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Supplementary Information
“How Crowded is the Prokaryotic Cytoplasm?”
Jan Spitzer and Bert Poolman
Email: jspitz@mcpolymers.com; jan.spitzer@gmail.com
Email: b.poolman@rug.nl
Contents
A. Vectorial character of prokaryotic cells
B. Examples of biomacromolecular crowding for the ‘Simple Coccoid Model’
A. Vectorial character of prokaryotic cells
In general, unequal cytoplasmic biomacromolecular crowding can have a multitude of
topologies, where biomacromolecular clusters can associate between themselves, with the
nucleoid and with the cytoplasmic side of the plasma membrane, creating a corresponding
topology of dilute reservoirs of ‘bulk’ concentrations of metabolites, nucleic acids, and
proteins, as shown schematically in Fig. 1 in the main text. However, within the
supercrowded clusters (where biomacromolecular surfaces remain hydrated and
biochemically functional), biomacromolecules are separated by electrolyte nano-pathways
and nano-pools with no ‘bulk’ concentrations of metabolites, and therefore biochemical
reactions within the clusters can be considered vectorial; they have semi-conducting
electrolytic character (Mitchell, 1979; Spitzer 1985; Spitzer, 2003; Poolman et al, 2004;
Spitzer & Poolman, 2005, Spitzer & Poolman, 2009; Spitzer, 2011).
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B. Examples of biomacromolecular crowding for the ‘Simple Coccoid Model’
Elaborating the simple coccoid model (Fig. 2 in the main article), Table 1 contains
calculations of the thickness of the submembrane gel layer over a wide range of cytogel
supercrowding and cytosol ‘dilutions’ according to eq. 2 in the main text.
Cytogel ‘supercrowding’
[%]
Cytosol ‘dilution’ [%]
0%
5%
10%
15%
20%
25
200
200
200
200
200
27
175
162
149
120
170
31
142
120
101
68
133
35
120
95
76
48
109
40
101
76
59
35
90
45
87
64
48
28
76
52
73
63
52
38
21
65
56
39
28
15
48
74
49
41
33
23
12
85
42
28
19
10
35
95
37
24
17
9
31
100
35
23
16
8
29
Suppl. Info. Table 1. Thickness (nm) of submembrane gel layer in a simple coccoid
model. The data cover wide ranges of unequal crowding within the cytoplasm at
constant (random) crowding of 25% volume fraction of biomacromolecules. The
highlighted conditions at 52% crowding correspond to Fig. 2 in the main text.
The highlighted (bold) data in the column with 5% dilute cytosol correspond to the
specific example shown in Fig. 2 of the main article. The 52% volume packing is the
lowest structural packing of spheres (simple cubic), and the 74% volume packing is the
highest (hexagonal) density packing attainable without the spheres becoming deformed;
in these ranges of supercrowding, vectorial biochemistry becomes operational because
there is not enough space for metabolites to attain ‘bulk’ compositions (chemical
potentials) independent of position. Under these ‘vectorial’ conditions, the thickness of
the submembrane gel decreases from 63 nm at 52% supercrowding to 41 nm, at 74%
supercrowding; in the extreme case of ‘dry’ cytogel (100% volume fraction of dry matter)
the cytogel thickness shrinks to 29 nm, while the cytosol thickness expands to 170 nm,
with still reasonable (from a chemical engineering point of view) ratios of volumes: 22%
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for the nucleoid, 62% for the cytosol, and 16% for the ‘dry’ cytogel. Such high ranges of
submembrane supercrowding conditions represent a physiological mechanism to protect
the interior of the cell – the nucleoid – from adverse environmental conditions, i.e. from
desiccation, while triggering new genetic and metabolic responses.
In the range of 0% -20% volume fractions of ‘dilute’ cytosol, the thickness of the
supercrowded cytogel changes only from about 70 nm to about 20 nm above the 52%
volume fraction of cytogel supercrowding, i.e. by no more than about 3 ‘ribosomal’
diameters (the cases with the thickness of less than 20nm in the last two columns of Table
1 reflect the effect of already very crowded cytosol).
200
180
Thickness of the cytogel (nm)
160
Random
Vectorial
140
120
Phase-inversion and
interpenetrating
networks
100
80
60
40
20
0
0.25
0.50
0.75
1.00
Degree of cytogel supercrowding at 0-20% crowding of cytosol
0%
5%
10%
15%
20%
Suppl. Info. Fig 1. The onset of transient vectorial structures (biomacromolecular
super-clusters) above 52% volume fraction crowding as described in the text.
The data in Table 1 are represented in Suppl. Info Fig. 1; the plot starts at 25% average
random crowding with no cytogel-cytosol boundary and a cytoplasmic shell 200 nm thick
(first line in Table 1). As the cytogel gets supercrowded, a cytogel/cytosol boundary
appears for any given level of cytosol ‘dilution’. Importantly, the cytogel thickness
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decreases relatively fast and begins to level out above ~ 52% of cytogel supercrowding. In
the ‘lower range’ of supercrowding (25% - 52% volume fraction), the cytogel structuring
is weak and hence not very persistent; above the 52% volume fraction (52% - 100%
volume fraction), the biomacromolecular clusters become more persistent and hence
mechanically and physiologically more significant.
An important reference point in this range is 74% volume fraction, corresponding to
the closest packing of hard spheres; above the 74% volume fraction, the probability of
deformation of protein tertiary structures increases, as well as the probability of a
large-scale ‘phase inversion’ leading to a mechanically stronger system of ‘functionally
agglomerated’ proteins and nucleic acids with interpenetrating aqueous channels through
which electrolyte and metabolites can percolate. Similar conclusion has been reached (Fu
et al, 2010) from the data obtained by photoactivated localization microscopy (PALM).
Alternatively, in this highly crowded range, ‘pure proteins’ may separate, crystallize, and
fuse (either physically, or via regulated biochemical cross-linking reactions) into
mechanically strong structures.
Supplementary Information References
Fu G, Huang T, Buss J, Coltharp C, Hensel Z, Xiao J (2010) In vivo structure of the E.
coli FtsZ-ring revealed by photoactivated localization microscopy (PALM). PLoS One;
5(9):e12682.
Mitchell P (1979) Compartmentation and communication in living systems. Ligand
conduction: a general catalytic principle in chemical, osmotic, and chemiosmotic reaction
systems. Eur. J. Biochem. 95:1-20.
Spitzer JJ (1984) A re-interpretation of hydration forces near charged surfaces. Nature
310:396-397.
Spitzer JJ (2003) Maxwellian Double Layer Forces: from Infinity to Contact. Langmuir
19:7099-7111.
Poolman B, Spitzer JJ, and Wood JM (2004) Bacterial osmosensing: roles of membrane
structure and electrostatics in lipid–protein and protein–protein interactions.
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Spitzer JJ and Poolman B (2005) Electrochemical structure of the crowded cytoplasm.
Trends Biochem. Sci. 30:536-541.
Spitzer JJ and Poolman B (2009) The role of biomacromolecular crowding, ionic strength
and physicochemical gradients in the complexities of life’s emergence. Microbiol. Mol.
Biol. Rev. 73:371-388.
Spitzer J (2011) From water and ions to crowded biomacromolecules: in vivo structuring
of a prokaryotic cell. Microbiol. Mol. Biol. Rev. 75:491-506.