Biochemical reactions equations

In writing chemical equations and biochemical equations it is important to be careful with names of reactants. Chemical reactions are written in terms of species. In chemical reaction equations, atoms of all elements and electric charges must balance. Biochemical reaction equations are written in terms of reactants, that is in terms of sums of species, H+ is not included as a reactant and electric charges are not shown or balanced. In biochemical reaction equations, atoms of all elements other than hydrogen must balance. The names of the reactants that must be used in making calculations with this data base are given later. 

A is the apparent conservation matrix, and y is the stoichiometric number matrix for the biochemical reaction system. This equation makes it possible to calculate a basis for the stoichiometric number matrix from the apparent conservation matrix by use of NullSpace. A has the dimensions C xA where C is the apparent number of components (C - 1) and N is the number of reactants (sums of species), y has the dimensions N R Note that N = C + R where R is the number of independent biochemical reactions. Equation 7.2-5 makes it possible to obtain a basis for the apparent stoichiometric number matrix by use of NullSpace. 

The form in which acetate is used in most of its important biochemical reactions is acetyl coenzyme A (Figure 26 la) Acetyl coenzyme A is a thwester (Section 20 13) Its for matron from pyruvate involves several steps and is summarized m the overall equation... 

Enzymatic reactions frequently undergo a phenomenon referred to as substrate inhibition. Here, the reaction rate reaches a maximum and subsequently falls as shown in Eigure 11-lb. Enzymatic reactions can also exhibit substrate activation as depicted by the sigmoidal type rate dependence in Eigure 11-lc. Biochemical reactions are limited by mass transfer where a substrate has to cross cell walls. Enzymatic reactions that depend on temperature are modeled with the Arrhenius equation. Most enzymes deactivate rapidly at temperatures of 50°C-100°C, and deactivation is an irreversible process. 

Each of the processes shown in Figure 2.8 can be described by a Michaelis-Menten type of biochemical reaction, a standard generalized mathematical equation describing the interaction of a substrate with an enzyme. Michaelis and Men ten realized in 1913 that the kinetics of enzyme reactions differed from the kinetics of conventional... 

Generally, in an equation of a chemical reaction rate, the rate constant often does not change with temperature. There are many biochemical reactions that may be influenced by temperature and the rate constant depends on temperature as well. The effect of temperature on... 

Although the importance of a systemic perspective on metabolism has only recently attained widespread attention, a formal frameworks for systemic analysis has already been developed since the late 1960s. Biochemical Systems Theory (BST), put forward by Savageau and others [142, 144 147], seeks to provide a unified framework for the analysis of cellular reaction networks. Predating Metabolic Control Analysis, BST emphasizes three main aspects in the analysis of metabolism [319] (i) the importance of the interconnections, rather than the components, for cellular function (ii) the nonlinearity of biochemical rate equations (iii) the need for a unified mathematical treatment. Similar to MCA, the achievements associated with BST would warrant a more elaborate treatment, here we will focus on BST solely as a tool for the approximation and numerical simulation of complex biochemical reaction networks. 

The approximation of biochemical rate equations by linear-logarithmic (lin-log) equations [318] seeks to avoid several drawbacks of the power-law formalism. Using the lin-log framework, all reaction rates are described by their dependencies on logarithmic concentrations, based on deviations from a... 

Biochemical reactions are interesting but they are not magic . Individual chemical reactions that comprise a metabolic pathway obey, obviously, the rules of organic chemistry. All too often students make fundamental errors such as showing carbon with a valency of 3 or 5, or failing properly to balance an equation when writing reactions. Furthermore, overall chemical conversions occur in relatively small steps, that is there are usually only small structural changes or differences between consecutive compounds in a pathway. 

Biochemical reactions are basically the same as other chemical organic reactions with their thermodynamic and mechanistic characteristics, but they have the enzyme stage. Laws of thermodynamics, standard energy status and standard free energy change, reduction-oxidation (redox) and electrochemical potential equations are applicable to these reactions. Enzymes catalyse reactions and induce them to be much faster . Enzymes are classified by international... 

During fermentation, the enhanced absorption rate of oxygen increases the bulk concentration and, as a consequence, the production rate of cells can be increased as well. To predict this effect, the enhanced transfer rate has to be incorporated into the differential mass balance equations of fermentation processes studied. If you know the mathematical expression of the biochemical reactions and their dependence on oxygen concentration as well as the enhanced absorption rates due to the dispersed organic phase,you can calculate the fermentation exactly after solving the equation system obtained. 

The rates of chemical and biochemical reactions usually increase with temperature. The dependence of the reaction rate on temperature can usually be represented by the following Arrhenius-type equation over a wide temperature range ... 

Perhaps most interesting are endothermic reactions that result in products of less entropy (Case IV). What is notable about these reactions is that they will not occur on their own without the continued input of energy. Also, the products of these reactions can be complex molecules. The classic example is photosynthesis, which is the biochemical reaction by which plants use solar energy to create carbohydrates and oxygen from carbon dioxide and water, as represented by the following equation ... 

Illustrate, using structural equations, the chemical mechanisms of the following biochemical reactions. 

Spectrophotometry is one of the best methods available for measuring the rates of biochemical reactions. Consider a general reaction as shown in Equation 5.5. 

A further important type of reaction (equations 3 and 4) corresponds to the intramolecular redox process. The formation of (S2)2 can formally occur via the intramolecular reaction of (S°) (produced according to equation 3) with S2-. This type of reaction is of decisive importance for molybdenum-sulfur chemistry (and probably in various catalytic and biochemical problems as well). 

Why can we equate internal energy and enthalpy for most biochemical reactions ... 

Limited pH changes may occur if water electrolysis reactions (Equations 3 and 4) occur at the same rate and efficiency. In a completely mixed reactor, the proton produced at the anode should neutralize the hydroxyl ion produced at the cathode. However, the results indicated that the pH decreased to less than 5.5 even under completely mixed conditions in fed-batch reactors. The pH drop indicate less hydroxyl production at the cathode, either because different electrolysis reactions occurred (other than Equation 4) or because of biochemical reactions in the reactor. The type and concentrations of ions in the solution will impact the pH changes and require further investigation. Sodium bicarbonate was used and was effective in buffering the system for the range of electric field strengths studied. 

This is referred to as the extended Debye-Huckel equation. It is an approximation that gives a good fit of data at low ionic strengths (Goldberg and Tewari, 1991) when B= 1.6 L1/2 mol 1/2. Better fits can be obtained with more complicated equations with more parameters, but these parameters are not known for solutions involved in studying biochemical reactions. The way that thermodynamic properties vary with the ionic strength is discussed in more detail in Section 3.6. 

The equations and calculations described in this chapter are very useful, but so far we have not discussed thermodynamic properties other than equilibrium constants. The other properties introduced in the next three chapters provide a better understanding of the energetics and equilibria of reactions. We will consider the basic structure of thermodynamics in Chapter 2 and then to apply these ideas to chemical reactions in Chapter 3 and biochemical reactions in Chapter 4. 

Fundamental Equation for a Biochemical Reaction System at Specified pH... 

When the pH is specified, we enter into a whole new world of thermodynamics because there is a complete set of new thermodynamic properties, called transformed properties, new fundamental equations, new Maxwell equations, new Gibbs-Helmholtz equations, and a new Gibbs-Duhem equation. These new equations are similar to those in chemical thermodynamics, which were discussed in the preceding chapter, but they deal with properties of reactants (sums of species) rather than species. The fundamental equations for transformed thermodynamic potentials include additional terms for hydrogen ions, and perhaps metal ions. The transformed thermodynamic properties of reactants in biochemical reactions are connected with the thermodynamic properties of species in chemical reactions by equations given here. 

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