GB2298046A - Measuring the concentration of intact cellular biomass in a medium - Google Patents

Abstract

The concentration of intact cellular biomass in a medium which comprises intact cellular biomass in suspension and further includes non-intact cells, and/or non cellular particles, which are liable to interfere with dielectric measurement of the cellular biomass, is determined. A set of measurements are made, at different frequencies, of the dielectric permittivity and also preferably of the dielectric conductivity of the medium, and the set of measurements are compared with one or more prestored characteristics. The measurements are made at different frequencies in the range 0.2 to 10 MHz, and the comparison may be performed using a calibrated neural network.

Description

Biomass measurement apparatus and method This invention relates to the measurement of cellular biomass using the dielectric permittivity at radio frequencies, under conditions in which there may be interfering substances present.

In the dielectric spectroscopy of biological and other systems, it is usual to find areas of strong frequencydependence, known as dielectric dispersions, in which the measured permittivity or capacitance decreases with increasing frequency, with a shape (when the frequency is plotted logarithmically) approximating an inverse sigmoid.These passive, non-faradaic electric or "dielectric" properties of cellular suspensions themselves (as opposed to those of the suspending medium or the electrodes usually used as interfaces between the exciting electrical apparatus and the system of interest) are generally characterised by three major areas of frequency-dependence, known (in order of increasing frequency) as the a-, ss- and -dispersions. To characterise the behaviour of the system of interest quantitatively, one often fits the measurements (permittivity and conductivity at different frequencies) to an appropriate equation, that proposed by the Cole brothers being perhaps the most popular in biological work.The Cole-Cole equation is a modification of the Debye formulation of molecular dielectric behaviour which contains, in addition to the dielectric increment (E), characteristic frequency (fc) and high-frequency permittivity (ek,), an empirical parameter, the Cole-Cole a, which may be used to describe (if not to explain) the fact that real dielectric spectra are much broader than those due to a simple Debye-like dispersion. Whilst the Cole-Cole a has no theoretical justification (although it is widely interpreted in terms of a distribution of relaxation times), it has been shown that a great many types of relaxation-time distribution could accurately fit the Cole-Cole function.In addition, the Cole Cole function permits one to extract the parameters describing an entire dielectric dispersion, even if, for technical reasons, one cannot measure over the whole frequency range across which it occurs. For these and other reasons the Cole Cole formulation remains very popular as a means of characterising the dielectric properties of biological systems.

We have shown that the radio-frequency dielectric properties of biological cells at one or more appropriate frequencies may be used as a rapid and on-line method for measuring the levels of intact cellular biomass in fermenters and elsewhere, and have accordingly disclosed for this purpose a method and apparatus capable of measuring said dielectric properties in the range 0.2 to 10 MHz (see European Patents Nos. 0281602 and 0282532).The method relies upon the fact that the ss-dielectric dispersion exhibited by all biological cells is dominated by the charging of their plasma membrane(s), and that intact biological cells, but nothing else likely to be found in a fermenter or a cell suspension of interest, possess relatively non-conducting plasma membranes, and that the dielectric increment of the D-dispersion, or indeed the dielectric permittivity at frequencies that are relatively low with respect to the fc of the D-dispersion, is proportional to the volume fraction of the intact cellular biomass present.

This approach broadly requires that at least one of the frequencies of measurement is low with respect to the fc of the 13-dispersion, but not so low that the dielectric permittivity (or the capacitance) of the system is raised artificially over the background due to the a-dispersion or to the set of phenomena collectively referred to as electrode polarization.

In a biomass monitor instrument in accordance with the above patents, biofouling can be obviated by the manual or automatic application of electrolytic cleaning pulses, although a similar system without cleaning pulses may be used to assess the extent of such biofouling. The output of this device may be chosen in terms of absolute capacitance, capacitance minus that upon inoculation, or (via a previously determined calibration) dielectric permittivity, mg biomass/ml and so on.

An output of the conductance of the broth can also be provided.

The biomass monitor is suitable for use in all kinds of fermentations, and has been applied to a variety of prokaryotic and eukaryotic microbes, pitching control in breweries, plant cells, animal cells, immobilised cells, solid-subtract fermentations, and (since it measures biomass possessed of an intact cell membrane, and not necromass lacking one) in assessing cytotoxicity. We have also found this a convenient means to control a turbidostat.

In some media, however, especially those long exploited in many industrial fermentations, there may be other particulate matter which exhibits a substantial a-dispersion, or there may be an unacceptable level of electrode polarization or indeed other interfering effects; these effects are often manifested as an increase in capacitance over the baseline at low radio frequencies, which may therefore interfere with the dielectric estimation of cellular biomass according to the methods described above. Because such media are normally sterilised by steam or by autoclaving, any such particulate matter, though it may once have been cellular, is after sterilization no longer cellular, in the sense of containing a substantially ion-impermeable phospholipid membrane capable of providing a significant 13-dispersion.

The distinction between substantially intact cellular material, substantially non-intact cellular debris, and clearly non-cellular material is known to those skilled in the art and these materials produce significantly different capacitance and conductance spectra. From this point of view, we have found that the measurement of the dielectric permittivity, preferably together with the electric conductivity, of such suspensions at a variety of radio frequencies may be used, together with any of a number of methods of multivariate calibration, to deconvolve dielectric spectra of systems which contain both cellular and non-cellular materials.

According to a principal aspect of the present invention, therefore, there is provided a method or apparatus for detecting, by dielectric spectroscopy, non-cellular substances and phenomena in the presence of cellular biomass, which substances and phenomena interfere with the dielectric measurement of cellular biomass, so as to provide a more accurate measurement of the biomass present.

According to a second aspect of the present invention there is provided a method or apparatus for determining, by dielectric spectroscopy, the concentration of such non-cellular interfering substances and/or the magnitude of such interfering phenomena in the presence of cellular biomass.

Also according to the invention there is provided a method or apparatus for deconvolving the dielectric spectrum of a biological and electrochemical system which contains both intact, cellular material and non-cellular material, by comparing the dielectric spectrum obtained with a stored characteristic. Preferably the stored characteristic is developed in a training or supervised learning process.

The invention may be more clearly understood by reference to the following Example and to the accompanying drawings, in which: FIGURE 1 is a set of curves showing the measured variations in capacitance, with frequency, of different suspensions of yeast cells or wheatgerm; FIGURE 2 is a set of curves showing the measured variations in conductance, with frequency, of different suspensions of yeast cells or wheatgerm; FIGURES 3A and 3B are schematic diagrams to explain the principles of artificial neural networks which may be used for the purposes of the present invention; FIGURE 4 is a learning curve produced in training a neural network for the purposes of the present invention, in respect of yeast concentration; FIGURE 5 is a predicted versus true value line of yeast cell concentration following the training performed in accordance with Figure 4;; FIGURE 6 is a similar learning curve to Figure 4, but in respect of wheatgerm concentration; FIGURE 7 is a similar line to Figure 5 but in respect of the wheatgerm; FIGURE 8 is a learning curve similar to Figure 4, using a second neural network; FIGURE 9 is a similar line to Figure 5, produced using the second neural network; FIGURE 10 is another learning curve produced using the second neural network; FIGURE 11 is a predicted versus true value line for wheatgerm, produced using the second neural network; FIGURES 12 and 13 are prediction lines for yeast concentration, using a partial least squares (PLS) technique; FIGURES 14 and 15 are prediction lines for wheatgerm concentration, using the PLS technique; and FIGURES 16 and 17 are prediction lines for yeast and wheatgerm concentrations, respectively, using a principalcomponents-regression (PCR) technique.

The Example is designed to clarify the ability of the present invention to discriminate intact cellular biomass (which is one determinand of interest) from other material which may also be present in a matrix of interest and which may yet constitute other potential determinands. In the examples, concentrations are determined in terms of mass per unit volume of suspension, concentrations can instead be measured in other terms e.g. volume of cells per unit volume of suspension.

Example Baker's yeast (to provide a typical cell suspension) was obtained locally as a paste and suspended in 50 mM KH2PO4, pH 6,5. Wheatgerm ('Natural' wheatgerm, W. Jordan Cereals, Biggleswade, UK) (to provide a typical non-cellular interferent) was obtained locally and suspended in the same medium.

The dielectric properties of a suspension of yeast cells and of wheatgerm, and of the background electrolyte, are shown in Fig. 1. Capacitance measurements were made using a dielectric biomass monitor in accordance with the above patents, at the frequencies and with the concentrations of yeast and of wheatgerm indicated. The cell constant was 0.613cam~', as determined conductimetrically, and no attempt was made to remove the background signal due to the capacitance of the probe itself.The following points are clear: (i) even in the absence of yeast or wheatgerm there is a noticeable electrode polarization at the lower frequencies, manifested as an increase in capacitance over that at the high frequencies; (ii) wheatgerm exhibits a dielectric dispersion in this frequency range even though it has no intact cellular membranes and is incapable of producing a classical 13-dispersion; (iii) accurate estimations of the yeast cell biomass in this frequency range could be substantially interfered with by the presence of wheatgerm.

Fig. 2 shows the conductance properties of suspensions of yeast cells and of wheatgerm at the same radio frequencies as those in Fig. 1. Conductance measurements were made using the dielectric biomass monitor at the radio frequencies and with the concentrations of yeast and of wheatgerm indicated.

The cell constant was again 0.613 cm1. The following points are clear: (i) in the absence of yeast or wheatgerm there is no significant conductivity dispersion at the lower frequencies, which would be manifested as a decrease in capacitance over that at the higher frequencies; (ii) yeast cell biomass does exhibit a measurable conductivity dispersion in this frequency range, especially noticeably here between some 1 MHz and 4 MHz. These differences are due to the differences in the relaxation time of the processes causing the dispersions of electrodes, wheatgerm and yeast respectively.

We therefore made up a variety of mixtures of yeast and wheatgerm by gravimetric means, and subdivided them into 'training' and 'test' sets, as in Table 1, where it may be observed that there are 21 objects or samples in the training set and 15 objects or samples in the test set: Training Set Test Set Yeast Wheatgerm Yeast Wheatgerm mg/ml mg/ml mg/ml mg/ml 0.00 0.00 5.3 13.65 0.00 27.30 5.3 40.95 0.00 54.60 5.3 68.25 0.00 81.90 5.3 95.55 0.00 109.20 5.3 122.85 0.00 136.50 15.9 13.65 10.60 0.00 15.9 40.95 10.60 27.30 15.9 68.25 10.60 54.60 15.9 95.55 10.60 81.90 26.5 13.65 10.60 109.20 26.5 40.95 21.20 0.00 26.5 68.25 21.20 27.30 37.1 13.65 21.20 54.60 37.1 40.95 21.20 81.90 47.7 13.65 31.80 0.00 31.80 27.30 31.80 54.60 42.40 0.00 42.40 27.30 53.00 0.00 We then applied multivariate calibration methods of supervised learning to these data, so as to deconvolute the data on dielectric permittivity and conductivity to output the concentrations of yeast and of wheatgerm. We first describe artificial neural networks.

Artificial neural networks (ANNs) consist of highly interconnected parallel-processing elements known as nodes, which are arranged into layers representing a set of inputs, one or more so-called hidden layers, and a set of outputs.

Each node acts to sum its own inputs (which are the outputs of the elements of previous layers), and the sum is passed through a transfer function (which must be continuously differentiable and is normally nonlinear) to the element(s) in the next layer.

In a classical version, the transfer function is sigmoidal (via the exponential term) and is normalised between 0 and 1, the output oj of node j being given by: Oj= 1 + e(x/Y) (Eq 1) where

In equation (2), Oj is a bias term, oj is the output from the i node of the previous layer, and w represents the so-called weight or strength between node i and node j. z is known as the gain. Other possible functions include the sinh, tanh and sine functions, and whilst the exact architectures may be varied the general principles of fully interconnected feedforward networks are illustrated in Fig. 3A and 3B.

It is possible to train such networks by setting the weights and biases initially to small random values, presenting the networks with known inputs and outputs, and comparing the output of the net with the "true" (known) outputs. By adjusting the weights using information based on the difference (the error, e,) between the net's output and the true values, a principle known as the backpropagation or error (or, more simply and more commonly, backpropagation or backprop), it is therefore possible to train the network accurately to deliver a desired output when presented with novel (previously unseen) inputs. This process is repeated from the output through each hidden layer to the input.The actual weight updates for this so-called delta rule are: wij. = W1j + LR,e,,xij + M.mij (Eq 3a) mij = wjj - W1j (Eq 3b) where LR and M are user-defined values of the so-called Learning Rate and Momentum, respectively. In this way, weights are changed according both to the error and the input to the connection of interest. Training may be continued until a defined root-mean-square error (between the "true" outputs of the training set and the network's outputs) is obtained, or simply for a fixed number of presentations of the training set.

Advantageously a cross-validation regime is applied such the learning is ceased at a point substantially similar to that at which a suitable statistic such as the RMS error of a separate test set is minimised. These properties of multivariate calibration are generally known to those skilled in the chemometric art.

We have found that it is possible to train ANNs using dielectric data (the permittivity and conductivity values, or equivalently the capacitance and conductance values, at a number of frequencies) as the inputs, and the concentrations of the different substances of interest as the outputs, and thereby enable the trained network to give (say) the concentrations of the different substances of interest when presented with a separate set of dielectric data. To this end, Fig. 4 shows a learning curve in which the RMS error between the predicted and true values for the outputs is plotted against the epoch number, using a fully interconnected feedforward net with 50 input variables (capacitance and conductance values at 25 frequencies) and therefore 50 input nodes, 3 nodes in a single 'hidden' layer, and one output node, viz. the yeast concentration.The training and test samples were those in Table 1. The neural net was trained using the standard back-propagation algorithm: the software was a commercial package (NeuDesk, Neural Computer Sciences, Unit 3, Lulworth Business Centre, Nutwood Way, Totton, Southampton S04 3WW, UK) running on a PC.

Fig. 5 shown the predicted vs true value of the yeast cell concentration for both the training and test data after 1000 epochs of the learning performed in Fig. 4. It is clear that the neural net has leaned to deconvolute the yeast signal from the wheatgerm signal.

Fig. 6 shows a similar learning curve to that in Fig.

4 using the examples of Table 1, save that now the predictions are for the wheatgerm (which gives a much smaller dielectric response in this range than does the yeast - see Fig. 1).

Fig. 7 shows the predicted vs true values of the wheatgerm concentration for both the training and test data after 500 epochs of the learning performed in Fig. 6. It is clear that the neural net has learned to deconvolute the wheatgerm signal from the yeast signal.

Fig. 8 shows a learning curve in which the RMS error between the predicted and true values for the estimate of the yeast concentration is plotted against the epoch number, using a fully interconnected feedforward net with only 25 input variables (the capacitance but not the conductance values at 25 frequencies) and therefore 25 input nodes, 3 nodes in a single 'hidden' layer, and one output node, viz. the yeast concentration. The training and test samples were those in Table 1.

Fig. 9 shown the predicted vs true values of the yeast cell concentration for both the training and test data after 500 epochs of the learning performed in Fig. 8. It is clear that the neural net has learned to deconvolute the yeast signal from the wheatgerm signal using the capacitance data alone.

Fig. 10 shows a learning curve in which the RMS error between the predicted and true values for the estimate of the wheatgerm concentration is plotted against the epoch number, using a fully interconnected feedforward net with only 25 input variables (the capacitance but not the conductance values at 25 frequencies) and therefore 25 input nodes, 3 nodes in a single 'hidden' layer, and one output node, viz. the wheatgerm concentration. The training and test samples were those in Table 1.

Fig. 11 shows the predicted vs true values of the wheatgerm cell concentration for both the training and test data after 200 epochs of the learning performed in Fig. 10.

It is clear that the neural net has learned to deconvolute the wheatgerm signal from the yeast signal using the capacitance data alone.

We have also discovered that other, linear multivariate techniques may be used advantageously to relate dielectric data such as those described to the concentrations of determinands of interest. In particular, we have used the techniques of partial least squares (PLS) and principal components regression (PCR), techniques known to those familiar with the multivariate statistical and chemometric arts.

Fig. 12 shows the predictions of a PLS model formed using full leave-one-out cross validation (the optimal model shown contained 2 PLS factors), using both capacitance (C) and conductance (G) data as in Fig. 5 with the samples in Table 1.

It is clear that the PLS method is also capable of forming a calibration model relating the dielectric data to the determinands of interest, here the yeast cell concentration.

Study of the loadings plot of the 2-factor model showed that whilst both contributed, the capacitance readings were noticeably more important than the conductance readings in forming the model.

Fig. 13 shows the predictions of a PLS model formed using full leave-one-out cross validation (the optimal model shown contained 2 PLS factors), now using only the capacitance (C) and not the conductance (G) data, as in Fig. 9 with the samples in Table 1. It is clear that the PLS method is capable of forming a calibration model relating only the capacitance portion of the dielectric data to the determinands of interest, here the yeast cell concentration.

Fig. 14 shows the predictions of a PLS model formed using full leave-one-out cross validation (the optimal model shown contained 2 PLS factors), using both capacitance (C) and conductance (G) data as in Fig. 5 with the samples of Table 1.

It is clear that the PLS method is also capable of forming a calibration model relating the dielectric data to the determinands of interest, here the wheatgerm concentration.

Fig. 15 shows the predictions of a PLS model formed using full leave-one-out cross validation (the optimal model shown contained 2 PLS factors), now using only the capacitance (C) and not the conductance (G) data, as in Fig. 9 with the samples in Table 1. It is clear that the PLS method is capable of forming a calibration model relating only the capacitance portion of the dielectric data to the determinands of interest, here the wheatgerm concentration.

Fig. 16 shows the estimated yeast cell concentrations based on a PCR model formed using full leave-one-out cross validation (the optimal model shown contained 2 principal components), using both capacitance (C) and conductance (G) data as in Fig. 5 with the samples in Table 1. It is clear that the PCR method is also capable of forming a calibration model relating the dielectric data to the determinands of interest, here the yeast cell concentration.

Fig. 17 shows the estimated wheatgerm concentrations based on a PCR model formed using full leave-one-out cross validation (the optimal model shown contained 2 principal components), using both capacitance (C) and conductance (G) data as in Fig. 5 with the samples in Table 1. It is clear that the PCR method is also capable of forming a calibration model relating the dielectric data to the determinands of interest, here the wheatgerm concentration.

It will be appreciated that in each of Figures 5, 7, 9 and 11 to 17, the line which is shown is the line of identity.

Claims (13)

Claims

1) A method of determining the concentration of intact cellular biomass in a medium which comprises intact cellular biomass in suspension and further includes non-intact cells and/or non-cellular particles, the method comprising the steps of making a set of measurements, at different frequencies over a range of frequencies, said measurements including measurements of the dielectric permittivity of the medium or measurements of a parameter dependent on said dielectric permittivity, and comparing said set of measurements with one or more prestored characteristics.

2) A method as claimed in claim 1, in which said set of measurements also includes measurements of the dielectric conductivity of the medium or measurements of a parameter dependent on said dielectric conductivity.

3) A method as claimed in claim 1 or 2, in which said set of measurements are made at different frequencies within the range 0.2 to 10 MHz.

4) A method as claimed in any preceding claim, further comprising the step of determining the concentration of the non-intact cells or non-cellular particles in the medium by comparing said set of measurements with one or more prestored characteristics.

5) A method as claimed in any previous claim, in which said step of comparing said set of measurements with one or more prestored characteristics is performed using a calibrated neural network.

6) A method as claimed in claim 5, in which the neural network comprises a layered, feed-forward network, calibrated by means of a gradient descent training algorithm, and comprising: an input layer, to which is applied a representation of said measurements; one or more hidden layers; and an output layer supplying the or at least one said concentration value.

7) A method as claimed in any of claims 1 to 4, in which said step of comparing said set of measurements with one or more prestored characteristics is performed using a partialleast-squares (PLS) algorithm.

8) A method as claimed in any one of claims 1 to 4, in which said step of comprising said set of measurements with one or more prestored characteristics is performed using a principal-components-regression (PCR) algorithm.

9) A method as claimed in claim 1 and substantially as herein described.

10) An apparatus for determining the concentration of intact cellular biomass in a medium which comprises intact cellular biomass in suspension and further includes non-intact cells and/or non-cellular particles, the apparatus comprising a vessel or conduit at least partially filled with said medium, measuring means for making a set of measurements, at different frequencies over a range of frequencies, said measurements including measurements of the dielectric permittivity of the medium or measurements of a parameter dependent on said dielectric permittivity, and processing means for comparing said set of measurements with one or more prestored characteristics.

11) An apparatus as claimed in claim 10, in which said measuring means is arranged to make measurements of the dielectric conductivity of the medium or of a parameter dependent on said dielectric conductivity, and include those measurements in said set of measurements.

12) An apparatus as claimed in claim 10 or 11, in which said processing means is also arranged to determine the concentration of the non-intact cells or non-cellular particles in the medium by comparing said set of measurements with one or more prestored characteristics.

13) An apparatus as claimed in claim 10 and substantially as herein described.