Edited by: Claudio Fabricio Gonzalez, University of Florida, United States
Reviewed by: Catrin Ffion Williams, Cardiff University, United Kingdom; Armen Trchounian, Yerevan State University, Armenia
*Correspondence: Shaoxun Tang
This article was submitted to Microbial Physiology and Metabolism, a section of the journal Frontiers in Microbiology
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The electrokinetic properties of the rumen microbiota are involved in cell surface adhesion and microbial metabolism. An
The rumen environment is characterized by a resident microbial population that rapidly colonizes and digests feed particles, thereby providing fermentation end products that are utilized by the host animal (Paracer and Ahmadjian,
Where ε0 represents the permittivity of free space, ερ is the dielectric constant and η is the dynamic viscosity of dispersion medium, μe is the electrophoretic mobility and ξ is the zeta potential. The ξ represents the potential difference between the dispersion medium and stationary layer of fluid attached to the dispersed particle. It implies that ξ is a key indicator of the stability of colloidal dispersions. It has been proven that lower ξ absolute value means low viability in organism cells, which leads to the aggregation of cells in a dispersion medium (Kłodzińska et al.,
In previous works, the experimental outcomes and predictive models have been reported based on perturbation values of cell physical properties (permeability and hydrophobicity) of
In this line of thinking, ideas from the Perturbation Theory (PT) can be used to model the previously mentioned problem. The PT models are useful to find an exactly related and simpler solution to an existing sophisticated problem. The main feature of PT is to break the sophisticated issue into “perturbation” or “solvable” components. Our group has developed different PT models that start with a known solution to a problem and add corrections considering the variations of various experimental conditions (cj) (Gonzalez-Diaz et al.,
This study is aimed at predicting ξ by fitting a linear model that uses the MA operators of all parameters along with different time scales as input values. In some cases, the linear model hypothesis may fail due to the high complexities of the natural system. In agreement with the previously mentioned concepts, some non-linear Machine Learning methods can be combined with time-series analysis methods, such as two of the most known examples of each area of Autoregressive Integrated Moving Average (ARIMA) and non-linear Artificial Neural Network (ANN). ARIMA and ANN algorithms have been compared to each other in time-series problems (Turias et al.,
The present work focuses on the integration of ANN and ARIMA as models with PT operators to seek a new model able to predict the values of ξ (ζ
The experiment was conducted to determine the effect of rumen culture medium at different ST levels and SSA of substrates on the electrokinetic properties of rumen microbes and fermented
In this study, an exogenous non-ionic surfactant, alkyl polyglucoside (APG) bought from Hunan Diyuan Co., Ltd., China, was provided to construct the different ST levels. The dosages of APG used in the present work were adjusted as described in our previous reports (Liu et al.,
In general, the fermentation microbial samples at each time-point were collected by centrifuging and washing with phosphate-buffered saline at least two times. The details for collecting microbial cells were described in our previous works (Liu et al.,
The ST of inoculum in the fermentation process was determined on a time scale t1. The ST of the ruminal culture medium at each point time was measured immediately using the surface tension analyzer (model K100 Tensiometer, KRÜSS GmbH, Hamburg, Germany) (Blake et al.,
In current study, VFAs include acetic acid (C2:0), propionic acid (C3:0), butyric acid (C4:0), isobutyric acid (isoC4:0), valeric acid (C5:0), and isovaleric acid (isoC5:0). Every 2 mL of incubation fluid from each fermentation bottle on a time scale t2 were centrifuged at 10,000 × g and 4°C for 15 min. 1.5 mL of supernatant solution was collected, which was immediately mixed and homogenized with 0.15 mL 25% metaphosphoric acid. The mixture solution was centrifuged again at 10,000 × g at 4°C for 15 min, and the supernatant solution was collected to determine each VFA content by gas chromatography (HP5890, Agilent 5890; Agilent Technologies Co. Ltd, USA). The DB-FFAP column (Agilent, No.: 122-3232, 30 m in length with a 0.25 mm i.d. and 0.25 um thickness) was used. The parameters of this column were set as the attenuation in a nitrogen split ratio of 1:50, hydrogen flow 30 mL/min, airflow 365 mL/min, injector temperature 250°C, column temperature 150°C and detector temperature 220°C with N2 as carrier gas at a flow rate of 0.8 mL/min. The relative response factor, represented as the peak of each VFA, was calculated against a standard VFA mixture analyzed following every 10 measurements.
In this work, the ξ and μe values of ruminal mixed microbes (RMMs), VFA and γ were obtained with the same initial combinatorial conditions of ST × SSA. The recorded data of pH, digestibility (D) of NDF, and c(NH3-N) were also collected from our previous works (Liu et al.,
Flow chart of the experimental section used for the construction of the dataset.
The experiment considered the initial combinatorial conditions made up of 4 ST × 3 SSA = ST1-SSA1, ST1-SSA2 …ST4-SSA3 for all the variables, such as (a) experimental variables: ξ, μe, γ, and VFA; (b) record data: pH, c(NH3-N), and D. However, the experimental variables were measured with a different time span of 6–72 h in t1 and 6–48 h in t2. More specifically, all variables combined with the time series can be expressed as ξ(t1), μe(t1), ST-a(t1), pH(t1), c(NH3-N)(t1), and D(t1) in time series of t1; VFA(t2): C2:0(t2), C3:0(t2), C4:0(t2), isoC4:0(t2), C5:0(t2), and isoC5:0(t2) in time series of t2. Therefore, in order to study the effect of the perturbations of all variables over zeta potential (ξ) of RMMs, an integrated input dataset, made up of combinations of all the variables presented in these two different time scales (t1 and t2), needs to be assembled. There were two blocks of experimental data: (n1) No.(t1) = 12 initial cj × 3 replicates × 6 point-of-time = 216 cases; (n2) No.(t2) = 12 initial cj × 3 replicates × 4 point-of-time = 144 cases. In this work, an integrated dataset made up of No. = 31 104 (= 216 No.(t1) × 144 No.(t2)) cases was constructed, combining all variables in these two blocks of data on different time scales. The ξ value was standardized using the mean for all ξ. Next, the ξ-ANN models were developed to predict the numerical simulation ξ of rumen microbes over the environmental variables or factors in rumen fermentation ecosystem. For further details on n1 and n2 stocks experimental data (please see the online files SM01_Variables_t1.pdf, SM02_Variables_t2.pdf, SM03_Zp_model_dataset.xlsx, and SM04_Zp_dataset_std_values.sta) (Liu et al.,
In this work, it was firstly assumed that the zeta potential of RMMs might associate with the environmental factors to some extent. Herein, it was assumed that a numerical model used to map the physicochemical properties of RMMs might be beneficial to reflect its mechanism or function. Therefore, the environmental factors such as pH, D, c(NH3-N), γ, and VFAs were taken into consideration. The variable symbols Vq(t1) and Vf(t2) were defined according to two different time scales, where the subscript “q” and “f” indicate the different input variables corresponding to the different time series, respectively. Vq(t1) or Vf(t2) indicates that the input variables change with the corresponding time scale. As the variability or the “
In this sense, this is a complex theoretical model which combined the methods of the PT, MA and Time Series Analysis (Fisher,
In this general formula, symbols such as a0, bq, and cf, are the intercept, or the coefficient of the corresponding variable. In this specific case, the ANN model is a linear additive function of all the terms mentioned above. The terms of ΔVϕ(tk) were added as corrections to the EM of zeta potential ξ(e) = a1. < ξ(tk)>, where a1 refers to the weighted value of < ξ(tk)>, and < ξ(tk)> refers to expected value of ξ calculated as the standardized value of ξ based on the mean value of each cj.
Next, the expected measurements < ξ> and its corrections ΔVϕ(tk) were obtained for the entire dataset. First the different ANN algorithms (Fisher,
Flow chart of experimental and theoretical sections of this work.
The experimental results of ζ
The experimental results of ξ and μe for ruminal microbiota cells in t1 (h) time series.
3.37 | 53.95 | 6 | −3.12 | −0.05 | −31.92 | −0.04 | 48.93 | 36 | −2.38 | 1.79 | −24.26 | 1.81 | 51.69 |
46.09 | −3.35 | −0.67 | −34.44 | −0.66 | 49.41 | −2.55 | 1.31 | −26.23 | 1.32 | 50.39 | |||
42.78 | −3.44 | −0.81 | −35.29 | −0.81 | 46.25 | −2.72 | 0.98 | −27.88 | 0.98 | 47.87 | |||
36.07 | −3.14 | −0.39 | −32.20 | −0.38 | 39.87 | −2.84 | 0.35 | −29.13 | 0.36 | 45.02 | |||
3.73 | 53.95 | −3.21 | −0.61 | −32.94 | −0.60 | 47.53 | −2.52 | 1.12 | −25.86 | 1.11 | 50.20 | ||
46.09 | −3.06 | −0.31 | −31.41 | −0.31 | 46.38 | −2.70 | 0.59 | −27.72 | 0.58 | 47.55 | |||
42.78 | −3.27 | −0.51 | −33.58 | −0.51 | 46.58 | −2.77 | 0.74 | −28.42 | 0.74 | 47.85 | |||
36.07 | −3.44 | −0.70 | −35.27 | −0.69 | 44.72 | −2.94 | 0.53 | −30.22 | 0.53 | 45.27 | |||
4.44 | 53.95 | −3.22 | −0.34 | −33.02 | −0.34 | 49.32 | −2.72 | 0.89 | −27.92 | 0.89 | 49.70 | ||
46.09 | −3.32 | −1.01 | −32.92 | −0.76 | 48.91 | −2.31 | 1.49 | −23.76 | 1.45 | 48.48 | |||
42.78 | −3.48 | −0.90 | −35.71 | −0.90 | 49.18 | −2.54 | 1.44 | −26.04 | 1.43 | 46.55 | |||
36.07 | −3.37 | −0.62 | −34.56 | −0.62 | 44.43 | −2.61 | 1.27 | −26.82 | 1.25 | 44.71 | |||
3.37 | 53.95 | 12 | −3.21 | −0.29 | −32.98 | −0.30 | 52.01 | 48 | −3.85 | −1.88 | −39.67 | −1.91 | 47.25 |
46.09 | −3.25 | −0.44 | −33.40 | −0.41 | 50.09 | −3.81 | −1.82 | −38.90 | −1.74 | 44.89 | |||
42.78 | −3.33 | −0.54 | −34.17 | −0.54 | 47.59 | −3.72 | −1.50 | −38.14 | −1.50 | 44.06 | |||
36.07 | −3.22 | −0.60 | −33.12 | −0.61 | 47.74 | −3.67 | −1.70 | −37.61 | −1.69 | 43.98 | |||
3.73 | 53.95 | −2.94 | 0.06 | −30.19 | 0.06 | 53.88 | −3.23 | −0.66 | −33.19 | −0.66 | 48.11 | ||
46.09 | −2.99 | −0.13 | −30.69 | −0.13 | 49.52 | −3.20 | −0.66 | −32.86 | −0.66 | 46.40 | |||
42.78 | −3.20 | −0.32 | −32.80 | −0.32 | 50.05 | −3.32 | −0.62 | −34.09 | −0.63 | 43.18 | |||
36.07 | −3.13 | 0.06 | −32.18 | 0.06 | 45.05 | −3.85 | −1.72 | −39.51 | −1.71 | 41.96 | |||
4.44 | 53.95 | −3.35 | −0.66 | −34.36 | −0.66 | 51.21 | −3.10 | −0.05 | −31.83 | −0.05 | 46.33 | ||
46.09 | −3.09 | −0.45 | −31.77 | −0.48 | 51.94 | −2.92 | −0.01 | −29.94 | −0.04 | 45.21 | |||
42.78 | −3.49 | −0.93 | −35.82 | −0.93 | 49.04 | −3.26 | −0.37 | −33.47 | −0.36 | 43.56 | |||
36.07 | −3.13 | −0.03 | −32.10 | −0.02 | 46.65 | −3.37 | −0.63 | −34.62 | −0.63 | 42.30 | |||
3.37 | 53.95 | 24 | −2.70 | 0.98 | −27.68 | 0.98 | 49.02 | 72 | −3.31 | −0.54 | −34.01 | −0.55 | 46.95 |
46.09 | −2.48 | 1.49 | −25.47 | 1.50 | 46.44 | −3.03 | 0.12 | −31.71 | 0.00 | 45.34 | |||
42.78 | −2.41 | 1.74 | −24.79 | 1.73 | 44.92 | −3.06 | 0.14 | −31.39 | 0.13 | 44.44 | |||
36.07 | −2.38 | 1.49 | −24.48 | 1.48 | 44.03 | −2.64 | 0.85 | −27.11 | 0.85 | 44.18 | |||
3.73 | 53.95 | −2.95 | 0.05 | −30.26 | 0.05 | 50.16 | −2.95 | 0.05 | −30.25 | 0.05 | 45.17 | ||
46.09 | −2.67 | 0.66 | −27.41 | 0.66 | 47.68 | −2.99 | −0.14 | −30.71 | −0.14 | 44.97 | |||
42.78 | −3.07 | −0.01 | −31.54 | −0.01 | 46.01 | −2.78 | 0.72 | −28.47 | 0.73 | 44.21 | |||
36.07 | −3.06 | 0.24 | −31.39 | 0.24 | 44.18 | −2.52 | 1.58 | −25.87 | 1.58 | 42.71 | |||
4.44 | 53.95 | −2.79 | 0.73 | −28.62 | 0.72 | 49.98 | −3.31 | −0.58 | −33.99 | −0.57 | 45.78 | ||
46.09 | −2.85 | 0.15 | −29.61 | 0.04 | 47.20 | −2.98 | −0.16 | −30.59 | −0.20 | 45.65 | |||
42.78 | −2.97 | 0.36 | −30.51 | 0.35 | 45.17 | −2.96 | 0.40 | −30.32 | 0.40 | 44.97 | |||
36.07 | −3.15 | −0.08 | −32.31 | −0.07 | 45.21 | −3.08 | 0.09 | −31.64 | 0.09 | 44.60 |
The VFA values of the present study were shown in Table
The VFAs concentrations with the designated initial combinatorial conditions (3 SSA × 4 ST) in time series t2 (h).
3.37 | 53.95 | 6 | 5.06 | 3.50 | 2.78 | 0.71 | 0.71 | 0.74 |
46.09 | 6.94 | 3.90 | 3.37 | 0.59 | 0.59 | 0.93 | ||
42.78 | 6.98 | 3.76 | 3.23 | 0.56 | 0.56 | 0.91 | ||
36.07 | 6.29 | 4.10 | 3.58 | 0.62 | 0.62 | 1.05 | ||
3.73 | 53.95 | 4.25 | 3.45 | 2.79 | 0.58 | 0.58 | 0.81 | |
46.09 | 6.24 | 3.84 | 3.25 | 0.60 | 0.60 | 0.90 | ||
42.78 | 4.96 | 3.50 | 3.30 | 0.59 | 0.59 | 0.96 | ||
36.07 | 5.60 | 4.03 | 3.69 | 0.63 | 0.63 | 1.12 | ||
4.44 | 53.95 | 5.12 | 3.64 | 3.20 | 0.40 | 0.40 | 0.88 | |
46.09 | 5.94 | 4.00 | 3.63 | 0.57 | 0.57 | 0.99 | ||
42.78 | 4.30 | 3.69 | 3.57 | 0.50 | 0.50 | 1.00 | ||
36.07 | 5.86 | 4.16 | 3.85 | 0.59 | 0.59 | 1.11 | ||
3.37 | 53.95 | 12 | 6.57 | 4.56 | 3.58 | 0.41 | 0.41 | 0.96 |
46.09 | 7.37 | 4.76 | 4.21 | 0.72 | 0.72 | 1.24 | ||
42.78 | 8.80 | 5.06 | 4.43 | 0.70 | 0.70 | 1.27 | ||
36.07 | 9.70 | 5.27 | 4.52 | 0.72 | 0.72 | 1.44 | ||
3.73 | 53.95 | 6.12 | 4.26 | 3.33 | 0.40 | 0.40 | 0.90 | |
46.09 | 5.49 | 4.30 | 3.70 | 0.64 | 0.64 | 1.10 | ||
42.78 | 6.77 | 4.61 | 4.32 | 0.69 | 0.69 | 1.25 | ||
36.07 | 9.49 | 5.30 | 4.60 | 0.72 | 0.72 | 1.40 | ||
4.44 | 53.95 | 5.07 | 3.91 | 3.02 | 0.51 | 0.51 | 0.83 | |
46.09 | 6.49 | 4.52 | 3.81 | 0.63 | 0.63 | 1.09 | ||
42.78 | 7.85 | 4.71 | 4.02 | 0.65 | 0.65 | 1.14 | ||
36.07 | 6.73 | 4.65 | 4.12 | 0.67 | 0.67 | 1.30 | ||
3.37 | 53.95 | 24 | 18.69 | 10.03 | 9.15 | 1.05 | 1.05 | 1.54 |
46.09 | 17.97 | 9.68 | 9.68 | 1.20 | 1.20 | 1.73 | ||
42.78 | 19.99 | 10.61 | 11.03 | 1.35 | 1.35 | 2.08 | ||
36.07 | 17.38 | 8.68 | 9.30 | 1.25 | 1.25 | 2.24 | ||
3.73 | 53.95 | 17.74 | 9.93 | 8.92 | 1.20 | 1.20 | 1.55 | |
46.09 | 16.57 | 9.23 | 8.57 | 1.05 | 1.05 | 1.50 | ||
42.78 | 22.18 | 12.13 | 12.07 | 1.47 | 1.47 | 2.22 | ||
36.07 | 20.88 | 11.00 | 11.94 | 1.65 | 1.65 | 2.75 | ||
4.44 | 53.95 | 17.55 | 10.88 | 9.17 | 1.13 | 1.13 | 1.46 | |
46.09 | 20.38 | 11.18 | 9.33 | 1.18 | 1.18 | 1.57 | ||
42.78 | 20.23 | 10.76 | 9.48 | 1.18 | 1.18 | 1.70 | ||
36.07 | 18.43 | 9.14 | 8.54 | 1.21 | 1.21 | 1.77 | ||
3.37 | 53.95 | 48 | 13.18 | 8.10 | 6.48 | 1.05 | 1.05 | 1.69 |
46.09 | 14.70 | 7.83 | 6.66 | 1.10 | 1.10 | 1.73 | ||
42.78 | 14.91 | 8.76 | 7.80 | 1.25 | 1.25 | 2.05 | ||
36.07 | 14.07 | 8.95 | 8.34 | 1.31 | 1.31 | 2.28 | ||
3.73 | 53.95 | 14.36 | 9.90 | 8.23 | 1.34 | 1.34 | 2.15 | |
46.09 | 11.74 | 8.57 | 7.29 | 1.15 | 1.15 | 1.86 | ||
42.78 | 14.50 | 10.20 | 8.73 | 1.41 | 1.41 | 2.24 | ||
36.07 | 12.70 | 8.71 | 6.97 | 1.10 | 1.10 | 1.77 | ||
4.44 | 53.95 | 14.24 | 9.96 | 7.27 | 1.11 | 1.11 | 1.77 | |
46.09 | 12.35 | 9.85 | 8.05 | 1.32 | 1.32 | 2.04 | ||
42.78 | 17.22 | 11.78 | 10.04 | 1.59 | 1.59 | 2.52 | ||
36.07 | 15.81 | 10.87 | 9.05 | 1.39 | 1.39 | 2.27 |
In the previous section, the output values of ξ (ζ
ANN Dual-time series models for ξ of rumen microbiota.
RBF 14:14-794-1:1 | T | 0.826 | 1.020 | 0.000 | 0.575 | KM |
V | 0.858 | 0.978 | 0.012 | 0.502 | KN | |
PI | ||||||
MLP 1:1-5-1:1 | T | 0.273 | 1.020 | −1.181 | 0.982 | BP100 |
V | 0.000 | 0.978 | −1.181 | 0.982 | CG20 | |
CG0b | ||||||
LNN 15:15-1:1 | T | 0.349 | 1.020 | 0.000 | 0.956 | PI |
V | 0.306 | 0.978 | 0.002 | 0.932 |
Table
RBF model sensitivity analysis compared to other models.
RBF 14:14-794-1:1 | 1.00 | 2.03 | 1.54 | 1.27 | 1.90 | 1.15 | 1.00 | 1.03 |
MLP 1:1-5-1:1 | 1.02 | — | — | — | — | — | — | — |
LNN 15:15-1:1 | 1.00 | 1.08 | 1.00 | 1.00 | 1.07 | 1.02 | 1.13 | 1.04 |
ANN/Var Ratio | — | t2(h) | ΔC(Ace)2 | ΔC(But)2 | ΔC(Pro)2 | ΔC(iBut)2 | ΔC(iVal)2 | ΔC(Val)2 |
RBF 14:14-794-1:1 | — | 1.20 | 1.19 | 1.19 | 1.28 | 1.12 | 1.15 | 1.12 |
MLP 1:1-5-1:1 | — | — | — | — | — | — | — | — |
LNN 15:15-1:1 | — | 1.00 | 1.00 | 1.00 | 1.00 | 1.7E+12 | 1.00 | 1.7E+12 |
Thus, for the case of the RBF model, all variables have sensitivity ratios >1. It shows that the perturbations on the variables measured on both time scales (t1 and t2) have a significant effect on the final value of ξ (ζ
The cellulose degradation is highly correlated to the activity and quantity of fibrolytic enzyme. The previous work had proved that the inclusion of a non-ionic surfactant in the culture media resulted in a significant increase in the production of extracellular celluloses and β-xylosidase
The adhesion of ruminal microbiota to the substrate is the prerequisite for bacterial colonization and proliferation (McAllister et al.,
In the present study, the results also showed that the ζ
On the other hand, the VFAs are the secondary metabolites of rumen carbohydrate degradation. The iso-acids are required absolutely to stimulate the growth of several rumen bacterial species, particularly for the fibrolytic organisms (Allison,
In general, the PT method sets with an initial of a known exact solution for an issue or problem by adding the corresponding corrections due to the variations of different experimental conditions (Liu et al.,
In our previous studies, we reported that the ideas of PT combining with the ANN modeling were successfully used to predict the physic-chemical properties (permeability and hydrophobicity) of rumen microbes based on the combinatorial conditions of the ST and SSA in the processes of
YL, CZ, and ZT designed the research; YL, TR, YY, and ST conducted the research; YL, CM, CF, AP, and HG analyzed the experimental original data and constructed the predictive model; YL, TR, ST, CM, HG, and ZT wrote the full manuscript. All authors approved the final manuscript.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
The authors are extremely grateful to the Key Laboratory of Subtropical Agro-ecological Engineering, Institute of Subtropical Agriculture, from the Chinese Academy of Sciences (CAS) for providing the experimental materials and apparatuses to complete the present experiment.