasing the LDs size. Different order of the processes could lead to slightly different results. e. In case of growth/reduction processes, each LD can vary in volume and the ratio final volume / initial volume is the same for all the LDs, and it is equal to the ratio total final volume / total initial volume.
Here, we refer to the first population of LD observed in basal conditions as “progenitor population”, and to the second population of LDs observed in differentiated conditions, obtained after lipidic or lipolytic stimulation, as “daughter population”. The number of LDs to be measured can be arbitrarily chosen in order to analyze a great number of LDs and, at the same time, to keep down the computational time. The number is not related to the total amount of LDs effectively present in a single cell but represents a more general population.
2.
Methods
2.1.
Cell culture and Oil Red O staining
The 3T3-L1 preadipocytes (ECACC, Sigma-Aldrich, St. Louis, MO, USA) were cultured in 250 ml polystyrene sterilized flasks equipped with 0.2 µm vented plug seal cap by BD (Becton Dickinson, Franklin Lakes, NJ, USA), with DMEM/GlutaMAX, supplemented with 10% of FBS, and 1% antibiotic antimycotic solution, to reach a concentration of 2.5–3.0 × 106 cells (confluence 85–90%). Then, 3T3-L1 cells were detached from flask with trypsin-EDTA and were seeded in 6-well dishes containing a pre-sterilized glass coverslips and incubate at 37°C and 5% CO2 until reaching 90% confluency. At 90% of confluence, cells were differentiated for 3 days at 37°C, 5% CO2 in DMEM/F12 containing 10% FBS, 1% antibiotic antimycotic solution, 0.2 mM IBMX, 10 µM rosiglitazone, 1 µM dexamethasone, and 10 µg/mL insulin. After 72 h post-induction, cells underwent PBS washing (three times), and medium was replaced with an adipocyte maintaining medium (AMM), composed of DMEM/ F12 enriched with 10% FBS, 1% antibiotic antimycotic solution, 10 µg/mL insulin, in which cells were cultured for 2 days for fusion experiments (or 7 days for fission experiments). For fusion experiments, after washing with PBS 0.1 M pH 7.4, cell cultures were fixed for 10 min with 10% neutral buffer formalin. Cells were washed with sterile double distilled water and subsequently with 60% isopropanol for 2 min and stained with a filtered 0.35% Oil Red O solution in 60% isopropanol for 10 min at room temperature. Then, cells were washed with sterile double distilled water and stained with Mayer’s Hematoxylin Bio-Optica ready to use solution for 1 min at room temperature and washed again with sterile double distilled water. Slides were treated with Dako faramount aqueous mounting medium ready to use and then was applied the coverslip. For fission experiments, 3T3-L1 9 days-differentiated cells were subjected to lipolytic conditions by treatment with lipopolysaccharide (LPS). LPS was added to the adipocytes maintaining medium (AMM) for 24 h.
2.2.
Imaging and LDs’ measurements
Cells were observed in an Olympus BX51 photomicroscope equipped with a KY-F58 CCD camera (JVC). The images, like the ones showed in Fig. 1, were analyzed and stored using the software Image-ProPlus on a personal computer. For each LD, the maximum Feret’s diameter (MFD) was measured. The Feret’s diameter (or Feret Diameter FD) is a measure of an object size
computer methods and programs in biomedicine 138 (2017) 65–71
67
Fig. 1 – Microscopic images of cultured cells 1 day (panel a) and 10 days (panel b) after the beginning of a lipidic treatment. Very small LDs are present in the first cell population, instead bigger LDs, with a broader size distribution, are visible in the second cell population. Different processes can be involved to explain the size increase: the de novo formation, the growth through additional neutral lipid deposition in pre-existing droplets and the fusion process. These processes, and the opposite ones which act in lipolytic condition, can be numerically simulated as explained in the text.
along a specified direction, defined as the distance between the two parallel planes (or lines in case of planar images) restricting the object perpendicular to that direction. FD is generally used in optical microcopy to measure the size of irregularly shaped particles [16]. Here, we report the MFD, the longest distance between any two points of the object, also known as maximum caliper diameter.
2.3.
MC simulations
The computational algorithms were written in Matlab R2007a (Mathworks). A personal computer with minimal requests is needed; we used an Intel(R) Corel(TM)2 Quad CPU Q8200, 2.33 GHz, 3.25 GB RAM personal computer. The computational time spans from fraction of seconds for the simplest simulation to about 12 minutes for models involving high number of simulation events.
2.4.
Step by step MC fusion simulation
1. Import the LDs’ measurements of the progenitor population of LDs in the computational algorithm. The data form a vector; each measurement is a component of the vector. 2. Calculate the kernel distribution of the vector and plot it (Fig. 2). The Kernel distribution is used here to avoid the dependence of the histogram to the bin selection of the histogram itself. 3. Select the two LDs undergoing the fusion process. In case of random selection, using a random generator of scalar values, select the two components corresponding to the two LDs undergoing the fusion process. The random choice of the progenitor LDs can be substituted with a guided selection based on criteria selected a priori. For example, it is possible to attribute to the
Fig. 2 – Size distribution of LDs: progenitor and daughter distribution. LDs’ size was measured in cultured cells 1 day and 10 days after the beginning of a lipidic treatment, respectively.
68
computer methods and programs in biomedicine 138 (2017) 65–71
Fig. 3 – Size distribution of LDs: progenitor and daughter distribution (1 day and 10 days after the beginning of a lipidic treatment, as in Fig. 2). The curves can be compared with the simulated daughter curves obtained after 800, 1000, 1200 and 1400 fusion events. The first population of 1500 LDs undergoes merging events in which two randomly chosen LDs fuse in bigger LDs with volume equal to the sum of the two progenitor volumes.
4. 5. 6. 7. 8. 9. 10. 11.
12.
smallest LDs the highest probability to undergoing a fusion. Remove the selected components. Calculate the total volume of the two removed LDs and the diameter of a single LDs with the same volume. Add the new diameter (component) to the vector. Repeat the steps 4–6 for the number of fusion events to be simulated. Calculate the kernel distribution of the final vector and plot it (Fig. 2). Import the LDs’ measurements of the experimental daughter population in the computational algorithm. Calculate the kernel distribution of the vector of the experimental daughter population and plot it. Compare the kernel distribution of the simulated daughter populations with respect to the experimental daughter population (Fig. 3). The difference between the curves can be measured computing the mean squared error (MSE). Low MSE values indicate high similarity between the curves. Please note that repeating the same simulation with random choice of the progenitors, slightly different results can be obtained due the stochastic nature of the simulation itself. Compare also the number of the components of the vector (the number of simulated daughter LDs) to the expected one (experimental daughter population).
2. 3.
4. 5.
6. 7. 8. 9.
10.
2.5.
Step by step MC fission simulation 11.
1. Import the LDs’ measurements of the progenitor population of LDs in the computational algorithm. The data
form a vector; each size measurement is a component of the vector. Calculate the kernel distribution of the vector and plot it. Select the LD undergoing the fission process using a random generator of scalar values in case of random selection option. Alternatively it is possible to attribute to the biggest LDs the highest probability to undergo a fission event. Remove the selected component. Calculate the volume of the removed LD. Calculate the diameter of the single LDs produced by the fission process, depending on the hypothesized number of the daughter LDs in which the progenitor is divided and the hypothesized ratio between the diameters of the daughter LDs. The total volume of the daughter LDs must be the same of the progenitor LD. Add the new diameters (components) to the vector. Repeat the steps 4–6 for the number of fission events to be simulated. Calculate the kernel distribution of the new vector and plot it. Import the LDs’ measurements of the experimental daughter population corresponding to the high lipid accumulation in the cells, in the computational algorithm. Calculate the kernel distribution of the vector of the experimental daughter population and plot it. Compare the kernel distribution of the simulated daughter population with respect to the daughter experimental population.
computer methods and programs in biomedicine 138 (2017) 65–71
12. Compare also the number of the components of the vector (the number of simulated daughter LDs) to the expected one (experimental daughter population).
2.6.
Step by step MC volume grow/reduction simulation
1. Import the LDs’ measurements of the progenitor population in the computational algorithm. The data form a vector; each size measurement is a component of the vector. 2. Calculate the kernel distribution of the vector and plot it. 3. Calculate the total volume of the LDs progenitors. 4. Import the LDs’ measurement data of the experimental daughter population in the computational algorithm. 5. Calculate the kernel distribution of the vector defined at point 4 and plot it. 6. Calculate the total volume of the LDs daughters. 7. Calculate the ratio between the two volumes (multiplying factor). This is greater than 1 in case of growth and lesser than 1 in case of reduction. 8. Multiply the first vector for the multiplying factor. 9. Calculate the kernel distribution of the simulated daughter population and plot it. 10. Calculate the kernel distribution of the experimental daughter population and plot it. 11. Compare the kernel distribution of the simulated daughter population with respect to the experimental daughter population. In this case, the number of simulated daughter LDs is the same of the progenitor LDs.
2.7.
MC more complex simulations
Two or more simulations can be combined together to mimic many processes acting together. The output vector obtained at the end of the first simulation can be used as the input vector for the second simulation. The results could vary depending on the order of the processes in the sequence. In case of multiple simulations, we suggest to evaluate the differences scrambling the order of the processes. In most cases, the differences are negligible due to the stochastic nature of each simulation. In our experience, differences were observed when the random choice of the progenitor LD in the fusion process is substituted by a guided selection based on the size of the LDs, for example attributing the highest probability to undergoing a fusion to the biggest LDs. In this case the biggest LDs disappear and cannot be considered more in the second simulation process.
3.
Results
The experimental data used for the fusion simulation process are shown in Fig. 2. It shows the size distributions of the progenitor and daughter LDs measured in cultured cells 1 day and 10 days after the beginning of the lipidic treatment, respectively. The numerical simulation computes the LDs size
69
distribution after 800, 1000, 1200 and 1400 fusion events. Increasing the number of fusion events the peak of the progenitor LDs distribution gradually moves toward higher size due to the fusion process which is hypothesized to be the only process acting on the LDs. Two LDs, randomly chosen, merge in only one LD with volume equal to the sum of the two initial LDs. Consequently, the number of the LDs decreases with the increase of the interactions. All the distributions are showed in Fig. 3. Moving from 800 to 1400 fusion events, the simulated distributions increase their similarity with the daughter distribution and after 1400 fusion events the simulated distribution well represents the experimental data. This result suggests that the simulated process could mimic the behavior of the LDs. Specific results and other hypothesis regarding the fusion process can be found in Ref. [13]. The de novo formation process, the growth through additional neutral lipid deposition in preexisting LDs, the fission process and the combination of two or three processes were simulated in Ref. [14]. The differences between simulated and experimentally obtained curves can be measured using the MSE. If the simulated distributions are different from the experimental daughter populations (high MSE values) also varying the number of simulated events, it is possible to conclude that the simulated process (and the related hypothesis) cannot be able to justify the experimental data. Due to the stochastic nature of the simulations the stability and reproducibility of the results was evaluated in five different simulations of the fusion process. The results of the first simulation are presented in Fig. 3, the results of the other four simulations are shown in Fig. 4 (panels a–d). The MSE values measured comparing the simulated distributions with the experimental data are reported in Table 1. The mean MSE value and the standard deviation are also reported at the bottom of the table. These outcomes show that the simulations are well reproducible.
4.
Discussion
In this paper, a computational approach to the study of the interaction between LDs was explained step by step in order to facilitate the readers to re-write the algorithms. The aim of this paper is to encourage the application of the computational approach to the dynamic of the cellular organelles. The proposed method allows the analysis of many different processes acting on the LDs, like fusion, growth/reduction through additional neutral lipid deposition in pre-existing droplets or lipid release in the cytoplasm. Here, the capability of the simulations to mimic the real processes was highlighted, and the stability of the simulations, due to the stochastic nature of the computational processes, was evaluated. Using the described algorithms, many different hypotheses can be verified in a very brief computational time for each single process, and more complex simulations, involving two or more different processes, can be tested. The use of computational simulation in the study of lipid storage can help in the comprehension of the associated mechanisms, and it is fundamental due to the increasing prevalence of obesity and the related pathologies in our society.
70
computer methods and programs in biomedicine 138 (2017) 65–71
Fig. 4 – Size distributions of LDs: progenitor and daughter distribution 1 day and 10 days after the beginning of a lipidic treatment shown with the simulated daughter curves obtained after 800, 1000, 1200 and 1400 fusion events in four different simulation (panels a–d).
Table 1 – Comparison between five fusion simulation processes. The MSE between the progenitor LDs size distribution and the experimental daughter distribution is shown in the first column. In the next columns, the MSE between the simulated daughter populations (after 800, 1000, 1200 and 1400 fusion events respectively) and the experimental daughter population are reported.
1 simulation (Fig. 3) 2 simulation (Fig. 4a) 3 simulation (Fig. 4b) 4 simulation (Fig. 4c) 5 simulation (Fig. 4d) Mean STD
MSE 1 day-10 days
MSE 800 events-10 days
MSE 1000 events-10 days
MSE 1200 events-10 days
MSE 1400 events-10 days
2.8486
1.0856
0.6132
0.2777
0.0109
2.8486
0.9650
0.5973
0.2526
0.0135
2.8486
0.9821
0.5993
0.2842
0.0144
2.8486
0.9708
0.5214
0.2184
0.0175
2.8486
1.0486
0.6309
0.2643
0.0118
2.8486 0
1.0104 0.0537
0.5924 0.0419
0.2594 0.0260
0.0136 0.0026
computer methods and programs in biomedicine 138 (2017) 65–71
Conflict of interest The authors declare that they have no conflicts of interest.
Acknowledgment This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
Appendix. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cmpb.2016.10.013.
REFERENCES
[1] T.C. Walther, R.V. Farese Jr., Lipid droplets and cellular lipid metabolism, Annu. Rev. Biochem. 81 (2012) 687–714. [2] S. Martin, K. Driessen, S.J. Nixon, M. Zerial, R.G. Parton, Regulated localization of Rab18 to lipid droplets: effects of lipolytic stimulation and inhibition of lipid droplet catabolism, J. Biol. Chem. 280 (51) (2005) 42325– 42335. [3] S. Martin, R.G. Parton, Lipid droplets: a unified view of a dynamic organelle, Nat. Rev. Mol. Cell Biol. 7 (5) (2006) 373– 378. [4] N. Krahmer, Y. Guo, F. Wilfling, M. Hilger, S. Lingrell, K. Heger, et al., Phosphatidylcholine synthesis for lipid droplet expansion is mediated by localized activation of CTP: phosphocholinecytidylyltransferase, Cell Metab. 14 (4) (2011) 504–515.
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[5] V. Rizzatti, F. Boschi, M. Pedrotti, E. Zoico, A. Sbarbati, M. Zamboni, Lipid droplets characterization in adipocyte differentiated 3T3-L1 cells: size and optical density distribution, Eur. J. Histochem. 57 (2013) e24. [6] D. Binns, T. Januszewski, Y. Chen, J. Hill, V. Markin, Y. Zhao, An intimate collaboration between peroxisomes and lipid bodies, J. Cell Biol. 173 (2006) 719–731. [7] S. Murphy, S. Martin, R.G. Parton, Quantitative analysis of lipid droplet fusion: inefficient steady state fusion but rapid stimulation by chemical fusogens, PLoS ONE 5 (2010) e15030. [8] L. Kuerschner, C. Moessinger, C. Thiele, Imaging of lipid biosynthesis: how a neutral lipid enters lipid droplets, Traffic 9 (2008) 338–352. [9] G. Kellner-Weibel, B. McHendry-Rinde, M.P. Haynes, S. Adelman, Evidence that newly synthesized esterified cholesterol is deposited in existing cytoplasmic lipid inclusions, J. Lipid Res. 42 (2001) 768–777. [10] A. Marcinkiewicz, D. Gauthier, A. Garcia, D.L. Brasaemle, The phosphorylation of serine 492 of perilipin a directs lipid droplet fragmentation and dispersion, J. Biol. Chem. 281 (2006) 11901–11909. [11] S. Or-Tzadikario, R. Sopher, A. Gefen, Quantitative monitoring of lipid accumulation over time in cultured adipocytes as function of culture conditions: toward controlled adipose tissue engineering, Tissue Eng C 16 (5) (2010) 1167–1181. [12] N. Shoham, A. Gefen, Stochastic modeling of adipogenesis in 3T3-L1 cultures to determine probabilities of events in the cell’s life cycle, Ann. Biomed. Eng. 39 (10) (2011) 2637–2653. [13] F. Boschi, V. Rizzatti, M. Zamboni, A. Sbarbati, Lipid droplets fusion in adipocyte differentiated 3T3-L1 cells: a Monte Carlo simulation, Exp. Cell Res. 321 (2) (2014) 201–208. [14] F. Boschi, V. Rizzatti, M. Zamboni, A. Sbarbati, Models of lipid droplets growth and fission in adipocyte cells, Exp. Cell Res. 336 (2) (2015) 253–262. [15] Y. Guo, T.C. Walther, M. Rao, N. Stuurman, G. Goshima, K. Terayama, et al., Functional genomic screen reveals genes involved in lipid-droplet formation and utilization, Nature 453 (2008) 657–661. [16] W.H. Walton, Feret’s statistical diameter as a measure of particle size, Nature 162 (1948) 329–330.
j o u r n a l h o m e p a g e : w w w. i n t l . e l s e v i e r h e a l t h . c o m / j o u r n a l s / c m p b
Simulating the dynamics of lipid droplets in adipocyte differentiation Federico Boschi a,*, Vanni Rizzatti b, Mauro Zamboni b, Andrea Sbarbati c a
Department of Computer Science, University of Verona, Strada Le Grazie 15, 37134 Verona, Italy Department of Medicine, Geriatric Section, University of Verona, Piazzale Stefani 1, 37126 Verona, Italy c Department of Neurological and Movement Sciences, University of Verona, Strada Le Grazie 8, 37134 Verona, Italy b
A R T I C L E
I N F O
A B S T R A C T
Article history:
Background: Lipid droplets are cellular organelles that regulate the storage and hydrolysis
Received 20 June 2016
of neutral lipids. The dynamic of lipid droplets (LDs), during the differentiation process from
Received in revised form
fibroblast-like cells into adipocyte, is strictly related to the lipid storage in cells. The number
3 October 2016
and size of the LDs depends on the lipidic or lipolytic stimulations to which the cells are
Accepted 18 October 2016
exposed. Method: Here, we propose a computational approach to study the processes regulating the
Keywords:
LDs’ number and growth/reduction in size using Monte Carlo simulations. The number and
Lipid droplet
size of LDs are measured before and after experimental treatment in 3T3-L1 cell cultures.
3T3-L1
The algorithms simulating the evolution from basal to differentiate (lipidic or lipolytic) con-
Adipocyte
ditions are here detailed step by step. The algorithms can mimic thousand interacting events
Fat
between LDs or squeezing/enlargement events of a single LD in a very brief computational
Triglycerides accumulation
time, from seconds up to few minutes.
Monte Carlo simulation
Results: The main processes regulating the interactions between LDs are here presented, and for each of them, all the needed information to re-write the computational routine are provided. More specifically, the results obtained, analyzing the fusion process between LDs, are here presented. Conclusions: Here, we would like to supply the basis to explore the dynamics of lipid storage in cells with a computational approach and to encourage the applications of numerical simulation to cell studies. © 2016 Elsevier Ireland Ltd. All rights reserved.
1.
Introduction
Lipid droplets (LDs) are cellular dynamic structures spanning in size from few to 100 µm in white adipocytes [1]. Their number and size is related to the cellular requests [2–4]. Their size dis-
tribution is a powerful tool useful to describe the differentiation of LDs in mature adipocyte and fibroblast like cells [5]. LDs can experience different processes: growth through additional neutral lipids deposition in existing droplets, de novo formation of LDs, fusion (interaction with other LDs), fission, decrease through neutral lipids exit from pre-existing LDs, and
* Corresponding author. Department of Computer Science, University of Verona, Strada Le Grazie 15, 37134 Verona, Italy. E-mail address: [email protected] (F. Boschi). http://dx.doi.org/10.1016/j.cmpb.2016.10.013 0169-2607/© 2016 Elsevier Ireland Ltd. All rights reserved.
66
computer methods and programs in biomedicine 138 (2017) 65–71
interaction with other organelles. In particular they can interact with endoplasmic reticulum, endosomes, mitochondria and peroxisomes [6]. The homotypic (LD-LD) fusion is a very rare process in which two smaller droplets fuse in only one droplet with volume equal to the sum of the original volumes. LDs can also grow in size through the addition of neutral lipids to the pre-existing LDs [7–9] or by transfer of neutral lipids from a smaller (donor) to a larger (acceptor) LD. Instead the inverse process, the fission process, is characterized by the fragmentation of LDs in many smaller LDs and it is observed in adipocytes after lipolytic stimulation [10]. The knowledge of the processes regulating the LDs growth and reduction is crucial for the comprehension of all the pathologies related to the lipid accumulation and to design new strategies to fight obesity. Stochastic modeling of adipogenesis was developed by Gefen and co-workers [11,12] in order to determine the probabilities of events in the cell’s life cycle. The researchers simulated the growth of LDs in cell culture with different insulin concentration in the medium. They reproduced the mean size of the LDs, the mean number of LDs for cell and the mean area of adipocytes. They simulated also the images representing the LDs in the adipocytes mimicking real micrographs. The aim of this paper is to highlight the potentialities of Monte Carlo (MC) simulations mimicking the processes responsible for the number and size of the LDs and to supply the basis to reproduce and extend their applications in this field. In particular here we explain step by step how an algorithm studying the behavior of the LDs can be written, as the algorithms used in our previous works simulate the fusion and other processes [13,14]. We focused our attention not on the mean value of the LDs’ size but on the shape of the LDs size distribution, which is well represented by the kernel distribution, and we monitored the similarities between computational and experimental data. We report here some noteworthy hypothesis used to simulate the processes. a. Two LDs can merge together (fusion process) or, alternatively, a LD can be split (fission process) in two or more LDs. Only one event occurs at each time. b. No new LDs are synthesized and no LDs can disappear apart for the simulated process (i.e. LDs do not interact with other organelles). c. The new formed LD has a volume corresponding to the sum of the volumes of the two initial LDs (fusion process) or, alternatively, the LDs’ daughters have the total volume of the progenitor (fission process). d. In case of simulations of more than a single process, the processes act in sequence, not simultaneously. This is suggested by the experimental observations regarding the growth of the LDs which are in agreement with the hypothesis that their formation occurs in steps [15]: first increasing the number of small droplets and then increasing the LDs size. Different order of the processes could lead to slightly different results. e. In case of growth/reduction processes, each LD can vary in volume and the ratio final volume / initial volume is the same for all the LDs, and it is equal to the ratio total final volume / total initial volume.
Here, we refer to the first population of LD observed in basal conditions as “progenitor population”, and to the second population of LDs observed in differentiated conditions, obtained after lipidic or lipolytic stimulation, as “daughter population”. The number of LDs to be measured can be arbitrarily chosen in order to analyze a great number of LDs and, at the same time, to keep down the computational time. The number is not related to the total amount of LDs effectively present in a single cell but represents a more general population.
2.
Methods
2.1.
Cell culture and Oil Red O staining
The 3T3-L1 preadipocytes (ECACC, Sigma-Aldrich, St. Louis, MO, USA) were cultured in 250 ml polystyrene sterilized flasks equipped with 0.2 µm vented plug seal cap by BD (Becton Dickinson, Franklin Lakes, NJ, USA), with DMEM/GlutaMAX, supplemented with 10% of FBS, and 1% antibiotic antimycotic solution, to reach a concentration of 2.5–3.0 × 106 cells (confluence 85–90%). Then, 3T3-L1 cells were detached from flask with trypsin-EDTA and were seeded in 6-well dishes containing a pre-sterilized glass coverslips and incubate at 37°C and 5% CO2 until reaching 90% confluency. At 90% of confluence, cells were differentiated for 3 days at 37°C, 5% CO2 in DMEM/F12 containing 10% FBS, 1% antibiotic antimycotic solution, 0.2 mM IBMX, 10 µM rosiglitazone, 1 µM dexamethasone, and 10 µg/mL insulin. After 72 h post-induction, cells underwent PBS washing (three times), and medium was replaced with an adipocyte maintaining medium (AMM), composed of DMEM/ F12 enriched with 10% FBS, 1% antibiotic antimycotic solution, 10 µg/mL insulin, in which cells were cultured for 2 days for fusion experiments (or 7 days for fission experiments). For fusion experiments, after washing with PBS 0.1 M pH 7.4, cell cultures were fixed for 10 min with 10% neutral buffer formalin. Cells were washed with sterile double distilled water and subsequently with 60% isopropanol for 2 min and stained with a filtered 0.35% Oil Red O solution in 60% isopropanol for 10 min at room temperature. Then, cells were washed with sterile double distilled water and stained with Mayer’s Hematoxylin Bio-Optica ready to use solution for 1 min at room temperature and washed again with sterile double distilled water. Slides were treated with Dako faramount aqueous mounting medium ready to use and then was applied the coverslip. For fission experiments, 3T3-L1 9 days-differentiated cells were subjected to lipolytic conditions by treatment with lipopolysaccharide (LPS). LPS was added to the adipocytes maintaining medium (AMM) for 24 h.
2.2.
Imaging and LDs’ measurements
Cells were observed in an Olympus BX51 photomicroscope equipped with a KY-F58 CCD camera (JVC). The images, like the ones showed in Fig. 1, were analyzed and stored using the software Image-ProPlus on a personal computer. For each LD, the maximum Feret’s diameter (MFD) was measured. The Feret’s diameter (or Feret Diameter FD) is a measure of an object size
computer methods and programs in biomedicine 138 (2017) 65–71
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Fig. 1 – Microscopic images of cultured cells 1 day (panel a) and 10 days (panel b) after the beginning of a lipidic treatment. Very small LDs are present in the first cell population, instead bigger LDs, with a broader size distribution, are visible in the second cell population. Different processes can be involved to explain the size increase: the de novo formation, the growth through additional neutral lipid deposition in pre-existing droplets and the fusion process. These processes, and the opposite ones which act in lipolytic condition, can be numerically simulated as explained in the text.
along a specified direction, defined as the distance between the two parallel planes (or lines in case of planar images) restricting the object perpendicular to that direction. FD is generally used in optical microcopy to measure the size of irregularly shaped particles [16]. Here, we report the MFD, the longest distance between any two points of the object, also known as maximum caliper diameter.
2.3.
MC simulations
The computational algorithms were written in Matlab R2007a (Mathworks). A personal computer with minimal requests is needed; we used an Intel(R) Corel(TM)2 Quad CPU Q8200, 2.33 GHz, 3.25 GB RAM personal computer. The computational time spans from fraction of seconds for the simplest simulation to about 12 minutes for models involving high number of simulation events.
2.4.
Step by step MC fusion simulation
1. Import the LDs’ measurements of the progenitor population of LDs in the computational algorithm. The data form a vector; each measurement is a component of the vector. 2. Calculate the kernel distribution of the vector and plot it (Fig. 2). The Kernel distribution is used here to avoid the dependence of the histogram to the bin selection of the histogram itself. 3. Select the two LDs undergoing the fusion process. In case of random selection, using a random generator of scalar values, select the two components corresponding to the two LDs undergoing the fusion process. The random choice of the progenitor LDs can be substituted with a guided selection based on criteria selected a priori. For example, it is possible to attribute to the
Fig. 2 – Size distribution of LDs: progenitor and daughter distribution. LDs’ size was measured in cultured cells 1 day and 10 days after the beginning of a lipidic treatment, respectively.
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computer methods and programs in biomedicine 138 (2017) 65–71
Fig. 3 – Size distribution of LDs: progenitor and daughter distribution (1 day and 10 days after the beginning of a lipidic treatment, as in Fig. 2). The curves can be compared with the simulated daughter curves obtained after 800, 1000, 1200 and 1400 fusion events. The first population of 1500 LDs undergoes merging events in which two randomly chosen LDs fuse in bigger LDs with volume equal to the sum of the two progenitor volumes.
4. 5. 6. 7. 8. 9. 10. 11.
12.
smallest LDs the highest probability to undergoing a fusion. Remove the selected components. Calculate the total volume of the two removed LDs and the diameter of a single LDs with the same volume. Add the new diameter (component) to the vector. Repeat the steps 4–6 for the number of fusion events to be simulated. Calculate the kernel distribution of the final vector and plot it (Fig. 2). Import the LDs’ measurements of the experimental daughter population in the computational algorithm. Calculate the kernel distribution of the vector of the experimental daughter population and plot it. Compare the kernel distribution of the simulated daughter populations with respect to the experimental daughter population (Fig. 3). The difference between the curves can be measured computing the mean squared error (MSE). Low MSE values indicate high similarity between the curves. Please note that repeating the same simulation with random choice of the progenitors, slightly different results can be obtained due the stochastic nature of the simulation itself. Compare also the number of the components of the vector (the number of simulated daughter LDs) to the expected one (experimental daughter population).
2. 3.
4. 5.
6. 7. 8. 9.
10.
2.5.
Step by step MC fission simulation 11.
1. Import the LDs’ measurements of the progenitor population of LDs in the computational algorithm. The data
form a vector; each size measurement is a component of the vector. Calculate the kernel distribution of the vector and plot it. Select the LD undergoing the fission process using a random generator of scalar values in case of random selection option. Alternatively it is possible to attribute to the biggest LDs the highest probability to undergo a fission event. Remove the selected component. Calculate the volume of the removed LD. Calculate the diameter of the single LDs produced by the fission process, depending on the hypothesized number of the daughter LDs in which the progenitor is divided and the hypothesized ratio between the diameters of the daughter LDs. The total volume of the daughter LDs must be the same of the progenitor LD. Add the new diameters (components) to the vector. Repeat the steps 4–6 for the number of fission events to be simulated. Calculate the kernel distribution of the new vector and plot it. Import the LDs’ measurements of the experimental daughter population corresponding to the high lipid accumulation in the cells, in the computational algorithm. Calculate the kernel distribution of the vector of the experimental daughter population and plot it. Compare the kernel distribution of the simulated daughter population with respect to the daughter experimental population.
computer methods and programs in biomedicine 138 (2017) 65–71
12. Compare also the number of the components of the vector (the number of simulated daughter LDs) to the expected one (experimental daughter population).
2.6.
Step by step MC volume grow/reduction simulation
1. Import the LDs’ measurements of the progenitor population in the computational algorithm. The data form a vector; each size measurement is a component of the vector. 2. Calculate the kernel distribution of the vector and plot it. 3. Calculate the total volume of the LDs progenitors. 4. Import the LDs’ measurement data of the experimental daughter population in the computational algorithm. 5. Calculate the kernel distribution of the vector defined at point 4 and plot it. 6. Calculate the total volume of the LDs daughters. 7. Calculate the ratio between the two volumes (multiplying factor). This is greater than 1 in case of growth and lesser than 1 in case of reduction. 8. Multiply the first vector for the multiplying factor. 9. Calculate the kernel distribution of the simulated daughter population and plot it. 10. Calculate the kernel distribution of the experimental daughter population and plot it. 11. Compare the kernel distribution of the simulated daughter population with respect to the experimental daughter population. In this case, the number of simulated daughter LDs is the same of the progenitor LDs.
2.7.
MC more complex simulations
Two or more simulations can be combined together to mimic many processes acting together. The output vector obtained at the end of the first simulation can be used as the input vector for the second simulation. The results could vary depending on the order of the processes in the sequence. In case of multiple simulations, we suggest to evaluate the differences scrambling the order of the processes. In most cases, the differences are negligible due to the stochastic nature of each simulation. In our experience, differences were observed when the random choice of the progenitor LD in the fusion process is substituted by a guided selection based on the size of the LDs, for example attributing the highest probability to undergoing a fusion to the biggest LDs. In this case the biggest LDs disappear and cannot be considered more in the second simulation process.
3.
Results
The experimental data used for the fusion simulation process are shown in Fig. 2. It shows the size distributions of the progenitor and daughter LDs measured in cultured cells 1 day and 10 days after the beginning of the lipidic treatment, respectively. The numerical simulation computes the LDs size
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distribution after 800, 1000, 1200 and 1400 fusion events. Increasing the number of fusion events the peak of the progenitor LDs distribution gradually moves toward higher size due to the fusion process which is hypothesized to be the only process acting on the LDs. Two LDs, randomly chosen, merge in only one LD with volume equal to the sum of the two initial LDs. Consequently, the number of the LDs decreases with the increase of the interactions. All the distributions are showed in Fig. 3. Moving from 800 to 1400 fusion events, the simulated distributions increase their similarity with the daughter distribution and after 1400 fusion events the simulated distribution well represents the experimental data. This result suggests that the simulated process could mimic the behavior of the LDs. Specific results and other hypothesis regarding the fusion process can be found in Ref. [13]. The de novo formation process, the growth through additional neutral lipid deposition in preexisting LDs, the fission process and the combination of two or three processes were simulated in Ref. [14]. The differences between simulated and experimentally obtained curves can be measured using the MSE. If the simulated distributions are different from the experimental daughter populations (high MSE values) also varying the number of simulated events, it is possible to conclude that the simulated process (and the related hypothesis) cannot be able to justify the experimental data. Due to the stochastic nature of the simulations the stability and reproducibility of the results was evaluated in five different simulations of the fusion process. The results of the first simulation are presented in Fig. 3, the results of the other four simulations are shown in Fig. 4 (panels a–d). The MSE values measured comparing the simulated distributions with the experimental data are reported in Table 1. The mean MSE value and the standard deviation are also reported at the bottom of the table. These outcomes show that the simulations are well reproducible.
4.
Discussion
In this paper, a computational approach to the study of the interaction between LDs was explained step by step in order to facilitate the readers to re-write the algorithms. The aim of this paper is to encourage the application of the computational approach to the dynamic of the cellular organelles. The proposed method allows the analysis of many different processes acting on the LDs, like fusion, growth/reduction through additional neutral lipid deposition in pre-existing droplets or lipid release in the cytoplasm. Here, the capability of the simulations to mimic the real processes was highlighted, and the stability of the simulations, due to the stochastic nature of the computational processes, was evaluated. Using the described algorithms, many different hypotheses can be verified in a very brief computational time for each single process, and more complex simulations, involving two or more different processes, can be tested. The use of computational simulation in the study of lipid storage can help in the comprehension of the associated mechanisms, and it is fundamental due to the increasing prevalence of obesity and the related pathologies in our society.
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Fig. 4 – Size distributions of LDs: progenitor and daughter distribution 1 day and 10 days after the beginning of a lipidic treatment shown with the simulated daughter curves obtained after 800, 1000, 1200 and 1400 fusion events in four different simulation (panels a–d).
Table 1 – Comparison between five fusion simulation processes. The MSE between the progenitor LDs size distribution and the experimental daughter distribution is shown in the first column. In the next columns, the MSE between the simulated daughter populations (after 800, 1000, 1200 and 1400 fusion events respectively) and the experimental daughter population are reported.
1 simulation (Fig. 3) 2 simulation (Fig. 4a) 3 simulation (Fig. 4b) 4 simulation (Fig. 4c) 5 simulation (Fig. 4d) Mean STD
MSE 1 day-10 days
MSE 800 events-10 days
MSE 1000 events-10 days
MSE 1200 events-10 days
MSE 1400 events-10 days
2.8486
1.0856
0.6132
0.2777
0.0109
2.8486
0.9650
0.5973
0.2526
0.0135
2.8486
0.9821
0.5993
0.2842
0.0144
2.8486
0.9708
0.5214
0.2184
0.0175
2.8486
1.0486
0.6309
0.2643
0.0118
2.8486 0
1.0104 0.0537
0.5924 0.0419
0.2594 0.0260
0.0136 0.0026
computer methods and programs in biomedicine 138 (2017) 65–71
Conflict of interest The authors declare that they have no conflicts of interest.
Acknowledgment This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
Appendix. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cmpb.2016.10.013.
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