If Enzymes Get Inactive Due to Hish Temp Acan the Become Active Again

Constructed Methods 6 – Enzymatic and Semi-Enzymatic

M. Bechtold , South. Panke , in Comprehensive Chirality, 2012

seven.5.3.1 Inactivation Mechanisms

Enzyme inactivation can principally be attributed to mechanisms related to the reactor, the medium components, or the protein. Enzyme inactivation is oftentimes induced past phase interfaces resulting, for example, from dispersed air bubbles or biphasic liquid/liquid systems. In the instance of air bubbling and droplets of nonpolar organic solvents, interfacial interaction with the enzyme results in hydrophobic forces that disturb the secondary construction of the enzyme. Other irreversible mechanisms include cleavage by proteases present, for case, in a CFE, precipitation, or aggregation, ²⁸ or chemical processes such equally oxidation, racemization, condensation, hinge region or tryptophan hydrolysis, or aspartate isomerization. ²⁹ Even so, at that place are also more subtle mechanisms that render enzymes inactive. As proteins are active only in a specific circuitous structural configuration, unfolding of some domains of the protein or subunit dissociation typically results in a drastically less agile or completely inactive enzyme. Consequently, mechanistic models of enzyme deactivation consider at least three primal protein states (1) the correctly folded active country E; (2) an inactive, at to the lowest degree partially unfolded state U (this country is frequently considered to exist randomly coiled, although many contempo studies indicate that it also includes partially folded structured variants); and (3) a completely denatured state D ^xxx that originates from the concrete and chemic irreversible inactivation mechanisms ²⁸ introduced above. Stabilization of the active state E with respect to unfolding can principally be attributed to a high activation energy barrier in example of a rate-controlled unfolding process, or to the position of the unfolding equilibrium favoring the active land in case of thermodynamically controlled unfolding. Experimental studies suggest that both mechanisms are ubiquitous in nature. ^28a,30a Apparently, in both situations operational conditions such as temperature, pH, or corporeality of denaturing agents determine the extent of unfolding and hence stability.

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Stability and Stabilization of Biocatalysts

M. Polakovič , ... V. Báleš , in Progress in Biotechnology, 1998

1 DRAWBACKS OF CONVENTIONAL EVALUATION [1]

Enzyme inactivation is by and large explained as a chemical procedure involving several phenomena like assemblage, dissociation into subunits, or denaturation (conformational changes), which occur simultaneously during the inactivation of a specific enzyme [2,three]. However, the principal information for elucidating the kinetics of enzyme inactivation is obtained through the measurement of enzyme activity, which is determined as the rate of enzyme reaction at specified weather condition. Consequently, enzyme action gives the best quantitative information on the miracle of activity loss, only it is hard to relate this to the changes occurring in the enzyme structure. The total enzyme activity, A, is generally equal to the sum of the activities of active enzyme forms, A_i . The activity, a, is commonly given as a relative value of the initial activity, A ₀,

(one) $a=\frac{A}{A_0}=\frac{{\displaystyle \sum _i{A}_i}}{{\displaystyle \sum _i{A}_{i0}}}=\frac{{\displaystyle \sum _i{\gamma }_i{c}_i}}{{\displaystyle \sum _i{\gamma }_i{c}_{i0}}}$

where ϒ_i are the molar activities and c_i are the molar concentrations of enzyme forms.

Equation (ane) reflects the methodological problems encountered in the analysis of the kinetics of enzyme inactivation. As the inactivation is represented by a set of reactions among dissimilar enzyme forms, for the evaluation of kinetics it would exist highly useful to know the content of individual enzyme forms. Further complications during the analysis of inactivation kinetics are that the molar activities of enzyme forms are generally unknown. Thus, it is difficult to determine from the inactivation bend solitary whether a reaction is reversible or irreversible, whether parallel reactions are taking place on the same enzyme class or not, or whether intermediates are active or inactive. Information technology has been demonstrated how uncomplicated kinetic equations (mainly starting time-lodge kinetics) can disguise a more complex kinetic behaviour [4–6].

Unlike inactivation mechanisms of equal complexity can notwithstanding correspond to the same integral activity-time relationship and the number of equivalent mechanisms increases exponentially with the number of parameters in the kinetic equation [i]. Thus, neither isothermal inactivation data exhibiting non-first order kinetics practice not provide sufficiently consistent information upon which a detail mechanism of inactivation could be declared. A careful statistical analysis of extensive ready of inactivation data found in literature showed that any pattern of enzyme inactivation behaviour (biphasic, grace-menstruation or activation-menses) tin can exist described past a relatively elementary exponential function [1]. Such functions represent lumped kinetic equations and any simple mechanisms which could be identified from them are dismissed if the validity of the mechanisms is tested at several temperatures [1].

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Stability and Stabilization of Biocatalysts

Vadim Five. Mozhaev , in Progress in Biotechnology, 1998

2.1 Denaturation mechanism

Mechanistic consideration of enzyme inactivation in organic solvents is based on the important prerequisite that the protein molecule is surrounded by a beat formed by h2o molecules bound to the protein surface by hydrogen bonds. This hydration shell or at least a portion of information technology represents an integral part of poly peptide construction and is essential for enzyme role [6]. Consequently, displacement of bound water molecules by organic solvent results in a dramatic alter of the whole protein construction and leads to denaturation. In line with these ideas, inactivation of enzymes in water-co-solvent mixtures consists of 3 main steps schematically shown in Fig. two:

Fig. ii. Schematic presentation of the mechanism of protein denaturation past organic solvents.

i.

dehydration of the protein molecule, i.east. removal of a sure disquisitional amount of water molecules from the poly peptide hydration beat out;

2.

binding of the organic co-solvent by the partially dehydrated protein;

iii.

conformational transition in the protein molecule resulting in the formation of a denatured course D with concomitant loss of catalytic activity.

Thermodynamic consideration of this model led to the following expression for the free free energy of protein denaturation (ΔG_D) by organic solvents [7]:

(i) $\text{Δ}{\text{M}}_{\text{D}}={\text{B}}_0+{\text{B}}_1{\text{n}+\text{B}}_2{\text{E}}_{\text{T}}\left(30\right)+{\text{B}}_{\mathrm{iii}}\text{n}\log \text{P}$

where B₀, B₁, B₂, and B_iii are numerical coefficients, which are abiding for a given protein regardless of the solvent nature; northward is the numerical parameter which depends on the size of co-solvent molecules and gives an idea of how many water molecules can be displaced from the protein surface by one molecule of the organic solvent; E_T(30) is the Dimroth-Reichardt parameter, which is directly related to the gratuitous energy of the co-solvent solvation; P, the sectionalization coefficient of the solvent in water/octanol biphasic system, is a measure of its hydrophobicity. The values of E_T(30), P and n for solvents tin exist either constitute or calculated from the data independent in comprehensive handbooks on organic and physical chemistry.

Equation 1 has a real predictive force in stating that co-solvents with loftier values of E_T(30) and logP are strong denaturants. In fact, the solvents that are both hydrophobic and have a high solvation capacity, like ane,iv-dioxane, tetrahydrofuran (THF), and higher alcohols (e.thousand., isomers of butanol) cause enzyme inactivation at concentrations as low as ten-30 vol. %. On the other manus, hydrophilic solvents like glycerol, ethylene glycol, and formamide accept a small denaturing capacity and at concentrations as loftier equally fifty-60 vol. % still do not inactivate many enzymes. Due to this fact, concentrated solutions of these solvents tin be a convenient medium for enzyme reactions in binary mixtures of co-solvents with water. Scaling of co-solvents co-ordinate to their denaturing capacity may have a full general character as its correctness has been proved correct in experiments with 8 proteins in more than 30 solvents [7].

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Drugs used in the treatment of disorders of pancreatic function

David B Church building , in Small-scale Animal Clinical Pharmacology (Second Edition), 2008

Pharmacokinetics

In an attempt to minimize enzyme inactivation during passage through the stomach, a number of preparations are enteric coated. There is some controversy every bit to whether this is an reward in dogs every bit (especially in the untreated exocrine pancreatic insufficiency patient) lack of alkaline-rich pancreatic secretions may event in generally lower pH levels in the duodenum, maintenance of the enteric coating and hence less enzyme availability. Although numerous publications recommend the apply of nonenteric-coated preparations, at that place are few published controlled clinical information to support this hypothesis.

The enzymes are but active as intact molecules and consequently any assimilation or distribution considerations are irrelevant to their therapeutic efficacy.

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Stability and Stabilization of Biocatalysts

Mylène Caussette , ... Brigitte Lindet , in Progress in Biotechnology, 1998

1 INTRODUCTION

Experimental observations in our laboratory accept shown that gas bubbling induced enzyme inactivation (1). The interest of this observation relies on the two following factors. On the one paw, to attain high yields of bioconversion and loftier productivities, information technology is essential to command the parameters acting on enzyme stability. On the other hand, in industrial processes, enzyme inactivation is more often than not required to stop the enzymatic reaction and to forbid product deterioration which can impact the final quality of the product.

Very few works correlate enzyme inactivation and the presence of interfaces. Some studies have focused on enzyme adsorption at solid-liquid interfaces (2-five). At liquid-liquid interfaces, enzyme inactivation has been mainly reported by the Pr. Halling's team (vi-nine). Some works have reported the poly peptide adsorption at static air-water interface (x-16). Enzyme inactivation at this interface has only been reported by few authors (17,18).

This commodity focuses on enzyme inactivation at dynamic gas-liquid interfaces. Inactivation studies take been performed past measuring residual enzymatic action after nitrogen bubbling in an enzyme aqueous solution. Three enzymes have been studied : Lysozyme, Lipase and Pectinmethylesterase.

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Oligomerization in Health and Disease

Doctor. Faiz Ahmad , Chris G. Dealwis , in Progress in Molecular Biology and Translational Science, 2013

ii.6 The X-ray structure of the dATP-induced hexamer of Class 1 RNR

To understand the structural ground of RR1 oligomerization and enzyme inactivation by dATP, we crystallized the ScRR1 hexamer complex. The circuitous crystallized in a hexagonal space group and diffracted to 6  Å. Although the depression-resolution structure does not provide atomic item, it is useful for indicating oligomer organization. To clarify the data, 2 models of ScRR1 hexamer packing were considered. In both models, ScRR1 α₆ is a trimer of dimers, in which the 3 dimers are related to each other past a threefold axis. Nonetheless, the models differ in the diameter of the cardinal pore of the hexamer and in how dATP would mediate hexamerization. In i model, only three of the six dATP-leap ATP-binding cones participate in forming the hexamer interface, the other three free to collaborate with the pocket-sized subunit. Hence, only three dATP molecules are present at the hexamer interface. In the other model, the interfaces that stabilize the hexamer are entirely formed past 6 dATP-leap ATP-binding cones. Furthermore, each of the iii interfaces is formed by two dATP-bound ATP-binding cones from next RR1 dimers that contact each other in an antiparallel conformation and are related by twofold symmetry ²⁹ (Fig. 14.fiveA ).

Effigy 14.5. Subunit oligomerization packing of RR1 based on the low-resolution Ten-ray crystal construction of the ScRR1 hexamer. (A) ScRR1 monomers are colored in cyan and blueish. ATP-binding cones are colored in red. (B) Electron micrograph of the α_{half dozen}–ββ′–dATP holocomplex; image showing the negative stain of holocomplex. Scale bar, 50   nm. Model of the α₆●ββ′●dATP holocomplex based on cryo-EM data.

Reproduced with permission from Ref. 29.

Since the hexamer model was built on the depression-resolution ScRR1 hexamer structure, information technology was pertinent to test the hexamer interfaces of both models biochemically. Hence, site-directed mutagenesis was used to disrupt the hexamer interface predicted past each model. Interestingly, only the D16R mutation, at the N-terminus, disrupts hexamer formation in both hRRM1 and ScRR1. The results of this biochemical study validated only one model—the ane in which all six ATP-binding cones participate in the hexamer interface (Fig. 14.5A).

It was hypothesized that since the D16R mutation abolishes the ability of hRRM1 to form a dATP-induced hexamer, D16R like the earlier reported mutation D57N which abolishes the ability to discriminate between ATP and dATP would forestall the allosteric inhibition of hRRM1 by dATP at physiological concentration. Interestingly, D16R hRRM1 retains the ability to reduce ADP and CDP substrates and, every bit expected, its activity is not inhibited by dATP. Unlike D57N, it is not activated by dATP either, notwithstanding. Furthermore, D16R hRRM1 retains the ability to bind dATP, and so this change is not caused by abolishing dATP binding at the A-site. Since D16R hRRM1 will still demark dATP but does non form hexamers as a effect and is not inhibited by it, this supports the idea that allosteric inhibition of RR by dATP under physiological conditions requires hRRM1 to exist in hexameric class. ²⁹

Our dATP-induced hexamer construction let us examine subunit packing for the first fourth dimension. The cryo-EM structure showed that the dATP holoenzyme has a subunit composition of α₆β₂ (Fig. 14.5B and C). In a similar study, site-directed mutagenesis studies showed that the ATP-induced hexamer adopts an interface different from that of the dATP-induced hexamer. It is quite easy to envisage that in that location must be structural differences between the ATP-induced hexamer and the dATP-induced hexamer for i to act every bit a functional entity and the other to be inactive.

Recently, it has been shown by carefully examining the ATP cone of ATP- and dATP-jump Class I RNR that the largest differences between the two complexes are in the loop region that spans residues 45–52. ⁵² This particular loop is believed to be an important part of the dimer–dimer interface in the eukaryotic hexamer. This observation led to speculation that subtle differences in the conformation of this region upon ATP and dATP binding are responsible for the different oligomeric structures of ATP- versus dATP-leap eukaryotic RR and for the different oligomerization behaviors of eukaryotic and Eastward. coli Class 1RR. ⁵² Rather than form hexamers as in human RR, E. coli RR appears to undergo oligomeric interconversion from α₂β₂ (the active oligomer for E. coli RR) to the ring-shaped α₄β₄ (the inactive oligomer for E. coli RR) under the influence of the allosteric effector. Moreover, this interconversion is linked with singled-out subunit rearrangements upon ATP and dATP binding, which gives further insight into the molecular machinery of the activated and inactivated states. ⁴⁵ Further extending the research on Due east. coli RR band structure, a later on study showed that the clinically canonical anticancer drug gemcitabine when added to a solution of both E. coli RNR subunits induces an unusual structure known as a concatamer, in which 2 α₄β₄ rings interlock to grade a unique (α₄β₄)_ii complex. ⁴⁶ This study exploited a hybrid approach to structural studies by using small-angle X-ray handful (SAXS) and electron microscopy (EM) along with X-ray crystallography to verify the formation of this unique complex. The proposed mechanism for the formation of the concatamer is that α₄β₄ ring formation occurs as described above and the ring afterwards opens to accommodate a second ring and and then recloses. The mechanism past which the concatamer forms was further confirmed past SAXS analysis, additionally demonstrating that the structure was not a crystallography artifact. It is important to mention here that despite the structural similarity between ScRR1 and the E. coli enzyme, East. coli RR does not class a hexamer. The only complexes reported for the Eastward. coli enzyme to this bespeak are α₂β₂, α₄β₄, and (α₄β₄). Information technology is noteworthy that the power to form different ring structures among Class ane RR provides to develop new strategies to inhibit the RRs. ⁴⁶

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Technology Fundamentals of Biotechnology

J. Ge , ... Z. Liu , in Comprehensive Biotechnology (Second Edition), 2011

2.67.5.two Enzyme Stabilization via the Polymer Network

Dissociation of the hydrophobic core is a major reason for enzyme deactivation at high temperatures. Every bit shown in Figure 7 , molecular simulation studies indicated that the presence of the acrylamide network increased the intramolecular hydrogen bonding in the lipase and, thus, contributed to the enhanced thermal stability of the enzyme. The strengthened intramolecular interactions allowed the encapsulated lipase to withstand higher temperatures, particularly afterwards polymerization that resulted in multipoint linkages with the porous acrylamide network. Moreover, calculations of the radial distribution office (RDF) of h2o and organic solvents such as DMSO indicated that the presence of the acrylamide network pushed the solvent molecules away from the surface of the lipase, resulting in enhanced stability of the lipase in the organic solvent, as shown in Figure 8 . Finally, an increase in the acrylamide concentration further reduced the root mean square deviation (RMSD) in the presence of DMSO. These results indicated that the gel thickness tin be tuned to yield an enzyme nanogel of required stability ( Figure 9 ).

Effigy vii. Intramolecular hydrogen bonding within the lipase in the presence of acrylamide.

Reproduced from Ge J, Lu DN, Wang J, et al. (2008) Molecular fundamentals of enzyme nanogels. Journal of Concrete Chemistry B 112: 14319–14324. With permission from American Chemic Guild [eight].

Effigy eight. The RDF of DMSO in a lipase–acrylamide aqueous solution.

Reproduced from Ge J, Lu DN, Wang J, and Liu Z (2009) Lipase nanogel catalyzed transesterification in anhydrous dimethyl sulfoxide. Biomacromolecules x: 1612–1618. With permission from American Chemic Club [ten].

Figure ix. The RMSD of the lipase in DMSO in the presence of acrylamide.

Reproduced from Ge J, Lu DN, Wang J, and Liu Z (2009) Lipase nanogel catalyzed transesterification in anhydrous dimethyl sulfoxide. Biomacromolecules ten: 1612–1618. With permission from American Chemic Society [ten].

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BROWNING | Enzymatic – Technical Aspects and Assays

J. Nicolas , ... J. Philippon (Retired) , in Encyclopedia of Food Sciences and Nutrition (2nd Edition), 2003

Heat

Rut treatment, or blanching, without doubt constitutes the simplest and near direct method of enzyme inactivation. It consists of brief immersion (from 1 to 6  min depending on size) of the product in h2o, humid syrup, or steam shut to 100   °C.

Catechol oxidases are inhibited higher up approximately 70   °C. Their heat stability is closely pH-dependent; information technology is maximal at almost pH half-dozen and decreases very speedily beneath and above this value.

In the deep-freezing of foodstuffs, blanching is principally applied to vegetables that are eaten cooked (potatoes, salsify, asparagus, etc.), but it is also selected to stabilize frozen fruit purées, particularly of apricots. Blanching is little used with whole or sliced frozen fruits that are eaten raw, since information technology results in loss of firmness and in flavor changes which are unacceptable to the consumer. This is why blanching is merely used for fruit with tissue sufficiently impermeable to oxygen, to escape deep browning. Examples are apricot and peach, for which the brief surface handling scarcely alters the organoleptic qualities. When blanching of pears and, particularly, apples (20–25% lacunae) is incomplete, marked deep browning occurs on thawing.

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Methods in Neurotransmitter and Neuropeptide Research, Part ane

Yuji Maruyama , ... W.B. Stavinoha , in Techniques in the Behavioral and Neural Sciences, 1993

Publisher Summary

This chapter describes recent progress in microwave musical instrument development. It discusses the current status of rapid enzyme inactivation through the utilise of microwave irradiation. It describes a commercial musical instrument that was developed for applying the magnetic field (H-field) with a tuning organisation. It is a microwave device with a 10 kW input operating at a frequency of 2450 MHz. To obtain a qualitative evaluation of microwave free energy distribution, succinic dehydrogenase activity was examined following microwave irradiation (MWR). Rats were killed by MWR at 9.0 kW for 0.4 or 0.8 s. Rats killed by decapitation served equally the control for enzyme activity. The brains were then removed from the skull and frozen in an acetone/dry-water ice mixture. Cholinesterase activeness in the rat brain was determined post-obit microwave heating to confirm the critical temperature for destroying the enzyme. Post-obit MWR, the temperature of the encephalon was measured with a needle containing a thermocouple in the tip. To elucidate the effects of MWR on rapid inactivation of enzymes, in vivo encephalon concentrations of regional substances with high turnover rates were determined after decease past decapitation and MWR.

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Stability and Stabilization of Biocatalysts

A. Illanes , ... A. Aillapán , in Progress in Biotechnology, 1998

two.i Enzyme inactivation

Enzyme thermal inactivation can exist conveniently modeled based on a serial type mechanism [v] . Reaction kinetics and enzyme inactivation for CIL co-ordinate to a ii-stage series machinery can be represented past the post-obit scheme:

Considering a final inactive stage, the following expression is obtained:

(one) ${}_{{\text{e}}_0}^{\text{e}}=\left[1+\text{A}\cdot \begin{array}{l}\hfill {\text{k}}_1\hfill \\ \hfill {\text{k}}_2-{\text{k}}_1\hfill \end{array}\right]\cdot \text{exp}\left(-{\text{k}}_1\cdot \text{t}\right)-\left[\text{A}\cdot \begin{array}{l}\hfill {\text{thousand}}_1\hfill \\ \hfill {\text{k}}_2-{\text{k}}_1\hfill \end{array}\right]\cdot \text{exp}\left(-{\text{m}}_{\mathrm{ii}}\cdot \text{t}\right)$

Based on the modulation hypothesis, different first-order transition rate constants will exist for each enzyme species (free enzyme E, and secondary complexes ES and EP, equation (one) existence applicable to any of them, with:

(2) ${\text{k}}_{\text{i}\text{J}}={\text{k}}_{\text{i}}\left(\mathrm{ane}-{\text{northward}}_{\text{i}\text{J}}\right)$

where subscript i refers to the inactivation stage, subscript J denotes the modulator and n_iJ are modulation factors.

In addition, the rate equation for lactose hydrolysis with CIL is [four]:

(3) $\text{σ}\left(\text{X}\right)=\begin{array}{l}\hfill \text{five}\left(\text{Ten}\right)\hfill \\ \hfill {\text{yard}}_{\text{cat}}\cdot \text{e}\hfill \end{array}=\begin{array}{l}\hfill \left(1-\text{X}\right)\hfill \\ \hfill \left[\begin{array}{ll}\hfill \begin{array}{l}\hfill {\text{One thousand}}_{\text{thousand}}\hfill \\ \hfill {\text{Grand}}_{\text{P}}\hfill \end{array}\hfill & \hfill -1\hfill \end{array}\right]\text{X}+\left[\begin{array}{l}\hfill {\text{K}}_{\text{m}}\hfill \\ \hfill {\text{southward}}_0\hfill \end{array}\right]+\mathrm{one}\hfill \end{array}$

From a material remainder of all enzyme species, considering the proposed 2-stage series mechanism, and the rate equation for lactose hydrolysis, enzyme inactivation under reactive conditions volition be described by:

(4) $\begin{array}{ll}-\begin{array}{l}\text{de}\hfill \\ \text{dt}\hfill \end{array}\hfill & =\text{e}\cdot {\text{thousand}}_1\cdot [\begin{array}{l}\hfill \left(1-\text{A}\right)\cdot \text{exp}\left(-{\text{k}}_1\cdot \text{t}\right)\cdot \left[1-\text{σ}\left(\text{10}\right)\cdot {\text{N}}_1\left(\text{X}\right)\right]\hfill \\ \hfill \text{exp}\left(-{\text{g}}_{\mathrm{ane}}\cdot \text{t}\right)+\left({\text{k}}_1\cdot \text{A}.\left({\text{k}}_2-{\text{k}}_1\right)\right)\cdot \left[\text{exp}\left(-{\text{k}}_{\mathrm{one}}\cdot \text{t}\right)-\text{exp}\left(-{\text{one thousand}}_2\cdot \text{t}\right)\right]\hfill \end{array}+\hfill \\ \hfill & +\begin{array}{l}\hfill \text{A}\cdot {\text{k}}_2\cdot \left[\text{exp}\left(-{\text{g}}_{\mathrm{ane}}\cdot \text{t}\right)-\text{exp}\left(-{\text{k}}_{\mathrm{ii}}\cdot \text{t}\right)\right]\cdot \left[1-\text{σ}\left(\text{Ten}\right)\cdot {\text{N}}_{\mathrm{two}}\left(\text{X}\right)\right]\hfill \\ \hfill \left({\text{g}}_{\mathrm{two}}-{\text{m}}_1\right)\text{exp}\left(-{\text{g}}_1\cdot \text{t}\right)+{\text{k}}_1\cdot \text{A}\cdot \left[\text{exp}\left(-{\text{chiliad}}_1\cdot \text{t}\right)-\text{exp}\left(-{\text{g}}_{\mathrm{two}}\cdot \text{t}\right)\right]\hfill \end{array}]\hfill \end{array}$

where:

${\text{N}}_1\left(\text{X}\right)={\text{due north}}_{1\text{S}}+{\text{due north}}_{\mathrm{one}\text{P}}\cdot {\text{M}}_{\text{1000}}\cdot \text{X}/\left[{\text{K}}_{\text{P}}\left(1-\text{10}\right)\right];{\text{N}}_2\left(\text{X}\right)={\text{northward}}_{2\text{S}}+{\text{due north}}_{2\text{P}}\cdot {\text{K}}_{\text{m}}\cdot \text{X}/\left[{\text{Chiliad}}_{\text{P}}\left(\mathrm{i}-\text{X}\right)\right]$

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