Temperature sensitivity of soil dehydrogenase activity determined by the TTC method: An exponential modelling approach

Introduction

As primary members of the family of oxido-reductase enzymes, soil dehydrogenases are to be mentioned (EC 1.1.1) (Gu et al., 2009) [4] . They appear within all living microbial cells (intracellularly), and are one of the most significant enzymes among all inhabiting the soil environment. Soil dehydrogenases are therefore also used as a suitable overall indicator for microbial activity in soil (Gu et al., 2009; Salazar et al., 2011; Tabatabai, 1982) [4,18,20] . They are also closely related to microbial oxido-reduction reactions (Moeskops et al., 2010) [14] . The additional important property of not accumulating extracellular in the soil makes them further suitable as microbial activity indicator. The variety of soil enzymes like ligases and lyases, as well as oxido-reductases, isomerases or hydrolases attribute each of them certain special biochemical roles or functions in the soil's energy and matter conversion process (Gu et al., 2009) [4] . The relevant role in biological soil organic matter oxidation by soil dehydrogenases results from the hydrogen-transfer towards inorganic acceptors, from the inhabiting organic material (Zhang et al., 2010) [25] . The transfer of hydrogen to nicotinamide adenine dinucleotide phosphate or either nicotinamide adenine dinucleotide occurs by dedicated dehydrogenases where the transferred hydrogen atoms take part in the biosynthetic reduction processes throughout these indicated co-enzymes (Subhani et al., 2001) [19] . By this, any given soil's entire DHA is framed by multiple individual dehydrogenase activities of different enzymes present in this soil's living micro-organisms and hence can become considered as biological indicator of the microbial redox-system and used as measurement proxy to quantify the overall micro biological oxidation activities in the soil environment (Subhani et al., 2001) [19] .

Soil dehydrogenase enzyme produced by diversity of rhizospheric micro-organisms are the natural catalysts of different metabolic strategies that occur in the rhizosphere i.e., biodegradation of agrochemicals, decomposition of humus and organics matter, accumulation of organic matter for metabolic activities, release of essential macro-as well as micro-nutrients and offering them for plant's usage through molecular nitrogen fixation (Xie et al., 2009; Małachowska Jutsz and Matyja, 2019) [24,13] . There are reports showing that a biological indicator for judgement of soil quality parameters with organic matter and xenobiotic compounds is possible by evaluating the different enzymes activities i.e., soil dehydrogenase, lipases, cellulose, xylanase, catalase and ureases (Małachowska Jutsz and Matyja, 2019) [13] . Active dehydrogenases is able to utilize O 2 as well as other compounds as terminal electron acceptors, although anaerobic microorganisms produce most dehydrogenases (Brzezińska et al., 2001) [1] . Because of this, the soil's metabolic ability is represented by the DHA and its activity level (or DHA value) may be used as suitable proxy for the soil's microorganism's biomass. Nevertheless, when dealing with the complex soil environment, with the highly diverse microorganisms and degradation processes, the relations between the overall microbial activity and the underlying particular biochemical characteristics are sometimes covered from the obvious (Salazar et al., 2011) [18] . It has been reported that several soil factors, like soil moisture, pH, temperature and, clearly also organic matter content, as well as the soil's aeration conditions (rate of oxygen diffusion and redox potential) are stimulating dehydrogenase activity (Wolinska and Stępniewska, 2012) [22] . Various studies have investigated the change of soil DHA results caused by variations of the incubation temperature (at DHA measurement) or/and the soil's microorganisms quantity level (Subhani et al., 2001; Ghaly and Mahmoud, 2006; Trasar-Cepeda et al., 2007) [19,5,21] . As the soil Dehydrogenase Activity takes place within the cells of viable soil microbes, an optimum temperature range for highest activity can be expected, which should correlate with the temperature for optimum growth conditions of the respective microorganisms (Wolinska and Stępniewska, 2011) [23] . As the enzyme catalysis rate correlates positive with rising temperature, until a level becomes reached where enzyme-denaturisation takes place (Wolinska and Stępniewska, 2012) [22] , a similar temperature pattern for the DHA results may be expected. Further, the physic-chemical properties of the rhizospheric soil may alter the results depending on the environmental factors. Organic matter content as well as the soil's sorption capacity shall be mentioned here as to become considered. Further-more, variations and/or modifications in the DHA determination strategies are creating a difficulty in comparing results from various experiments (researchers/DHA measurement methods) when changes in TTC concentration, soil sample type/weight (1-10 g) or incubation time (1-40 hrs) and incubation temperature (20-37ºC), and use of various organic matter additions (glucose, dextrose, yeast extract, etc.) take place. Sometimes a linear increase of the TPF over time, starting with the TTC inoculation, is assumed at least for certain duration (incubation time range). This (variable and unknown) range where a linear increase in triphenyl formazon can be considered, and becomes relevant in case the entire kinetic of enzymes is unknown, and was not described in various research. It is worth pointing out that the parameters incubation time, incubation temperature and/or selected TTC concentration were often selected based on former research experiments, or had been selected according other boundary conditions. Such data may create the risk of comparing and interpreting results which were measured on different pre-conditions (Januszek et al., 2015) [9] . Last but not least, the selected TTC concentration level is preferable sufficient elevated for saturating the active site of enzymes in the ETC system, but shall not be harming (toxic) to the diversity of rhizospheric micro-organisms; a relevant parameter often not determined (Małachowska-Jutsz and Matyja, 2019) [13] . There are also various mathematical models mentioned for the TPF formation during the incubation time, either based on the exponential function or modified models as the Michaelis-Menten kinetic model (Małachowska-Jutsz, A., and Matyja, K., 2019) [13] , which are in contrast to the assumption of an (initial) phase where TPF increase in a linear way. Having a suitable mathematical model allows also to interpolate TPF levels between different incubation durations and therewith compare results more accurate, especially if the TPF formation process does not follow a linear increase. Therefore, one objective of the presented work was conducting a detailed modelling approach to determine the dynamics of the TPF formation at different incubation time and temperatures and comparing against result according the existing Casida method (Casida et al., 1964) [2] .

Materials and Methods

Collection and Physico-chemical characterization of soil samples

The study was conducted at the Agriculture Research Station, Mandor, Agriculture University, Jodhpur, Rajasthan, India (25°23.115′ N latitude, 72°30.726′ E longitude; 150 m above sea level). The region is characterized by an arid climate with sandy soils typical of western Rajasthan. Soil samples were collected following the harvest of pearl millet during the 2022-2023 cropping season. Rhizospheric soil samples were collected from a depth of 0-20 cm, representing the active root zone, from adjacent experimental plots under two treatments (T 1 and T 5 ). The samples were collected using standard soil sampling procedures, ensuring minimal disturbance and contamination, and were transported to the laboratory for further analysis. Treatments T 1 (Control): Soil without the application of Recommended Dose of Nutrients (RDN) or biofertilizers; T 5 (Treatment): Soil collected from plots treated with Recommended Dose of Nutrients (RDN), plant growth-promoting rhizobacteria (PGPRs) as biofertilizers, and an appropriate quantity of Farm Yard Manure (FYM). The samples got air-dried at 25 °C to a water content of around 2/3 of field capacity (~ 0.26 g g -1 soil). For removing stones and to homogenize the samples, the soil became sieved using a 2mm mesh. Physic-chemical soil parameter analyses were carried out in four replicates; numbers presented are the arithmetic average of the replicates (table 1). Soil texture was classified according the Casagrande aerometric method by separating the sand subfraction in sieves with mesh sizes of 1, 0.5, 0.25, and 0.1 mm (Małachowska-Jutsz and Matyja, 2019) [13] . Particle size groups were determined as per Polish Society of Soil Science classification (PTG, 2011). Measurement of soil pH H 2 O and pH KCl in 1 mol KCl dm -3 was done potentiometrically according to (PN-ISO 10390:1997 1997), with a combined electrode. The Kappen method (Jaremko and Kalembasa, 2014) [10] was used to determine the cation exchange capacity (CEC). Hydrolytic acidity values and CEC permitted gravimetric moisture content determination according ISO 11465:1993 (drying of 100 g soil sample for 24 hrs at 105 °C). The Kjeldahl method (ISO 11261:1995) was applied to measure total nitrogen and Tiurin method, as per standard protocol suggested by Mebius (1960) [15] , to measure overall organic carbon content. Overall phosphorus level was determined from Soil Science Lab of IARI New Delhi, according to (ISO 11263:1994).

Estimation of soil dehydrogenase activity (DHA) at different temperature and incubation periods

For both soil probes, DHA was measured according the standard protocol published by Casida et al., (1964) [2] , with additional sampling at different incubation times. The reagents were mixed in the test tubes using a glass rod (in a way avoiding sample-aeration). For soil probe T 1 the incubation temperature was set to 28 °C and selected incubation time were 2, 4, 8, 12, 22, 32, 72 and 96 h, lightning condition was dark during incubation. This T 1 results were used to get base data and to select a suitable parameter estimation process. For soil probe T 5 we selected with 4, 8, 24, 48, 72 and 96 hours in the dark slightly different incubation times and, besides the 28 °C incubation temperature, two additional temperatures maintaining 40 °C on the high side and 15 °C on the low side during the incubation time.

Following the incubation duration, the probes were centrifuged for 7 minutes (at 3000 rpm), the supernatant was discarded. Afterwards, the produced TPF was then extracted in 5 ml of methyl alcohol. After shaking the samples properly, they were centrifuged a second time. The light absorbance of the supernatant was then determined with a Systronics Spectrophotometer Model 482-Sl at the optical wavelength of 485 nm. The final TPF concentration of the probe was then determined according a calibration curve which was prepared beforehand according to established standard procedure. For each sample defined by soil-probe (treatment), incubation-temperature and incubation-time, three replicates have been analyzed, resulting in 24 probes for T 1 and 54 probes for treatment T 5 . All analysis work was done at at the Basic Science Laboratory (BSL) at Agriculture University Jodhpur, Rajasthan, India.

Function modeling and parameter optimization

According to Małachowska-Jutsz and Matyja, (2019) [13] the formation of TPF concentration can be approximated by the differential equation:

The change (increase) of TPF at any given time (t) after incubation can be described as delta between a final saturation level (TPF max ) and the actual TPF level (TPF(t)), multiplied with a constant factor (k). Solving this differential equation for the initial condition TPF t = 0 = 0 and substitution of τ = 1/k gives:

with "e" denoting Euler's number (2,71828...) and "τ" a characteristic constant value. By this, the generated TPF amount can be described as a function of incubation time by an exponential function with TPF max as saturated TPF value (after "infinite" incubation time) and the characteristic time constant τ, indicating the incubation time (duration) after which the TPF value reaches ~63% (value: 1-e -1 ) of the saturation level TPF max .

Variation of the two unknown parameters (TPF max , τ) and comparing against the measured data lead to an optimum combination to approximate the measured values best, as per selected model. For finding the best parameter combination the "Coefficient of determination" (R²) was used as quality metric (optimization target: R² → max).

With n: Sample size (9 for T 1 and 7 for T 5 , each including t = 0); p: Number of model parameters (2, for the selected exponential function)

Statistical Analysis

The calculated soil parameters (

Results

Different soil physic-chemical properties i.e. pH, Hydrolytic acidity, moisture, cation exchange capacity (CEC), total nitrogen and phosphorous, total organic carbon, particle percentage distribution are essential factors of the microbial enzymatic activity (Soil biological Indicator). This basic physical-chemical properties were measured and are provided as suitable information about the collected rhizospheric soil in the table 1.

The pH value of rhizospheric soil collected for the experiment was at 7.12 and this was optimum for generating maximum soil dehydrogenase activity. Similarly, mean content of total organic carbon was 1.90 g kg -1 DW. Soil dehydrogenase enzyme activity highly correlated with presence of total organic carbon content in the rhizospheric soil. In physic-chemical properties of soil, a relatively low amount of nitrogen and phosphorous (1.463 g kg -1 DW and 0.58 g kg -1 DW, respectively) was found and also depicted in the table 1. Soil dehydrogenase enzyme activity might be also affected by the soil texture. In this regard we have estimated soil texture of rhizospheric soil. In estimation, rhizospheric soil samples, the sand (diameter 0.005-2 mm)dominated (84%), silt (0.002--0.005 mm)-5% and clay (< 0.002 mm)-11%.

The In order to find reasonable ranges for the optimum model parameters, the model parameter search was repeated using the values on the 95% confidence range of the TPF mean values (TPF mean ± confidence interval). The dotted curves in the figures A1 … A4 indicate the resulting model values when using the upper/lower confidence boundaries of the measured values as input for the parameter modeling. The herewith found parameter combinations are indicated in the contour plots as ▵ symbols for results on the upper bound and as ▿ symbols for the lower bound results. showing that both parameters are not only temperature but also treatment depending. All the data are depicted in the table 2 and table 3. The enzymatic activity in soil DHA is usually expressed as (µg TPF) (g soil) -1 (hours incubation time) -1 . Following the Casida method, the DHA is therefore the TPF level after 24 h incubation time, divided by 24 h. This is equivalent to the "secant activity" described by Małachowska-Jutsz, A., and Matyja, K., (2019) [13] . The "tangent activity" referred-to in that paper equals to the first derivative at the beginning of incubation, or the TPF max value divided by the time constant τ. Having a suitable mathematical model permits to compare the model output with the measured data and/or predicted values. Figure 3 shows the predicted DHA values and the results achieved with the measured data (as per Casida method). The predicted DHA is highest at the beginning of the incubation time and then reducing, as expected by the used model. The DHA levels at time = 0 are naturally also corresponding to the values achieved with the "tangent method" (see Małachowska-Jutsz, A., and Matyja, K., 2019 → tangent activity) [13] . ). The values at incubation-time = 0h correspond to "tangent method" according Małachowska-Jutsz, A., and Matyja, K., (2019) [13] . The ' x ' markers denote the model predicted DHA values at 24 h, also for the soil treatment T1.

We finally tested the exponential model against a linear function for the TPF formation. For this, the mean of the measured data from T 1 and T 5 up to 22 h respectively 24 h incubation time were used and a linear regression coefficient was calculated. We then compared the adjusted R² resulting from this linear model (R² adj lin ) against the respective ones from the exponential model (R² adj exp ), and used this to judge the model quality; higher R² adj indicate better fit of the model data to the measured values. With our data we achieved better model fit (higher R² adj ) for 3 out of the 4 treatments with the exponential model. The exception was T 5 -28 °C, where the linear model achieved a marginally higher R²adj (0.996) than the exponential model (0.989), likely because TPF had not reached saturation within the 24 h range used for the linear comparison. (Table 4).

Discussion

In our estimation of physic-chemical soil properties, most of these were found to be optimal for higher soil dehydrogenase enzyme activities efficiency. However, minor differences in described rhizospheric soil properties and selected appropriate approach for soil dehydrogenase enzyme estimation can affect the efficiency of the measured enzyme activities (Liu et al., 2008; Xie et al., 2009; Cross and Sohi, 2011) [12,24,3] . The presented experiment, carried out on one soil type in two different fertilization treatment conditions, reveal that the soil treated with recommended (bio-) fertilizer amount shows 1.8-fold increase in Dehydrogenase activities, compared to our control (T 1 ). This result is not a surprise, as DHA is reflecting the amount of enzymatic activity in soil, where elevation is expected with the application of bio-fertilizer. We also see a dependency of the TPF level (and the DHA results) on the incubation temperature with a maximum at 28 °C (the midone of the selected temperatures), where the DHA is 1.7fold higher compared to the 40 °C, and 5.6-fold higher compared to 15 °C incubation temperature, at the same soil. As the variants on incubation temperature for T 5 were carried-out on the same soil sample the differences come from the change in the temperature of the analysis (the measurement) procedure. They may result from either in slower reaction dynamics or a lower reaction amount, or a combination of both. While in the first case the TPF is expected to still reach the same level after longer incubation, only taking more time, the second case would mean a comparable reaction dynamic at a lower reaction intensity, indicating the TPF will not reach same amount, even after long incubation.

To answer these questions, we turned to mathematically modeling the TPF formation process as exponential function and investigated the temperature dependency, reflected by the achieved model parameters. The findings reveal a faster reaction with higher temperature (ref. Fig 2 B), where reaction speed increases by ~20% at 40 °C incubation, indicated by smaller time-constant parameter τ (change from 34.6h to 29.8h), but slows down by ~30% at 15 °C incubation temperature, always with 28 °C as reference. In terms of reaction intensity, we see a peak at 28 °C, where model predicted TPF saturation level TPF max (after "infinite" incubation time) reduces to ~60% at 40 °C and to ~28% at 15 °C incubation temperature (Fig. 1). The combination of reaction dynamics and intensity result into a model predicted maximum DHA (determined by the TPF level after 24h incubation) at 28 °C, with a drop to ~65% (from 6.68 to 4.37 µg TPF/g soil/h) at 40 °C and a drop to ~22% (from 6.68 to 1.45 µg TPF/g soil/h) at 15 °C incubation temperature (see Table 1). All model predictions are well supported by the measured results, we therefore may use model predicted values also to estimate values at other incubation times, especially at t = 0 (start of incubation) where soil enzyme reaction is highest. The mathematical model predicts a DHA calculated according the "tangent method" (Małachowska-Jutsz and Matyja, 2019) [13] tangent activity) of 9.27 µg TPF/g soil/h for the T 5 at 28 °C incubation temperature. At 40 °C the tangent model-predicted DHA shows a value of 6.37 µg TPF/g soil/h, which is a drop to ~69% and 1.83 µg TPF/g soil/h at 15 °C incubation temperature, at drop to nearly 20% of the value at 28 °C incubation temperature. Comparing the two fertilizer treatments (T 1 , T 5 ) we see an increase of nearly 1.6-fold in the tangent DHA results at 28 °C incubation for the T 5 treatment with bio fertilizer applied (see Table 1). Our findings confirm that an exponential function as mathematical model, as proposed by several authors, fits well to the measured data with resulting high values for the correlation quality indicator (R² adj ) between 0.952 and 0.993. Both variable model parameters converge for each series towards a unique combination, leading to a maximum (optimum) R² for each investigated treatment (data series), as seen in the related contour plots; the exponential function hence defines a suitable model for this purpose. The achieved model parameters clearly confirm a temperature dependency of the TPF formation. Results from soil treatment T 5 reveal a tendency towards faster reaction (smaller value of the time constant parameter) with rising incubation temperature for the TPF formation, which is in line with many reports on faster chemical reactions with rising temperatures, within a certain temperature range. We also observed a temperature dependency for the TPF saturation level (TPF max ) achieved. In the range of the investigated temperature levels between 15 °C to 40 °C we identified a peak value for the TPF max parameter, in our case at an incubation temperature of 28 °C, for the soil treatment T 5 . Also, this observation is backed-up by other authors (Gu et al., 2009) [4] , where a rise in the level of the reaction product (i.e., TPF level) has been observed when increasing the reaction temperature with a following drop of this level when temperature is exceeding a certain optimum level. Results from treatment T 1 were gathered only at 28 °C and confirm that maximum TPF level as well as reaction rate (time constant) are not only temperature depending but change also with the soil treatment/type.

Conclusion

Soil dehydrogenase enzyme activity mainly depends on the environmental factors and associate methods used to determine it, even when estimated from the same rhizospheric soil. Measuring the enzyme activity is influenced not only by the soil itself but also by the measurement method. The widely used Casida method relies on incubation of the soil sample with a TTC suspension and the subsequent formation of TPF. We observed (among others) that this process is strongly influenced by the temperature during the incubation time and the TPF formation rate changes over the incubation duration. From our findings we conclude that the exponential model is a suitable mathematical model for the TPF formation process in the course of soil DHA analysis. The effort for model parameter fitting (to the measured data) is modest and straight forward and can be carried-out with any mathematics software, capable of basic functions. The numbers of additional samples required are also modest; where we recommend to skip some sampling times (incubation times) used and plan instead for 6, 12, 24, 48, 96 hrs as incubation times for the purpose of soil DHA analysis. Applying the dispersion parameters (e.g. standard deviation) from the measured replicates to the model parameters is not a straight-forward procedure, as the selected model is not linear in the measured data and the exponential factor (time-constant) has a different unit. We therefore applied the optimization procedure additionally onto the data given by the 95% confidence range derived from the replicates of the individual samples. Even though these resulting model parameters do not denote the 95% confidence range for the best-fit model parameters, they indicate a range for the sensitivity of the model parameters with respect to the variations seen in the measured data. Having a suitable mathematical model for a bio-chemical reaction provides benefits, but comes mostly at the cost of additional measurements required and the modeling work to be done. In case of the selected TPF dynamics model with the two parameters, the minimum required measured values are two, compared to the Casida method, where one data sample after 24h incubation time is mandated. Using the bare minimum of measured data bears the risk of low model quality as any (not avoidable) measurement uncertainty becomes fully transferred into model uncertainty. The advantage of a valid mathematical model is the gain of insight into the bio-chemistry process, especially for timeevolving processes, with unknown reaction velocity. In our case we found a clear trend in reaction dynamics (faster reaction at higher temperature) and a peak in reaction intensity (i.e., the created TPF amount) with rising temperature during the incubation. Choosing the right amount of measured data at suitable sample points (sample time) can optimize the cost/benefit ratio between smaller cost for data collection at constant high model quality.

Acknowledgement

AcknowledgmentAuthors acknowledge Agriculture University Jodhpur for providing all necessary resources for completion of this research and the authors declare no competing interests.

References

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