Which Condition Is Related To An Increase In The Size And Number Of Fat Cells In The Body?

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Hypertrophy and/or Hyperplasia: Dynamics of Adipose Tissue Growth

• Junghyo Jo,
• Oksana Gavrilova,
• Stephanie Pack,
• William Jou,
• Shawn Mullen,
• Anne Eastward. Sumner,
• Samuel W. Cushman,
• Vipul Periwal

10

• Published: March 27, 2009
• https://doi.org/x.1371/journal.pcbi.1000324

Figures

Abstruse

Adipose tissue grows by 2 mechanisms: hyperplasia (cell number increase) and hypertrophy (cell size increase). Genetics and diet affect the relative contributions of these two mechanisms to the growth of adipose tissue in obesity. In this written report, the size distributions of epididymal adipose cells from two mouse strains, obesity-resistant FVB/N and obesity-prone C57BL/6, were measured after 2, 4, and 12 weeks under regular and high-fat feeding weather condition. The full prison cell number in the epididymal fat pad was estimated from the fat pad mass and the normalized cell-size distribution. The prison cell number and book-weighted hateful jail cell size increase every bit a office of fat pad mass. To address adipose tissue growth precisely, we adult a mathematical model describing the evolution of the adipose prison cell-size distributions equally a function of the increasing fat pad mass, instead of the increasing chronological time. Our model describes the recruitment of new adipose cells and their subsequent development in unlike strains, and with dissimilar diet regimens, with common mechanisms, but with diet- and genetics-dependent model parameters. Compared to the FVB/North strain, the C57BL/6 strain has greater recruitment of small adipose cells. Hyperplasia is enhanced by high-fat diet in a strain-dependent way, suggesting a synergistic interaction between genetics and diet. Moreover, loftier-fatty feeding increases the rate of adipose cell size growth, independent of strain, reflecting the increase in calories requiring storage. Additionally, loftier-fat nutrition leads to a dramatic spreading of the size distribution of adipose cells in both strains; this implies an increase in size fluctuations of adipose cells through lipid turnover.

Author summary

Obesity is an enlargement of adipose tissue to shop excess energy intake. Hyperplasia (jail cell number increase) and hypertrophy (cell size increase) are 2 possible growth mechanisms. The in vivo dynamic change of fat tissue cannot exist monitored in real time due to current technical limitations. Nonetheless, we can measure cell-size distributions of fat cells in individual animals. Our fundamental goal is to extract dynamic features of tissue remodeling from snapshots of prison cell-size distributions. We develop a mathematical model that interpolates between the jail cell-size distribution measurements and predicts the continuous change of the cell-size distribution with respect to fat pad mass increase. Our adipose tissue growth model includes three essential components: new jail cell recruitment, size-dependent cell growth, and jail cell-size fluctuations. In item, we compared the adipose tissue growth of obesity-prone and obesity-resistant mice under a standard or a high-fatty diet to examine the genetic and diet effect on adipose tissue growth. Past applying our model to these different conditions, we constitute that the size increase of fat cells is dependent on nutrition. On the other hand, the nutrition-induced number increase of fatty cells is dependent on strain, suggesting a synergy between genetics and nutrition.

Citation: Jo J, Gavrilova O, Pack Southward, Jou W, Mullen S, Sumner AE, et al. (2009) Hypertrophy and/or Hyperplasia: Dynamics of Adipose Tissue Growth. PLoS Comput Biol 5(3): e1000324. https://doi.org/10.1371/journal.pcbi.1000324

Editor: Jason A. Papin, University of Virginia, United States of America

Received: September 15, 2008; Accustomed: Feb 9, 2009; Published: March 27, 2009

This is an open-access article distributed nether the terms of the Creative Eatables Public Domain declaration which stipulates that, in one case placed in the public domain, this work may exist freely reproduced, distributed, transmitted, modified, congenital upon, or otherwise used by anyone for any lawful purpose.

Funding: This work was supported by funding from the intramural enquiry programme of the NIH, NIDDK. The funders had no part in study blueprint, data drove and assay, decision to publish, or preparation of the manuscript.

Competing interests: The authors have alleged that no competing interests be.

Introduction

Obesity is an enlargement of adipose tissue to store excess energy intake. Hyperplasia (cell number increase) and hypertrophy (jail cell size increase) are two possible growth mechanisms. Adipose tissue obesity phenotypes are influenced by diet and genetics, as well as by their interaction [ane]–[4]. Starting from Johnson and Hirsch'south studies [five], in that location is an extensive literature on adipose tissue growth in normal and abnormal development, characterizing the state of the tissue in terms of the mean jail cell size and cell number. Hyperplastic growth appears only at early stages in adipose tissue evolution [6],[seven]. Hypertrophy occurs prior to hyperplasia to run across the need for additional fatty storage capacity in the progression of obesity [8]. However, it has proven difficult to empathise how diet and genetics specifically bear on hyperplasia and/or hypertrophy of adipose cells, because of limited longitudinal data well-nigh adipose tissue growth.

Beyond these studies, it has recently become possible to measure cell-size distributions precisely. This detailed information, compared with the hateful cell size and total cell number, tin can be used to compute many size-related quantities that permit a finer characterization of the adipose tissue growth process. Cumulants of the cell-size distribution tin can exist used to compute other physiological quantities such as the volume-weighted mean cell size. The cell-size distribution can be used to gauge total cell number inside a fat pad from its mass. Furthermore, it is believed that some specific metabolic properties, east.g., insulin resistance [ix] and adipokine secretion [ten], depend on the precise cell-size distribution rather than the hateful cell size. Indeed, several studies accept addressed the alter of the size distribution of adipose cells under diverse conditions in chick embryo development [eleven], lean and obese Zucker rats [12],[13], partially lipectomized Wistar rats [14], rabbit biopsy [15], and human adipose tissue [sixteen],[17]. These studies focused only on the static differences betwixt cell-size distributions nether different atmospheric condition. Notwithstanding, cross-sectional static prison cell-size distributions for a range of snapshots of brute development can exist used to deduce the dynamics of adipose tissue growth, if nosotros can appropriately clarify the snapshots with the help of mathematical modeling. Given present technical limitations, this may be the best bachelor approach to a microscopic and longitudinal understanding of in vivo adipose tissue growth, although a recent experiment has obtained microscopic observations of lipid accumulation in lipid droplets of adipose cells [eighteen].

To address genetic and dietary effects on the dynamic procedure of adipose tissue growth, we obtained prison cell-size distributions of epididymal fat of obesity-resistant FVB/N (hereafter FVB) and obesity-prone C57BL/6 (C57) mouse strains under standard chow and loftier-fat diets. The C57 mouse is the best characterized model of diet-induced obesity [19], and the FVB mouse is a preferable model for generating transgenic mice [20]. These two commonly-used inbred mouse strains are genetically quite afar [21],[22], and they have distinct metabolic phenotypes: Compared with FVB mice, C57 mice have depression circulating triglyceride levels [21] and increased triglyceride clearance [23],[24]; FVB mice are characterized by relatively higher hepatic insulin resistance, counter-regulatory response to hypoglycemia, and reduced glucose-stimulated insulin secretion [25]; FVB mice are as well known to be spontaneously hyperactive [26] and relatively lean since they announced to be less responsive to loftier-fatty nutrition than C57 mice [27]. Withal, the development of diet-induced obesity in these two strains has not been formally compared. In this report, we developed a mathematical model predicting the modify of the prison cell-size distribution as a function of the epididymal fat pad mass to clarify quantitatively the dynamic characteristics that depend on genetics and/or diet. The model of adipose tissue growth describes how many new cells are formed, how each prison cell grows depending on its size, and how lipid turnover leads to size fluctuations that cause a spreading in the cell-size distribution. As the epididymal fat pad mass increases, the jail cell-size distribution changes in a systematic mode depending on both genetics and diet. Comparing experimental results with the theoretical growth model, we found that hypertrophy is strongly correlated with diet. Hyperplasia, on the other hand, is dependent on genetics. Nutrition-induced changes in hyperplasia are strain-dependent, suggesting an interaction between diet and genetics.

Results

Effect of High-Fat Diet on Body Limerick in FVB and C57 Mice

At the beginning of the experiment (5 weeks of historic period), C57 mice were significantly lighter than FVB mice (Fig. 1A) due to a difference in lean mass, although total fat mass was not different (Fig. 1B). When mice were maintained on regular chow diet, the difference in trunk weight disappeared by the age of eleven weeks (week 6 of experiment, Fig. 1A). Under regular diet weather condition, FVB and C57 mice maintained comparable fat mass throughout the whole grade of the experiment (Fig. 1B). Loftier-fat diet caused significant increase in body weight and fat mass in both strains; however, changes in body weight and fatty mass were more dramatic in C57 mice. The C57 mice had twice as much fatty after 12 weeks of high-fat feeding (Fig. 1B). The overall difference in total fat mass betwixt FVB and C57 mice correlated with proportional differences in the amounts of epididymal (intra-abdominal), inguinal (subcutaneous), and brown fat (Table 1). Caloric intake and activity were comparable in FVB HF and C57 HF mice; even so, FVB HF mice had higher resting and total oxygen consumption, and higher rectal temperature, suggesting that increased energy expenditure rather than reduced caloric intake was the reason for relative resistance to high-fatty nutrition-induced obesity in the FVB mice. Interestingly, during the commencement 2 weeks of high-fat feeding, FVB and C57 mice showed comparable increment in total fat mass (Fig. 1B). C57 HF mice continued to increase fatty mass quickly until week 10 of the experiment, whereas FVB HF mice slowed down accumulation of fatty around week 3. In C57 mice, high-fatty feeding caused a gradual increase of both epididymal and inguinal fatty pads; in contrast, in FVB mice, epididymal fat mass increased just slightly afterward 4 weeks on high-fatty feeding, while inguinal fat pad continued to increase in size throughout the form of experiment (Fig. S1). High-fat feeding acquired significant increase in blood glucose and insulin levels in both FVB and C57 mice (Table one). Insulin levels and glucose intolerance were higher in C57 HF mice than in FVB HF mice, suggesting more than severe insulin resistance (Fig. 2A). Consistent with previous reports [23],[24], C57 REG mice showed reduced serum triglyceride levels, compared with FVB REG mice with no difference in FFA (Table i). This was non due to college fat utilization, since respiratory exchange ratio (Table 1) and the rates of fatty acid oxidation measured in vivo (Fig. 2B) and in isolated skeletal muscle (Fig. 2C) were comparable in FVB REG and C57 REG mice. More probable, lower serum triglycerides in C57 REG mice were caused by much more than efficient clearance of circulating triglycerides as suggested by triglyceride clearance exam (Fig. 2D). High-fatty feeding reduced circulating triglyceride levels in both FVB and C57 mice and improved triglyceride clearance in the latter strain (Table 1 and Fig. 2D). Both strains showed comparable reduction of respiratory exchange ratio, suggesting comparable increase of fatty acid utilization under loftier-fat diet condition (Table 1). Taken together, these data suggest that the power to efficiently clear triglyceride from circulation may contribute to the high chapters of fatty accumulation in C57 mice.

Figure 1. Changes in trunk composition of FVB and C57 mice under standard grub (REG) and high-fat (HF) atmospheric condition.

(A) Torso weight. (B) Fatty mass. Body limerick was measured at indicated fourth dimension points in eight mice per group using Repeat iii-in-one MRI analyzer. High-fatty and control feeding were initiated at the age of v weeks. Ten-axis indicates weeks of controlled feeding. One of 3 independent experiments is shown. Values given are mean±SEM.

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Figure ii. Physiological characteristics of FVB and C57 mice.

(A) Glucose tolerance test was performed on week 10 of controlled feeding with grub and high-fat diet. Mice were fasted overnight and injected with glucose (ii mg/g, i.p.). Each group was represented past eight mice. (B) Whole body oxidation of oleic acid was measured x-week old male person FVB advertizement C57 mice in non-fasted state (viii mice per group) as described in Gautam et al. [47]. (C) Oxidation in palmitic acids was measured in soleus muscle dissected from 10-week-quondam FVB and C57 mice maintained on grub nutrition (eight mice per grouping). Samples were collected at 8 am from randomly fed mice or mice fasted for 18 hours [methods in Toyoshima et al. [46]]. (D) Triglyceride clearance in FVB and C57 male mice later on 11 weeks of controlled feeding with chow and high fat nutrition. Mice were fasted for 4 h and then given 400 µl of peanut oil by a gavage. Plasma was collected hourly for v h from the tail vein for triglyceride measurement. Each grouping was represented by viii mice.

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Hypertrophy and Hyperplasia with Fat Mass Increase

To test the underlying mechanism of different rate of fat aggregating in epididymal fat of FVB and C57 mice, we measured mass and cell-size distribution in tissue samples of epididymal fatty collected at 0, 2, 4, and 12 weeks of controlled feeding (Fig. 3). Since histological analysis does not allow authentic determination of adipocyte cell size, which volition exist discussed after, we measured prison cell size distribution using a Coulter Counter and estimated book-weighted hateful jail cell size and total cell number of epididymal fat pad from these measurements, which had similar values in other mouse study [v]. Strong correlations were observed betwixt fat pad mass and book-weighted mean jail cell size, and between fatty pad mass and total cell number, regardless of strain and diet divergence (Fig. four). The first correlation gave a scaling relation, , between fat pad mass, , and volume-weighted mean cell size, (Figs. 4A and 4B). In addition, an exponential relation was found betwixt fat pad mass, , and full prison cell number, : where the initial fat pad mass, , was obtained from control mice; and the initial cell number, , and the rate of increment of jail cell number in fat pad mass, , were estimated from data (Figs. 4C and 4D; Tabular array 2). The initial cell number, , in C57 mice was larger than the initial cell number in FVB mice (Table two; Figs. S2C and S2D). Every bit the fatty pad mass increases, the total cell number increases. The rate of increase of jail cell number, , was larger under regular diet than nether high-fat diet, a tendency more axiomatic in C57 mice (Figs. 4C and 4D; Table 2), suggesting a genetic departure. The ratios of between the results of regular and loftier-fat diets are 1.42 and 3.22 for FVB and C57 mice, respectively (Tabular array two). This may bespeak an interaction between genetics and nutrition on the increase of cell number. Annotation that nosotros also observed similar results with body weight and fatty mass, since the three quantities (epididymal fat pad mass, fat mass, and torso weight) are correlated with each other. However, the results with epididymal fat pad mass were the all-time fits: The mean square difference betwixt information and fit in Figs. 4A–D was 9.73, 7.94, 3.56×10^v, and five.54×x^six, respectively; the result with body weight was eleven.82, 15.35, 3.65×10⁵, and four.82×10⁶; the consequence with fat mass was viii.58, eight.61, four.28×10^five, and 6.xi×10^six.

Figure 3. Normalized prison cell-size distribution in epididymal fat pad.

One typical instance of five-week-old control FVB mice is plotted. Circles indicate measured data points, while the line represents a fitting curve that is the sum of ane Gaussian and ii exponential functions.

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Figure 4. Size and number increment of epididymal fat cells with respect to epididymal fatty pad mass.

(A) and (B): the correlation between epididymal fatty pad mass and volume-weighted mean prison cell size is fitted with a power constabulary with (A) and (B) , which is plotted with solid lines. (C) and (D): the correlation between epididymal fat pad mass and full prison cell number is fitted into an exponential function with initial fat pad mass , initial jail cell number , and cell-number increasing charge per unit , plotted with dashed lines (chow diet) and solid lines (high-fat diet). Fitted parameter values are summarized in Tabular array 2.

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Genetic and Dietary Effects on Adipose Tissue Growth

These ii strong correlations, between fat pad mass and hypertrophy, and betwixt fatty pad mass and hyperplasia, suggest that the increment in adipose tissue can be described equally a systematic growth process with respect to fat pad mass increment. We bundled cell-size distributions sorted with respect to epididymal fat pad mass (Fig. 5). Remarkably, the adipose tissue growth model in Eq. (1) describes the evolving pattern of cell-size distributions with respect to the fat pad mass increase. The model fitted experimental cell-size distributions quantitatively, despite the fact that all distributions are cross-sectional information obtained from individual animals. The different parameter values in the model, which fit each private jail cell-size distribution from both strains and both diet regimens, gave quantitative differences in the epididymal adipose tissue growth process between strains and between diets (Table 2). Kickoff, the maximal size-dependent growth charge per unit, , and the rate of cell-size fluctuations due to lipid turn over, , demonstrated a diet-induced divergence, and a smaller strain-induced difference. Size-dependent growth and size fluctuations, which resulted in hypertrophy, announced to be regulated mainly by diet. Specifically, the size-dependent growth moved the large prison cell mode of the cell-size distributions in Fig. 5 to larger sizes, and the lipid turnover fluctuations increased the spread of the distribution effectually the large cell mode. It is important to annotation that the results must be advisedly interpreted considering every rate is a rate per unit fat pad mass increase, non per unit of measurement fourth dimension increase. Second, the geometrical parameters ( , and ), which make up one's mind the shape of the size-dependent growth rates, had essentially the aforementioned values regardless of the diet and strain difference, except for . Therefore, the lower disquisitional size, which gives the size initializing cell size-dependent growth, and two scale parameters could exist stock-still at southward_l  = 37 µm, η_l  = 12 µthousand, and η_u  = 63 µm, respectively. On the other hand, the upper critical size limiting cell size-dependent growth of large cells depended on diet; under the high-fatty feeding, this cutoff size shifted to a larger size (Fig. half dozen). Nether high-fat diet, the changes of parameters ( , , and ) overstate the lipid-storage capacity of fat tissues through both hyperplasia and hypertrophy. Lower serum triglycerides in the high-fat diet condition (Tabular array 2 and Fig. 2nd) may be correlated with the increasing lipid storage in enlarged fatty cells considering no pregnant difference in fat acid oxidation was found as suggested by no difference in respiratory exchange ratio (Table 1).

Effigy 5. Changes of cell-size distributions with the mass increment of epididymal fat pad under chow and high-fat diets.

Initial jail cell-size distributions of 5-calendar week-sometime command mice are given at the first row of each column with dashed lines. Dots show experimental results. Annotation that the results are ordered with epididymal fat pad mass, not with the chronological fourth dimension (weeks of controlled feeding) shown in parentheses. Solid lines represent the normalized cell-size distributions corresponding to the given epididymal fatty pad mass, predicted by the adipose tissue growth model.

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Discussion

Our central finding is that hyperplasia and hypertrophy of adipose cells in the epididymal fat pad is a office of the fat pad mass, even though it may take individual animals dissimilar time periods to attain a given fat pad mass. Therefore, adipose tissue growth, represented every bit changes of the cell-size distribution, can be systematically modeled equally a growth procedure with respect to fat pad mass increase; this may reflect a correlation between fat pad mass and the secretion of adipokines and other signaling molecules decision-making adipose tissue growth. Accordingly, it should be noted that the rates in our model are not the usual rates per unit of measurement fourth dimension increase just the rates per unit of measurement mass increase. Thus, several rates ( , , and ) in the model had larger values for animals on a chow nutrition than for those on a high-fatty diet. However, if these rates were converted to the usual rates per unit time increase, they had larger values for the high-fatty diet, because it takes less time for a unit increment in the fatty pad mass from larger, and more numerous, cells on a high-fat diet than for an increase of the same magnitude from smaller, and fewer, cells on a chow diet (Fig. S1). It has been suggested that when obesity progresses, hypertrophy of adipose cells occurs early, and then triggers hyperplasia [8]. Our study showed that new prison cell recruitment increases exponentially every bit fatty pad mass increases. Hypertrophy of adipose cells is the main contributor to fat pad mass increase, whereas hyperplasia does not contribute much to this increase because it occurs in small cells that have a much smaller volume of fatty stored. Therefore, our model naturally embodies the concept that hyperplasia is affected by the hypertrophic growth of cells. On the other manus, information technology has been reported that hyperplasia of adipose cells occurs only at early development stages; hence, no new cell recruitment would be expected at late stages fifty-fifty under obesogenic weather condition [6],[7]. It may exist the case that the age of the animals in our study (6 weeks quondam) allows the occurrence of hyperplasia.

The model developed here may give microscopic insights into the size-dependent growth of adipose cells that cannot be addressed by static cross-sectional studies. For case, we found the following specific properties of size-dependent cell growth: the lower critical size, , initializing lipid accumulation, did non depend on diet in the ii mouse strains, whereas the upper critical size, , limiting cell growth from reaching an extraordinary size, was elevated on a loftier-fat diet. This size-dependence of cell growth is a testable hypothesis. Next, the cell-size fluctuation parameter, , was different between regular and high-fat diets; it is larger under high-fat diet, when it is transformed to units appropriate for per unit time change instead of unit fatty pad mass change. Thus, the random procedure for fatty cells to release and take upwardly fat occurs more actively nether a high-fat diet than under a regular diet. Information technology may be of involvement to see if these results tin can exist generalized to other strains and organisms.

Compared with the studies observing a unmarried pinnacle in prison cell-size distributions of fat cells [11], [xv]–[17],[28], nosotros accept observed bimodal cell-size distributions as reported past others [12], [13], [29]–[32]. Near studies [12],[thirteen],[31],[32] observing the bimodality used the Coulter Counter technology which has several advantages to assess the unabridged distribution of cell sizes [31]: First, the analyzed cells tin be proven to be authentic adipose cells based on morphology and flotation; 2nd, the book of each cell is assessed regardless of shape and free of the artifacts of off-middle sectioning every bit is the rule rather than the exception using histological approaches; finally, sufficient numbers of particles tin be counted and sized to provide statistically significant complex curves. In contrast, microscopic methods for histology may not notice minor cells due to the influence of microscope magnification [thirty], pocket-sized sample number, and sampling bias. Notwithstanding, when the Coulter Counter is used, not-adipocyte contagion may contribute to the cell-size distribution especially at small sizes, although our minimal cell diameter, 22 µm, is above the possible contamination ranges, x to twenty µone thousand, mentioned past Mersmann and MacNeil [31]. To be sure, nosotros again analyzed the modified data using only cell-size distributions above 35 µm diameter with the model, and reached the same conclusions (data not shown). The nadir in the cell-size distribution (Fig. 3) may separate ii cell populations. DeMartinis and Francendese divers the pocket-sized cells, with diameter smaller than 35 µm, as "very pocket-size fatty cells" [29]. Based on our model, these cells take negligible size-dependent growth, because their size is smaller than the lower critical size, s_l  = 37 µone thousand. Therefore, the size-dependent growth machinery tin can naturally explain the origin of bimodality in the prison cell-size distribution of fat cells. Cells with size but higher up can grow with the size-dependent manner, merely cells with size below tin randomly abound with the size-fluctuation through lipid turnover. This separation causes the jail cell accumulation below the size, , which gives the lower peak in cell-size distributions. This cell population may serve as a potential reservoir for mature adipose cells. Their maturation process may be interpreted equally follows: The fatty cells reaching the disquisitional size, , past random size fluctuations, so, can abound with a size-dependent growth mechanism. As mentioned above, the size fluctuation occurs more actively nether a high-fat nutrition; therefore, the reservoir can accelerate the maturation process under the stimulating condition.

In the tissue growth model, we included the recruitment of new cells and the growth of existing cells, only non the expiry of old cells, because the model was consequent with the data without the apoptosis of adipose cells. This result is also consistent with a study observing that epididymal fat tissue of C57BL/half dozen mice does not show pregnant cell decease before 12 weeks under a high-fat diet [33]. However, extended high-fatty diet finally induces apoptosis of fat cells [33]. Furthermore, one recent written report has reported that human fatty cells plough over on a x-twelvemonth time calibration [7]. Our model, therefore, still needs enhancement to be more than generally applied in various conditions. Cell death should be considered and the diet dependence of the model parameters should exist formally incorporated. In this study, we focused on i fat depot, epididymal fat, with several reasons: 1) the weight of epididymal fat pads tin can be accessed more accurately than the weight of inguinal fat pads due to the ease of dissection; 2) the morphology of adipose cells in epididymal fat is more homogeneous than in inguinal fat which contains a lot of brown adipose tissue-like cells, particularly in mice resistant to diet-induced obesity; and 3) the difference between the genotypes was more axiomatic in growth of epididymal fat, which reaches a plateau at iv weeks in FVB mice, just continues to abound in C57 mice throughout the course of experiment, in contrast to the inguinal fatty shows sustained growth in both strains (Fig. S1). Although we have not measured the cell-size distribution of other fat depots, we measured the mass change of inguinal and brown fatty depots, which shows similar pattern with epididymal fat depot (Fig. S1). Thus, it is of interest to utilise the model to other fat depots that accept functional differences [34],[35], and to other species such as human, which is left for future study. We expect the model tin be applied to such various data sets but by adjusting the model parameters, because the model contains general tissue growth mechanisms for the recruitment of new cells and their subsequent development.

Our data advise that at least three factors may explain why C57 mice gain more fat than FVB mice practise under high-fat diet: First, FVB mice have increased metabolic rate and increased rectal temperature, nearly likely due to the increased sympathetic tone. Although nosotros did non notice significant differences in action between the strains in our study, more comprehensive behavior measurements suggested that FVB mice are spontaneously hyperactive, compared with C57 mice [26]. They besides take increased centre charge per unit [36] and respond with hyperglycemia to a variety of treatments [37]. In addition, they are more responsive to stress associated with restraint and fasting [38]. All these data taken together suggest that the activity of sympathetic nervous organization increased more in FVB mice than the action in C57 mice. Second, compared with the FVB mice, C57 mice clear circulating triglycerides more efficiently [23],[24], which at least in part could be attributed to higher serum lipase activeness [23] and higher capacity to store triglycerides in the liver [23],[24] and the adipose tissue (shown in this study). Although molecular mechanisms of triglyceride clearance are non fully understood, adipose tissue conspicuously contributes to clear triglycerides considering the ability to clear circulating triglycerides is impaired in lipoatrophic mice [23]. In particular, information technology has been reported that high-fat diet enhanced triglyceride clearance [39], which may be related to the induction of lipoprotein lipase activeness in the adipose tissue [twoscore]. Finally, compared with FVB mice, C57 mice showed greater recruitment of pocket-sized adipose cells, particularly under high-fat diet. It has been suggested that new adipose cells can arise from progenitor cells which reside within the adult white fat depots [41],[42], and from other sources such equally bone marrow-derived circulating progenitor cells [43]. Recruitment of both types of progenitors has been shown to be stimulated by loftier-fat diet [41],[43]. Information technology is possible that greater recruitment of smaller fatty cells in C57 mice might exist acquired past a higher pool of precursor cells or thier higher intrinsic capacity for adipocyte differentiation. However, in vitro mesenchymal stem jail cell, isolated from the outer ear of FVB and C57 mice, differentiate into adipose cells equally well [44]. The try to compare differentiation of bone marrow stromal jail cell from FVB and C57 mice into adipose cells was not conclusive due to the very low yield and poor proliferative capacity of the cells isolated from C57 mice [45]; however, bone marrow does non appear to be the major source of new fat cells at least in mice [43]. Our model suggests the departure between genotypes in the recruitment of small adipose cells might be fat pad autonomous, merely the molecular machinery underlying this difference is unclear. Fat pad is a circuitous organ containing a variety of different cell types, including mature adipose, preadipose and vascular cells, nerves, macrophages, and fibroblasts. The number of adipocyte precursors and their proliferation in response to external signals varies between fat depots [35]. Farther studies would be needed to decide how genotype specific interaction betwixt different cell blazon and secreted factors may affect the charge per unit of adipocyte recruitment to the specific fatty depots.

In summary, we have derived a mathematical model describing the growth of adipose tissue with cell-number and prison cell-size increases as a function of epididymal fat pad mass. Based on this dynamic model, we examined the effects of genetics and diet on adipose tissue growth. Comparing the cell-size distributions from ii strains and two diets, we ended that cell size change depends on diet, and prison cell number alter depends on genetics and diet, equally well as their interaction.

Materials and Methods

Animals

All procedures were approved by the Creature Care and Use Committee of the National Establish of Diabetes and Digestive and Kidney Diseases. Male FVB and C57 mice were obtained from The Jackson Laboratory (Bar Harbor, ME). Mice were reared four per muzzle on a 12-h lite/dark bicycle (lights on 06:00–18:00). At the age of 5 weeks, mice of each strain were split up into 2 groups. Half of the mice were fed regular grub NIH-07 nutrition (hereafter REG; Zeigler Brothers, Inc., Gardners, PA), containing 4.08 kcal/g (11% calories from fat, 62% from carbohydrates and 26% from protein). The other half was fed loftier-fat nutrition, F3282 (futurity HF; Bio-Serv, Frenchtown, NJ), containing five.45 kcal/one thousand (59% fatty, 26% saccharide, and fifteen% protein). Water and diets were provided ad libitum. Five independent experiments were conducted, each using 4 groups of mice: FVB REG, FVB HF, C57 REG and C57 HF. In three experiments, mice were maintained on controlled diets for 12 weeks and used for body composition assay, physiological characterization , and cell size distribution. Two additional sets of mice were euthanized after 2 weeks and iv weeks of loftier-fatty and control feeding for cell-size distribution only.

In Vivo Experiments

Body limerick, nutrient intake, metabolic rate, glucose tolerance, triglyceride clearance, and fat acid oxidation in isolated soleus musculus were measured equally described previously [46]. Whole body fatty acid oxidation was measured as described in Gautam et al. [47]. Claret for biochemical assays was obtained from the tail vein in the not-fasted state. Glucose levels were measured using Glucometer Aristocracy (Bayer, Elkhart, IN). Serum insulin was assayed using radioimmunoassay (Linco Research, St. Charles, MO). Serum triglycerides, cholesterol (Thermo DMA, Louisville, CO) and free fatty acid (FFA) (Roche Practical Scientific discipline, Indianapolis, IN) were measured according to the manufacturers procedures.

Measurement of Cell Size in Epididymal Fatty

Cell-size distribution in epididymal fat was measured after 2, 4, and 12 weeks of loftier-fatty and control feeding using Beckman Coulter Multisizer III as previously described [9]. Briefly, 20–30 mg of fat tissue were sampled from the midsection, by autopsy and so removing the sample for fixation from the center of the cutting epididymal fat. Tissue samples were immediately fixed in osmium tetroxide [48], incubated in a water bath at 37°C for 48 h, and so adipose prison cell size was adamant past a Beckman Coulter Multisizer III with a 400 µm discontinuity. The range of jail cell sizes that tin effectively exist measured using this aperture is twenty–240 µyard. The instrument was ready to count half-dozen,000 particles, and the fixed-cell suspension was diluted and so that coincident counting was <10%. Later collection of pulse sizes, the information were expressed every bit particle diameters and displayed as histograms of counts confronting bore using linear bins and a linear scale for the x-axis (Fig. 3). Cell-size distribution was measured in four samples from each grouping, except for the C57 mice after 4-calendar week high-fatty nutrition exposure, which had merely iii available samples. A sample was taken from each fat pad and processed separately. Each sample was then counted at least twice. The curves from the two samples are and so averaged, but but after examining the reproducibility between the 2 samples.

Adipose Tissue Growth Model

The cell-size distribution includes all the information related to cell sizes in a tissue and its changes give a statistical view of the detailed growth process of each prison cell. To examine adipose tissue growth in terms of underlying microscopic processes, we consider a mathematical model quantifying the processes that change the prison cell-size distribution. The model tin can predict how many new cells are formed and how cells with different sizes grow as fatty pad mass increases. The cell-number density of a certain size (diameter) at a given fat pad mass is the specific quantity to be considered. We consider how this cell-size distribution changes with an incremental change in fat pad mass . The evolution of the cell-size distribution with fatty pad mass can exist modeled by a partial differential equation, (1) This equation comprises three general components of the adipose tissue growth process. Starting time, we assume that new prison cell recruitment occurs but at the minimal cell size observed, which is mathematically expressed as the delta function . The recruitment rate with respect to fat pad mass is given by the exponential function, (2) where is the initial total cell number at a given initial fatty pad mass , and is the rate of increase in prison cell number per unit alter in fat pad mass. The modify of total prison cell number is the recruitment rate of new cells if cell death is negligible; we found no need to include apoptosis at any jail cell size to fit these experimental data. Therefore, this recruitment rate can be straight obtained from the experimental result using the relation between total cell number and fat pad mass by differentiating the role with respect to . Second, there is jail cell-size dependent cell growth. After maturation of adipose cells to a specific size, they may be able to accumulate fat, causing hypertrophy. In addition to this limiting growth charge per unit of small adipose cells, in that location may exist also an upper growth limit because large adipose cells cannot grow indefinitely by this growth process, though they may attain larger sizes by size fluctuations caused by lipid turnover. The rising and fall of cell-growth charge per unit depending on jail cell size tin be described with the general functional form multiplying ii sigmoidal functions, (3) where represents the maximal growth charge per unit; and are the lower and upper critical sizes, respectively, which requite the half-maximal growth rate; and give their scale (Fig. half-dozen). Finally, the final term in Eq. (1) represents prison cell-size fluctuations with the constant charge per unit, , which reflect lipid turnover randomly occurring in adipose cells. This lipid turnover is the only growth mechanism for large cells above the upper critical size . Generally, the size-dependent growth of cells moves their size distribution to larger sizes, while size fluctuations spread the size distribution.

Optimization Method

To optimize model parameters then that they can closely describe the development of jail cell-size distribution in experiment, we used the minimization of a "cost function" which quantifies the divergence between the model and experimental results. To ascertain the price part, the normalized prison cell-size distribution at a given fat mass was compared with simulation data with a parameter gear up : (6) where is the total number of jail cell size bins and is the total number of given fat mass. The scale of the cost function was calculated from the intrinsic fluctuation of experimental data, which tin can be defined as the squared deviation between the measured prison cell-size distribution and a shine fitting function : (vii) This intrinsic fluctuation is numerically virtually x percent of the squared divergence between experimental and model data. Every bit the plumbing fixtures function in Fig. three, nosotros used a sum of two exponentials and a Gaussian, (8) a form that has been used to fit adipose cell-size distributions [ix]. These parameter fits were performed using the nonlinear bend-fitting routine in MATLAB R2007a (Natick, MA, USA). For the optimization process, we specifically used the parallel tempering Monte-Carlo method to observe the global minimum of the toll part [50]. Nosotros used 10 uniformly spaced values (0.ane to ane) for the tempering parameter and ran ten bondage in parallel with the updating probability . At every 20 steps, a pair of adjacent simulations on x tempering parameters were randomly chosen and their parameter states were exchanged with probability . After equilibrium, twenty,000 iterations were used with the fixed tempering parameter to judge the optimal parameter values and their standard errors.

Nosotros also used this method to estimate the initial total prison cell number, , and its charge per unit of increase, , from the relation between fat mass and total cell number (Figs. 4C and 4D). In the minimization betwixt the fitting function and experimental data, we used a constraint that the initial jail cell number is equal regardless of diet conditions, i.due east., regular and high-fatty diets. The boilerplate fatty mass of four control mice before regular and loftier-fat diets was used every bit the initial fat mass, , which is 0.34 g and 0.29 thousand for FVB and C57 mice, respectively. Nosotros estimated the uncertainties, and , by propagating the ten percentage statistical fluctuations observed in the experimental data.

Numerical Solution of Fractional Differential Equation

We solved the following discrete version of our model, given as a continuous fractional differential equation in Eq. (1): (ix) with mass interval δm = 0.1 mg and size interval δs = 0.73 µm.

Supporting Information

Effigy S1.

Changes in epididymal (A, B), inguinal (C, D), and brownish (E, F) fatty pad mass of FVB (A, C, Eastward) and C57 (B, D, F) mice under chow and high-fat diet weather condition. Ten-axes indicate weeks of controlled feeding initiated at the age of v weeks old. Y-axes in console (A–D) shows combined weight of right and left fat pads. Each time betoken has four sample per group with exception of calendar week 12 (viii samples per grouping) and 4 week C57 HFD (three samples per group). Lines are drawn for guide.

https://doi.org/10.1371/journal.pcbi.1000324.s001

(0.09 MB TIF)

Figure S2.

Changes in epididymal fat pad of FVB and C57 mice under chow and high-fat diet. (A) and (B) Book-weighted mean prison cell size. (C) and (D) Total cell number. X-axes indicate weeks of controlled feeding initiated at the age of 5 weeks sometime. Each time point has four samples at the time point, four weeks (three bachelor samples). Lines are drawn for guide.

https://doi.org/x.1371/journal.pcbi.1000324.s002

(0.07 MB TIF)

Acknowledgments

We give thanks Arthur Sherman for helpful discussions and a critical reading of the manuscript.

Author Contributions

Conceived and designed the experiments: JJ OG AES SWC VP. Performed the experiments: OG SP WJ SM. Analyzed the data: JJ OG VP. Wrote the newspaper: JJ OG SWC VP.

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Which Condition Is Related To An Increase In The Size And Number Of Fat Cells In The Body?,

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