12.1: Biochemical Reactions and Energy Changes

Search Fundamentals of Biochemistry

Learning Goals (ChatGPT o3-mini)

(Learning goals written by Claude, Sonnet 4.6, Anthropic)

Thermodynamics and Kinetics of Enzyme Catalysis

• Explain how breaking a C–X bond generates carbocation, carbanion, or free radical intermediates, and describe why each is inherently unstable.
• Interpret free energy diagrams for uncatalyzed and enzyme-catalyzed reactions, distinguishing between thermodynamic (ΔG) and kinetic (activation energy) parameters and explaining how enzymes lower activation energies without altering the energies of free reactants or products.
• Use resonance and inductive effects to predict the relative stability of reactants, intermediates, and products in structurally similar molecules.

Oxidation and Carbonyl Reactivity

• Determine whether a carbon atom has been oxidized or reduced by tracking changes in bonds to electronegative atoms or by calculating formal oxidation numbers.
• Predict the products of nucleophilic addition to aldehydes and ketones (hydration, hemiacetal/acetal formation, and imine/Schiff base formation) and explain how acid or base catalysis facilitates each pathway.
• Rank carboxylic acid derivatives by their reactivity toward nucleophilic substitution using resonance stabilization of the carbonyl carbon and leaving group stability as criteria.

Carbon–Carbon Bond Formation and Cleavage

• Describe how the carbonyl carbon functions as an electrophile and how the alpha-carbon carbanion (enolate) functions as a nucleophile in aldol and Claisen condensation reactions.
• Explain why decarboxylation of β-keto acids is mechanistically favorable while analogous cleavage of α-keto acids is not, citing electron flow to an appropriate sink.

Introduction

We have already discussed How Enzymes Work and Enzymatic Reaction Mechanisms in great detail in Chapter 6. Here, we will focus on a lighter, less granular review of key reaction mechanisms and the changes in Gibbs' free energy associated with them, both in uncatalyzed and enzyme-catalyzed reactions. Consider it a simple review of basic organic reactions and thermodynamics in preparation for the comprehensive focus on reaction mechanisms in Unit 2: Bioenergetics and Metabolism.

Breaking C-X bonds

Organic reactions involve the formation and breaking of carbon-carbon bonds. There are three ways to break a bond to a C-X bond, producing either a carbocation, carbanion, or free radical intermediate, all unstable and reactive, as illustrated in Figure \(\PageIndex{1}\). Both the carbocation and the free radical are electron-deficient, and the carbanion, although not electron-deficient, carries a negative charge on C, an atom with relatively low electronegativity.

Figure \(\PageIndex{1}\): Ways to break a C-X bond

These unstable intermediates are higher in energy than the reactants. Hence, the transition state, which is even higher in energy than the intermediates, must have a structure that resembles the intermediates more than the reactants, as shown in Figure \(\PageIndex{2}\). The charged carbanion and carbocation intermediates have a developing charge in the transition state.

Figure \(\PageIndex{2}\): Gibbs' free energy of reactants, transition state, and intermediate in breaking a bond.

The thermodynamics of the reactions is determined by the change in free energy between the intermediates and the reactants. In contrast, the kinetics of the reaction is determined by the difference in free energy between the transition states and the reactants, as shown in Figure \(\PageIndex{3}\). A catalyst lowers the energy of the transition state without affecting the energies of the reactants or intermediates (assuming that these are free and not bound to the catalyst.

Figure \(\PageIndex{3}\): Activation energy and ΔG for a simple uncatalyzed and catalyzed reaction

The free energy diagram shown in Figure 3 is very simplistic. We need a diagram that better fits an enzyme-catalyzed reaction using the simple reaction equation below.

E + S ↔ ES → EP ↔ E + P

A free energy diagram for the binding of E and S followed by the conversion of bound S to bound and then the free product is shown in Figure \(\PageIndex{4}\).

Figure \(\PageIndex{4}\): Simple free energy curve for the enzyme-catalyzed substrate conversion to product. https://commons.wikimedia.org/wiki/F...y_levels_2.svg

Even this diagram is overly simplified, since it suggests that the bound substrate in the ES complex is converted to the bound product in a single step, with no intermediates.

The free energy diagram should include intermediates along the reaction pathway. An example of this is shown in Figure \(\PageIndex{5}\) for the reversible conversion of a 3-carbon sugar, dihydroxyacetone phosphate (DHAP), to another 3-carbon sugar, glyceraldehyde-3-phosphate, in a reaction catalyzed by the enzyme triose phosphate isomerase (we will study the enzyme in the next chapter).

Figure \(\PageIndex{5}\): Complete free energy profile for all the elementary steps of the triosephosphate isomerase-catalyzed reaction. Aqvist J, Fothergill M. Computer simulation of the triosephosphate isomerase-catalyzed reaction. J Biol Chem. 1996 Apr 26;271(17):10010-6. doi: 10.1074/jbc.271.17.10010. PMID: 8626554. Creative Commons Attribution (CC BY 4.0)

Note that the enzyme lowers the activation energy of each step in the overall reaction. Enzymes can also catalyze reactions by altering the reaction pathway, though in this case all intermediates in the conversion are the same in both the uncatalyzed and catalyzed pathways.

A comparison of the thermodynamic reactivity of molecules of similar structures can be made by determining the relative stability of the reactants and products from structural considerations. Consider two reactants, R₁ and R₂, which produce products P₁ and P₂, respectively. Any structural features that preferentially stabilize R2 compared to R1 or P2 compared to P1 but don't stabilize R2 and P2 to the same extent will lead to a greater driving force for R2 → P2 compared to R1. This is shown graphically in Figure \(\PageIndex{6}\):

Figure \(\PageIndex{6}\): Free energy reaction diagrams for two similar molecules

Mechanisms that stabilize a reactant, intermediate, or product include resonance and inductive effects (electron release or withdrawal).

An example of how the comparative acidity of two similar molecules can be determined by comparing their structures is shown below for acetic acid and ethanol in Figure \(\PageIndex{7}\).

Figure \(\PageIndex{7}\): Comparative acidity of two similar molecules

The stronger acid, acetic acid, has the more stable (and hence less basic) charged product (the conjugate base)

An example of how an intermediate can be stabilized through resonance is shown in Figure \(\PageIndex{8}\) for the keto-enol tautomerization reaction, which is favored in the direction of the keto form, a weaker acid than the enol.

Figure \(\PageIndex{8}\): Comparative stability of keto and enol intermediates

An example of how the inductive effect (electron release and withdrawal) stabilizes/destabilizes carbocations and cations is shown in Figure \(\PageIndex{8}\).

Figure \(\PageIndex{8}\): Factors contributing to stabilization of carbocations and carbanions

Also, remember that electron-withdrawing by the F's in the negatively charged conjugate base of trifluoracetic acid helps explain its lower pKa than acetic acid.

Lastly, consider how stabilizing a tertiary carbocation below helps explain the preferential formation of the tertiary alcohol over the secondary alcohol, as shown in Figure \(\PageIndex{9}\).

Figure \(\PageIndex{9}\): Preferential formation of tertiary alcohol

Oxidation of Organic Molecules

Organic molecules are usually oxidized in two-electron steps. Two methods can be used to determine if a C atom in an organic molecule has been oxidized.

• C is oxidized if the number of bonds from C to oxygen increases or the number of bonds to H decreases. More generally, if the number of bonds from C to a more electronegative atom increases or the number of bonds from C to a less electronegative atom decreases, the carbon is oxidized.
• A more robust method involves determining the oxidation number of the carbon atoms in the reactant and product. If the oxidation number becomes more positive, the C is oxidized.

The general rules for determining the oxidation numbers of the atoms in a molecule are:

1. O is generally 2-
2. H is usually 1+
3. in molecules consisting of one type of atom (like O₂) - i.e., a polyatomic element, the atoms have an oxidation number of 0.
4. the sum of the oxidation numbers of the atoms in a molecule equals the net charge on the molecule or ion.

In general, the oxidation number can be calculated as follows:

1. assign all nonbonded electrons of an atom to that atom
2. assign all bonded electrons to the more electronegative atom of the two atoms bonded
3. assign one electron of a bond to each atom if the two are identical.
4. sum up the assigned electrons from 1-3. Subtract this number from the total number of electrons in the atom's outer shell (the group number). The result is the oxidation number.

An illustration of the sequential two-step oxidation of ethane to acetic acid and assigned oxidation numbers is shown in Figure \(\PageIndex{10}\). Focus on the C with red bonds. One electron is assigned to the C for the non-bolded red bond and 2 for the bolded red bond.  Remember that C has a higher electronegativity than H, so we assign both electrons in a C-H bond to C to determine C's oxidation number. Each carbon in a C-C bond shares one electron from the bond, since they have the same electronegativity.

Figure \(\PageIndex{10}\): Change in oxidation number on the stepwise conversion of ethane to acetic acid

Note that the red carbon connected to the NH₂ in ethylamine has the same oxidation state as the red carbon in ethanol. Hence, the conversion of ethane to ethylamine is an oxidation reaction that requires an oxidizing agent.

Reactions of Carbonyls: Aldehydes and Ketones

When water reacts with an aldehyde in a nucleophilic addition reaction, a 1,1-diol or a geminal diol results. This reaction can be catalyzed by a base, which acts as the nucleophile (it's a stronger nucleophile than water) and adds to the carbonyl C. OH- is regenerated when the alkoxide produced abstracts a proton from water, regenerating OH-.

When an alcohol adds to an aldehyde or ketone, a hemiacetal or hemiketal, respectively, is formed. In the presence of an acid catalyst, the acid protonates the carbonyl oxygen, making the carbonyl more electrophilic. After the alcohol adds to form a hemiacetal or hemiketal, the acid can protonate the OH group, leading to its expulsion as water in an acid-catalyzed elimination. The carbocation or resonant-form oxonium ion can react with another ROH to form an acetal or ketal. These steps are summarized in Figure \(\PageIndex{11}\).

Figure \(\PageIndex{11}\): Nucleophilic addition to an aldehyde

If the nucleophile is an amine, an addition can occur, followed by an elimination to form an imine or Schiff base, as shown in Figure \(\PageIndex{12}\).

Figure \(\PageIndex{12}\): Schiff base formation

An acetal or ketal is a geminal ether (as water addition to aldehydes or ketones produces geminal diols). As with other ethers, these geminal ethers are stable to bases and are often used as protecting groups to prevent undesired reactions of aldehydes and ketones in basic solution. Acetal formation is favored by excess anhydrous alcohol in acetic conditions, while high water concentrations and an acid catalyst accelerate acetal breakdown.

Why are ethers and, hence, acetals/ketals resistant to bases? They resist nucleophilic attack, such as by base, since the expelled group (alkoxide) is unstable. (Epoxides, in contrast, will react with OH- nucleophiles since the epoxide ring is strained and of high energy.). Ethers can react with acids, which protonate the ether O to form an oxonium ion. Nucleophilic attack (such as by Br-) on an adjacent C can occur (S_N2), with electrons flowing to the protonated oxonium ion (a great electron sink) as it departs.

Reactions of Carboxylic Acid Derivatives

Carboxylic acid derivatives undergo nucleophilic substitution reactions.  They have better leaving groups than aldehydes and ketones (which undergo addition reactions). With the substitution reaction, the carbonyl's double bond stability is retained. Two things control the reactivity of these derivatives: the stability of the reactants compared to the products. Figure \(\PageIndex{13}\) shows the relative reactivity of carboxylic acid derivatives.

Figure \(\PageIndex{13}\): Relative reactivity of carboxylic acid derivatives

A reactant is less reactive if stabilized by resonance. Hence, the relative reactivity is amide < ester < anhydride < acid chloride.

The nonbonded electron pair on N of the amide, a less electronegative atom than O, can delocalize and form a resonant structure with a double bond between the N and carbonyl C more readily than the O in the ester. An electron pair on the bridging O in the anhydride could delocalize and split between the two carbonyls C (called competing resonances). This process is less stable than with the other carboxylic acid derivatives.  The reactant least stabilized by resonance is the acid chloride, since a nonbonded pair of electrons on the larger chlorine molecule can't delocalize as readily, given the C-Cl bond distance.

Notice that this order of decreasing stability based on resonance stabilization is also the order of increasing electrophilicity of the carbonyl C (which is most electrophilic in the absence of electron delocalization from the adjacent N, O, or Cl).

Product stability is also important. If the deprotonated leaving group is considered one of the products (which distinguishes the reactions), then the order of decreasing stability of the products is Cl^- > RCOO^- > RO^- > RHN^-.  This is shown in Figure \(\PageIndex{14}\). (Note: the pKa of ROH = 16 and R₂NH = 40)

Figure \(\PageIndex{14}\): Relative stability of carboxylic acid derivative leaving groups

What determines the stability of products relative to reactants is the strength of the bonds formed and broken during the reaction.

In nucleophilic addition to aldehydes and ketones, the strength of the bond to the nucleophile must be greater than the strength of the pi bond broken in the carbonyl. A C-Cl bond strength is 81 kcal/mol (340 kJ/mol) compared to a pi C-O bond strength of 93 kcal/mol (389 kJ/mol). Hence, a Cl- is not likely to add to a carbonyl C. Consider the hydration of formaldehyde (carbonyl with 2 H's), acetaldehyde (with 1 H and 1 methyl group, and acetone (with 2 methyl groups). The ΔG^o for hydration of these is -19, -1, and +15 kcal/mol (63 kJ/mol), respectively, showing that increased electron release toward the carbonyl C, which makes it less electrophilic and more stable, decreases the carbonyl's reactivity.

In nucleophilic substitution, the leaving group (anion) must be more stable than the nucleophile.

Kinetics of Reactivity of Carbonyls

The relative kinetic reactivity of various carbonyls toward nucleophiles follows the order of electrophilicity of the C. (i.e, the extent of the positive charge on the carbonyl C.) The slow step in a nucleophilic attack is breaking the pi-carbonyl bond. If the reactant is stabilized by resonance in ways that reduce the electrophilicity of the carbonyl C, the reaction is slowed.

Nucleophilicity is a measure of the "affinity" of an atom or ion for an electrophilic C with a nucleophilic lone pair. This is similar to basicity, which is a measure of the "affinity" of an atom or ion for a proton. Halides are not good nucleophiles for reactions with acid derivatives since the halide (like Cl-) is a better leaving group than the actual leaving group.

Making C-C Bonds

Metabolism can be divided into catabolic (breaking down) and anabolic (synthetic) reactions. To obtain energy, sugars and fatty acids are converted to carbon dioxide. Hence, C-C bonds must be broken. In contrast, C-C bonds must be synthesized in photosynthesis. In all reactions, electrons from broken bonds flow to atoms where bonds will be made. Flow is from a source (a pair of electrons possibly with a negative charge) to a sink (a slightly or fully positive atom). Figure \(\PageIndex{15}\) shows a couple of ways to make a C-C bond using either the reaction of two carbon-centered radicals (free radical mechanisms are uncommon biologically) or a carbocation with a carbanion.

Figure \(\PageIndex{15}\): Making C-C bonds

A carbocation is unstable unless incorporated into a molecule in which it is stable, so instead of using them, the carbonyl C is used as the electrophilic carbon. (Instability of carbocations is reflected in their propensity to rearrange.) Taking into account the resonance form of the C=O carbonyl bond with a positive charge on C and a negative charge on O, the net charge on the carbonyl is about +0.5. A carbanion, often stabilized as an enolate, is a negatively charged carbon. These features are illustrated in Figure \(\PageIndex{16}\).

Figure \(\PageIndex{16}\): Carbonyl carbons as electrophiles and carbanions as nucleophiles

One method of making a C-C bond is an aldol condensation, in which a carbanion formed by the deprotonation of a C-H alpha to a carbonyl (which is stabilized by the enolate resonance form) acts as a nucleophile that adds to a carbonyl C in an aldehyde or ketone. The reaction is illustrated in Figure \(\PageIndex{17}\).

Figure \(\PageIndex{17}\): Aldol condensation

In another C-C bond synthesis reaction, a Claisen Condensation, a carbanion formed by the deprotonation of a C-H alpha to a carbonyl (which is stabilized by the enolate resonance form) acts as a nucleophile that substitutes at a carbonyl C in a carboxylic ester or thioester. This is illustrated in Figure \(\PageIndex{18}\).

Figure \(\PageIndex{18}\): Claisen condensation

Breaking C-C Bonds

In addition to a retroaldol condensation, a common method to break a C-C bond is through a decarboxylation reaction at a beta-keto acid. Notice in Figure \(\PageIndex{19}\) that the analogous reaction at an alpha-keto acid is unlikely since the electrons from the C-C bond that is cleaved have no "sink" to which to flow.

Figure \(\PageIndex{19}\) C-C bond cleavage by decarboxylation of beta-keto acids.

Alpha-keto acids can be decarboxylated using thiamine cofactors, as discussed in Chapter 6.

Summary

(Summary written by Claude, Sonnet 4.6, Anthropic)

This chapter provides a mechanistic foundation for the metabolism chapters that follow, reviewing core principles of organic reactivity and thermodynamics as they apply to biochemical systems.

Breaking a bond between carbon and a heteroatom produces one of three unstable intermediates — carbocations, carbanions, or free radicals — each higher in energy than the starting material. Because transition states are even higher in energy and structurally resemble these intermediates, factors that stabilize an intermediate also lower the activation energy for its formation. Enzymes exploit this principle by selectively stabilizing transition states, thereby lowering the activation energies for every elementary step along a reaction pathway without altering the reaction's overall thermodynamics (ΔG). Free energy diagrams for enzyme-catalyzed reactions, such as the triose phosphate isomerase reaction, illustrate this multi-step reality clearly.

Resonance delocalization and inductive effects are the primary structural features governing relative stability. Comparing acetic acid and ethanol illustrates how resonance stabilization of the conjugate base explains differences in acidity, while the keto–enol tautomerization example shows how resonance favors the keto form. Electron-withdrawing or electron-releasing groups similarly modulate carbocation and carbanion stability, with real consequences for reaction outcomes such as preferential tertiary alcohol formation via a more stable tertiary carbocation.

Carbon oxidation state is tracked either by monitoring changes in bonds to more or less electronegative atoms or by calculating the formal oxidation number. Organic molecules are typically oxidized in two-electron steps, as illustrated by the stepwise conversion of ethane to acetic acid.

Carbonyl compounds are central to biochemical reactivity. Aldehydes and ketones undergo nucleophilic addition — with water, alcohols, or amines — yielding geminal diols, hemiacetals/acetals, or imines (Schiff bases). Acetals are stable to base but susceptible to acid, making them useful as protecting groups. Carboxylic acid derivatives instead undergo nucleophilic substitution, and their reactivity follows the order acid chloride > anhydride > ester > amide, reflecting the degree to which resonance donation from nitrogen or oxygen reduces electrophilicity at the carbonyl carbon.

Carbon–carbon bond formation relies on pairing an electrophilic carbonyl carbon with a nucleophilic enolate carbanion. Aldol condensation achieves this through addition, while Claisen condensation proceeds through substitution at a thioester or ester. The reverse — C–C bond cleavage — occurs efficiently at β-keto acids via decarboxylation because the electrons from the broken bond are captured by the adjacent carbonyl as an electron sink. The analogous reaction at α-keto acids is disfavored for lack of such a sink, requiring instead the specialized thiamine cofactor mechanism discussed in Chapter 6.