Cells often transfer electrons between reactions using small organic redox coenzymes rather than transferring free electrons directly through water.

Three major carrier systems are

$$\mathrm{NAD^+/NADH},$$

$$\mathrm{NADP^+/NADPH},$$

and

$$\mathrm{FAD/FADH_2}.$$

Each pair has an oxidized form and a reduced form that can be interconverted reversibly.

NAD carries a two-electron reducing equivalent

Nicotinamide adenine dinucleotide (NAD) contains a nicotinamide group that can accept a hydride equivalent, corresponding to two electrons and one proton:

$$\mathrm{NAD^+ +2e^-+H^+\rightleftharpoons NADH}.$$

In biochemical shorthand, oxidation of a substrate is often written

$$\mathrm{substrate_{red}+NAD^+\rightarrow substrate_{ox}+NADH+H^+}.$$

The substrate loses reducing equivalents and is oxidized; NAD$^+$ accepts them and is reduced. The reverse process oxidizes NADH back to NAD$^+$ and transfers its reducing power elsewhere.

NADP uses the same redox chemistry in a distinguishable carrier pool

NADP$^+$ is closely related to NAD$^+$ but contains an additional phosphate group outside the nicotinamide redox center. Its reduction is analogous:

$$\mathrm{NADP^+ +2e^-+H^+\rightleftharpoons NADPH}.$$

The extra phosphate does not supply the transferred electrons. Instead, it lets enzymes distinguish the NAD/NADH and NADP/NADPH pools.

Cells commonly use NAD$^+$/NADH strongly in pathways that oxidize fuels, while NADPH commonly supplies reducing power for biosynthesis and other reductive processes. These are tendencies of metabolic organization, not different definitions of oxidation and reduction.

FAD can accept two electrons and two protons

Flavin adenine dinucleotide (FAD) is another redox coenzyme. Its common two-electron reduction is summarized as

$$\mathrm{FAD+2e^-+2H^+\rightleftharpoons FADH_2}.$$

FAD is often held tightly by an enzyme as a bound cofactor, allowing flavin redox chemistry to operate as part of that enzyme's catalytic mechanism.

Oxidized versus reduced carrier state

The notation encodes redox state:

NAD+    → NADH    reduction
NADP+   → NADPH   reduction
FAD     → FADH2   reduction

A reduced carrier is not itself ATP. It stores reducing power: electrons that can later be transferred through another redox process.

Carrier recycling is essential

A finite carrier pool cannot support continuous oxidation if every oxidized molecule becomes reduced and remains that way. For example, a pathway using NAD$^+$ requires eventual regeneration of NAD$^+$ from NADH.

Conversely, a pathway that repeatedly consumes NADPH requires some process that reduces NADP$^+$ again.

The general cycle is

one reaction reduces the carrier
        ↓
carrier transports reducing equivalents
        ↓
another reaction oxidizes the carrier
        ↓
carrier is available for reuse

NAD, NADP and FAD therefore connect otherwise separate reactions into larger redox networks by transporting reducing equivalents between them.