Model based study of the first stage of biological nitrification (NH₄⁺ oxidation to NO₂⁻)

Abstract

Reaction mechanisms are generated for the first stage of biological nitrification (NH₄⁺⇒NO₂⁻) by using graph theoretical methods and the chemical information for reaction intermediates. On this basis, a large number of kinetic models are obtained. As a result of model discrimination, a kinetic model is derived to describe the kinetics of the biological nitrification reaction appropriately. The kinetic constants of the model were estimated by implementation of a differential method for parameter estimation. The selection of a correct reaction mechanism and kinetic model is performed on the basis of the experimental data obtained using laboratory scale equipment. A kinetic model which appropriately describes the kinetics of ammonia oxidation into nitrite and its parameter estimates is obtained. It is in correspondence with the mechanism including the reaction step of formation and decomposition of an intermediate complex between ammonia, bacteria and oxygen.

Introduction

The biological removal of nitrogen in water is a combination of the processes of autotrophic nitrification and heterotrophic denitrification. The nitrification is a two-step process, which proceeds as a result of metabolism of nitrogen-oxidative bacteria species Nitrosomonas and Nitrobacter (Anthonisen et al., 1974). The oxidation to nitrite, catalyzed by Nitrosomonas sp., the so called “nitritation” process, is the first oxidation step, expressed according to EPA (1975) as follows:

$$\text{NH}{}_{\mathrm{<mtext>4</mtext>}}{}^{\mathrm{<mtext>+</mtext>}}\text{+1.5}\text{O}{}_2\text{→}\text{NO}{}_{\mathrm{<mtext>2</mtext>}}{}^{\mathrm{<mtext>-</mtext>}}\text{+2}\text{H}{}^{\mathrm{+}}\text{+}\text{H}{}_2\text{O}\text{+58}\text{–}\text{84}\text{kcal}$$

To explain the reaction mechanism, the participation of intermediates such as NH₂OH, NHO, [NO₂·NHOH] in the reaction mechanism was quite frequently postulated (Aleem, 1970, Painter, 1970, Focht and Chang, 1975).There are strong indications that hydroxylamine is likely to be an intermediate in the initial phase of ammonia oxidation (Aleem, 1970). The reaction of hydroxylamine formation is expressed by the following equation:

$$\text{NH}{}_4{}^{\mathrm{+}}\text{+0.5}\text{O}{}_2\text{→}\text{NH}{}_2\text{OH}\text{+}\text{H}{}^{\mathrm{+}}$$

The initial oxidation of ammonium ions involves a two-electron transfer to form hydroxylamine (Focht and Chang, 1975). In the special literature, there is speculation that the ammonia transformation causes the chemical instability of hydroxylamine and the other possible intermediates. A logical two-electron transfer from hydroxylamine would produce the hypothetical nitroxyl. It can exist as an intermediate with a short life time. Aleem (1970) found that cell-free extracts of Nitrosomonas, when incubated with hydroxylamine and cytochrome. c. Fe³⁺, catalyzed an oxidative condensation resulting in 2 mol of nitrite. They concluded that the nitrification was thus a semicyclic process involving the participation of ferrocytochrome in the oxidation of hydroxylamine to a hypothetical nitroxyl, which condenses with nitrogen dioxide to form nitrohydroxylamine:

$$\text{NH}{}_2\text{OH}\text{+2}\text{cyt.}\text{c}\text{. Fe}{}^{\mathrm{3+}}\text{→}\text{(NHO)}\text{+2}\text{cyt.}\text{c}\text{. Fe}{}^{\mathrm{2+}}\text{+2}\text{H}{}^{\mathrm{+}}\text{(NHO)}\text{+}\text{HNO}{}_2\text{→}\text{NO}{}_2\text{·}\text{NHOH}\text{NO}{}_2\text{·}\text{NHOH}\text{+0.5}\text{O}{}_2\text{→2}\text{HNO}{}_2\text{2}\text{cyt.}\text{c}\text{. Fe}{}^{\mathrm{2+}}\text{+2}\text{H}{}^{\mathrm{+}}\text{+0.5}\text{O}{}_2\text{→2}\text{cyt.}\text{c}\text{. Fe}{}^{\mathrm{3+}}\text{+}\text{H}{}_2\text{O}\text{NH}{}_2\text{OH}\text{+}\text{O}{}_2\text{→}\text{HNO}{}_2\text{+}\text{H}{}_2\text{O}\text{+}\text{energy}$$

In the absence of oxygen, Anderson (1965) suggests that nitrous oxide is formed, by a non-enzymatic reaction. The same non-enzymatic generation of nitrous oxide was observed in resting-cell suspensions of Nitrosomonas europaea (Yoshida and Alexander, 1964). However, chemical production of nitrous oxide at neutral pH from hydroxylamine and nitrite has also been shown to occur with relative ease (Focht and Chang, 1975).

As a result, it is generally accepted that the mentioned mechanism of nitrification is a semicyclic process involving the oxidation of ammonia as a first step to the complex X₀[NH₂OH], where X₀ denotes enzyme or/and bacteria. However, the kinetic description of the nitrification process in many cases is rather complicated due to the formation of complexes between the reagents and enzyme or/and bacteria. The latter can be bound directly to the cell wall of specific bacteria and the reaction rate depends on the bacterial concentration.

Based on the above, we tried to specify the intermediates and the reaction steps that could take part in the transformation of ammonia to nitrite.

The intermediates (complexes) for the nitrification process in which two reagents (ammonia and oxygen) and three reaction products (NO₂⁻, H⁺ and H₂O) are involved are presented in Table 1.

There is biochemical evidence, as well as supposition, for the involvement of complexes 1, 2 and 4 (Table 1) in the nitrification process. The other complexes from Table 1 are also thought to take part in this reaction, but there is no clear proof of this.

The reaction steps that can be generated from the complexes given in Table 1 are summarized in Table 2.

Information on the topological structure of the mechanism (topological information), which is related to the formal kinetic information, can be expressed conveniently by means of cyclic graphs (Kamenski et al., 1992, Kamenski and Nenov, 1997, Petrov, 1987, Petrov, 1992), which are called kinetic graphs (KGs). The vertices and edges in such a graph correspond to intermediates and reaction steps, respectively. On the other hand, the minimum number of independent cycles, i.e. graph cyclomatic number, equals the number of linearly independent reaction routes.

The two routes (cycles) in the two-route reaction can be linked in two different ways: by a common intermediate (vertex) and a common step (edge) (Fig. 1). As a result, two possible mechanism types, denoted by B and C, correspond to these two possibilities.

For these types of mechanisms, the complexes listed in Table 1 are regarded as intermediates. The possible one-route mechanisms are constructed on the basis of the graph theoretical approach described above, as well as by using the limitation of only four reaction steps in each mechanism. From the intermediates given in Table 1, as well as from the reaction steps presented in Table 2, five such possible reaction mechanisms are obtained. They are summarized in Table 3. The edge numbering in Table 3 corresponds to that of the reaction steps in Table 2. Three indices are used in Table 3 to denote these mechanisms. The first one indicates the number of reaction routes, the second one marks the number of intermediates in the route, and the third one stands for the mechanism serial number.

The 1.2.1 and 1.3.1 mechanisms in Table 3 correspond to the case in which the rate determining step is the reaction of intermediate X₁ with the oxygen. In the case of the 1.2.2 mechanism there is a step sequence featuring the oxygen attack on the bacteria–NH₄⁺ complexes as a rate determining step. The 1.3.2 mechanism incorporates the formation of binary complex bacteria–NHO while the 1.4.1 mechanism includes an additional step for the formation of the X₄ ternary complex (bacteria-NO₂–NHOH). These complexes react further with oxygen.

Two-route mechanisms for the nitrification reaction corresponing to types B and C can be generated from the one-route ones presented in Table 3. Aiming to derive the reaction mechanisms given in Table 4, the chemical evidence for the existence of different intermediates (presented in Table 1) are used. On this basis, some possible reaction steps is generated. For e.g. the products of the two-route mechanism 2.3.1 (Table 4) can be obtained by steps “2” and “10” starting from different intermediates with the same bacteria. Based on the chemical evidence and the graph theoretical approach, all pairs of graphs that have only one vertex in common are combined with each other, forming bicyclic graphs of type B (e.g. X₀ for mechanisms 1.2.1 and 1.2.2, 1.3.1, 1.3.2, 1.4.1, and 1.2.2). The two-route mechanisms corresponding to type C are generated by assembling those of the one-route ones that have a common graph edge (e.g. 1.3.1 1.3.2 1.4.1 and 1.2.1), or two common edges, e.g. edges 1 and 5 are common for the 1.3.2 and 1.4.1 mechanisms. The resulting two-route mechanisms are shown in Table 4. The vertex, edge, and mechanism numbering correspond to those in Table 3.

In order to retain the canonical graph presentation (Bonchev et al., 1982), the two edges that the two cycles have in common may be located on the enveloping cycles corresponding to the initial one-route mechanisms, as is the case with mechanism 2.4.2 in Table 4. As can be seen from Table 4 for the 2.4.2 mechanism, edge 5 belong to both (X_o, X₁, X₃) and (X_o, X₁, X₃, X₄) cycles, the second one being an enveloping cycle for canonical representation II, where another minimal cycle (X_o, X₃, X₄) appears. The latter, however does not corresponds to any one-route mechanism, since it contains arcs with opposite directions (6 and 7,8).

An inspection of the mechanisms in Table 4 indicates that most of the cases of class C contain the comparative transformation of one and the same intermediate into reaction products with or without the involvement of other intermediates (e.g. X₁⇒X₀ and X₁⇒X₃⇒X₄⇒X₀ in 2.4.1.)

It should also be mentioned that the generation procedure generally produces mechanisms having more than two routes. However, these mechanisms are not considered here because of the problem of kinetics. In fact, the simultaneous direct transformation of an intermediate into a reaction product and the three indirect transformations involving another intermediate do not seem likely.

In the specific case of the nitrification reaction, all elementary steps (Table 2) included in the routes, except those standing for irreversible reactions, can be regarded as quasi-equilibrium steps.

In quasi-equilibrium approximation, as well as in the presence of the rate determining steps, the rate of a one-route reaction is expressed by the equations

$$\text{r=A}\text{/}\text{F}{}_{\mathrm{k}}$$

$$\text{F}{}_{\mathrm{k}}\text{=1+}\text{∑}\text{j}\text{K}{}_{\mathrm{j}}\text{C}{}_{\mathrm{j}}{}^{\mathrm{n}}\text{C}{}_{\mathrm{<mtext>p</mtext>}}{}^{\mathrm{m}}$$

Here, k_L is the rate constant of the rate determining step, K_d is the constant of the quasi-equilibrium step in the route, [E]_Σ is the total concentration of all enzyme or/and bacteria species and C_j (C_p) is the concentration of the reactants (reaction products).

According to the assumption made above, the rate of nitrification reaction in the case of a two-route mechanism is the sum of the rates of nitrification on the first and second route:

$$\text{r=r1+r2}$$

The denominator of Eq. (3) represents all the forms of the enzyme or/and bacteria complexes and comprises the K_j equilibrium constants of all elementary reactions in which enzyme or/and bacteria complexes are formed.

The kinetic models obtained by using , , are shown in Table 5.

The selection of a correct reaction mechanism and kinetic model in this particular case is performed on the basis of experimental data obtained in laboratory scale equipment. The details of the kinetic measurements are described in the following section.