Mathematical Models of Adipose Tissue Dynamics - The Mechanobiology of Obesity and Related Diseases - page 18

In addition, larger cells are likely to be more fragile to physical stress [ 9 ].
Therefore, the size-dependent death rate of adipose cells can be modeled as:

1 þ tanh s s k
g k

;

k ð s Þ ¼ k m
2

ð 14 Þ

where k m is the maximal death rate; s k is the characteristic size giving half-
maximal death rate; and g k is the width of the size dependence transition. The
death of adipose cells starts to occur when adipose tissues have to meet continuous
demand to enlarge under long-term high-fat diet [ 28 ]. Surprisingly, adipose tissue
mass starts decreasing after a prolonged period of positive energy balance. This is
due to the limited ability of some fat depots such as epididymal fat to keep on
expanding to accommodate the excessive demand. Eventually, adipose cell death
will dominate over cell growth. To describe this phenomenon, we assumed that
adipose cell death starts to occur when overall adipose cells expand too much. This
condition is mathematically described by a step function:

H ð s s c Þ; ð 15 Þ
where s ¼ R ds sn ð s Þ= R ds n ð s Þ is the mean size of adipose cells. Therefore, the
death process of adipose cells is active, H ð s s c Þ ¼1 ; only if the mean cell size
exceeds a certain critical size s c , otherwise H ð s s c Þ ¼0[ 17 ].
In addition to the passive death of enlarged adipose cells, it has been observed
that small cells are removed under negative energy balance [ 17 ]. Two hypotheses
are possible to explain the removal of small cells. Apoptosis is one simple pos-
sibility [ 29 ]. Note that this is a programmed cell death to actively remove
unnecessary capacity for storing lipids, in contrast to the passive cell death
(necrosis) of enlarged adipose cells. The other possibility is that the disappearing
small adipose cells may just shrink below an observable size limit (\25 lm).
Based on Bayesian model comparison, the latter model was more likely to explain
the evolution of adipose cell-size distribution under negative energy balance [ 17 ].
Therefore, the tiny adipose cells shrinking below the observable size window can
reappear when the energy balance turns positive.

4.5 Cell Turnover

Spalding et al. [ 3 ] have reported that human adipose cells have a life span of about
10 years. The dynamic processes of adipose cells inferred above can describe their
entire lifespan. New cells appear, and experience stochastic size fluctuations. Once
a cell reaches a lower critical size, it starts to grow in a size-dependent manner.
After reaching another upper critical size, it is removed by cell death. This
hypothetical model raises an explicit conjecture that larger adipose cells are older.
The processes of removal of old large cells and recruitment of new small ones
form a cycle. Indeed, the cycle in individual cells has also emerged in the