Integral Structural–Functional Method for Characterizing Microbial … · 2015. 4. 2. ·...

ISSN 1064�2293, Eurasian Soil Science, 2015, Vol. 48, No. 4, pp. 378–394. © Pleiades Publishing, Ltd., 2015.Original Russian Text © A.V. Yakushev, 2015, published in Pochvovedenie, 2015, No. 4, pp. 429–446.

378

INTRODUCTION

One of the objectives of a soil biologist is to deter�mine the nature and rates of the processes fulfilled bymicroorganisms in soil. This can be reached by meansof the structural–functional characterization of themicrobial community. The structural characterizationinvolves the taxonomic composition of the soil micro�bial community. The functional characterizationinvolves information on the development of microbio�logical processes in the soil. The structural–functionalcharacterization by determining the physiologicalgroups of microorganisms in the soil using the inocu�lation on selective agar media showed its limited appli�cability long ago [5]. The physiological state of themicroorganisms remains unknown. The abundanceand activity are different characteristics of microor�ganisms. The functional specialization of soil micro�organisms has been overestimated. There are few soilmicroorganisms specializing in a single process: amicroorganism fulfills different processes purposefullyor in cometabolism. No uniform structural–func�tional method has yet been developed.

We develop the idea of separating physiologicalmicrobial groups on the new level of microbial associ�ations. In nature, a microorganism transforms thenutritive substrate not alone (as on a selective agarmedium) but syntrophically in association with othermicroorganisms.

The aim of this work is to develop an integral cul�ture method for the simultaneous study of the compo�sition and physiological diversity of microbial popula�tions, their growth strategy, and physiological statefrom the growth parameters and the taxonomic com�position of liquid accumulative cultures (associa�tions). The principle and novelty of the approach con�sist in the integration of several methods into a logi�cally bound entity: the Winogradsky method of soilaccumulative culture (succession approach) [2] isimplemented for different physiological conditions ofgrowth by means of the inoculation of liquid mediawith a soil suspension analogously to multisubstratetesting (Biolog EcoPlates and FungiLog) [3] with thetheoretical description of the growth dynamics analo�gously to the kinetic method of determining themicrobial biomass in a soil [9, 21]. The compositionsof the initial suspension and the appearing associa�tions are determined by the plate method [7] supple�mented with the description of the appearancedynamics of the microbial colonies [17] and themolecular–genetic identification of the microorgan�isms by sequencing the nucleotide sequences of theDNA fragment of the gene coding for 16S rRNA usingBLAST software. The method was tested for soil�envi�ronmental studies, but the approach is universal andcan be used for microbial complexes of water bodiesand industrial microbial associations in biotechnologyand in the physiological study of pure cultures. The

SOIL BIOLOGY

Integral Structural–Functional Method for Characterizing Microbial Populations

A. V. YakushevFaculty of Soil Science, Moscow State University, Moscow, 119991 Russia

e�mail: [email protected] August 13, 2014

Abstract—An original integral structural–functional method has been proposed for characterizing microbialcommunities. The novelty of the approach is the in situ study of microorganisms based on the growth kineticsof microbial associations in liquid nutrient broth media under selective conditions rather than on the level of taxaor large functional groups. The method involves the analysis of the integral growth model of a periodic culture.The kinetic parameters of such associations reflect their capacity of growing on different media, i.e., their phys�iological diversity, and the metabolic capacity of the microorganisms for growth on a nutrient medium. There�fore, the obtained parameters are determined by the features of the microbial ecological strategies. The inocu�lation of a dense medium from the original inoculate allows characterizing the taxonomic composition of thedominants in the soil community. The inoculation from the associations developed on selective media charac�terizes the composition of syntrophic groups, which fulfill a specific function in nature. This method is of greaterinformation value than the classical methods of inoculation on selective media.

Keywords: microbial associations, microbial growth kinetics, ecological strategies of microorganisms, earth�worms, peat

DOI: 10.1134/S1064229315040110

EURASIAN SOIL SCIENCE Vol. 48 No. 4 2015

INTEGRAL STRUCTURAL–FUNCTIONAL METHOD FOR CHARACTERIZING 379

integral structural–functional method for characteriz�ing microbial populations (hereafter, integral method)is a development of the kinetic method for the in situdetermination of the physiological state of microor�ganisms [14].

OBJECTS AND METHODS

Natural bacterial and fungal complexes were stud�ied. The objects of the study were cultured het�erotrophic aerobic and facultative anaerobic bacteriaand fungi forming syntrophic associations. Thesyntrophic associations are microbial cultures cogrow�ing on the same nutritive medium under mixing condi�tions, when they can interact directly or via metabolites.The associations represent a new type of operationaltaxonomic units used as an object of study. Vermicom�posts from cattle manure prepared using Eisenia fetidacompost worms by JSC Flora�L and JSC RusskiiGumus (pHwater = 8.15 ± 0.19; Norg = 1.797 ± 0.003%;Corg = 21.89 ± 0.135%) were studied. Model compostsand vermicomposts were prepared by the laboratorycultivation of F. fetida on small�leaf litter (pHwater =8.9 ± 0.5; Norg = 1.34 ± 0.03%; Corg = 36.76 ± 0.15%)and cattle manure (pHwater = 8.87 ± 0.24; Norg = 1.39 ±0.01; Corg = 21.40 ± 0.16), as well as Aporrectoda caligi�nosa earthworms on low�moor peat (pHwater = 6.33 ±0.22; Norg = 2.18 ± 0.01%; Corg = 35.06 ± 0.3%), for6 months. Microbial complexes of fresh (24�h old)coprolites and cattle manure (a substrate inhabited byEisenia fetida (food) during three model experiments),coprolites of Aporrectoda caliginosa and its food(Ap horizons of a leached chernozem, agro�peat soil,and soddy�podzolic soil; the A horizon of an ordinarychernozem + 10% oak waste; and the A horizon of anurbanozem), coprolites of Lumbricus terrestris, excre�ments of March fly (Bibio sp., Bibionidae) larva, and itsfood (broad�leaf litter) were also studied. Leaf litter(food) and old excrements of vegetable�eating milli�pedes (Pachyiulus flavipes) were compared, as well assamples from high�moor (pHKCl 2.5–4; degree ofdecomposition 5–10%) and low�moor (pHKCl 5.6–6.1;ash 7–13%) peat soils sampled to a depth of 1 m in theWestern�Dvina forest�bog station of the Research Insti�tute of Forestry (Tver oblast) in June and August of 2010and to a depth of 3 m in the bogs of Western Siberia(Tomsk oblast) in July–August of 2009: an oligotrophicbog (Polynyanka, 57°03′ N, 82°42′ E; pHKCl 2.6–5.2;ash 3–6%) and an eutrophic bog (Tagan, 56°21′ N,84°47–48′ E; pHKCl 5.7–6.2; ash 9–14%).

The pH values were determined by potentiometry.The contents of C and N in the dried and ground sam�ples were determined using an Elementar Vario EL IIIHCNS elemental analyzer. The content of ash wasdetermined by incineration in a muffle furnace accord�ing to the conventional procedure.

RESULTS AND DISCUSSION

Model of periodic microbial growth in liquid media.The method is based on the description of the growth ofmicrobial associations. A maximally simplified (withthe minimum number of parameters and equations) butmechanistic (theoretical) structurized quasi�homoge�neous integral model of a pure culture is proposed.

The model operates with an environmentalparameter (s0, the initial concentration of the grow�ing substrate, g/L) and culture parameters (x0, theinitial concentration of culture х in the nutrientmedium; tlag, the end point of the lag period, h; μm, themaximum value of the specific growth rate μ, h–1; ρ0,the initial value of growing culture’s physiologicalstate variable ρ; γ = –ln(ρ0), the metabolic capacityof the culture for growth on the nutrient medium; Kρ,the semisaturation constant (g/L), Kρ = s atρ = 0.5ρm, where ρm = 1 is the maximum ρ value; Y,the economic coefficient of the microbial growth onthe nutritive substrate, Y = (xm – ⎯ x0)/s0, where xm isthe maximum culture concentration; am, the maxi�mum specific dying rate, h–1; τdy, the time of thebeginning of the exponential dying, h; η0, the valueof the physiological state variable η of the dying cul�ture at the beginning moment of exponential dying;and ln (ln(η0) = δ, the metabolic capacity of the cul�ture to resist dying).

At t < τdy,

At t ≥ τdy,

The integral model of the lag period describes thedynamics of the exit of separate cells from the lagphase by the equation

ρ

ρ

= μ

μ = μ ρ+

μ= −

⎛ ⎞ρ = μ ρ − ρ⎜ ⎟+⎝ ⎠

,

,

,

,

m

m

dx xdt

sK s

xdsdt Y

d sdt K s

ρ= −

μlag

0ln( ).

m

t

= −τ

= − ητ

η= − η − η

τ

,

,

(1 ).

m

m

dx axd

da ad

da

d

−µ

ρρ =

− ρ + ρ'

' 0

0 0

'( ) ,

' '(1 ) mtt

e

380


YAKUSHEV

where is the maximum specific preparation rate ofthe metabolic cell system for the growth on themedium, and is the integral physiological state of thegrowing microbial culture, which determines the initialcapacity of a specific cell to exit from the lag phase.

To justify the integral model, let us consider the lagperiod, i.e., the preparation of the microorganisms forgrowing on the nutritive medium, which includes thefollowing stages: (1) primary dying; (2) stationary;(3) transition to exponential growth. The entire lagperiod or its separate stages can be absent. We examinethe models leaving out the dying stage. We separate themodels into the differential models describing thelagperiod of the culture via the growth of separate cellsand the integral models operating with changes in thetotal concentration of microorganisms. The lag periodis characterized by the duration of the lag phase, forwhich several concepts exist [24]. Within the frame�work of the integral approach, the duration of the lagphase for the entire culture includes the following:

(1) tlag_ini, the beginning of proliferation of the firstcell in the population [17]; however, it does not con�sider the transition to exponential growth, which is agreat disadvantage;

(2) tlag_fin, the final moment of the transition phase,when the specific growth rate of the culture is maxi�mum: µ = µm [10]; however, μ asymptoticallyapproaches µm, and tlag_fin cannot be expressed mathe�matically exactly;

(3) tlag_extr, the time when the value in the

modified Gompertz model reaches an extremum(maximum) [15]; the application of tlag_extr is limitedby the specific model;

(4) the duration of the lag phase in the integralmodel is calculated using the conventional Perthmethod [10] for the determination of tlag, which is the

µ 'm

ρ0'

⎛ ⎞⎜ ⎟⎝ ⎠

2

02

ln xdx

dt

graphical version of the Lodge–Hinshelwood method[20]; tlag is the intersection time of the tangents to theinitial concentration х0 (y1) and to the exponentialgrowth segment (y2) in the plot of the natural loga�rithm of the microorganism concentration ln(x) as afunction of time t (Fig. 1a) [10]. The same plot in thecoordinates x(t) is given in Fig. 1b. To clarify the bio�logical sense of tlag, we consider the structured inte�gral deterministic models.

According to Lodge and Hinshelwood [20], x =xNG + xG, where xNG and xG are the concentrations ofnongrowing and growing microorganisms, respec�tively. In the lag phase, the value of xG does notincrease, but the microorganisms synthesize thegrowth�limiting metabolite xP. At tlag_ini, the reachedconcentration xP corresponds to the beginning of theexponential increase of xG:

At tlag_ini = 0, the model is reduced to the continu�

ous–discrete–continuous model = [19]. The models have the following shortcomings:(1) in reality, there is no instant end of the lag phase,but a gradual transition of the cells in the lag phase(xlag) to the exponential growth phase (xexp) occurs;(2) nongrowing cells (xNG) are not always present dur�ing the lag phase.

We present the graphical Perth method in algebraicterms to clarify its relationship with the Lodge–Hin�shelwood method. We denote the ordinate segmentfrom the intersection point with y2 to 0 as L0, and the

( )

µ −

⎧ = ≤⎪⎪⎪ μ μ −= =⎨⎪⎪= μ − >⎪⎩

lag_ini

lag_ini

lag_ini

at

at

( )0

0

( )

1 .

m t tm G m NG

NGm

dx t tdt

x e x xdx x xdt x x

xx t t

x

( )x t µ+ 0

mtNG Gx x e

3

700 605040302010

6

9

20

0 302010

60

100

40

80

y2 = µmt + ln(L0)y1 = ln(x0) y2 = L0exp(µmt)

y1 = x0

tlag tlagW0L0

ln(L0)

ln(x

)

x

t t

(a) (b)

Fig. 1. Illustration for the determination of the lag phase by the Lodge–Hinshelwood graphical method in (a) semilog and(b) linear coordinates. Dots indicate the experimental data.



segment from the intercept with y2 to x0 as W0 (Fig. 1b).Hence, At the moment of tlag,

y1 = y2,

Let then, the algebraic form of the Perth

method is as follows:

It follows from the Perth method that the functionx(t) describing the exponential and lag phases shouldfulfill the following conditions: (1) x(0) = x0; (2) at t →

–∞, x(t )→ W0; (3) at t → ∞, (4) tlag =

The function x(t) = y1 + y2 fulfills all the con�

ditions if –L0 is added as an additional term, becausey1(0) + + y2(0) = x0+ L0.

Then,

Expressing L0 and W0 through х0 and ρ0, we obtain

Let us derive :

As and , then

We express W0 through L0 and obtain

, which is a logistic equation with

K = 1.

= +0 0 0.x L W

µ

= + =

lag

0 0 0 0 ,mtx L W L e

⎛ ⎞+⎜ ⎟⎝ ⎠=μ

lag

0 0

0

ln

.m

L W

Lt

= ρ

+

00

0 0

,L

L W

ρ= −

μlag

0ln( ).

m

t

µ→ 0( ) ;mtx t L e

ρ−

μ

0ln( ).

m

µ

= + −

= +

1 2 0

0 0

( ) ,

( ) .mt

x t y y L

x t W L e

µ= − ρ + ρ0 0 0( ) (1 ),mtx t x e

= μ ρ .mdx xdt

ρd

dt

ρ =+

( )( ) ,

( ) ( )L t

tL t W t

= 0( )W t W µ= 0( ) mtL t L e

µ

µρ =

+

0

0 0

( ) .m

m

t

t

L et

L e W

− ρ

=

ρ

0 00

0

(1 ),

LW

µ

µ

ρ =− ρ

+ρ

0

0 00

0

( ) ,(1 )

m

m

t

t

L et

LL e

−µ

ρρ =

− ρ + ρ

0

0 0

( ) ,(1 ) mt

te

ρ= μ ρ − ρ(1 )m

d

dt

The biological sense is that tlag – L(tlag) = x0,

ρ(t) = where is the parameter characterizing

the difference between μ and μm caused by the internalphysiological features of the culture rather than by theexternal factors (e.g., the lack of growing substrate).The equations coincide with the continuous–dis�crete–continuous model [19] given W0 = xNG andL = xG. However, this biological interpretation of theparameters W0, L, and ρ(t) is unacceptable, and we findanother by examining the structured model of the bot�tleneck [22]. In the chemical composition of the micro�organisms, we separate хP, the concentration of intrac�ellular components: the enzymes, enzymatic complex,ribosomes, etc., which play the role of a bottleneck in

metabolism, i.e., regulate μ.

its value varies from the minimum Pmin to the maxi�mum Pmax. The variable Q (termed the metabolicactivity functional) is proposed as a quantitative indexof the physiological state of the microbial population:

, where λ is a constant. At the same time, Q isthe specific consumption rate of the limiting substrate(metabolic coefficient). From the Mono equation

(cited from [10]), where is the eco�

nomic coefficient. Then, and

For the lag phase of a periodic culture,

The synthetic chemostatic model (SCM) [9],which develops the bottleneck model, describes theconcentration of microorganisms as x = хP + хU, whereхP is the totality of intracellular high�molecular�weight components essential for the growth (RNA,ribosomal proteins, etc.), an even more extended con�cept of хP than that in [20, 22], and хU is the totality ofintracellular high�molecular�weight componentsensuring the slow growth and survival under unfavor�able conditions (storage compounds, cyanide�resis�tant oxidases, pigments, etc.). U =

U varies from Umin to Umax. The

values of P and U are inversely proportional. Themodel expands the equality which wasderived for stationary chemostatic conditions [22], to

other cultivation conditions. =

µ

µ

( )

m

t µ

µ

( )

m

t

⎛ ⎞= ⎜ ⎟

⎝ ⎠

g component

g biomass;Px

Px

= λQ P

µ= ,Q

Y=

dxYds

µ = YQ µ =max.m YQ

= µ − µ

= − µ = µ −

= = µ

max max( )

.

mdQ Q Qdt

YQ Q Q Q Q

dx YQx xdt

⎛ ⎞⎜ ⎟⎝ ⎠

(g component

g biomass;Ux

x

µ = µ ( ),mr t

−

=

−

min

max min

( )( )

Q t Qr t

Q Q

382


YAKUSHEV

= is the variable of the

physiological state with the initial value r0, which reg�ulates the metabolism of a microorganism and repre�sents the development of the Q concept [22]. It is takenin the SCM that the maximum specific rate of хP syn�thesis is v ≠ μm.

Then, the SCM describes the lag phase as follows:

Later on, the author took that v = μm, and theSCM equations coincided with the integral model.Hence,

= ,

which is true, and

W(t) = = (1 – r(t))x(t) =

, which is wrong, because, in the com�

plex model, = = =

is a constant.

Therefore, although in mathematical terms ρ(t) =r(t), in reality, ρ(t) ≠ r(t). In distinction from r0, ρ0 notonly characterizes the physiological state of the cul�ture at the beginning of the lag period, but it is also theratio between the lengths of the L0 and W0 segments onthe ordinate (Fig. 1), which are determined from thefurther growth curve; hence, the ρ0 value of a microor�ganism varies among the nutritive media. Therefore,the medium for which the value of ρ was determinedshould be indicated: ρglucose, ρAshby, etc. In distinctionfrom r0, ρ0 can be higher than 1. In this case, the tran�sition to the active state of the microorganisms notincluded in x0 (e.g., those not cultivated on agarizedmedia) occurs in the lag phase. Therefore, to discrim�inate the physiological state variable r(t) from ρ(t), wedesignate the latter as the physiological state of thegrowing culture.

Initially, the physiological state indicated the fea�tures of the culture that could be described by models[18]. Later on, this concept involved all available infor�mation on the composition and metabolism of cells [12]or, on the contrary, a specific kinetic quantity deter�mined by the culture history (the Powell metabolicactivity functional Q) [22]. These two approachesreflect two sides of the same phenomenon. Therefore,

−

−

min

max min

( )P t P

P P

−

−

−

min

max min

( )1

U t U

U U

= µ

= −(1 ).

mdx rxdt

dr r rdt

v

−

=

−

min

max min

( )( ) ( )

P t PL t x t

P P

−

=

−

min

max min

( )( ) ( ) ( )P P

P P

x t xr t x t x t

x x

−

−

min

max min

( )( )

U t Ux t

U U−

−

min

max min

( )( )U U

U U

x t xx t

x x

( )W t −

−

min

max min 0(0)U U

xU U

− 0 0(1 )r x

−

−

min

max min 0(0)U U

U U

x xx

x x

the physiological state should characterize (1) the ini�tial state of the culture under the new medium condi�tions and (2) its state during the growth. It is incorrectto define the physiological state as the value h0 = µmtlag,which the authors interpret as the metabolic work thatmust be fulfilled by microorganisms to adapt to the newconditions and prepare for reproduction [24], becauseh0 does not describe the changes in the physiologicalstate of the microorganisms during their growth. Toavoid confusion, we introduce the term metaboliccapacity for growth γ = µmtlag = – ln(ρ0). The higher theγ value, the lower the metabolic capacity for growth; thevalue of γ characterizes both metabolically active anddormant microbial cultures.

In the bi�phasic Baranyi model of the lag phase [16]based on the bottleneck principle and according to theMichaelis–Menten enzymatic kinetics model, theμ value depends on the concentration of the growth�limiting metabolite (probably RNA or ATP), xP(t), andthe Michaelis semisaturation constant (KP):

The synthesis of xP(t) is described by a first�orderequation with constant ν:

The values of xP(t) and KP cannot be determined;

is determined from the growth curve:

.

Then,

If it is taken that

then

⎛ ⎞= μ ⎜ ⎟+⎝ ⎠

( ).

( )p

mP p

x tdx xdt K x t

= ν .PP

dxx

dt

=

( )P

P

x tq

K

ν= = = ν

P P

P P

dx xdqq

dt K dt K

−ν

= = = = α

+ + ++

0

0

( )

( )( ).

( )( ) 11

P

P Pt

PP P

P

x tqx t K q

tx tK x t q q eK

ρ= = = =

− ρ −0

( )( ) ( ) ( ),

1 ( ) 1 ( )P

P

tx t L t r tq

K t W r t

−ν

−ν

−α = = =

+ −+

−

0

0 0

0 0 0

0

1( ) ( ).

(1 )1

tt

r

r rt r t

r r r eer



The only true condition is ν = µm. At ν < µm, thegrowth will stop with time because of the decrease ofxP. This contradicts the possibility of the permanentcultivation of a microorganism. The condition ν > µm

results in the absurd equality х = xP. Hence, one enzy�matic system controls the growth of microorganismsand the synthesis of xP, and ν = µm. Then,

, and the bi�phasic Baranyi modelcoincides with the integral model. This explains whyv = μm for the description of the lag phase in theSCM. From the coincidence of the integral model,the bi�phasic Baranyi model, and the SCM, xP = kLand KP = kW0, where k ≠ 1 is an empirical constant. Inthe lag and exponential phases, the change in the rela�tive specific metabolic work of the microorganisms(with respect to the maximum possible value) with time

is as follows: = =

In the presence of the lag

phase, the growth curve asymptotically approaches the

exponential form ( at t → ∞); therefore,

should be found for the determination of the addi�tional specific metabolic work (Aad) that should be ful�filled by microorganisms to adapt to new conditionsand prepare for reproduction (transit to the exponen�

tial phase). At = At ρ0 = 1,

the maximum possible work is reached; then,

= =

Let us calculate tlag_extr [15] for the integral model.

Note that = and the Buchanan–

Cygnarowicz approach can be applied to any model of

the lag phase, because = Then,

α = ρ =( ) ( ) ( )t t r t

= ρ∫0( ) ( )t

A t t dt−µ

ρ

− ρ + ρ∫ 0

00 0(1 ) m

t

tdt

e−µ

− ρ + ρ+

μ

0 0ln((1 ) ).

mt

m

et

µ→ 0( ) mtx t L e

∞A

→ ∞t ∞

→A Aρ

+μ

0ln( ).

m

t

∞

=mA t

∞ ∞

= −

adm mA A A

ρ− −

μ

0ln( )

m

t tρ

− =μ

lag0ln( )

.m

t

⎛ ⎞⎜ ⎟⎝ ⎠0

ln xdx

dt= µ

0

,dxx dtx

⎛ ⎞⎜ ⎟⎝ ⎠

2

02

ln xdx

dt

µ.

d

dt

μ ρ= μ ,m

d d

dt dt

−µ

−µ

− µ −µ

−µ

μ ρ − ρμ=

− ρ + ρ

μ ρ − ρ − ρ − ρμ=

− ρ + ρ

20 0

20 0

3 220 0 0 0

2 30 0

(1 ),

((1 ) )

(1 )((1 ) ).

((1 ) )

m

m

m m

m

tm

t

t tm

t

ed

dt e

e ed

dt e

In the extremum point,

At at

→ –∞.

At ρ0 > 0.5, tlag_extr < 0; i.e., it loses the biologicalsense. Therefore, tlag_extr is unsuitable for assessing theduration of the lag period in the integral model.

The equation is similar to that for the determina�tion of the lag phase duration from the respiratoryresponse of microbes to the addition of glucose to thesoil using the SCM [1].

As then tlag_extr = =

where is the initial rate of the blank

microbial respiration (unrelated to the growth), and

is the initial rate of productive microbial respira�

tion (related to the growth). In all the cases, ≥ therefore, the equation always has a biological sense,because tlag_extr > 0.

Let us consider the differential approach to thedescription of the lag phase. The integral and differen�tial approaches describe the same phenomenon andshould use identical equations. We describe the exitdynamics of separate cells from the lag phase withinthe integral model. To distinguish the parameters cal�culated on the basis of the exit dynamics of separatecells from the lag phase and those determined from thegrowth curve of the whole culture, we use the super�script “'”. We denote the concentration of viable cells

in the medium at t = 0 as .

The exit dynamics of the separate cells from the lagphase is directly proportional to the physiological state

of the growing culture = =

where μm is the maximum specific

− µ −µ

−µ

μ =

μ ρ − ρ − ρ − ρ =− ρ + ρ

⎛ ⎞− ρ⎜ ⎟ρ⎝ ⎠=μ

lag_extr lag_extr

lag_extr

lag_extr

2

2

230 0 0 0

30 0

0

0

0,

(1 )((1 ) )0,

((1 ) )

1ln

.

m m

m

t tm

t

m

d

dt

e e

e

t

ρ →0 0,

− ρ⎛ ⎞⎜ ⎟ρ ρ⎝ ⎠ → −μ μ

0

0 0

1ln

ln( ),

m m

ρ →0 1,

− ρ⎛ ⎞⎜ ⎟ρ⎝ ⎠μ

0

0

1ln

m

=

+

pr0

bl pr0 0

00.1

,0.1

Vr

V V

⎛ ⎞⎜ ⎟⎝ ⎠μ

bl0pr

0

max

lnV

V

⎛ ⎞−⎜ ⎟⎝ ⎠μmax

0

0

0.1(1 )ln

,

r

r bl0V

pr0V

bl0V pr

0 ;V

0'x

ρ :0' exp( )x t ρ'0' ( )x t

−µ

ρ

− ρ + ρґ

0 0

0 0

' ',

' '(1 ) m t

x

e

384


YAKUSHEV

preparation rate of the cell metabolic system for thegrowth.

The biological sense is that –

xexp(tlag) =

If the detection time (td) (necessary for the forma�tion of a visible colony on a dense nutritive medium) isdirectly related to the first division of the single parentcell of the colony (before td, the radial growth rate ofthe colony Kr is constant), then the duration of the lag

phase for each cell and the value for the whole cul�ture can be assessed from the appearance time of col�onies on Petri dishes. At the initial stage, Kr is con�stant, which is undoubted for fungi and actino�mycetes.

Then, xexp(t)~N(t) is the number of colonies on the

medium at the moment t, and ~ Nfin is the number

of colonies grown on the medium; characterizesthe initial capacity to form colonies on a dense nutri�tive medium:

We denote the metabolic capacity for growth on a

dense medium as γap = –ln( ) and the maximum spe�cific preparation rate of the metabolic cell system for

growth on a dense medium as . The superscrip ap(apparent) is used, because, even in an ideal case, thetime td passes between the exit of the cell from the lagphase and the registration of the colony, which distortsthe parameter values.

The proposed theoretical deterministic integralmodel more adequately describes the appearancedynamics of macrocolonies on dense media than theempirical stochastic (probabilistic) Hattori model [16]based on the Poisson distribution:

where σ is the probability of colony development. Theintegral model explains and theoretically describes theexistence of the lag period; it predicts the acceleratedand then slowed appearance of colonies, which is fre�quently observed in practice, and explains the increasein the time of appearance of the first colony withdecreasing CFU number on the medium by the factthat the smaller the number of cells on the medium, thebetter the ρ(t)ap corresponds to the appearance of thefirst colony. The Hattory model postulates the lag phasebut does not explain it. This model predicts only theslowing appearance of colonies, which contradicts theexperimental data: it does not consider the increase in

ρ= −

μlag

0'ln( )''m

t

− ρ

0

0

'.

'2

x

ρ0'

0'x

ρap0

−µ

ρ= ρ =

− ρ + ρap

apap fin

fin ap ap

0

0 0

( ) ( ) .(1 ) m t

NN t N t

e

ρap0

µapm

−σ −

= ≤⎧⎪⎨

= − >⎪⎩lag_ini

lag_ini

fin lag_ini( )

( ) 0,

( ) (1 ), ,t t

N t t t

N t N e t t

the appearance time of the first colony with decreasingCFU number and assigns an inadequately great biolog�ical sense to the appearance of the first colony (tlag_ini isthe appearance time of the first colony). The appear�ance kinetics of colonies on a dense medium allowsobtaining independent data on the in situ physiologicalstate of the microorganisms without analyzing the dataderived from the growth kinetics in liquid cultures. Note

that γ' ≠ γ ≠ γap and ≠ μm ≠ because of the differ�ence between the conditions in the liquid and densemedia.

The Mono equation [10] adequately describes thegrowth�deceleration and stationary phases; therefore,the integral model relates the decrease of μ with thesubstrate limitation according to the Michaelis–Menten enzymatic kinetics model. The limitationshould be manifested in the decrease of ρ(t), because,as was shown above, one enzymatic system controlsthe growth of microorganisms and the synthesis of xP,and ν = μm. This is another difference between ρ(t)and r(t). We introduce the corresponding equations inthe integral model:

where s0 is the initial concentration of the growingsubstrate s; Y = (xm – x0)/s0 is the economic coefficientof growth, where xm is the maximum concentration ofthe culture during the growth; and the semisaturationconstant Kρ = s at ρ = 0.5 ρm, where ρm = 1 is the max�imum ρ value.

For the description of the culture dying, we intro�duce the following parameters: a, the specific dyingrate, h–1; τdy, the time when a = am (the maximum

dying rate), h; and , the concentration of microor�ganisms at t = τdy. Let τ = t – τdy exists at t ≥ τdy. Thegrowth and dying are so different processes that weintroduce the parameter η for the physiological state ofthe dying culture. For this purpose, we divide the dyingculture into the exponentially dying component J(τ) =f2 and the undying component Z(τ) = f1 (Fig. 2). J(τ) isanalogous to L(t), and Z(τ) is analogous to W(t). Wedenote the ordinate segment from the intersection point

of f1 with the ordinate to 0 as Z0 and its segment to as

J0. Hence, = There is a biologically mean�ingful time moment τ1, when f2 = f1:

µ 'm µapm

ρ

ρ

μ = μ ρ+

μ= −

⎛ ⎞ρ = μ ρ − ρ⎜ ⎟+⎝ ⎠

,

,

,

m

m

sK s

xdsdt Y

d sdt K s

x0dy

dy0x

dy0x +0 0.J Z

− τ − τ

= + =

dy 1 10 0 0 0( ) ,m ma ax e J Z e Z



600 5040302010

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

f1 = Z0

f2 = x0dyexp(–amτ)

x

τ

t1

J0

Z0

Fig. 2. Simulation of culture dying. Dots indicate the experimental data.

Let be the physiological state η of the

dying culture at t = τdy; then,

The biological sense is that τ1 – x(τ1) = 2Z0. Wedenote the metabolic capacity of the culture to resistdying as δ = –ln(η0) = amτ1. Within this approach, thefunction x(τ) describing the dying of the culture

should fulfill the following conditions: (1) x(τdy) =

(2) at τ → τdy, x(τ) = (3) at τ → ∞ x(τ) → Z0;

and (4) The equation x(t) = f1 + f2 meets

all the conditions if is substituted by J0, because

f1(0) + f2(0) = + Z0. Then,

Expressing J0 and Z0 through and η0, we obtainthat

⎛ ⎞⎜ ⎟+⎝ ⎠τ = −

0

0 01

ln

.m

Z

J Z

a

η =+

00

0 0

Z

J Zη

τ = −0

1ln( )

.ma

dy0 ;x

− τdy0 ;max e

ητ = −

01

ln( ).

mady0x

dy0x

− τ

τ = +) 0 0( .max Z J edy0x

− τ

τ = − η + η

= −

τ

= − η

τ

η= − η − η

τ

dy0 0 0( ) ((1 ) ),

,

,

(1 ),

ma

m

m

x x e

dx axd

da ad

da

d

where is the parameter characterizing the

difference between a and am caused by the internalphysiological features of the culture rather than theexternal factors (e.g., the lack of growing substrate).

The integral model is structured, because it subdi�vides (structures) the microbial culture into compo�nents with different properties (L, W, J, and Z).

The proposed experimental procedure for the struc�tural–functional characterization of the natural micro�bial complex. All the operations are performed understerile conditions. The sterility control should be pro�vided for each analysis. The experimental design isgiven in Fig. 3.

The homogenization and desorption of microor�ganisms from the solid substrates are performed in anaqueous suspension (1 : 5) on a Heidolph Multi Reaxvortex mixer at 2000 rpm for 20 min. Coarse samplesare preliminarily ground. The growth of fungi in thesuspension is inhibited by adding an antibiotic (0.05%nystatin). To suppress bacteria, 0.25% chlorampheni�col is added. Excess substrate particles are removed bycentrifugation at 3200 g for 5 min. The concentrationand composition of the cultivated microorganisms inthe original substrate are determined by inoculationfrom the supernatant on an agar medium using theconventional procedure with the description of theappearance dynamics of colonies on Petri disheswithin the above�described integral model. The super�natant is added by 100�μL portions into the wells of acapped 96�well flat�bottom culture plate containing100 μL of different liquid media in each well. Thecomposition of the liquid media depends on the objec�tive of the study. It is desirable that the media be trans�

η =( )m

ata

386


YAKUSHEV

parent and colorless or does not change the color duringthe growth of microorganisms. A control treatmentcontaining the nutritive medium without the growingsubstrate is necessary to not confuse the growth causedby the attendant compounds in the inoculated suspen�sion of the test sample with the growth on the organicsubstance of the nutritive medium. The nutritive mediaare sterilized by autoclaving or filtering through mem�brane filters with a pore diameter of 0.22 μm. To pre�vent the evaporation of water from the wells, the plateis covered from the sides with parafilm. The plate is setinto an immunoassay analyzer (e.g., Tecan Sunrisemicroplate reader), which automatically records thegrowth dynamics of the microorganisms from theoptical density (at 620 nm) with the periodic shaking ofthe plate. To maintain the target temperature, theinstrument is placed in a climatic chamber or a thermo�stat. The temperature is determined by the experimen�tal task; a temperature of 25°C (standard for soil micro�biology [8]) is recommended. After the end of thegrowth period (up to several weeks), agarized versions ofwell media or glucose–peptone–yeast (GPY) mediaare inoculated from the wells to reveal the taxonomic

composition of the associations developed in the wells.The microorganisms are identified using the modernmolecular–genetic method. The growth of the periodicmixed culture (microbial association) in the wells isdescribed by the integral model developed for pure cul�tures and described above.

The substrate concentration s0 is experimentallyset; the growth of the biomass х as a function of time tand the parameters x0 and τdy are determined. Fromthese data, other parameters are calculated usingModelMaker 3.0 (Cherwell Scientific, Oxford, UK).The growth of associations is frequently stepwise;therefore, each stage is separately described by theintegral model equations.

The integral method gives a number of parameters:(1) The taxonomic structure of the microbial popula�tions determined by the conventional inoculationfrom the initial suspension and the microbial associa�tions spontaneously developed on selective liquidmedia. (2) The specific physiological diversity deter�mined from the growth in a broth medium under spe�cific physiological conditions (per 1 g of substrate).Given that the integral model developed for the peri�

2.00E+061.60 1.41.21.00.80.60.40.2

1.00E+09

2.00E+09

3.00E+09

4.00E+09

5.00E+09

00

0.2

0.4

0.6

0.8

1.0

1.2

20 40 60 80 100 120 140

C(O

D62

0)

OD620

1

2

3 4

5

6

9

8

7

а b

Incubation time, h

Opt

ical

den

sity

, 6

20 n

mFig. 3. Experimental design: (1) analytical soil sample; (2) soil suspension in a vortex tube; (3) culture plate with liquid brothmedia; (4) culture plate inoculated with a suspension; (5) Petri dish with microorganisms isolated from the initial suspension;(6) Sunrise immunoassay analyzer; (7) optical density growth curves in the plate wells plotted by the immunoassay analyzer((a) coprolites, (b) food); (8) microorganisms grown on a Petri dish after inoculation from a nutrient medium on which a micro�bial association was developed; (9) linear correlation of the bacterial concentration in the suspension С(OD620) with the opticaldensity (OD620) at the inoculation from wells on a universal GPY medium (n = 150; r2 = 0.52).



odic growth of a pure culture is used for describing thegrowth of associations, the term “microbial culture”in the indication of the kinetic parameters should besubstituted by the term “cultivated microbial associa�tion.” For example, the in situ physiological state ofthe microorganisms is expressed through γ and γap (themetabolic capacity of the cultivated microbial associ�ation for growth in different broth and agar media,respectively). (3) The growing strategies of the culti�vated microbial association determined from the

parameters μm, Y, Kρ, δ, and am.

Proposed liquid and agarized nutritive media. Inthe methods of multisubstrate testing and BiologEcoPlates [3], the trophic diversity is determinedusing a medium with a certain metabolite (aminoacid, sugar, polyatomic alcohol, organic acid, etc.) asa single source of carbon. The new method proposesto determine the physiological diversity of the micro�organisms, i.e., to use media simulating differentphysiological conditions. In our experiments, uni�versal rich media for auxotrophs were used: GPYbroth, nitrogen�free Ashby’s medium for oligonitro�phils, a medium for copiotrophs [23], a urea�con�taining medium free from mineral nitrogen for theconsumption of organic nitrogen forms, and GPYbroth with an citrate buffer (pH 3–7) for studying themicrobial growth at different pH values. Media con�taining one organic compound at 2.5 g/L were used,which were prepared from the mineral basis of Cza�pek’s medium (0.5 g/L NaNO3, 0.25 g/L MgSO4 ·7H2O, 0.12 g/L KCl) [11] diluted with tap water by4 times. The list of nutrients was significantlyexpanded [3], including biopolymers of animal andplant origin (starch, carboxymethyl cellulose(CMC), chitin, casein, Tween�20, pectin, xylan,dextrane�500), aromatic compounds, biologicallyactive compounds and hormones (salicin, indolace�tic acid, cinnamic acid, phenylalanine, histidine),salts of organic acids (sodium dodecyl sulfate, potas�sium citrate, potassium pyruvate, calcium lactate,potassium oxalate, sodium acetate, potassium succi�nate), monomers (glucose, xylose, mannose, arabi�nose, alanine, cysteine, glutamine, valine, lysine),oligosugars (lactose, cellobiose), and alcohols(methanol (for methylotrophs), ethanol, sorbite,dulcite, inosite).

A GPY broth, each component of which is taken ata concentration of 1 g/L, or an agarized version of oneof the above media is recommended for the inocula�tion of agarized media from liquid media and the ini�tial soil suspensions in soil�environmental studies.

Substantiation of the sample preparation. The sam�ple preparation by vortexing allows homogenizing anddesorbing cells from the surface of the solid phase (if itexists) by the mildest method. Centrifugation reducesthe amount of interfering substrate particles (becausethe growth in a liquid culture is determined from a tur�bidity measurements), which could be additional

µap,m

sources of microbial growth in liquid media. The dis�solved nutrients of the sample can be removed by filtra�tion followed by the washing out of cells from the sur�face of the filter.

For comparison purposes, it is important to stan�dardize the microbial community under study in termsof the number of microorganisms getting into the wellsor the weight (or volume) of the analytical sample. Thelatter operation is simpler; therefore, it was used in thiswork: a 1�g sample of dry substance (soil) was taken asthe standard. All the kinetic parameters can varydepending on the sample weight. The physiologicaldiversity should be the most sensitive parameter. Thephysiological diversity determined for 1 kg of soil cansignificantly exceed that for 1 g of soil. Therefore, itshould be realized that the integral method determinesthe specific physiological diversity per unit weight of theportion or microbial concentration in the suspension.

Substantiation of the method for determining thebacterial growth. The optical method has a number ofshortcomings [10]. There is a rule that, at the suspen�sion absorption below 1.1 and the volume of bacterialcells of 0.4–2 μm3, the relationship between the lightabsorption and the biomass concentration in the sus�pension does not depend on the shape of the cells(cocci, coliforms) [8]. This rule is confirmed by theinoculation from liquid media in wells on a dense GPYmedium (Fig. 3). The statistical analysis of the equa�tionС(OD620) = a + b OD620 (where С(OD620) is the con�centration of bacteria, CFU/mL; OD620 is the opticaldensity of the suspension at 620 nm measured on a Sun�rise analyzer; and а and b are the target coefficients)showed that the coefficient a is statistically insignifi�cant, and the equation is simplified to the statisticallysignificant equation С(OD620) = b OD620 (p > 0.95) withr2 = 0.52 (sample set n = 150) and b = (2.0 ± 0.51) × 109.The sensitivity limit of the Sunrise analyzer is 2 ×106 CFU/mL. The coefficient b obtained for the GPYbroth is the same for all the media used and differentsoils. It should be determined permanently, because itcan be different for new nutritive media and habitats.The universality of the coefficient can be related to themorphological diversity of mixed cultures, which isobserved under a microscope and levels the opticalparameters of cultures. The microscopic study confirmsthat mobile solitary plankton cells predominantlydevelop; the formation of biofilms, aggregates, andmicrobial deposits is of secondary importance. This factallows the quasi�homogeneous model, which repre�sents the uniform distribution of the culture in the sam�ple volume, to be applied for describing the growth ofmicroorganisms in the wells. The wavelength of 620 nmis selected for the detection of microbial growth becauseof the lower light absorption by humus and microbialpigments, which interfere with the determination of themicroorganism concentration at higher wavelengths.

Substantiation of statistical data processing. Thegrowth curves of suspensions in wells with the samemedium almost coincide: the variation coefficient for

388


YAKUSHEV

the kinetic parameters of the integral model is Сv <10%, because the growth rate is determined by theinitial composition of the suspension. The suspen�sions obtained from different samples of the same soilcan give different growth curves, and the frequencydistributions of the kinetic parameters do not followthe Gauss law; therefore, the results should be pre�sented as a range of distributions or medians withquartiles. Hence, the following rule should beadhered: one replicate for each sample.

Substantiation of the integral model applicability.The integral model well describes the growth of purecultures, e.g., at the study of the effect of sphagnols onbacteria [4]. In the study of microbial associations ondense and liquid media, two or three growth stages with

an intermediate lag phase are frequently observed. It isproposed to present the development of microbial asso�ciations as the independent growth of several groupsseparately described by the integral model (Figs. 4, 5)and to index their parameters according to the growthstages (μm1, μm2, …). It is shown in Fig. 4 how theappearance dynamics of the colonies on a densemedium (Fig. 4a) are described through two indepen�dent processes. The dynamics of the first association are

described by the equation (Fig. 4b),

and the dynamics of the second association are

described by the equation N2(t) =

(Fig. 4c). Figure 5 illustrates how, for the interpreta�tion of the integrated stepwise growth of the associa�tion in a liquid medium (Fig. 5a) on the basis of sta�tistical analysis, the single curve is converted intofour curves described by separate equations of theintegral model (Fig. 5b). It is taken for stages 1–3that x0 = 1650 ± 530 CFU/mL; stage 1 of the initialgrowth is characterized by μm1 = 0.81 ± 0.23, Кρ1 =4.84 ± 1.42 g/L, γ1 = 1.66 ± 0.57, and Y1 = 1.40 ±0.28 million CFU/g. At the initial stage, microorgan�isms usually grow slowly. After this stage, intermediatestages are sometimes observed. In Fig. 5b, this is stage 2:μm2 = 0.36 ± 0.22; Кρ2 = 0.001 ± 0.0006 g/L; γ2 = 5.11 ±3.17; Y2 = 9.40 ± 0.36 million CFU/g. The last growthstage is usually the main growth stage (in Fig. 5b,stage 3): μm3 = 0.12 ± 0.08; Кρ3 = 1.83 ± 0.74 g/L; ρ03 =13 ± 7; Y3 = 105.20 ± 0.19 million CFU/g. The laststage is single� or multistep dying of the association,frequently with stabilization at some final concentra�tion level (stage 4): am = 0.024 ± 0.014; τdy = 111 h;δ = 0.59 ± 0.11. At the third growth stage, ρ03 = 13 > 1;therefore, the participation of bacteria from the pre�ceding stages in the final growth stage can be sup�posed for the association considered.

A similar division of single�step processes into two�and, more rarely, three�step processes was reported ear�lier for the description of the soil microbial communityfor the appearance dynamics of colonies on Petri dishesaccording to Hattori [6], the Michaelis–Menten enzy�matic kinetics model [9], the kinetics of the respiratoryresponse to the addition of glucose to the soil (Fig. 1 in[25]), and the biokinetic fractionation of soil organicmatter by the Semenov method [13]. It follows that thesoil microbial community has two–three groups ofstrategies strongly differing in enzyme systems andgrowth kinetics (probably K, L, and r strategies) ratherthan a continuum of ecological strategies. Note that, ondense media, the first wave of colony appearance can berelated to the exit from the lag phase not only of Bacillus[6] but also of many other bacteria (Flavobacterium,Cytophaga, Pseudomonas, etc.).

−µ

ρ

− ρ + ρap

apfin1

ap ap1

01

01 01(1 ) m t

N

e

−µ

ρ

− ρ + ρap

apfin2

ap ap2

02

02 02(1 ) m t

N

e

1800 16014012010080604020

2E8

4E8

6E8

8E8

1E9

1.2E9

1.4E9

0

2E8

4E8

6E8

8E8

1E9

1.2E9

1.4E9

0

2E8

4E8

6E8

8E8

1E9

1.2E9

1.4E9

Time, h

Bac

teri

al c

once

ntr

atio

n,

CF

U/g

(a)

(b)

(c)

Fig. 4. Appearance kinetics of colonies on a Petri dish

described (a) by one equation, where r2 = 0.95, = 4.5,

= 0.05, and Nfin = 1.2 × 109, and as a combination of

two populations: (b) = 0.07, = 3.7, Nfin1 = 3.9 × 108;

(c) = 0.05, = 5.1, Nfin2 = 7.7 × 109.

γap1

µapm1

µapm1 γ

ap1

µapm2 γ

ap2



Let us consider a small part of the results obtained bythe integral method, which illustrate the potential of themethod in the ecology of microorganisms. The data onthe kinetic parameters Y, μm1, and γ1; the physiologicaldiversity; and the taxonomic composition of associa�tions were derived from 640 growth curves obtained on12 nutritive media for 87 portions from 16 samples(8 excrements and 8 feedstuffs). The data for peats werederived from 349 growth curves obtained on 14 nutritivemedia for 48 samples from 8 peat horizons [14].

Taxonomic composition of bacterial associationsafter growth on broths in wells. The determination ofthe parameter b for the function С(OD620) describingthe relationship between the concentration of cellsand the optical density of suspensions showed that b =(2.5 ± 0.63) × 109 for the inoculation of bacteria fromwells on the tryptone soya broth, (2.0 ± 0.51) × 109 onthe GPY broth, and (4.1 ± 1.5) × 108 (i.e., lower by anorder of magnitude) on selective media (agarized ver�sions of the media in the wells from which the inocu�late was taken). The coefficient of determination forС(OD620) was as follows: r2 = 0.26 (n = 21) for theselective media, r2 = 0.50 (n = 23) for the tryptonesoya broth, and r2 = 0.52 (n = 150) for the GPY broth.These facts and the twofold decrease of the Shannonindex at the inoculation of selective media comparedto the GPY broth indicate that, in the stationary anddying phases of bacterial associations, the abundanceof bacteria capable of directly utilizing the organicsubstrate from the liquid medium is lower than that ofsatellite bacteria by an order of magnitude on the aver�age. In the polymer�containing media, the destructionof the association is directly fulfilled by species of theorder Myxococcales and the genera Bacillus, Fla�vobacterium, Cytophaga, and Nocardia, as well as theorder Rhodococcus for phenylalanine and histidine;satellite bacteria include the more abundant generaAquaspirillum, Comamonas, Pseudomonas, andArthrobacter. From the inoculation data, one to seven

bacterial cultures develop in each well with two–threespecies being predominant. The same species is fre�quently found on different media. For a specific soil,10–20 bacterial species are isolated from associationson 12 media (CMC, starch, pectin, xylan, chitin,Tween�20, casein, glucose, xylose, phenylalanine,cinnamic acid, sodium acetate). For the food–animalexcrement pair, 30 to 50% of the species are common;these are usually dominants in the wells. The biodiver�sity in the associations is low: the Shannon index isabout 1. In most wells, one species is predominant (theBerger–Parker index > 0.7). Antagonistic bacteria candominate in the same well, as is confirmed by thezones of inhibited growth on Petri dishes after inocu�lation from the wells.

Appearance dynamics of colonies on dense media.To determine the parameter x0 of the integral modelnecessary for the calculation of the other kineticparameters and the taxonomic composition of the nat�ural community, the inoculated suspension is platedon a dense medium. For the studied samples of bacte�rial and fungal complexes from different vermicom�posts, peats, and animal excrements, the appearancedynamics of the colonies is adequately described bythe integral model (r2 = 0.95 ± 0.02), which proves itsvalidity. To illustrate, we note the increase in the CFUnumber of fungi in the excrements of the millipedePachyiulus flavipes compared to the food (leaf litter)from 8750 ± 2250 to 14900 ± 2900 CFU/g with their

values of being similar: 0.29 ± 0.02 and 0.27 ±0.009 h–1, respectively. The metabolic capacity forgrowth, γap, increases in the excrements from 12.1 ±0.2 to 12.6 ± 0.3. The comparison of the bacterialcommunities in the excrements and the food of Lum�bricus terrestris at the first stage of the exit of the bac�terial cells from the lag phase (Fig. 4) revealed anincrease in the metabolic capacity for growth (decreaseof γap) during the intestinal transit: γap is 6.47 ± 1.67 in

µapm

2400 2001601208040

2E8

4E8

6E8

8E8

CF

U/m

L

Time, h

1 2 3

4

(a) (b)

Fig. 5. Example of bacterial growth in a liquid culture: (a) actual growth and (b) growth divided into four (1–4) independent pro�cesses (lines) described by the integral model; (circles) experimental data.

390


YAKUSHEV

the food and 3.81 ± 0.46 in the excrements. At the

same time, of the preparation for growth on themedium increased from 0.048 ± 010 to 0.12 ± 0.055.

Specific physiological diversity of bacteria. Thephysiological diversity of a microbial communityimplies the capacity of its members to grow and repro�duce under different physiological conditions of themedium (temperature, salinity, redox potential, etc.).The trophic diversity implies the capacity of the com�munity members to utilize different food sources(capacity to grow on polymers, fulfill photosynthesis,etc.). The functional diversity implies the capacity ofthe community members to perform their ecologicalfunctions (decomposition of plant residues, ecosystemsupply with nitrogen (via N fixation), symbiosis withplants or causing of plant and animal diseases, etc.).The trophic diversity, which is a specific manifestationof the physiological diversity, is determined from thenumber of media with different organic substrates onwhich associations appeared after the inoculation ofthe studied soil suspensions. The comparison of thefood and excrements of the soil invertebrates (earth�worms, March flies) showed a decrease in the specifictrophic diversity of the bacterial complex in the excre�ments (in 1 g). Associations do not appear on rarelyutilized compounds (cinnamic and tartaric acids,sodium dodecyl sulfate). This phenomenon is relatedto the decrease in the taxonomic diversity of bacteriain coprolites (confirmed by the classical plate methodwith the inoculation from the food and coprolites). Onthis basis, it can be supposed that functionally simplerbacterial communities are selected in the intestines ofsaprotrophic invertebrates than in the substrate onwhich they food (soil, semidecomposed plant resi�dues). However, in an experiment on the comparisonof the bacterial communities in the food and excre�ments of the earthworm Aporrectoda caliginosa, thenumber of experimental treatments with growth onthe CMC biopolymer increased by 25%.

The inoculation of broths with peat suspensionsalways resulted in the formation of associationsactively growing on starch, pectin, xylan, xylose, glu�cose, phenylalanine, acetate, Ashby’s medium, GPYbroth, Tween�20, and casein. The exceptions wereCMC, chitin, and cinnamic acid. The abundance ofbacteria capable of growing on them in peats was sosmall that associations did not developed in all wellseven at the 1 : 10 dilution of the peat suspension.Growth on cinnamic acid was recorded in 3 out of40 samples taken from different horizons of high�moor peat (at a depth of 0–15 cm), which indicates alow abundance of bacteria capable of growing on cin�namic acid as a single source of carbon. The absenceof destructive bacteria in high�moor peats is related tothe accumulation of benzene carboxylic acids inhibit�ing the microbial activity. In the low�moor peat,growth was recorded in 36 out of 40 samples. Thisindicated the higher abundance of bacteria capable of

µapm

growing on cinnamic acid in the low�moor peats thanin the high�moor peats. The portion of wells in whichgrowth on the CMC medium was observed was signif�icantly larger in the low�moor peat soils. This indi�cated a higher abundance of bacteria (cellulolytics inlow�moor peats) and a higher hydrolytic potential ofthe communities in the low�moor peats. The decreaseof the water content and the rise of the air tempera�ture, which were observed in August compared to July,resulted in a significant increase in the abundance ofboth chitinolytic and cellulolytic bacteria in the stud�ied peats; hence, the portion of wells with growth onchitin and CMC increased [14]. Thus, the decrease ofthe water content stimulates the appearance of bacte�rial associations of chitinolytics and cellulolytics inpeats, which accelerates the decomposition of peat.

Parameter Y of bacterial associations. The param�eter Y of the integral model is similar to the economiccoefficient used in microbial kinetics: the higher theY value, the higher the efficiency of the food assimila�tion by the microbial associations in the broths. Thecomparative analysis of the Y values for the food andexcrements of the earthworms Eisenia fetida, Aporrec�toda caliginosa, and Lumbricus terrestris and larvae ofthe March fly Bibio sp. showed no regularities at thelevel of the specific nutrient medium. The coefficientY on the specific medium can increase or decreaseduring the intestinal transit. An analogous tendency isobserved for the values of μm1 and γ1 for the food andexcrement samples, as well as for the peats. However,the summation of all the rank distributions of theY values among all seven objects shows a decrease inthe efficiency of the substrate assimilation in the tran�sit bacterial community. This indicates a change in thepredominant ecological strategy in the bacterial com�munity during the intestinal transit. The effect of bac�teria with less efficient metabolism increases, and theportion of media on which Y > 5 × 1011 CFU/g sub�strate decreases (Fig. 6a). The less efficient metabo�lism of the intestinal associations allows the cells ofanimal intestine walls to intercept some food. Thelower Y values indicate more copiotrophic conditionsin the intestine under which the high efficiency of thesubstrate assimilation is not necessary.

The bacterial associations of high�moor peats dif�fer from those of low�moor peats by the more effi�cient metabolism (higher portion of associations withY > 3.6 × 1011 CFU/g substrate) (Fig. 6b). This indi�cates the more oligotrophic conditions of the high�moor peats for microorganisms and the orientationof the microbial associations toward the more com�plete and efficient utilization of small resources.

The parameter µm1 of bacterial associations. Forsimplicity of comparison, the rank distributions of μm1were analyzed (Fig. 7a). Because of the passagethrough the intestines of the March fly larvae andearthworms, the bacterial associations of the freshexcrements, in distinction from the food communi�ties, become capable of more rapidly growing in the



presence of excess food (the portion of associationswith μm1 > 0.8 h–1 is larger, and those with μm1 < 0.2 h–1

are almost absent). The invertebrates create favorableconditions for the decomposition of soil organic mat�ter in their intestines and thus stimulate fast�growingbacteria able to provide the host with food. To win thecompetition for food in the animal intestines, the bac�teria should have higherμm1 values.

The bacterial associations of high�moor peats dif�fer from those of low�moor peats by the lower growthrate in the presence of excess food (the portion of asso�ciations with μm1 > 0.2 h–1 is smaller) [14]. This indi�cates the potential incapacity of the bacterial associa�tions to rapidly decompose organic matter even underfavorable nutritive conditions. This fact explains theslow decomposition of high�moor peat even after dry�ing, in distinction from low�moor peat, whose micro�bial associations do not strongly differ from those ofautomorphic soils in terms of μm1.

The parameter γ1 of bacterial associations. For sim�plicity of comparison, the rank distributions of γ1 wereanalyzed (Fig. 7b). The associations of fresh excrementsmore rapidly responded to the appearance of nutritivesubstrates than the food associations (the portion ofassociations with γ1 < 2 increases from 32 to 65%),which indicates the higher metabolic capacity for the insitu growth of the excremental bacteria. The intestinaltransit community occurs in the intestines of a saproph�agous invertebrate for only several hours; therefore, forthe efficient digestion, the associations composed of themicroorganisms most rapidly responding to theimprovement of the medium conditions and immedi�ately beginning to grow should win the competition.

The bacterial associations of high�moor peats dif�fer from those of low�moor peats by the slowerresponse to the appearance of nutritive substrates (theportion of the most metabolically active associationswith γ1 < 5 is smaller than in the associations of low�

moor peats by 2 times) [14]. In undecomposed moss ormoss litter, the intense decomposition of organic mat�ter occurs, which slows down only in the waterloggedhorizons of low�moor peats; therefore, the bacterialassociations, which are buried when the thickness ofthe peat layer increases, retain the capacity of rapidlyactivating under favorable conditions. In the high�moor peats, the sphagnum moss is slowly decom�posed; therefore, the bacterial associations do notacquire the capacity for rapid activation.

Optical density study of the growth of mixed fungalassociations in broths. Fungi frequently form inten�sively colored spores and films on the surface of themedium, which interfere with the determination ofthe biomass from optical density measurements. If adirectly proportional relationship is supposed betweenthe optical density and the biomass of fungi for eachseparate association, γ (dimensionless parameter) andμm (h–1) can be determined, although under the addi�tional assumption that the conversion factor does notchange during the incubation. The values of theseparameters do not depend on the conversion factor;they are determined by the growth curve shape and aresimilar for optically different fungi. The growth of fun�gal complexes from the food and old excrements ofPachyiulus flavipes on biopolymers (starch, chitin,xylan, CMC, dextrane�500, pectin, casein, Tween�20)was studied. Growth was observed in all the replicatesfor all the substrates. The growth curves of the fungaland bacterial associations are similar in shape; there�fore, we describe the growth of fungi similarly to thatof bacteria. To describe the kinetics, we conventionallytake that the inoculation of the soil suspension on Petridishes gives only fungal spores n (CFU/mL), and thesize of the raw biomass of an average soil spore is 5 ×10–11 g [7]. Then, x0 (g/mL) = n × 5 × 10–11. We takefrom the experimental data that the raw biomassx(t) (g/mL) = 0.0008 OD620 for the Sunrise immu�

01.2E11 2.4E11 3.6E11 4.8E11 6E11 7.2E11

5101520253035404550556065

1.2E11 2.4E11 3.6E11 4.8E11 6E11 7.2E11

Ave

rage

por

tion

of c

lass

, %

Y, CFU/g substrate

1

2

3

4

(a) (b)

Fig. 6. Averaged rank distributions of the Y values for the bacterial associations obtained on nutritive media from (1) animal excre�ments, (2) animal food, (3) high�moor peat, and (4) low�moor peat.

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YAKUSHEV

noassay analyzer. Under these assumptions, we calcu�late the mean values of γ1 and μm1 for the fungal asso�ciations on all the substrates. In the excrements, μm1

increases from 0.28 ± 0.05 to 0.34 ± 0.03 and γ1

decreases from 3.5 ± 0.7 to 2.1 ± 0.6. These facts con�firm the activation of the fungal block in the experi�ments, which was described above on the basis of theappearance dynamics of colonies on the agar medium.Inoculation from wells showed that the associationsinclude actinomycetes and zygomycetes. The portionof yeast�like fungi and yeasts, which gain an advantagein broths, increased in the associations compared tothe initial fungal complex. Inoculation and the

microscopy of wells revealed a low abundance of bac�teria (<106 CFU/mL) because of the use of chloram�phenicol. The microscopy of the wells under 50�foldmagnification after incubation for 117 h revealed thepredominance of one to three species in each well withtwo species being most frequently predominant. Thiswas confirmed by inoculation from the wells on anagarized medium.

CONCLUSIONS

The integral method is based on the expansion ofthe concept of the ecological strategy to not only pop�

02.01.41.21.00.80.60.40.2

5

10

15

20

25

30

35

40

45

0222

5

10

15

20

25

30

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40

45

4 6 8 10 12 14 20

50

55

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75

Ave

rage

por

tion

of c

lass

, %

Ave

rage

por

tion

of c

lass

, %

μm1, h–1

γ1

1

2

(a)

(b)

Fig. 7. Averaged rank distributions of (a) the µm1 values and (b) capacity of growing γ1 for the bacterial associations obtained onbroths from (1) animal excrements and (2) food.



ulations but also microbial associations; the applica�bility of the kinetic model describing the growth of apure culture to associations; the renouncement of thestudy of the microbial behavior in soil in favor of themore standard and homogeneous conditions in liquidmedia, where simpler microbial associations, whichare amenable to exact mathematical analysis, aredeveloped; and the consideration of the behavior ofmicroorganisms in a microcosm (wells of a cultureplate) analogous of their behavior in the real soil (sim�ulation of a microzone on a macroscale). These con�ditions implicitly lie behind the application of the suc�cession approach, which is based on the dynamicstudy of the microbial communities after any initiationof succession in the soil under controlled conditions ofsoil microcosms. This approach is widely used by soilbiologists; it proved its efficiency in the study of thesoil microbial complex. The dynamics of the microbialassociations in microcosms after the addition ofchitin, glucose, or oil differs from that under field con�ditions. All the above assumptions imply the expan�sion of the properties assigned to a biological species toartificial associations. Thus, the object of the in situstudy of microorganisms by the integral method is anew operational taxonomic unit: a complex (compos�ite) species (microbial association considered as a spe�cies). The complex species represents the concept of aspontaneous culture [2] followed to its logical end: thestudy of the soil microbial community by the growthanalysis of mixed (spontaneous) cultures appearing atthe addition of some growing substrate to the soil,which creates a selective advantage for the reproduc�tion of the studied organisms. However, only the timeand the use of the integral method by different special�ists will show the accuracy, reliability, and relevance ofthe analysis of spontaneous associations appearing inliquid nutritive media for basic and applied research.

The terms of “the physiological state of the growing

microbial culture” and “the physiological

state of the dying microbial culture” are pro�

posed. It is supposed that

and where xP(t) is the concentration of the

growth�limiting metabolite in the cell, KP is theMichaelis semisaturation constant with this metabo�lite, and k ≠ 1 is an empirical constant.

The passage of microorganisms through the intes�tines of March fly larvae and earthworms results in asignificant difference between the bacterial associa�tions of the fresh excrements and food. In the intes�tines, the bacteria most metabolically capable of grow�ing (lower –ln(ρ01)) and fast�growing (higher μm1)with the lower degree of conversion of food to biomass(lower Y) gain an advantage in the transit community:

μρ =

μ( )

m

t

η =( )m

ata

ρ =+0

( )( ) ,

( )L t

tW L t

=

( )( ) ,Px t

L tk

=0 ,pKW

k

a part of the monomers resulting from the microbialactivity remains for the host animal. Decomposablebiopolymers (cellulose) are predominantly selected atthe expense of destroyers of hardly decomposablecompounds (sodium dodecyl sulfate, cinnamic andtartaric acids, potassium oxalate): the physiologicaldiversity decreases.

The bacterial associations of high�moor peats moresignificantly differ from those of automorphic soilsthan the associations of low�moor peats potentiallycapable of rapidly decomposing polymers. The associ�ations of high�moor peats are incapable of rapidgrowth even under favorable conditions (lower μm1).The associations more slowly respond to the appear�ance of nutritive substrates (higher γ1). However, theyhave a more efficient metabolism (higher Y). All thisindicates the presence of internal reasons related tothe structure of the microbial associations for the slowdecomposition of high�moor peat even after drying, indistinction from the external reasons (insufficient aer�ation, absence of soil animals, etc.) in the low�moorpeat, which is rapidly mineralized after the removal ofexternal limitations (drying).

ACKNOWLEDGMENTS

The author thanks E.V. Blagodatskaya, S.A. Blago�datskii, T.G. Dobrovol’skaya, and O.S. Kukharenko.

This work was supported in part by the RussianFoundation for Basic Research (project nos. 12�04�01170�a and 13�04�00536�a (experiments with peat))and the Russian Science Foundation (project nos. 14�14�00625 (experiments with earthworms) and 14�50�00029 (experiments with millipedes)).

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Translated by K. Pankratova

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