Method and device for characterizing the inhibitory capacity of a molecule on a microorganism

Abstract

A method for determining a quantity G.sub.inhib quantifying the inhibitory capacity of a molecule on a type of microorganism includes: preparing a plurality of samples, including microorganisms of the type, a nutrient medium for the microorganism and an initial amount of the molecule per microorganism increasing in a range [Q.sub.min,Q.sub.max] as a function of a classification of the samples; measuring the growth of the microorganisms in the samples as a function of time; and determining the quantity G.sub.inhib as a function of the measurements of the growth. Determination of the quantity G.sub.inhib includes: for each sample, calculating a value reflecting the growth of the microorganism of said type based on measurements of growth; classifying the values calculated for the samples as a function of the classification of the samples; and determining the quantity G.sub.inhib as a function of the variation of the classified values.

Claims

1. A method for determining a quantity G.sub.inhib, comprising: preparing a plurality of samples comprising microorganisms, a nutrient medium for the microorganisms, and an amount of an inhibitory molecule per microorganism that increases in a range [Q.sub.min,Q.sub.max] as a function of a predetermined classification of the samples; incubating the plurality of samples for a time period; measuring growth of the microorganisms in each of the plurality of samples at different incubation times within the time period to obtain growth measurements for each of the plurality of samples; and determining the quantity G.sub.inhib based on the growth measurements, wherein: (i) the microorganisms are of a predetermined type; (ii) Q.sub.min as a lower limit of the range [Q.sub.min,Q.sub.max] results in no inhibition of the growth of the microorganisms in the plurality of the samples; (iii) Q.sub.min to Q.sub.max of the range [Q.sub.min,Q.sub.max] strictly increases; (iv) Q.sub.max as an upper limit of the range [Q.sub.min,Q.sub.max] results in complete inhibition of the growth of the microorganisms in the plurality of the samples; (v) the quantity G.sub.inhib represents a capacity of the inhibitory molecule to inhibit the growth of the microorganisms; (vi) determination of the quantity G.sub.inhib comprises: calculating a plurality of growth values for the microorganisms based on the growth measurements; correlating the plurality of growth values with the predetermined classification of the plurality of samples to obtain classified growth values; and determining the quantity G.sub.inhib as a function of variation found within the classified growth values; (vii) the quantity G.sub.inhib comprises a range [Q.sub.min.sup.MIC,Q.sub.max.sup.MIC] for which the growth of the microorganisms in the plurality of samples is at least partially inhibited; and (viii) determination of [Q.sub.min.sup.MIC,Q.sub.max.sup.MIC] comprises identifying a transition zone in the variation of the classified growth values and identifying corresponding samples from the plurality of samples that are within the transition zone.

2. The method of claim 1, wherein each growth value is an estimate of a maximum slope μ in a logarithmic growth phase and/or an estimate of a duration of a lag phase λ.

3. The method of claim 1, wherein identification of the transition zone comprises determining two inflexion points of the variation found within the classified growth values.

4. The method of claim 1, wherein identification of the transition zone comprises modeling the variation found within the classified growth values by a piecewise linear continuous function comprising two endmost straight-line segments and an intermediate straight-line segment that is the transition zone between the two endmost straight-line segments.

5. The method of claim 1, wherein the quantity G.sub.inhib comprises an initial minimum inhibitory amount Q.sub.MIC of the inhibitory molecule that completely inhibits the growth of the microorganisms, and the initial minimum inhibitory amount Q.sub.MIC is equal to an upper limit Q.sub.max.sup.MIC of the range [Q.sub.min.sup.MIC,Q.sub.max.sup.MIC].

6. The method of claim 1, wherein the lower limit Q.sub.min of the range [Q.sub.min,Q.sub.max] is a zero amount of the inhibitory molecule.

7. The method of claim 1, wherein: the growth of the microorganisms in each of the plurality of samples is measured at increasing incubation times within the time period to obtain the growth measurements for each of the plurality of samples; a plurality of quantities G.sub.inhib are determined over time based on the growth measurements as a function of the increasing incubation times; the plurality of the quantities G.sub.inhib are analysed to determine when the quantities G.sub.inhib stabilize over time to identify a stabilized quantity G.sub.inhib; the stabilized quantity G.sub.inhib represents the capacity of the inhibitory molecule to inhibit the growth of the microorganisms; and the stabilized quantity G.sub.inhib comprises the range [Q.sub.min.sup.MIC,Q.sub.max.sup.MIC] for which the growth of the microorganisms in the plurality of samples is at least partially inhibited.

8. The method of claim 1, wherein the plurality of samples each comprise at least 100 microorganisms.

9. The method of claim 1, wherein the plurality of samples each comprise at least 500 microorganisms.

10. The method of claim 1, wherein the plurality of samples comprise an amount of another inhibitory molecule per microorganism.

11. The method of claim 1, wherein the microorganisms are at a constant concentration among the plurality of samples.

12. The method of claim 1, wherein the microorganisms are a type of bacteria and the inhibitory molecule is an antibiotic.

13. The method of claim 1, wherein the microorganisms are a type of yeast or mold and the inhibitory molecule is an antifungal.

14. The method of claim 1, wherein the nutrient medium comprises an element that is metabolized by the microorganisms to form fluorescent molecules during the growth of the microorganisms and the growth of the microorganisms is measured by measuring fluorescence from the fluorescent molecules.

15. The method of claim 1, wherein absorbance among the plurality of samples is variable as a function of quantity of the microorganisms and the growth of the microorganisms is measured by measuring optical density.

16. The method of claim 1, wherein preparation of the plurality of samples comprises producing a train of droplets as the plurality of samples in oil.

17. A device for determining a quantity G.sub.inhib, comprising: means for preparing a plurality of samples comprising microorganisms, a nutrient medium for the microorganisms, and an amount of an inhibitory molecule per microorganism that increases in a range [Q.sub.min,Q.sub.max] as a function of a predetermined classification of the samples; means for incubating the plurality of samples for a time period; means for measuring growth of the microorganisms in each of the plurality of samples at different incubation times within the time period to obtain growth measurements for each of the plurality of samples; and means for determining the quantity G.sub.inhib based on the growth measurements, wherein: (i) the microorganisms are of a predetermined type; (ii) Q.sub.min as a lower limit of the range [Q.sub.min,Q.sub.max] results in no inhibition of the growth of the microorganisms in the plurality of the samples; (iii) Q.sub.min to Q.sub.max of the range [Q.sub.min,Q.sub.max] strictly increases; (iv) Q.sub.max as an upper limit of the range [Q.sub.min,Q.sub.max] results in complete inhibition of the growth of the microorganisms in the plurality of the samples; (v) the quantity G.sub.inhib represents a capacity of the inhibitory molecule to inhibit the growth of the microorganisms; (vi) determination of the quantity G.sub.inhib comprises: calculating a plurality of growth values for the microorganisms based on the growth measurements; correlating the plurality of growth values with the predetermined classification of the plurality of samples to obtain classified growth values; and determining the quantity G.sub.inhib as a function of variation found within the classified growth values; (vii) the quantity G.sub.inhib comprises a range [Q.sub.min.sup.MIC,Q.sub.max.sup.MIC] for which the growth of the microorganisms in the plurality of samples is at least partially inhibited; and (viii) determination of [Q.sub.min.sup.MIC,Q.sub.max.sup.MIC] comprises identifying a transition zone in the variation of the classified growth values and identifying corresponding samples from the plurality of samples that are within the transition zone.

18. The device of claim 17, wherein each growth value is an estimate of a maximum slope μ in a logarithmic growth phase and/or an estimate of a duration of a lag phase λ.

19. The device of claim 17, wherein identification of the transition zone comprises determining two inflexion points of the variation found within the classified growth values.

20. The device of claim 17, wherein identification of the transition zone comprises modeling the variation found within the classified growth values by a piecewise linear continuous function comprising two endmost straight-line segments and an intermediate straight-line segment that is the transition zone between the two endmost straight-line segments.

Description

BRIEF DESCRIPTION OF THE FIGURES

(1) The invention will be better understood on reading the description given hereunder, supported by the appended figures, in which:

(2) FIG. 1 is a simplified schematic view of the analyzer described in the article “Millifluidic droplet analyser for microbiology”;

(3) FIG. 2 is an example of droplets produced by the analyzer of FIG. 1;

(4) FIG. 3 is a scheme describing the production of fluorescence signals by the analyzer of FIG. 1;

(5) FIGS. 4A and 4B are plots of fluorescence measurements as a function of the number of the droplets produced, at 0 minute and 400 minutes, respectively;

(6) FIG. 5 is a plot of fluorescence measurements as a function of the number of the droplets produced and time;

(7) FIGS. 6A to 6C are diagrams illustrating determination of the minimum inhibitory concentration by a cutting method of the prior art, for tests performed on E. coli with three different antibiotics;

(8) FIG. 7 is a flowchart of one embodiment of the method according to the invention;

(9) FIG. 8 is a diagram illustrating an initial concentration profile of antibiotic in the droplets generated during the method according to the invention;

(10) FIG. 9 is a diagram illustrating settings of flow rate of the syringes of the analyzer of FIG. 1, generated as a function of the profile in FIG. 8;

(11) FIG. 10 is a plot of the fluorescence measurements of the droplets produced by the settings in FIG. 9 as a function of time;

(12) FIG. 11 is a diagram illustrating measurements of fluorescence as a function of the number of the droplets for different measurement time points;

(13) FIGS. 12A and 12B are diagrams illustrating estimation of the true initial concentration of antibiotic in the droplets for two different tests;

(14) FIG. 13 is a diagram illustrating bacterial growth in the presence of nutrients and as a function of time;

(15) FIG. 14 is a diagram illustrating transformation of the fluorescence measurements into a sequence of maximum growth rates of the bacteria as a function of the number of the droplets;

(16) FIG. 15 is a diagram illustrating transformation of the fluorescence measurements into sequences of lag phase times of the growth of the bacteria as a function of the number of the droplets;

(17) FIGS. 16A and 16B are diagrams illustrating respectively a transition phase in a sequence of maximum growth rates and the approximation of the sequence of maximum growth rates by a piecewise linear function;

(18) FIGS. 17 and 18 are diagrams illustrating transition zones obtained respectively on a sequence of maximum growth rates and a sequence of lag phase times; and

(19) FIGS. 19A to 19C are diagrams illustrating determination of the minimum inhibitory concentration according to the invention, for the tests performed on E. coli with three different antibiotics in FIGS. 6A to 6C.

DETAILED DESCRIPTION OF THE INVENTION

Embodiment Example

(20) An embodiment of the method according to the invention will now be described in relation to the flowchart in FIG. 7, steps of this method being illustrated in FIGS. 8 to 19. The method is applied for determination of a minimum inhibitory concentration MIC of the growth of bacteria, by means of the device 10 described in the article “Millifluidic droplet analyser for microbiology” and briefly described above in relation to FIG. 1. Control of the components of this device and processing of the measurements are performed by means of a conventional data processing unit, for example a computer.

(21) The method comprises the production, at 50, of experimental data on the growth of bacteria in the presence of a gradient of antibiotic, and analysis, at 52, of the data produced to determine the MIC concentration.

(22) The production step 50 comprises a first step 54 of determining parameters for production of the data. Step 54 notably comprises definition of a concentration range [C.sub.min; C.sub.max] which is assumed to include the MIC concentration, namely C.sub.min<MIC<C.sub.max. This range is determined as a function of preceding studies, notably as a function of a regulatory MIC concentration or clinical studies. Notably, the concentration C.sub.max is a concentration for which the antibiotic completely inhibits bacterial growth and is above the MIC concentration. As a variant, the method described below serves for adjusting the range [C.sub.min; C.sub.max]. For example, if the MIC concentration determined is very far from the maximum concentration C.sub.max, the latter is decreased and the method is carried out once more. Similarly, if the MIC concentration is too close to the maximum concentration C.sub.max, the latter is increased and the method is restarted. Preferably, the minimum concentration C.sub.min is selected so as to guarantee that the bacteria are more or less free to grow, said free growth being exploited subsequently in data processing, as will be explained in more detail below. For example, the concentration C.sub.min is equal to 0.

(23) An initial concentration profile of antibiotic [ATB].sub.ini as a function of the number k of the droplets subsequently produced is then generated as illustrated in FIG. 8. This profile comprises: a first plateau P.sub.C.sub.min for which ∀k∈[1; N.sub.C.sub.min], [ATB].sub.ini(k)=C.sub.min; followed by a ramp R.sub.gradient for which the concentration [ATB].sub.ini(k) increases linearly from the minimum concentration C.sub.min to the maximum concentration C.sub.max, i.e. ∀k∈[N.sub.C.sub.min+1; N.sub.gradient], [ATB].sub.ini(k+1)−[ATB].sub.ini(k)=constant; followed by a second plateau P.sub.C.sub.max for which ∀k∈[N.sub.gradient; N], [ATB].sub.ini(k)=C.sub.max.

(24) The lengths of the plateaux P.sub.C.sub.min and P.sub.C.sub.max are selected so as to identify automatically portions of straight lines with roughly zero slope as a function of the number k in the data produced subsequently. These lengths depend for example on the accuracy of the algorithm used. The inventors noted, however, that a plateau length equal to about a hundred droplets allows good-quality identification. Regarding the length of the ramp R.sub.gradient, it is defined as a function of the desired precision for the MIC concentration, in the limits imposed by the device for producing the droplets.

(25) Flow rate settings for the syringes 12, 14, 16 are then produced, at 56, as a function of the initial concentration profile of antibiotic [ATB].sub.ini. These settings are illustrated in FIG. 9. Notably, the flow rate setting of syringe 12 of bacterial solution is constant in order to produce droplets comprising roughly the same initial number of bacteria. This number is advantageously greater than 500 so as not to exacerbate the particular features of each bacterium, for example 1000 bacteria. The flow rate setting of syringe 16 of antibiotic for its part follows the profile [ATB].sub.ini and the flow rate setting of syringe 18 of nutrient medium has an inverted profile in order to produce droplets of constant volume.

(26) In parallel, the solutions of bacteria, of nutrient medium and of antibiotic are prepared and then put in their respective syringes. Advantageously, and optionally, a fluorescent marker, for example sulforhodamine, of known concentration, is also added to the antibiotic solution. This marker, whose fluorescence is measurable by the detection system 28, advantageously at a wavelength different than that used for measuring the population of the bacteria, makes it possible to determine the true concentration of antibiotic in each droplet, as will be explained in detail below. This additional fluorescence is measured by the detection system 38, which is equipped for example with a set of filters for selecting the measured wavelength, as described for example in the document “Millifluidic droplet analyser for microbiology”.

(27) In a next step 60, the device 10 is controlled as a function of the flow rate settings thus defined in order to produce a train of N droplets, and the fluorescence of each droplet is measured regularly using the reciprocating motion described above. Still at 60, the measurement signal from the detection system 28 is processed to produce and store the fluorescence values {x.sup.k(t.sub.1.sup.k), x.sup.k(t.sub.2.sup.k), . . . , x.sup.k(t.sub.p.sup.k), . . . , x.sup.k(t.sub.P.sup.k)} of each droplet for the acquisition time points {t.sub.1.sup.k, t.sub.2.sup.k, . . . , t.sub.p.sup.k, . . . , t.sub.P.sup.k}. An example of quantities x.sup.k(t.sub.p.sup.k) is illustrated in FIGS. 10 and 11, either as a function of time t.sub.p.sup.k (FIG. 10) or as a function of the number of the droplets for different measurement cycles (FIG. 11).

(28) For its part, the data processing step 52 comprises estimation, at 62, of the true initial concentration of antibiotic in the droplets. In practice, there is a difference between the flow rate settings and the true flow rates so that there is a difference between the desired profile [ATB].sub.ini and the true concentration profile. Notably, the true profile may not be perfectly linear. The true concentration of antibiotic is estimated from the measured fluorescence of sulforhodamine {z.sup.1(t.sub.L.sup.1), z.sup.2(t.sub.L.sup.2), . . . , z.sup.k(t.sub.L.sup.k), . . . , z.sup.N(t.sub.L.sup.N)} at the start of incubation of the droplets. The measurement cycle L is notably within the lag phase of the bacteria, and is for example the first measurement cycle. At this time point, the bacteria have not begun to grow and they induce a constant or zero fluorescence in the droplets. The variation of the fluorescence among the values {z.sup.1(t.sub.L.sup.1), z.sup.2(t.sub.L.sup.2), . . . , z.sup.k(t.sub.L.sup.k), . . . , z.sup.N(t.sub.L.sup.N)} therefore corresponds to the fluorescence of the sulforhodamine added to the solution of antibiotic. Knowing the concentration of sulforhodamine, the fluorescence of the latter is therefore proportional to the initial concentration of the antibiotic [ATB].sub.ini.

(29) The estimate .sub.ini of the true concentration is calculated notably by: applying a smoothing filter on the measurements {z.sup.1(t.sub.L.sup.1), z.sup.2(t.sub.L.sup.2), . . . , z.sup.k(t.sub.L.sup.k), . . . , z.sup.N(t.sub.L.sup.N)}, for example a standard Loess smoothing filter, so as to obtain smoothed measurements {z.sup.1, z.sup.2, . . . , z.sup.k, . . . , z.sup.N}; identifying the start and end of the antibiotic gradient in the smoothed measurements. For example, the minimum value z.sup.N.sup.min=min{z.sup.1, z.sup.2, . . . , z.sup.k, . . . , z.sup.N} of the smoothed measurements is identified and the start of the gradient is identified as the smallest number N.sub.g.sup.min>N.sub.min of the droplet whose smoothed measurement z.sup.N.sup.g.sup.min is X % higher than the value z.sup.N.sup.min, for example 1% higher. Similarly, the maximum value z.sup.N.sup.max=max{z.sup.1, z.sup.2, . . . , z.sup.k, . . . , z.sup.N} of the smoothed measurements is identified and the end of the gradient is identified as the largest number N.sub.g.sup.max<N.sub.max of the droplet whose smoothed measurement z.sup.N.sup.g.sup.max is X % lower than the value z.sup.N.sup.max, for example 99%. Of course, any method for determining the start and end of the gradient may be used; putting:

(30) $\begin{array}{cc}& \left(1\right)\end{array}$
with

(31) $a=\frac{C_{\mathrm{ma}x}-C_{min}}{{\stackrel{\_}{z}}^{N_g^{\mathrm{ma}x}}-{\stackrel{\_}{z}}^{N_g^{min}}}\mathrm{and}b=\frac{C_{\mathrm{ma}x}+C_{min}}{2}-a\times \frac{{\stackrel{\_}{z}}^{N_g^{\mathrm{ma}x}}+{\stackrel{\_}{z}}^{N_g^{min}}}{2}.$
The estimated concentration .sub.ini(k) is stored for later use as described above.

(32) The known concentrations C.sub.min and C.sub.max thus serve as an anchorage point for linear transformation of the fluorescence gradient within the range [z.sup.N.sup.g.sup.min; z.sup.N.sup.g.sup.max] into a concentration gradient .sub.ini in the range [C.sub.min; C.sub.max]. Notably, this makes it possible to preserve the nonlinearities of the true profile of initial concentration induced by the errors in production of the droplets. FIGS. 12A and 12B illustrate estimation of the concentration profile [ATB].sub.ini for two experiments conducted for two strains of E. coli respectively. The noisy curves represent the measured fluorescence {z.sup.1(t.sub.L.sup.1), z.sup.2(t.sub.L.sup.2), . . . , z.sup.k(t.sub.L.sup.k), . . . , z.sup.N(t.sub.L.sup.N)}, the smoothed curves (in bold) superimposed on the noisy curves correspond to the smoothed fluorescence {z.sup.1, z.sup.2, . . . , z.sup.k, . . . , z.sup.N}, and the curves anchored on the values C.sub.min and C.sub.max (shown with thin lines) are the estimated concentration .sub.ini. These figures, and particularly FIG. 12B, show the considerable nonlinearity of the measured fluorescence, caused by the imperfections of the device 10, and the estimate .sub.ini of the concentration, which reproduces, to within a scaling factor, the fluorescence profile.

(33) The processing 52 also comprises a step 64 carried out in parallel with the measurement step 60, namely each time a new measurement cycle P delivers new measurements {x.sup.1(t.sub.P.sup.1) x.sup.2(t.sub.P.sup.2), . . . , x.sup.k(t.sub.P.sup.k), . . . , x.sup.N(t.sub.P.sup.k)} of the fluorescence of the droplets, for as long as a stop criterion described below is not satisfied. When step 64 is triggered, measurements {x.sup.k(t.sub.1.sup.k) x.sup.k(t.sub.2.sup.k), . . . , x.sup.k(t.sub.p.sup.k), . . . , x.sup.k(t.sub.P−1.sup.k)}, corresponding to the preceding measurement cycles 1, 2, . . . , P−1, have therefore already been stored for each droplet k.

(34) More particularly, for each droplet k, step 64 comprises a first step 66 of transforming the sequence {x.sup.k(t.sub.1.sup.k) x.sup.k(t.sub.2.sup.k), . . . , x.sup.k(t.sub.p.sup.k), . . . , x.sup.k(t.sub.P.sup.k)}, derived from concatenation of the stored sequence {x.sup.k(t.sub.1.sup.k) x.sup.k(t.sub.2.sup.k), . . . , x.sup.k(t.sub.p.sup.k), . . . , x.sup.k(t.sub.P−1.sup.k)} with the new fluorescence measurement x.sup.k(t.sub.P.sup.k) of the droplet, into a value D.sup.k(t.sub.P) containing information about the dynamics of growth of the bacteria in the droplet k for an incubation period between t.sub.1 and t.sub.P. The objective of this transformation is to take into account, for the measurement cycle of time point t.sub.P, the history of the fluorescence up to execution of this cycle, while qualifying this history qualitatively, advantageously via a growth model.

(35) This history is advantageously taken into account by means of a model of the growth of bacteria in a nutrient medium, more preferably the model in FIG. 13, which illustrates the natural logarithm of the bacterial population as a function of time. As is known, the growth of bacteria comprises: a first lag phase of duration λ during which the bacteria synthesize enzymes that they will need in order to use the nutrient medium, and in which there is no cell division of the bacteria; followed by an exponential growth phase: after an acceleration, the growth reaches a maximum growth rate μ, or equivalently, the growth curve has a maximum slope μ; followed by a stationary phase, which corresponds to exhaustion of the nutrient medium. Growth slows down and becomes roughly zero, the bacterial population being roughly stabilized at a value A. The stationary phase is followed by a phase of decline, not shown here, following complete exhaustion of the nutrients.

(36) The lag, growth and stationary phases are estimated for example by one and/or other of the temporal models y(t) in the following table:

(37) TABLE-US-00001 Parameters Name of to be the model Formula y(t) identified Logistic $y\left(t\right)=\frac{A}{1+\exp \left(\frac{4.Math.\mu }{A}.Math.\left(\lambda -t\right)+2\right)}$ A, μ, λ Gompertz $y\left(t\right)=A.Math.\exp \left(-\exp \left(\frac{\mu .Math.e}{A}.Math.\left(\lambda -t\right)\right)+1\right)$ A, μ, λ Modified Gompertz $y\left(t\right)=A.Math.\exp \left(-\exp \left(\frac{\mu .Math.e}{A}.Math.\left(\lambda -t\right)\right)+1\right)+A.Math.\exp \left(\alpha .Math.\left(t-t_{\mathrm{shift}}\right)\right)$ A, μ, λ, α, t.sub.shift Richards $y\left(t\right)=A.Math.{\left(1+v.Math.\exp \left(1+v+\frac{\mu }{A}.Math.{\left(1+v\right)}^{1+\frac{1}{v}}\right).Math.\left(\lambda -t\right)\right)}^{\left(-\frac{1}{v}\right)}$ A, μ, λ, v where e is Euler's constant.

(38) For each measurement cycle P and for each droplet k, step 66 thus consists of identifying at least one of the parameters of a model y(t) containing information on dynamics as a function of the measured fluorescences {x.sup.k(t.sub.1.sup.k), x.sup.k(t.sub.2.sup.k), . . . , x.sup.k(t.sub.p.sup.k), . . . , x.sup.k(t.sub.P.sup.k)} for the droplet, and notably a maximum slope μ.sup.k(t.sub.P) and/or a lag time λ.sup.k(t.sub.P) for this sequence (D.sup.k(t.sub.P)=μ.sup.k(t.sub.P) or D.sup.k(t.sub.P)=λ.sup.k(t.sub.P)). Identification of the parameters of the model (t), which consists of minimizing an estimation error formed from the difference between the vector of the measurements (x.sup.k(t.sub.1.sup.k) x.sup.k(t.sub.2.sup.k) . . . x.sup.k(t.sub.p.sup.k) . . . x.sup.k(t.sub.P.sup.k)).sup.T and the vector of estimation of the measurements (y(t.sub.1.sup.k) y(t.sub.2.sup.k) . . . y(t.sub.p.sup.k) . . . y(t.sub.P.sup.k)).sup.T, is performed in a manner known per se from the domain of the identification, for example by nonlinear least squares.

(39) As a variant, the parameters are identified without using a model y(t), for example by calculating a polynomial by the method of splines approximating the sequence (x.sup.k(t.sub.1.sup.k) x.sup.k(t.sub.2.sup.k) . . . x.sup.k(t.sub.p.sup.k) . . . x.sup.k(t.sub.P.sup.k)). The parameters λ and μ are then estimated empirically, for example by the finite-difference method. For example, the maximum slope μ is obtained by calculating the derivative of the polynomial approximating the sequence and selecting the maximum value of the derivative as the slope μ. As another variant, the models or the approaches may be mixed.

(40) Identification of the parameters of the growth of a bacterial population is well known from the prior art. For example, this identification may be performed using the “grofit” software package described in the document by Kahm M. et al. “grofit: Fitting Biological Growth Curve with R”, Journal of Statistical Software, Vol. 33(7), February 2010.

(41) As the calculation of the parameters is of a statistical nature, identification is preferably carried out once a minimum number of measurements have been acquired. The minimum number of measurement cycles is for example equal to 10, step 64 therefore being carried out for measurement cycles once this minimum number is reached.

(42) At the end of step 66 of calculation of the parameters of growth of the bacteria, the following sequences are therefore produced:
M(t.sub.P)={μ.sup.1(t.sub.P),μ.sup.2(t.sub.P), . . . ,μ.sup.k(t.sub.P), . . . ,μ.sup.N(t.sub.P)}
Λ(t.sub.P)={λ.sup.1(t.sub.P),λ.sup.2(t.sub.P), . . . ,λ.sup.k(t.sub.P), . . . ,λ.sup.N(t.sub.P)}

(43) A sequence M(t.sub.P) and a sequence Λ(t.sub.P) are illustrated in FIGS. 14 and 15 respectively, as a function of the number k of the droplets, for a time point t.sub.P equal to 6 hours.

(44) The processing 52 continues, at 68, with determination of a true minimum inhibitory concentration MIC(t.sub.P) for the time point t.sub.P as a function of at least one of the sequences of parameters determined, for example the sequence M(t.sub.P). This determination is based on searching for a transition zone in the sequence of parameters comprising the concentration MIC(t.sub.P). This zone is defined as the range of initial concentrations of antibiotic of minimum width for which the antibiotic has an observable inhibitory effect on the growth of the bacteria. Referring to FIG. 16A, which illustrates the sequence M(t.sub.P) of FIG. 14 as a function of the number k of the droplets, it is observed that the curve M(t.sub.P) is roughly constant and equal to μ.sub.max over a range [1; N.sub.0] with N.sub.0>N.sub.g.sup.min. Similarly, the curve M(t.sub.P) is roughly zero over a range [N.sub.MIC(t.sub.P.sub.); N] with N.sub.MIC(t.sub.P.sub.)<N.sub.g.sup.max of the droplets with initial concentration of antibiotic C.sub.max. The range [N.sub.0; N.sub.MIC(t.sub.P.sub.)] therefore corresponds to the transition zone, the upper limit of this range corresponding to the required concentration N.sub.MIC(t.sub.P.sub.).

(45) Identification of the transition zone [N.sub.0; N.sub.CMI(t.sub.P.sub.)] in step 66 may be performed by any known mathematical method, notably any method for identifying inflexion points on a curve, and therefore for identifying two inflexion points flanking the transition zone.

(46) For example, the curve M(t.sub.P) is approximated by a piecewise linear continuous function {circumflex over (ƒ)}(k) according to the relation:

(47) $\hat{f}\left(k\right)=\{\begin{array}{cc}a.Math.k+b& \forall k\in [1;N_0[\\ a.Math.k+\beta & \forall k\in \left[N_0;N_{\mathrm{MIC}\left(t_P\right)}\right]\\ c.Math.k+d& \forall k\in ]N_{\mathrm{MIC}\left(t_P\right)};n]\end{array}$
where the values of the parameters N.sub.0, α, β, a, b, c, d, and N.sub.MIC(t.sub.P.sub.) are calculated in a manner known per se as the optimal solution of an optimization problem minimizing an estimation error between the sequence M(t.sub.P) and the sequence {{circumflex over (ƒ)}(1), {circumflex over (ƒ)}(2), . . . , {circumflex over (ƒ)}(k), . . . , {circumflex over (ƒ)}(N)}.

(48) Other approximations of the sequence M(t.sub.P) are possible, for example a polynomial approximation, notably obtained by the method of splines.

(49) Step 64 then continues, at 70, with the determination, and storage, of the initial concentration of antibiotic corresponding to the droplet number N.sub.MIC(t.sub.P.sub.) according to the relation:
MIC(t.sub.P)=.sub.ini(N.sub.MIC(t.sub.P.sub.))

(50) In a next step 72, a stability test of the concentration MIC(t.sub.P) is performed. The test consists for example of verifying whether the sequence formed from the concentrations MIC(t.sub.P) calculated for T last fluorescence measurement cycles, for example the last 3 cycles, is stable. The concentration is deemed stable for example when it varies by less than S %, for example 5%, for the last T measurement time points. The stability test notably makes it possible to stop the process at the earliest moment so that it is not necessary to select a minimum incubation time a priori.

(51) FIGS. 17 and 18 illustrate calculation of the range [N.sub.0; N.sub.MIC(t.sub.P.sub.)] respectively for the sequences M(t.sub.P) and Λ(t.sub.P) in FIGS. 14 and 15. The range [N.sub.0; N.sub.MIC(t.sub.P.sub.)] determined for the sequence M(t.sub.P) is equal to [157; 196], which corresponds to the concentration range [0.97; 2.17]. The range [N.sub.0; N.sub.MIC(t.sub.P.sub.)] determined for the sequence Λ(t.sub.P) is equal to [189; 199], which corresponds to the concentration range [0.97; 2.3]. Note that the numbers N.sub.MIC(t.sub.P.sub.) determined for the two parameters are very close (196 and 199 respectively). For its part, the range [N.sub.0; N.sub.MIC(t.sub.P.sub.)] is determined with greater precision by means of the sequence Λ(t.sub.P), whose transition zone is more abrupt than the transition zone of the sequence M(t.sub.P).

(52) If the concentration MIC(t.sub.P) is not stable, step 72 loops back to step 66 for calculating a concentration MIC(t.sub.P) as a function of the new fluorescence measurements. In contrast, if the concentration MIC(t.sub.P) is stable, stopping of the measurements is then commanded at 74. The last concentration MIC(t.sub.P) calculated and stored is then the minimum inhibitory concentration of the antibiotic for the bacterium that is the object of the measurements.

(53) FIGS. 19A to 19C illustrate the results of the embodiment just described. Production of the measurements is that described in relation to FIGS. 6A to 6C. More particularly, the measurements described in these figures form the object of data processing in the processing step 52 described above using the sequence M(t.sub.P) for calculating the concentration MIC(t.sub.P). As can be seen, the concentration MIC(t.sub.P) quickly reaches a stable value that is within the tolerance range of the regulatory MIC. Concerning replicate 3 in FIG. 19B, the particular form of MIC(t.sub.P) results from a calibration error of the droplet production system detected a posteriori.

(54) Variants

(55) A particular embodiment of the invention has been described. Obviously the invention is not limited to this embodiment. Notably the following variants, alone or in combination, form part of the invention.

(56) The embodiment is described for application to estimation of a minimum concentration of antibiotic inhibiting the growth of bacteria and a range of inhibitory concentrations. The invention also applies to determination of other quantities that are characteristic of the inhibitory capacity of the antibiotic.

(57) A particular embodiment has been described, applied to analysis of the inhibitory capacity of an antibiotic on bacterial growth. The invention applies in the same way to analysis of the inhibitory capacity of any molecule on a microorganism, notably analysis of the inhibitory effect of an antifungal on a mold, fungus or yeast.

(58) A particular embodiment has been described in which a single type of antibiotic is present in the samples. As a variant, the samples may comprise a second antibiotic of known concentration. Investigation of the synergies of the antibiotics may thus be undertaken. For example, the method according to the invention is carried out for different concentrations of the second antibiotic.

(59) An embodiment has been described in which the bacteria are initially in large number to avoid exacerbating particular features. As a variant, a smaller bacterial count, or even a single bacterium, is present in the samples in order to study the latter in particular.

(60) An embodiment has been described in which a gradient of initial concentration of antibiotic is produced. As a variant, the concentration of the antibiotic is constant and a bacterial concentration gradient is produced. In general, the invention thus relates to the formation of a gradient of an initial amount of a molecule per microorganism, between a minimum amount Q.sub.min and a maximum amount Q.sub.max.

(61) A gradient has been described that increases linearly from an initial value to a final value. A linear gradient allows each concentration zone to be considered with equal importance. Other types of gradient, notably nonlinear, are of course possible. For example, plateau gradients, where a large number of droplets, for example some tens to about a hundred, are generated for a limited number of concentration values, for example about ten, distributed over the concentration range [C.sub.min; C.sub.max] of the antibiotic in question. Advantageously, these concentration values are selected as a function of the recommendations of the regulatory authorities relating to application of the reference method by microdilution such as the CA-SFM (Antibiogram Committee of the French Society of Microbiology) or EUCAST (European Committee on Antimicrobial Susceptibility Testing), so as to perform multiple repetitions (some tens to about a hundred, depending on the number of drops per plateau) of a microdilution experiment, in a single experiment.

(62) Processing of fluorescence measurements x.sup.k has been described. Of course, the invention also applies to processing carried out on any value deduced bijectively from the measurements x.sup.k, for example the number of bacteria, which is calculated as a function of x.sup.k in a manner known per se.

(63) Calculation of parameters of a growth model has been described, for taking into account the history of growth of the bacteria in the determination of a quantity, for example the MIC.

(64) As a variant, the history is taken into account by calculating a variation V.sup.k of the measurement x.sup.k as a function of time. For example, this variation V.sup.k(t.sub.P) is equal to (x.sup.k(t.sub.P.sup.k)−x.sup.k(t.sub.P−1.sup.k)), or equal to the mean

(65) $\frac{1}{P}\underset{p}{\overset{}{.Math.}}\left(x^k\left(t_p^k\right)-x^k\left(t_{p-1}^k\right)\right),$
or equal to max.sub.p(x.sup.k(t.sub.p.sup.k)−x.sup.k(t.sub.p−1.sup.k)). Calculation of MIC(t.sub.P) as a function of V.sup.k(t.sub.P) is performed identically or similarly to that described in relation to the values μ.sub.k(t.sub.P) and λ.sub.k(t.sub.P).

(66) Moreover, determination of the quantity as a function of a parameter (μ.sup.k(t.sub.P) or λ.sup.k(t.sub.P)) has been described. As a variant, a quantity, for example the MIC, may be calculated for each parameter of a set of parameters and the final MIC is calculated as a function of, or is selected from, the calculated MIC values. For example, the final MIC is equal to the mean value of the MICs.

(67) An embodiment has been described in which the MIC is equal to the last value calculated that is deemed stable. As a variant, the method continues for several cycles once the MIC has converged and the final MIC is calculated as the average of the values of MIC calculated once convergence was obtained.

(68) An embodiment has been described using the analyzer described in the article “Millifluidic droplet analyser for microbiology”. Of course, the invention applies to any type of device and method producing a plurality of samples having a gradient of inhibitor and/or a gradient of a microorganism sensitive to said inhibitor. Notably, the invention applies for example to samples that do not have the same volume.

(69) Determination of an MIC has been described, namely the MIC that is deemed to be true, the latter being equal to the upper limit of the range [N.sub.0; N.sub.CMI(t.sub.P.sub.)]. Of course, the regulatory MIC, for example that fixed by the French government or the US government, may also or alternatively be estimated from this range. In fact, as determination of the range is stable, it is possible to determine a correspondence table, or any other suitable conversion rule, between this range and the regulatory MIC. As an example, it is possible to determine whether the microorganism is sensitive, intermediate or resistant to the molecule according to a regulatory classification comparing an MIC at the critical concentrations of the molecule tolerable by humans. A regulatory classification of this type is for example established by the CA-SFM (Antibiogram Committee of the French Society of Microbiology) or EUCAST (European Committee on Antimicrobial Susceptibility Testing).