22
2.2 Architecture of Organisms, Tissues, and Cells and the Bits Between
So, there is some interesting size regulation occurring, which links droplet biophysics and
their biological functions. LLPS droplets in effect are a very energy efficient and a rapid way
to generate spatial compartmentalization in the cell since they do not require a bounding lipid
membrane, which is often slow to form and requires energy input. Instead, LLPS droplets
can form rapidly and reversibly in response to environmental triggers in the cell and can
package several biomolecules into one droplet to act as a very efficient nano-reactor bio
chemical vessel since the concentration of the reactants in such a small volume can be very
high. LLPS droplets research is very active currently, with droplets now being found in many
biological systems and being associated with both normal and disease processes. As you will
see from Chapter 4, research is being done using super-resolution microscopy to investi
gate these droplets experimentally, but as you will also see from Chapter 8 much modeling
computational simulation research tools are being developed to understand this interesting
phenomenon.
2.2.7 VIRUSES
Worked Case Example 2.1: Biomolecular Liquid Condensates
One type of biomolecule B dissolved in solvent S has an exothermic interaction enthalpy
of 3kBT between 2 B molecules, 2kBT between 2 S molecules, and 1.5 kBT between 1 B and
1 S molecule. If there are no differences between the number of accessible microstates
between well-mixed and demixed, what is the probability that a well-mixed solution of B
will phase separate? Assume each B or S molecule must either bind to another B molecule
or an S molecule.
Answer:
With no difference in the number of accessible microstates between well-mixed
and demixed, this implies that here there is no entropy difference upon phase tran
sition, and so the likelihood of phase transition occurring is determined solely by
the net enthalpic differences. To determine the probability of a transition for any
thermodynamic process, we use the Boltzmann factor since the probability of any
transition occurring, which has a total free energy activity barrier of E, is propor
tional to the Boltzmann factor of exp(–E/kBT) where kB is the Boltzmann constant
and T the absolute temperature. So, the total probability for phase separation
occurring is given by the sum of all relevant Boltzmann factors for phase separ
ation to occur, divided by the total sum of all possible Boltzmann factors (i.e. for all
transitions for demixing of the biomolecules and the solvent molecules in phase
separation, but also for those for well-mixed solvent with biomolecule)—for those
acquainted with statistical physics, this sum is often referred to as the parameter
Z, known as the canonical partition function (often omitting the word “canonical”)
and here in effect serves as a normalization constant to generate the probability.
We are told that each B or S molecule must either bind to another B or S molecule.
Thus, the possible combinations of molecule pairs are SS, BB, SB or BS. SS and BB are
demixed, SB and BS are well-mixed. Interaction enthalpies here are all exothermic
(attractive), so the associated energy barriers are all negative: –2.0, –1.5. –1.5. –3.0
kBT. The phase transition probability therefore goes as:
exp
E
k T
exp E
k T
exp
E
k T
exp
E
k T
exp
SS
B
BB
B
SS
B
BB
B
(
)
(
)
(
)
(
)
(
−
+
−
+
−
+
/
/
/
/
−
+
E
k T
expt E
k T
SB
B
BS
B
/
/
)
(
)
After substituting in the values given, this probability comes out as ~0.75, or 75%.
This sort of analysis doesn’t of course give you any information about the spatial
dependence of droplet formation. But it does illustrate that relatively small energy