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Volume 16, 2005

 

 

 

Examination of some possibilities for growth prognostication of bacteria Escherichia Coli in presence of heavy metals’ complexes with neural network’s help

 

Sotir Sotirov* , Ljudmila Dimitrova**, Evdokia Sotirova***

“Prof. D-r Asen Zlatarov” University – Bourgas Bulgaria

ssotirov@btu.bg* , ldim@btu.bg**, esotirova@dir.bg***

 

 

 

Abstract

Some metals are absolutely necessary for the welfare of the human’s vital activity and relate to so called biogene elements. Other metals – so called toxic metals, provoke opposite effects – getting into a living organism they cause poisoning and death. About their examination however are necessary many experiments and compound mathematical methods for tracking their influence and for growth prognostication of bacteria.

This material exposes a different point of view at the subject. The work team propounds neural network’s using in prognostication of the growth curves of bacteria Escherichia Coli in presence of heavy metals’ complexes.

 

Keywords: neural networks, prognosis, growth curves of bacteria Escherichia Coli,

 

Introduction

Between the chemical elements, capturing the interest like biosphere’s pollutants, heavy metals (with atom weight over 40) represent particular interest. This to high degree is connected to the biological activity of many of them. Physiological influence of metals to the human’s and animal’s organism is different and depends on metal’s nature, on connection type in which it exists in the environment and its concentration. Many heavy metals display salient complex-forming properties. For example, in water solutions, the ions of these metals are hydrated and they are able to form different hydroxide-complexes, which composition depends on the solution’s acidity. If in the solution there are anions or molecules of organic compounds, the ions of these metals form varied complexes with different structure and stability.

Some heavy metals are absolutely necessary for the welfare of the human’s vital activity and they relate to so called biogenic elements. Others – so called toxic metals, provoke opposite effects – when they get into the living organism they cause poisoning and death.

Along of long period of time have been existed the conviction that important biological functions make only sodium, potassium, manganese, iron and calcium which compose 99% of all metal’s atoms in human’s organism and  except the iron they relate to the macro elements’ group. The interest in the transitional elements’ functions relating to the heavy metals (including the iron) and are contained in the organism like tracks, appears from a short of time. Because of their low contents in the organism, they are called microelements (magnesium, zinc, molybdenum, fluorine, selenium etc.) The mentioned microelements function in organism in form of hydrated ions or like the iron – in form of coordination compounds. Metal cations execute many important biochemical reactions like nitrogen’s fixation, breathing through oxygen or nitrate, one-electron catalyst, tearing of C-C relation, assimilation of hydrogen, biodegradation of urea and etc. Heavy metals’ complexes catalyze all these reactions. In high concentrations however the heavy metals form nonspecific complex compounds, which drive to toxic effects.

Purpose of the current work is developing of a mathematical model based on restricted capacity experimental data, allowing quality and quantity evaluation of the influence of the different heavy metal’s complexes on the growth of bacteria Escherichia Coli.

 

 

Growth curves of microbial population in periodical reactor.

 

For growth and development of microbial cells are necessary the following conditions 1) viable sowing material; 2) carbon-containing substratum; 3) easy-absorbed energy source; 4) source of nitrogen; 5) oxygen; 6) mineral salts; 7) absence of inhibitors which oppressive cells’ growth; 8) appropriative physical-chemical conditions (pH, temperature, heat- and mass-exchange). The growth process of biomass could be presented in a diagram like this:

  Substrates + Cells  Extracellular Products + More Cells

                                                                                           (1)

 

Microbial growth is an autocatalytic reaction - the rate of growth is directly related to cell concentration. The growth process is characterized by the net specific growth rate:

 

                                                                                                                (2)

Where X is the biomass quantity and t is time.  

The net specific growth rate is the difference between a gross specific growth rate () and the rate of loss of cell mass due to cell death ():

                                                                                                    (3)

 

In strict periodical processes every components of nutritious environment and sowing material are charged only once at the beginning of the process. After some time, also only once, is drowning out the cultural liquid of the apparatus, after that the biomass and the other products get detached. Their characteristic is a non-interrupted alteration of physiological state of population and composition of nutritious environment which is related to vital process flowing in the microbial cells.

Growth of microbial population in periodical culture graphically is described with so called growth curve (fig.1). It is dependence of parameter characterizing the quantity of microorganisms (for example the optical density) of time. On the typical growth curve of the bacterial culture are distinguished some phases:

·        Lag-phase;

·        Log-phase or phase of exponential growth;

·        Phase of growth delay;

·        Hospital phase / Station phase;

·        decline phase or phase of death

Fig.1. Typical batch growth curve

Sowing material fall in fresh nutritious environment does not start immediately to multiply. Cells go through adaptation stage and during that time their enzymes become active or new enzymes start synthesize. This period is called lag-phase.

 

·        Occurs immediately after inoculation and is a period of adaptation for the cells to their new environment

·        New enzymes are synthesized, synthesis of other enzymes is repressed

·        Intracellular machinery adapts to the new conditions

·        May be a slight increase in cell mass and volume, but no increase in cell number

·        The lag phase can be prolonged by low inoculum volume, poor inoculum condition (high % of dead cells), age of inoculum, nutrient-poor medium

 

After it the maximum growth speed is observed, the population grows exponentially. Duration of this phase depends on initial concentration of the substratum and also of the condition of sowing material ( log  or exponential phase).

 

In this phase, the cells have adjusted to their new environment

·        At this point the cells multiply rapidly (exponentially)

·        Balanced growth –all components of a cell grow at the same rate

·        Growth rate is independent of nutrient concentration, as nutrients are in excess

·        The first order exponential growth rate expression is

 

                                                      (4)

Integrating

                                                                                      (5)

An important parameter in the exponential phase is the doubling time (time required to double the microbial mass)

                                                                                           (6)

 

In consequence the growth delays because of lack of nutritious substratum or because of accumulation of inhibition metabolites, or because some other physical-chemical changes in environment properties. Deceleration phase is very short phase, during which growth decelerates due to either depletion of one or more essential nutrients or the accumulation of toxic by-products of growth (e.g. Ethanol in yeast fermentations). This is period of unbalanced growth -cells undergo internal restructuring to increase their chances of survival. Deceleration phase is followed quickly by the stationary phase. Through it the speed of the neoformed and perished cells is equal, which provokes plateau’s appearance in diagram. After a fixed time the number of dying cells become vastly to outnumber the neoformed ones. Culture become to LIZIRA – go over to dying phase which is presented by reverse slope of the curve.

Analysis of the growth curves is a fundamental moment in learning mechanism of enzymes’ reactions and the influence of the particular factors over it [6]. Exposed mathematical model founds on the received growth curves in presence of different complexes of heavy metals in nutrition environment.

 

Neural network for prognosis realization

 

In examined case it prognosticates one-dimensional function. Main part in this process is a realization of possibility based on gained experience of preliminary learning to prognosticate the next value of function  growth curve of bacteria Escherichia Coli.

Neural network (fig.2) which is used has eight entries and one exit. In its middle layer, the main “intelligent” part, there are ten neurons.

 Network learns with experimentally removed results of process which will be prognosticated. In this learning, a part of these results (like series of consecutive measurements) submits on the network’s entry and the next in the series of measurements – on the exit.

 

 

 

 

 

 

 

 

 

 


Learning process could be presented in the following sequence:

-      of the series  of measuring, on the network’s entry submit so many values m as its entries are(in this case m=5) -  (when  i=0,1,2 3,4,5…, p=N-m-1);

-      the following value of the series submits on the network’s exit s;

-      series of measuring on the entry P and the next value of the series T make learning pair (), after that the learning purpose is the T –value. Learning is by algorithm “Backpropagation”;

-      i increases with a one  while   and this is the end of learning.

 

Prognostication of values is realized in the following sequence:

-      the last m values of the learning series submit on the trained system’s entry. The received value of the exit is the first of prognosticated ones;

-      the received prognosticated value is added to these learning series P like ;

-        the next prognostication is based on the entry series with N +1 elements. From it is taken the last m values and they submit on the network’s entry.

 

 

Prognostication of growth curve of bacteria Escherichia Coli

 

Data learning the neural network and which are experimentally received (table 1) submits on the network.

Table 1

t

Without Gly

Prognosis

With Gly

Fe(Gly)2

Vo(Gly)2

MoO2(Gly)2

As(Gly)2

0

0.75

 

0.8

0.94

0.8

0.8

0.94

1

0.78

 

0.78

1.16

1.1

1.08

0.88

2

0.82

 

0.9

1.6

1.35

1.32

0.92

3

0.86

 

1.1

1.68

1.53

1.48

0.9

4

1.21

 

1.38

1.685

1.6

1.6

0.96

5

1.38

 

1.56

1.68

1.62

1.7

0.97

6

1.58

 

1.76

1.67

1.65

1.72

1

7

1.65

 

1.82

1.7

1.6

1.65

0.88

8

1.65

 

1.8

1.69

1.58

1.56

0.84

9

1.72

 

1.82

1.66

1.58

1.58

0.84

10

1.69

 

 

 

 

 

 

11

1.69

 

 

 

 

 

 

12

 

1.6582

 

 

 

 

 

13

 

1.6359

 

 

 

 

 

14

 

1.6055

 

 

 

 

 

 

 

Their visual representation is given on fig.3

                                       

fig.3

 

On the figure are presented seven different growth curves, in which are used different metals. Only one of them is prognosticated (Without Gly- dark blue). Prognosticated averages are three and their diagram is presented in purple.

 

Realization of prognostication is accomplished in environment of MATLAB and are used some analogues of [5]. Neural network have a structure 8-10-1. Learning is realized with accelerated algorithm [1], which is a modification of algorithm “Backpropagation” [2,3,4].

 

Conclusions:

Proposed method allows being prognosticated growth curves of bacteria Escherichia Coli in the presence of different metals’ complexes and in different concentration based on organic experimental data. In this way, the quantity of high-priced experiments vastly decreases by using the possibilities of the neural networks.

 

References:

 

1.      Sotir Sotirov, A method of accelerating neural network learning, Neural Processing Letters, Springer Science+Business Media B.V., Formerly Kluwer Academic Publishers B.V., Volume 22, Issue 2, Oct 2005, Pages 163 - 169

2.      D. E. Rumelhart, G.E. Hinton and R.J. Williams, “Learning representation  by back-propagation errors”, Nature, vol.323, pp 533-536, 1986.

3.      D.B. Parker, “Learning-logic: Casting the cortex of the human brain in silicon”, Technical report TR-47, Center for computational research in Economics and management Science, MIT, Cambridge, MA, 1985.

4.      Sotir Sotirov Modeling the algorithm Backpropagation for learning of neural networks with generalized nets – part 1, Proceedings of the Fourth International Workshop on Generalized Nets, Sofia, 23 September 2003, 61-67

5.      Àíàíèåâ Â.Ò., Èâàíîâ Ò. È.,Ñîòèðîâ Ñ. Í., Ìåòîä çà ïðîãíîçèðàíå íà èçíîñâàíåòî íà ìåòàëîðåæåùè èíñòðóìåíòè ÷ðåç íåâðîííè ìðåæè, Íàó÷íî – ïðèëîæíà êîíôåðåíöèÿ ñ ìåæäóíàðîäíî ó÷àñòèå 2004ã., Íàóêà òåõíèêà òåõíîëîãèè è îáðàçîâàíèå, ßìáîë,  òîì 2, ñòð.48-53

6.      Ë. Äèìèòðîâà, Ê. Âàñèëåâ, Ñ. Ñîòèðîâ, Ì. Äèìèòðîâà, Ìîäåëèðàíå íà áèîòåõíîëîãè÷íè ïðoöåñè ÷ðåç èçïîëçâàíå íà îáåêòíèÿ ìîäåë íà JAVA, Ìåæäóíàðîäíà íàó÷íà êîíôåðåíöèÿ Óíèòåõ,  Ãàáðîâî,  24 – 25 íîåìâðè 2005

 

 

 

 

 

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