The quantity-antibacterial effect relationship of fluoroquinolones studied by microcalorimetry

Gao Wenying, Liu Yi, Qu Songsheng
(Department of Chemistry, College of Chemistry and Molecular Sciences, Wuhan University, Wuhan 430072, China)　

Abstract The effect of fluoroquinolones was investigated through microcalorimetry and mathematical method was applied to study the effect of different concentration of the drugs. With the concentration of fluoroquinolones increasing, the inhibitory effect keeps on increasing, however,  two kinds of fluoroquinolones, Norfloxacin and Pefloxacin, are of paradoxical effect.
Keywords  Fluoroquinolones, biological systems, mathematical model, microcalorimetry

1. INTRODUCTION      
Fluoroquinolones is the in hibitor of Topoisomerase2 ,which can selectively interact with Monera and permeate into cell wall of microganism.Conseqently this kind of drugs can kill most of bacteria and they are of extensive spectrum of activity.
    Microcalorimetry is very suitable for the measurements of heat production of slight exothermic or endothermic processes, such as the heat production of anaerobic microbial, cell cultures and organelles. Calorimetry is completely nonspecific which is often a valuable property when the method is used for the monitoring of complex and poorly characterized biological systems. However, for many applications, it would be of great value if the calorimetric signal contains specific information concerning a given property of a biological system. With the inherent high specificity of such systems，it can frequently be achieved by specific activation or inhibition of the metabolic processes on line.
    At present, it is important to use the mathematical method in many areas. By means of the mathematical method, investigations on the mechanism of interaction between drug and cells can obtain more information that which can not be got through the chemical or biological methods.

2. EXPERIMENTAL
2.1 Reagents
Three kinds of fluoroquinolones: Lomefloxacin, Norfloxacin, Pefloxacin, was provided by Yichang Medicine Factory, Hubei 441001, P. R. China.
2.2 Bacteria
Escherichia coli (CCTCC AB91112) was provided by the Chinese Center for Type Culture Collections, Wuhan University, Wuhan 430072, P. R. China.
2. 3 Growth medium
Escherichia coli was grown on a peptone culture medium. The peptone culture medium contained per 1000mL (pH=7.2): NaCl 5g, peptone 5g, beef extract 3g. The medium was sterilized by autoclaving for 30 minutes at 120ºC.
2.4 Instrument
A 2277 Thermal Activity Monitor (Thermometric AB, Sweden) was used. The performance of this and the details of its construction have been described previously [1,2]. The LKB 2210 recorder was used in this experiment which allowed continuous recording of the power-time curves for growth. All measurements were made at 37.0ºC.
2.5 Microcalorimetric measurements
The microcalorimetric measurement used is the stopped-flow method. In all of the microcalorimetric experiments, the flow cell was completely cleaned and sterilized by 0.1mol/L NaOH, 0.1mol/l HCl, 75% ethanol solution and sterilized water respectively. Once the system was cleaned and sterilized, and the baseline had been stabilized, mixture of E. coli and fluoroquinolone , at a concentration 1×10⁶ cells/mL, was pumped into the microcalorimeter at a flow rate of 50 mL/h by an LKB2132 MicroPerpex pump. When the measuring cell of 2277-204 microcalorimeter (measuring volume, 0.6mL) was full, the pump was stopped and monitor was used to record the power-time curves.
    Escherichia coli was inoculated in the prepared culture medium, containing 1×10⁶ cells/ml. And the cells were suspended in the culture medium, then the fresh solution was added into the cell suspension.

3 THERMOGENIC CURVE ANALYSIS
3.1 Escherichia coli growth thermogenic curve
The temperature remained at 37.0ºC. We obtained the thermogenic curves of E. coli, the growth curves of E. coli under three kinds of fluoroquinolone with different concentrations, using the stopped-flow method. Research and observation reveals that the results have good repeatability at the same condition.
3.2 Growth rate constants of Escherichia coli 
According to a typical growth curve for E. coli, it can be divided into four phases, that is, lag phase, log phase , stationary phase and decline phase. Figs.1-3 show the growth rate constant of E. coli at 37ºC in the presence of three kinds of fluoroquinolones of different concentrations. The power-time curves in the presence of fluoroquinolones of different concentrations can be still divided into four phases, in which the lag phase, log phase and decline phase are very similar to, but the stationary phases are significantly different from those of E. coli without fluoroquinolones. During the lag phase and the log phase for E. coli, fluoroquinolones has the capacity to inhibit its growth to different extent.
    By analysis of the power-time curves for E. coli, it can be seen that the heat power increased exponentially during the log phases. So, we can calculate the growth rate constants（k）of E. coli, obeying the following equation：If the cell number is n₀ at time 0, and n_t at time t,
n_t = n₀ exp(kt)
Where k is the growth rate constant. If the power output of each cell is w, then
n_t w = n₀ w exp(kt)
If the heat output power is P₀ at time 0, and P_t at time t, then
P₀ = n₀ w
And P_t = n_t w, giving
P_t=P₀ exp(kt)
or ln P_t=lnP₀ + kt.
According to the equation, we use the data ln P_t and t taken from the curves to fit a linear equation and calculate the values of k and the correlation coefficient R，which are listed in Table 1.

Table 1 Growth rate constant of Escherichia coli at 37ºC

Table 2 Growth rate constant of Escherichia coli at different concentrations of different fluoroquinolones

3.3Relationship between growth rate constant k and C
Figs1,2 and 3 show the relationship between k and C, from which we can see that the growth of E. coli is inhibited within some range of concentration, so the value of k decline continuously. However, the growth rate constant k has various effective stage in the presence of different drugs.
    In the presence of Lomefloxacin, Fig.1 indicates the growth rate constant k decreases with decreasing concentration of Lomefloxacin.

Fig.1 The growth rate constant k of Escherichia coli at different concentrations of Lomefioxacin at 37ºC

    In the presence of Norfoxacin, Fig.2 show the value of k decrease generally during he value of k decrease to zero generally duringthe the regions of 0.015-0.06mg/ml. It is seen that the drug has the maximum inhibition when the concentration is 0.06mg/ml. If the concentration goes on increasing, the values of k increase steadily. In all the complete curve it is of paradoxical effect obviously.

Fig.2 The growth rate constant k of Escherichia coli at different concentrations of Norfloxacin at 37ºC

In the presence of Pefloxacin, similarly, Fig.3 demostrates the value of k decreases in the range of 0.0025-0.01mg/ml. It can be seen that E. coli almost does not grow with the concentration being 0.01mg/ml, beyond which the values of k increase steadily. The results of analysis show that Pefloxmacin is of paradoxical effect. However, they are different from the effect under Norfloxacin.

Fig 3 The growth rate constant k of Escherichia coli at different concentrations of Pefloxacin at 37ºC

In conclusion, the biological effect of some drugs is of paradoxical effect apparently. The value of k decrease in the range of certain concentration, while after the maximum inhibitory concentration, k increases with C increasing.

4. STUDIES ON QUANTITY-ANTIBACTERIAL EFFECT
4.1 Data fitting and functional choice
Generally speaking, we obtain a range of isolated data in the experiment in order to grasp the rule of data information. We expect to determine the relationship about two variables to analytical equation. Thus we have to find out an advisable function. As far as function is concerned, in addition to considering the data regularities of distribution, the function feature are included. Therefore, we can choose an approximate function exactly.
4.2 Survey of mathematic model              
In terms of data and the Figs1,2 and 3, we can use the mathematical method to analyze standard equation which can fit the model of change and the graph used in biology. Denote the growth rate constant by Y and concentration by X.
    In the presence of Lomefloxacin, according to Fig.1.,it can be expressed as:
standard equation: Y＝A/[1+B(D-X)ⁿ];
Line plot of ln(A/Y-1) versus ln(D-X), and lnB is intercept. n is rate of slope. The value of parameter was determined with a coefficient R. From Fig.1 and values in Tab.2, the experiment curve can be expressed as:
linearisation: [ln(A/Y-1)]=lnB+n[ln(D-X)];
With the help of the computer, we obtain the following results:
A＝26.0842; B＝276.5082; D＝0.12575; n＝-0.4433; R＝0.9984.
    In the presence of Norfloacin，according to Fig.2, increasing interval and decreasing interval both can be expressed as:
standard equation: Y＝AXⁿ + B;
linearisation: [ln(Y-B)]=lnA+n[lnx];
    Line plot of ln(Y-B) versus lnX, and lnA is intercept. n is rate of slope. The value of parameter was determined with a coefficient R.
    Using the similar method, we can obtain:
decreasing interval: A＝-1260.33; B＝0.02552; n＝3.845; R＝0.9975.
increasing interval: A＝32.99: B＝-0.01165; n＝2.8288; R＝0.9994.
   In the presence of Pefloxacin, according to Fig.3, the curve is similar in the increasing interval to that in decreasing interval. The curve in the increasing interval can be expressed as:
standard equation: Y＝A/（1+Be^nx）;
linearisation: [ln(A/Y-1)]=lnB+n[X];
    Line plot of ln(A/Y-1) versus X, and lnB is intercept. n is rate of slope. The value of parameter was determined with a coefficient R.
The curve in the decline interval is expressed as:
standard equation: Y＝A/[1+B×e^n(D-x)];
linearisation: [ln(A/Y-1)]=lnB+n[D-X];
    Line plot of ln(A/Y-1) versus [D-X], and lnB is intercept. n is rate of slope. The value of parameter was determined with a coefficient R.
We obtain the following results:
decreasing interval: A＝0.02767; B＝26058.5; D＝0.0105; n＝-8048.03; R＝0.9957.
increasing interval :A＝0.02852; B＝7.0192×10¹⁸; n＝-3808.81; R＝0.9985.
4.3 Comparation of Ic₅₀
Half of inhibition concentration Ic₅₀ is defined as concentration of drug with inhibition rate equal to 50%,which can judge the sensibility of bacteria to drug. We can not only readout the value of Ic₅₀ on the curve with k equal to a half of k_0, but also get the value through solving the math equation.

Table.3 The value of Ic₅₀

It is apparent that the results obtained by the two methods are very close, which proves that the mathematic model is reliable.

5. DICUSSION
5.1 The paradoxical effect and mechanics
Paradoxical effect k is one of important constants which can represent the growing ability of cells.With drug of different concentration added under the same condition,the change of k can be used to evaluate the inhibitory effect of drugs. The results of experiment indicate the maximum heat output and growth rate constant of microbes take on paradoxical effect when they grow in the presence Norfloxacin(0.015-0.08) or Pefloxacin(0.0025-0.025).
    Fluoroquinolones can combine with Subunit A of rotany enzyme which is required for duplicating bacteria's DNA. As a result, the drug can inhibit the duplication of DNA. Because fluoroquinolone have osmotic effect on cell wall, it can kill many kinds of bacteria. The relationship between bacteria action and the amount of drug is of paradioxical effect. The mechanics may result from two factors, one of which is rotary enzyme's mutation lead to alteration of action spot, which results in the value of k being paradioxical change; the other of which is that, according to studies on cell's level, drug can change the permeability of membrane. When its concentration increases, macromoleculer of drugs will block off the passway, which cause drug can not be absord easily. Consequently, the paradioxical effect appear.
5.2 The theoretical source of mathematical model used in biology
It was said:"One scientific area can reach anchievement throughly only when it has been applied mathematic model to". Because mathematics and mathematic model is reasonable form which can describe thing's change, studies on anything will unavoidably depend on mathematic method and model. At the same time ,due to complexity of life phenomenon and the difference between life phenomenon and non-life phenomenon, we have to formulate special mathematic model in accordance with different life phenomenon, so as to obtain some information about vital movement from macroscopic view.
5.3 The advantage of mathematic model
As to the advantage of mathematic model, firstly, mathematic model can describe dynamic rule of biological system, and predict its action in different environment, on the basis of which researchers can analyze the more advanced system . Secondly, the formulation of mathematic model is helpful to build up some hypothesis. Through comparing result between calculation, important information are obtained for further study. Thirdly, the formulation of mathematic model and determination of parameter will help us to get quantitative data about biological system. Accordingly, the mathematic model can make contribution to the development of medicine and benefit the patients.
If methods in different fields are employed, we can get some necessary information to further study. When we face up to new challenges and opportunities, this findings have theoretical and practical importance.

ACKNOWLEDGEMENT      
The authors gratefully acknowledge the financial support of the National Natural Science Foundation of China, the National Science Foundation of Hubei Province, Young Mainstay Teacher Program of Chinese Education Ministry, and Young Excellent Teacher's Teaching and Science Research Award Program of Chinese Education Ministry.

REFERENCES         
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[2] Xie Changli, Tang Houkuan, Song Zhaohua et al. Thermochim. Acta, 1988, 123: 33.
[3] Chowdhry B Z,  Beezer A E, Greenhow E J. Talanta, 1983, 30: 209.
[4] Buckton G, Russel S J, Beezer A E. Thermochim Acta, 1991, 193: 195.
[5] Feng Gaohong. Practical Drug Note. Jiangxi Science and Technology Press, 1996, 4.
[6] Cui Qiwu, Liu Jiagang. Kinetics of Biological Populus Growth. Science Press, 1991, 4.

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