Supplementary materials for:
A new approach to decoupling of bacterial adhesion energies measured by AFM into
specific and nonspecific components
Asma O. Eskhan and Nehal I. Abu-Lail
The Gene and Linda Voiland School of Chemical Engineering and Bioengineering, Washington
State University, Pullman, WA 99164-2710
1
Details of Atomic Force Microscope (AFM) Experiments. Bacterial cells grown until late
exponential phase of growth and centrifuged twice at 5525g for ten minutes each round were
attached to gelatin-coated mica disks according to previously published protocols [1]. All AFM
experiments were performed with a PicoForceTM scanning probe microscope with Nanoscope
IIIa controller and extender module (Bruker AXS Inc., Santa Barbara, CA). Silicon nitride
cantilevers (DNP-S, Bruker AXS Inc., Santa Barbara, CA) were used in all experiments as our
model inert surface. Silicon nitride was chosen as our model surface because it is characterized
by a similar surface potential to that of sand and glass [2], both substrates to which L.
monocytogenes attach to frequently in nature [3] and in food industry units [4]. The force
constant of each cantilever was determined at the beginning of each experiment from the power
spectral density of the thermal noise fluctuations in deionized (DI) water [5]. On an average, the
spring constant was found to be 0.07 ± 0.01 N/m (n = 5). Prior to force measurements, L.
monocytogenes were imaged in TappingModeTM under DI water. Images were used to locate the
cells for force measurements. We have chosen to perform our measurements under water since it
is the main solvent used during food processing, preparation and storage, all processes during
which L. monocytogenes strains contaminate food [6]. For all pH values investigated, fifteen
cells from three cultures were examined. For each bacterial cell, force measurements were
performed on fifteen locations selected using the point and shoot feature of the AFM software to
cover the entire surface of the bacterial cell [7]. Both approach and retraction force-distance
curves were measured at a rate of 580 nm/s to minimize the hydrodynamic drag [8] and at a
resolution of 4096 points. Force measurements were performed on a bacteria-free area of the
gelatin-coated mica before and after taking the measurements on the bacterial cell. Equality of
2
the measurements ensured that the used tip was not contaminated due to contact with the
bacterial surface biopolymers.
The rationale behind applying Poisson statistical model to decouple AFM energies into
specific and nonspecific components. A Poisson process is one in which events are randomly
distributed in time, space or some other variable with the number of events in any nonoverlapping intervals statistically independent. It is often referred to as the law of rare events.
This definition applies to forces and energies measure by AFM as a function of time. If we think
about the energy calculated as the area under each retraction curve or each approach curve as an
event that occurs at a given time, the probability of that event occurring is independent of the
probability of an energy event happening at the next or prior time point. In addition, these
energies are randomly distributed in time.
A homogeneous Poisson process is one in which the long-term average event rate is
constant. If the average rate was denoted  and in any interval t, the expected number of events
will be:
 =t
(1)
A nonhomogeneous Poisson process is one in which the average rate of events changes
with time. Therefore, the rate of events occurring can be expressed as some function (t). The
number of events expected in an interval from t1 to t2 would then be the integral:
t2
   (t )dt
(2)
t1
While the expected number of events “” for a given experiment needs not to be an
integer, the number of events “n” actually observed must be an integer. The exponential
3
probability density function that describes the probability per unit time that an event will occur
can be given by:
dP = dt
(3)
Where dP is the differential probability that an event will occur in the in the infinitesimal
time interval dt. Equation 3 also can be used to describe the decay process of the adhesion
events. Generally, adhesion events observed in the retraction curve decrease in number as the
cantilevers retracts farther away from the surface due to dropping more and more of the surface
biomolecules attached to it. Equation 3 can be shown to lead directly to the Poisson probability
distribution (equation 3 in the manuscript). For details on the derivation, the reader can refer to
[9].
The assumptions we used to apply Poisson analysis to the adhesion energies are: (1) the
adhesion energy (E) develops as the sum of discrete bond-rapture energies and (2) these bonds
form randomly and all have similar bond energy values (Ei). The first assumption reflects the
first Poisson requirement discussed above which is in a given experiment, the number of events
“n” actually observed must be an integer. The second assumption reflects the randomness of the
Poisson event. A Poisson event is independent of the previous or following event in time. This is
true for adhesion energies measured by AFM. Finally, if we assume a homogeneous Poisson
process, then the long-term average event rate is constant. This is why we assume Ei to be
constant as we are assuming the specific energies that occur at distances less than 1 nm to be
constant in magnitude and are well represented by the average strength of a hydrogen bond.
If many AFM measurements were made, the set of measured energies will be described
by a binomial distribution. However, if the probability of forming a bond is small (<5%) (rare
event) so that the number of bonds formed (n) is much smaller than the possible number of
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bonds (N), then the distribution of the number of bonds formed will be well approximated by a
Poisson distribution [10, 11]. One of the main properties of a Poisson distribution is that the
mean and variance of the distribution are equal. For our AFM energy measurements, that reflects
equations 5 and 6 in the manuscript (equations 4-6 here):
µ𝐸 = µ𝑛 𝐸𝑖
(4)
𝜎𝐸2 = 𝜎𝑛2 𝐸2𝑖
(5)
 n Ei   n2 Ei2 ,  n   n2 Ei
(6)
Beebe et al. were the first to utilize Poisson model to quantify bond ruptures measured
between ligands and receptors by AFM [11]. When they applied the Poisson analysis to their
data using equation 6 above, a line was always obtained when the variance was plotted against
the mean of adhesion data. However, the intercept of the line was not zero. They attributed that
observation to several variables. These include:
1. Bond-formation probability between data sets could vary due to sample variations.
However, the physical mechanisms of why that would happen were not clear. Subtle
geometry or alignment issues were among the reasons discussed for the variations
possible in bonds strength.
2. In addition to variations in the bond strength, additional energies not associated with
chemical bonds may be present in the system. These energies could be related to
nonspecific interactions, electrostatic interactions, or instrument noise. In their discussion
of this possibility, they considered three cases: a constant additional energy, a random
additional energy, and a proportional additional energy. The choice of one type energy
over the other depends on the system under investigation and was well discussed in [9].
When constant additional energy is considered, the total energy measured for each pull5
off event becomes greater by the same amount. The effect is to increase the mean without
changing the variance and to shift the variance vs. mean plot to the right by an amount
equal to the added energy, dropping the intercept below the origin (for a positive added
energy). A constant added energy has no effect on the slope. We have used this approach
here as a means to discern the presence of nonspecific interactions between the tip and
sample. This was chosen based on validation by the Beebe et al. group as discussed
earlier when they measured AFM forces between chemically functionalized surfaces and
the magnitudes of the nonspecific forces estimated by Poisson model were very similar to
those calculated by DLVO theory [9, 10].
6
Table S1. A summary of the mean (µE), variance (σE2) and the number (n) of adhesion energy
events measured between the surface biopolymers of L. monocytogenes EGDe cells cultured at
five different pH values and silicon nitride in water in (aJ).
pH 5
pH 6
pH 7
pH 8
pH 9
Cell
1
2
3
4
5
6
7
8
9
10
Total
µE
σE2
n
µE
σE2
n
µE
σE2
n
µE
σE2
n
µE
σE2
n
72.57
48.10
59.16
43.06
24.59
24.17
34.80
36.88
31.77
43.66
41.87
1310
680
900
630
280
250
520
580
370
490
---
15
15
15
11
15
14
15
12
11
14
173
110.46
18.49
43.66
65.21
59.01
37.37
60.71
63.47
92.35
23.76
57.45
4630
240
980
1660
1150
560
1320
1290
3520
170
---
15
15
10
15
15
13
13
15
13
7
131
146.01
119.39
24.64
44.31
26.94
73.64
120.06
192.00
203.91
39.16
99.00
7110
4730
100
340
600
1600
4620
9200
10190
190
---
15
15
15
13
15
10
12
13
12
7
127
46.00
44.00
64.00
28.44
41.00
35.61
29.61
31.73
131.13
79.04
53.05
780
440
1230
360
630
580
240
340
3140
1600
---
14
15
15
14
15
15
14
14
12
9
137
31.92
32.53
32.21
43.25
63.77
107.73
122.08
25.97
49.88
34.85
54.42
440
480
470
630
1100
2030
2700
280
790
390
---
14
11
9
7
10
14
12
9
10
9
80
7
pH 5
pH 6
pH 7
pH 8
0.5 nN
pH 9
(A)
0.2 m
1.4
(B)
pH 5
pH 6
pH 7
pH 8
pH 9
1.2
Force (nN)
1.0
0.8
0.6
0.4
0.2
0.0
0
20
40
60
80
100
120
140
Distance (nm)
Fig S1. Examples of AFM force-distance (A) retraction and (B) approach curves measured
between a silicon nitride AFM tip and L. monocytogenes EGDe surface biopolymers in water for
each pH of growth investigated.
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2
Variance of Adhesion Energy (aJ )
1400
A) pH 5
1200
1000
800
600
400
200
(r2= 0.95)
0
0
20
40
60
80
2
Variance of Adhesion Energy (aJ )
2
Variance of Adhesion Energy (aJ )
Mean of Adhesion Energy (aJ)
B) pH 6
5000
4000
3000
2000
1000
0
(r2= 0.92)
-1000
0
20
40
60
80
100
120
140
3500
C) pH 8
3000
2500
2000
1500
1000
500
(r2= 0.98)
0
0
20
40
60
80
100
120
140
160
Mean of Adhesion Energy (aJ)
2
Variance of Adhesion Energy (aJ )
Mean of Adhesion Energy (aJ)
3000
D) pH 9
2500
2000
1500
1000
500
(r2= 0.96)
0
0
20
40
60
80
100
120
140
160
Mean of Adhesion Energy (aJ)
Fig S2. (A-D) Scatter plots of the variance, σE2, versus the mean, µE, of the adhesion energies
measured between the surface biopolymers of L. monocytogenes cells cultured at four different
pH values and silicon nitride in water. Each point has the coordinates of mean of all adhesion
energies quantified from retraction force-distance curves collected on one cell and the variance
of these points. Solid lines represent linear regression fits to the data and were used to obtain the
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specific and nonspecific components of the adhesion energies (Table 1 in the main text)
according to eq. 8 in the supplementary methods. Error bars represent the standard errors of the
means.
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