Download Supplementary Information (doc 140K)

Supporting Information
Supporting Methods
Composition of Synthetic Wastewater. SI Table 1 provides the composition of the synthetic
wastewater used as the feed for the chemostats. The media was prepared every 3 days from Stock
Media and Trace Element Solutions that were prepared monthly. Specifically, 10 mL/L of Stock
Media Solution was combined with distilled water, which was then autoclaved and stored at 4 oC.
One mL/L of sterile-filtered Trace Element Solution and 0.5 g/L of sodium bicarbonate were then
added to the mixture for use in the reactors.
Real-time PCR methods: Design and Procedures. Real-time PCR (TaqMan) was used to
quantify 16S-rRNA genes from the different guilds of bacteria of interest. The goal was to use
guild-level probes that would permit the monitoring of guild dynamics rather than population
dynamics in the chemostats. Given that each guild contained distinct sub-groups of organisms, a
series of probes were needed to encompass as many populations within each relevant guild as
possible. As such, a suite of primers and probes (Sigma-Genosys, TX, USA) were adopted or
constructed to target semi-conserved regions of genes specific to clades of ammonia-oxidizing
bacteria and nitrite-oxidizing bacteria.
The AOB suite of primers and probe were selected based on their specificity for most
ammonia-oxidising -proteobacteria, although we recognize this suite is weak for detecting
bacteria represented in the N. communis and N. oligotropha clusters (Purkhold et al., 2000).
Despite this issue, this suite was the best option available for AOB quantification because we
only require precise “relative” abundances for the LE calculations; i.e., this AOB suite is
imperfect, but it is consistently imperfect, which is most important. The NOB primers/probes
were newly designed using Beacon Design software (v. 5.10; Premier Biosoft International, Palo
1
Alto, CA, USA). A single TaqMan® primer/probe set was designed to detect Nitrobacter spp.,
whereas another set was designed for Nitrospira spp. that specifically detected desired products,
rather than PCR artifacts (e.g., primer dimers). For the quantification of both AOB and NOB,
DNA template (2 µL), appropriate primers (15 pmol) and probes (6.25 pmol) were combined
with iQ Supermix PCR reagent (BioRad, Hercules, CA, USA) to create 25 µL reaction volumes.
Reactions were then performed using a BioRad iCycler with an iCycler iQ fluorescence detector
and software v. 2.3 (BioRad). Temperature cycle was 95 oC (10 min), and 40 cycles of 94 oC (20
sec), anneal temperature (Table 1) for 1 min, and 72 oC (40 sec).
Real-time PCR methods: Specificities. Specificities of AOB, NOB, and “total bacteria”
primer/probe sets were checked using BLASTn tool (http://www.ncbi.nlm.nih.gov/blast/) and
Probe-Match program in the RDP Database (http://rdp.cme.msu.edu/; last accessed 5/2007) to
compare matches among “full-length” (>1200 base) sequences. The specificity for the total
bacteria suite of primers and probe ranged from 46.6% to 78.1% for no mismatches and 74.8% to
98.7% for one mismatch (note that the stringencies may have been affected with the low
annealing temperature of 50 oC). Specificities for the AOB suite are reported elsewhere (Koops et
al., 2003). The Nitrobacter spp. primers/probe matched 96-100% sequences with little or no
binding to non-targeted sequences, wheresas Nitrospira spp. analysis consisted of genus-specific
reverse primer and Taqman® probe, and a less specific forward primer. Together, they targeted
~85% of known sequences in the Nitrospira genus.
Real-time PCR methods: Precision. The variability of analysis was examined by extracting 8
replicates of a common sample and comparing its coefficients of variation (usually around 17%).
The presence of inhibitory substances in the sample matrix were checked by spiking the samples
2
with known amounts of template and comparing differences in concentration threshold values
(CT) between the matrix and controls (always less than one cycle difference). PCR efficiencies
were further examined by comparing serial dilutions of selected samples (those with high
concentrations of DNA) and plasmid controls. Correlation coefficients were more than 0.99 for
all calibration curves, and sample log gene abundances (except those below detection limits)
were within the linear range of the calibration curve.
Bacterial Biomass Conversions. Although only relatively precise abundances are required for
the LE calculations (and biomass conversation is not really needed), bacterial gene abundance
were converted to biomass equivalents for comparisons with protozoa data. As such, these
conversions were performed using existing data from the literature, including assumed gene copy
numbers/cell, cell biovolumes, and allometric biomass conversion factors. Specifically, rRNA
operon per cell was assumed to be 4.3 for “total bacteria” (Klappenbach et al. 2001) and 1.0 for
AOB (Klappenbach et al. 2001; GenBank #NC008344 and #NC007614, both unpublished;
#NC004757, Chain et al., 2003), Nitrospira spp. (assumed), and Nitrobacter spp. (GenBank
#NC007964, unpublished; #NC007406, Starkenberg et al. 2006). Biovolumes were assumed to
be: total bacteria, 0.7 μm3 (Posch et al., 2001); AOB, 1.57 μm3 (Koops et al., 2003); Nitrobacter
sp., 0.58 μm3 (Bergey et al., 1994); and Nitrospira sp., 0.28 μm3 (Abeliovich, 2001). Allometric
biomass conversions were assumed to be 125-288 fg/ μm3 (Loferer-Krössbacher et al., 1998).
Demonstrating Non-linear Determinism in the Time Series. Given that guild dynamics must
follow a non-linear deterministic model as a pre-condition for chaos to exist within the time
series, two additional tests were performed to show that non-linear determinism described the
data better than a linear stochastic model with error. In the first test, linear and non-linear
3
Volterra-Wiener expansions were fitted to the data (Barahona & Poon, 1996) and the average
error from each fit was calculated in-sample. When the error from the non-linear model was
smaller than that of the linear model we concluded that there was likely a visible non-linear
component to the data. In the second test, error in the non-linear Volterra-Wiener model was used
as a statistic in a surrogate data test using Matlab and TISEAN software (Hegger et al, 1999).
As background, the Volterra-Wiener series of order d, with system memory  , is defined as
follows (Barahona & Poon, 1996):

d


xˆ (n)  h0    h( j1 ,, jl ) x(n  j1 )  x(n  jl )
l 1 j1 1 j2 1
(1).
jl 1
For   1,,6 the order-1 series (linear) and order-2 series (non-linear), respectively, were fitted
to guild abundance time-series in a least squares sense, minimizing the root mean square (rms)
N
error e , where e2 ( , d )   xn  xˆ (n) 
n 
2
N
 x
nR
n
 x  . The parameter  serves the same
2
function as the embedding dimension, m , in the LE calculations, and its range was chosen to be
consistent with LE calculations. For each d, with   {1, ,6} , eˆ( ) was chosen to minimize
C (r )  log( e) 
r
, with r being the number of polynomial terms in the series model, and N =
N
104 the length of the time-series. For d = 2, the model was truncated to obtain the best fit with the
smallest number of non-linear terms.
In-sample rms error in the non-linear Volterra-Wiener model was also used in surrogate
testing of the null hypothesis that abundance data is generated by a linear process with Gaussian
inputs. Polished, amplitude-adjusted-Fourier-transform (AAFT) surrogates were generated from
the Fourier power spectrum of abundance data for all guilds in each reactor. Surrogate time-series
share linear properties of abundance data while non-linear properties are randomized. This
method is described in Schreiber and Schmitz (2000) and was implemented using TISEAN
4
software (Hegger et al, 1999) (http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.1).
Specifically, the Volterra-Wiener series of order 2,



j 1
j 1 k 1
xˆ (n)  h0  h1 ( j ) x(n  j )   h2 ( j, k ) x(n  j ) x(n  k ),
was fitted without truncation to abundance time-series and to surrogate time series; ê was
determined on each series in the manner described above. A one-sided test was then carried out:
if abundance data had lowest ranking of ê (i.e. smallest error) in an ê -distribution over 19 AAFT
surrogates, the null hypothesis was rejected with a significance of 95%.
Examination of Noise and Variability in Time-series Data. Two approaches were used to
characterize noise and fluctuations in the time series: a modified Pimm-Redfearn analysis of
variability and detrended fluctuation analysis (DFA). Pimm and Redfearn (1988) previously
showed “reddening” (or “pinkness”) in population density time series by comparing the standard
deviations of log-transformed values taken from the time series at different segment (census)
lengths. Specifically, as one calculates variability over a longer period of time, values would
increase if there is an underlying dynamical behavior in the time series. However, Rohani et al
(2004) suggested that all possible segments of a time series with each census length be
calculated, thus creating pseudo-replication; from those multiple values, a statistical average
could be calculated, which was assessed here.
DFA was performed based on the method presented by Peng et al (1995) using a modified
algorithm provided in PhysioToolkit (Goldberger et al, 2000). The data series was integrated and
divided into boxes of equal length, and a least-squares line fitted to the data. The average
fluctuation (i.e., rms) of the detrended time series is determined as a function of box size. A
5
scaling exponent (α) can be calculated from log-log plot of the results, which reflects random
versus non-random patterns.
Supporting Results
Reactor Operation Period. The chemostats were operated for over 300 days in the experiment;
however, only 207 days of data were used in the analysis. The first 30 days were operated as
batch and then fill-and-draw units (which are quite different than later chemostat operations), and
those data were not used. Further, three hydraulic retention times of data after the reactors were
switched to continuous-flow operations were also not used (~ 30 days based on the 0.1 d-1
reactor) because this is the customary period allowed for acclimation after changes in system
operations. Finally, the last 30 days operating data were not used because a mistake was made
making the media, which destabilized the systems at around day 275 to 285. Specifically, on day
285, nitrification in both the 0.83 and 0.3 d-1 chemostats suddenly ceased and could not be
recovered despite one month of additional effort. Given that we could not identify exactly when
the mistake was made, we conservatively chose an “end” date well before the suspected error.
This stop date decision was somewhat arbitrary, but was made prior to data analysis so that we
did not bias any subsequent guild or performance analyses.
Measures of Non-linearity, Variability, and “Noise”. The in-sample rms errors of a linear
Volterra-Wiener model and a non-linear Volterra-Wiener model are tabulated for all guilds to 4
significant figures in SI Table 2. The non-linear error is smaller (dopt = 2) for all chemostats and
all guilds, which implies that the time-series data is fitted better by a non-linear rather than a
linear process.
6
SI Table 3 presents rankings of error ‘e’ measured on abundance data in a distribution over
19 surrogates, where e is the rms error in a non-linear Volterra-Wiener model. As background, if
the abundance data error has the smallest ranking (i.e., one) in the distribution then the null
hypothesis that abundance data is generated by a linear process with noisy inputs is rejected with
a significance of 95%. SI Table 3 indicates that the most frequently-occurring rank for guild data
is one. Although conclusions cannot be made universally to a 95% confidence level, results
clearly show that our time-series data has the smallest or near the smallest ranking, which is
strong confirmation of non-linearity given the short, noisy nature of the time-series.
Modified Pimm-Redfearn tests on each time series indicates the data in each series was
“pink”, meaning that long-term trends dominated the data, rather than just short-term random
events (i.e., white noise). SI Figure 1 shows that AOB and NOB variability became greater as
census lengths increased, but also reached an asymptotic limit for census lengths greater than
about 32 days. The same general pattern was observed for other guilds (total bacteria and
protozoa are not shown). The only exception was in the 0.1 day-1 reactor for NOB, which reached
a limit at a census length of only 10 days.
Dominance of longer term patterns was also confirmed by DFA, where αAOB were 1.1, 0.8
and 0.9 for the 0.1, 0.3 and 0.83 day-1 chemostats, respectively. In this analysis, values greater
than 0.5 but less than 1 suggest long-range power-law correlations (“red”-shifted patterns). All
values for αNOB also were ~ 1, except for the 0.1 day-1 reactor, which reported αNOB ~ 0.7,
suggesting more randomness, but this does not imply significantly “random.” Finally, αTotal Bacteria
and αProtozoa were in the range 1-1.1 for the 0.1 and 0.83 day-1 chemostats, whereas values from
the 0.3 day-1 unit were slightly lower, 0.8 to 0.9, but (again) were not significantly random.
References
7
Abeliovich A (2001) The Nitrite oxidizing bacteria. In: Dworkin M, et al. (Eds) The Prokaryotes:
An Evolving Electronic Resource for the Microbial Community, Springer-Verlag, New
York
Barahona M & Poon C-S (1996) Detection of nonlinear dynamics in short, noisy times series.
Nature 381: 215-217.Bergey DH, Holt JG, Krieg NR & Sneath PHA (1994) Bergey's
Manual of Determinative Bacteriology. Lippincott Williams & Wilkins, Baltimore, MD,
USA
Chain P, Lamerdin J, Larimer F, Regala W, Lao V, Land M, et al. (2003) Complete genome
sequence of the ammonia-oxidizing bacterium and obligate chemolithoautotroph
Nitrosomonas europa. J. Bacteriol. 185: 2759-2773.
Goldberger AL, Amaral LAN, Glass L, Hausdorff JM, Ivanov PC, Mark RG, et al. (2000)
PhysioBank, PhysioToolkit, and PhysioNet – Components of a new research resource for
complex physiologic signals. Circulation 101, e215-e220.
Harms G, Layton AC, Dionisi HM, Gregory IR, Garrett VM, Hawkins SA, et al. (2003) Realtime PCR quantification of nitrifying bacteria in a municipal wastewater treatment plant.
Environ Sci Technol 37: 343-351
Hegger R, Kantz H & Schreiber T (1999) Practical implementation of nonlinear time series
methods: The TISEAN package. Chaos 9: 413-435.
Hermansson A & Lindgren PE (2001) Quantification of ammonia-oxidizing bacteria in arable
soil by real-time PCR. Appl Environ Microbiol 67: 972-976
Klappenbach JA, Saxman PR, Cole JR & Schmidt TM (2001) rrndb: the Ribosomal RNA Operon
Copy Number Database. Nucl Acids Res 29: 181-184
Koops H-P, Purkhold U, Pommerening-Röser A, Timmermann G & Wagner M (2003) The
Lithoautotrophic ammonia oxidizing bacteria. In: Dworkin M, et al. (Eds) The
8
Prokaryotes: An Evolving Electronic Resource for the Microbial Community, SpringerVerlag, New York
Kowalchuk GA, Stephen JR, DeBoer W, Prosser JI, Embley TM & Woldendorp JW (1997)
Analysis of ammonia-oxidizing bacteria of the beta subdivision of the class
Proteobacteria in coastal sand dunes by denaturing gradient gel electrophoresis and
sequencing of PCR-amplified 16S ribosomal DNA fragments. Appl Environ Microbiol
63: 1489-1497
Loferer-Krössbacher M, Klima J & Psenner R (1998) Determination of bacterial cell dry mass by
transmission electron microscopy and densitometric image analysis. Appl Environ
Microbiol 64: 688-694
Peng C-K, Havlin S, Stanley HE & Goldberger AL (1995) Quantification of scaling exponents
and crossover phenomena in nonstationary heartbeat time-series Chaos 5: 82-87
Pimm SL & Redfearn A (1988) The variability of population-densities. Nature 334: 613-614
Posch T, Loferer-Krossbacher M, Gao G, Alfreider A, Pernthaler J & Psenner R (2001) Precision
of bacterioplankton biomass determination: a comparison of two fluorescent dyes, and of
allometric and linear volume-to-carbon conversion factors. Aq Microb Ecol 25: 55-63
Purkhold U, Pommerening-Roser A, Juretschko S, Schmid MC, Koops, H-P, & Wagner, M.
(2000) Phylogeny of all recognized species of ammonia oxidizers based on comparative
16S rRNA and amoA sequence analysis: Implications for molecular diversity
surveys..Appl Environ Microbiol 66: 5368-5382
Rohani P, Miramontes O & Keeling MJ. (2004) The colour of noise in short ecological time
series data. Math Med Biol 21: 63-72
Schreiber T & Schmitz A. (2000) Surrogate time series. Physica D 142: 346-382.
9
Starkenberg SR, Chain PS, Sayaverda-Soto LA, Hauser L, Land ML, et al. (2006) Genome
sequence of the chemolithoautrophic nitrite-oxidizing bacterium Nitrobacter winogradskyi
Nb-225. Appl Environ Microbiol 72: 2050-2063
10
SI Table 1. Stock solutions for preparing the synthetic wastewater media.
100x Stock Media Solution
(add 10 mL to 1000 mL volume DI water,
autoclave, and store at 4oC)
(g/L-stock)
Peptone
32.0
“Lab Lemco” powder (Oxoid)
19.0
Yeast extract
3.0
Urea
3.0
(NH4)2SO4
6.7
K2HPO4
1.4
KH2PO4
1.1
CaCl2·6H2O
0.4
MgSO4·7H2O
0.2
1000x Trace Element Solution
(sterile filter and add 1 mL to 1000 mL
Media Solution after autoclaving)
(g/L-stock)
FeCl3·6H2O
0.75
H3BO3
0.075
CuSO4·5H2O
0.015
KI
0.09
MnCl2·4H2O
0.06
NaMoO4·6H2O
0.03
ZnSO4·7H2O
0.06
CoCl2·6H2O
0.075
EDTA
0.5
Concentrated hydrochloric acid
1 mL
11
SI Table 2. In-sample rms errors of a linear Volterra-Wiener Model versus and a non-linear
Volterra-Wiener model.
0.1 d-1
Dilution Rate
Total bacteria
AOB
NOB
Protozoa
0.33 d-1
0.83 d-1
e
r

e
r

e
r

Linear
0.5148
6
5
0.586
6
5
0.3358
3
2
Non-linear
0.2080
28
6
0.217
27
6
0.1322
28
6
Linear
0.5775
6
5
0.349
6
5
0.5780
2
1
Non-linear
0.3320
24
6
0.147
28
6
0.1071
26
6
Linear
0.8699
4
3
0.463
7
6
0.4906
4
3
Non-linear
0.6986
11
5
0.167
28
6
0.0882
28
6
Linear
0.3979
7
6
0.382
6
5
0.4659
2
1
Non-linear
0.2865
28
6
0.265
28
6
0.3530
25
6
SI Table 3. e -rankings for guild abundance data among chemostats with surrogate series.
Dilution Rate
0.1 d-1
0.33 d-1
0.83 d-1
Total bacteria
1
1
1
AOB
4
1
1
NOB
2
1
2
Protozoa
6
7
8
12
SI Figure 1. Variability versus census length for AOB and NOB guild abundances for the three
chemostats.
AOB
1.0
0.9
avg. SDL
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.10 day-1
0.1
0.33 day-1
0.0
0.83 day-1
0
50
100
150
200
250
census interval
NOB
1.8
1.6
avg. SDL
1.4
1.2
1.0
0.8
0.6
0.10 day-1
0.4
0.33 day-1
0.2
0.83 day-1
0.0
0
50
100
150
census interval
13
200
250