Biomedical Engineering Reference
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Fig. 3 Cell fate trajectories of individual cells according to different stem cell concepts. Cells of
a defined differentiation state were selected (t = 0) and cultivated. a Pedigree concept: The cells
loose stem cell properties due to a random process. Over time they accumulate again in a defined
but more differentiated state. b Plasticity concept: The cells loose and gain stem cell properties in
any state. The population approaches a stationary distribution over time. Solid lines denote
sketches of the distribution of cell states at different time points. Dashed lines are trajectories of
individual cells
Each value of a may represent a set of regulatory network activation patterns.
From the molecular point of view, a may depend on abundance and subcellular
localization of proteins and RNAs, as well as other types of signalling and met-
abolic molecules [ 50 ]. In general, cell differentiation is assumed to be reversible.
Each cell's a -value fluctuates randomly with a state-dependent noise amplitude
r(a) (Fig. 4 a). From its current a-value a cell adopts a new value a 0 with a
randomization rate R which may in general depend on a. We assume R to be
constant. a 0 is drawn from a Gaussian distribution p(a 0 |a), centred around a with
standard deviation r(a).
p ð a 0 j a Þ/ exp ðð a 0 a Þ 2 = 2r 2 ð a ÞÞ
ð 1 Þ
The state dependence of r(a) is assumed to be determined by the environment.
We describe this dependency by:
r ð a Þ¼ r 0 1 a f ð E Þ
½
0
ð 2 Þ
Here, r 0 denotes the noise amplitude for stem cells, i.e. r(a = 0). f(E) is a function
describing the environmental impact. Positive fluctuation amplitudes require that
f(E) \ 1. In a simple approach it can be a constant f(E) = f 0 . In this case f 0 \ 0
describes stem cell supporting environments and 1 [ f 0 [ 0 describes differenti-
ating environments [ 37 ]. Differentiation is assumed to occur independently of cell
proliferation as found in progenitor systems [ 8 ].
In contrast, cell proliferation is assumed to be differentiation state dependent.
We assume that only cells in intermediate differentiation states with a s \ a \ a d
proliferate (see Fig. 4 b). For these states we assume an identical growth time s.
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