### Study area

The river Beas originates in the southern side of the Rohtang Pass above Kullu in Beas Kund, in central Himachal Pradesh, India (32.36° N lat. and 77.08° E long.) and merges into river Sutlej at Harike (31.17° N lat. and 75.2° E long.) in the state of Punjab, India, after traversing a distance of about 470 km. Plant samples were collected from the surroundings of the river bed between the towns of Beas and Harike. Identification and authentication of the plants was done at the Botanical Survey of India, Dehradun, India.

### Organic acids quantification using GC-MS

#### Preparation of sample

The organic acids in the plant leaves were determined by following the procedure earlier described by Sharma et al. (2016). Organic acids were extracted from 50 mg of the oven dried (80 °C, 24 h) powdered leaves of different plant species by adding 0.5 ml of 0.5 N HCl and 0.5 ml of methanol. After that, the samples were shaken for 3 h followed by centrifugation at 12,000 rpm for 10 min. To the supernatant, 300 μl of methanol and 100 μl of 50% sulphuric acid were added followed by overnight incubation in water bath at 60 °C. The mixture was cooled down to 25 °C, and 800 μl of chloroform and 400 μl of distilled water were added to it followed by vortexing for 1 min. The lower chloroform layer was used to estimate organic acids using GC-MS.

### Investigation using GC-MS

For the determination of organic acids, 2 μl of plant sample, i.e., the lower chloroform layer, was injected in the system. GC conditions: Helium was used as carrier gas, the starting column temperature was 50 °C held for 1 min which was raised to 125 °C at 25 °C/min followed by additional enhancement to 300 °C at 10 °C/min, held for 15 min. Injection temperature was 250 °C, injection mode was split, gas flow in the column was 1.7 ml/min, and analytical column DB-5ms was used. MS conditions: Ion source temperature was set at 200 °C and interface temperature was 280 °C, solvent cut time was 3 min, and detector gain mode was relative. Since the sample preparation procedure resulted in the derivatization of organic acids, the studied organic acids were citric acid trimethylester, succinic acid dimethyester, fumaric acid dimethyester, and malic acid dimethyester, and their contents were estimated using standard curve.

### Simulation of rate transfer coefficients

The rates of change of different components may be described by a system of linear differential equations for a constant size of the first component viz. citric acid (*x*
_{1}) to malic acid (*x*
_{4}).

$$ \frac{dx_2}{dt}={ax}_1-{bx}_2 $$

$$ \frac{dx_3}{dt}={bx}_2-{cx}_3 $$

$$ \frac{dx_4}{dt}={cx}_3-{dx}_4 $$

where *x*
_{
i
} are the concentrations of the acids and *a*, *b*, *c*, and *d* are the rates of transfer from one component to the next one. The differential equations can be solved for the size of the component with respect to time. With time, the system will tend to a steady state, and the rate of change of each component will be zero:

The system can be simulated using a set of difference equations:

$$ {x}_2\left(t+1\right)={x}_2(t)+{ax}_1(t)-{bx}_2(t) $$

$$ {x}_3\left(t+1\right)={x}_3(t)+{bx}_2(t)-{cx}_3(t) $$

$$ {x}_4\left(t+1\right)={x}_4(t)+{cx}_3(t)-{dx}_4(t) $$

where *x*
_{
i
} (*t*) and *x*
_{
i
} (*t* + 1) are the sizes of the components at times (*t*) and (*t* + 1), respectively. The matrix model representation of the difference equations given above will be as follows:

$$ \left[\begin{array}{l}{x}_1\left(t+1\right)\\ {}{x}_2\left(t+1\right)\\ {}{x}_3\left(t+1\right)\\ {}{x}_4\left(t+1\right)\end{array}\right]=\left[\begin{array}{l}1\kern1.44em 0\kern1.56em 0\kern1.56em 0\\ {}a\kern1.2em 1-b\kern0.84em 0\kern1.56em 0\;\\ {}0\kern1.2em b\kern1.68em 1-c\kern0.72em 0\\ {}0\kern1.2em 0\kern1.68em c\kern1.32em 1-d\end{array}\right]\kern0.36em \left[\begin{array}{l}{x}_1(t)\\ {}{x}_2(t)\\ {}{x}_3(t)\\ {}{x}_4(t)\end{array}\right] $$

or

$$ X\left(t+1\right)=M\;X(t) $$

where *M* is the rate transfer matrix and *X*(*t*) and *X*(*t + 1*) are vectors for organic acid contents at times (*t*) and (*t* + 1), respectively. At steady state,

$$ X\left(t+1\right)=X(t) $$

The system of difference equations was simulated using a self-coded software in MS-Excel to determine the rate transfer coefficients *a*, *b*, and *c*, by inputting the values of *x*
_{1,}
*x*
_{2}, *x*
_{3}, *x*
_{4}, and *d*.

### Statistical analysis

All the analyses were done in triplicate, and the results were expressed in mean and standard deviation values. The data were analyzed by using principal component analysis (PCA), factor analysis (FA), multiple linear regression analysis (MLR), and artificial neural network analysis (ANN) (Sokal and Rohlf 1995; Bailey 1994; Kumar et al. 2016, 2017). First-order linear difference equations were used for the simulation of the transformation of acids to a steady state. System analysis software was coded in MS-Excel. The software used were PAST, Minitab-14, and Statistica-12.