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Tunneling occurs when a molecule penetrates through a potential energy barrier rather than over it. Although not allowed by the laws of classical dynamics, particles can pass through classically forbidden regions of space in quantum mechanics based on wave-particle duality.

The potential energy well of a tunneling reaction. The dash-red arrow shows the classical activated process, while the red arrow shows the tunneling path.

Analysis of tunneling can be made using Bell’s modification of the Arrhenius equation which includes the addition of a tunneling factor, Q:

$k=QAe^{-E/RT}$

where A is is the Arrhenius parameter, E is the barrier height and

Failed to parse (syntax error): {\displaystyle Q=\frac{e^α}/{β-α}(βe^{-α}-αe^{-β})}
$Q={\frac {1}{2}}$
where $a={\frac {E}{RT}}$
and Failed to parse (syntax error): {\displaystyle b=\frac{2ap^2(2mE)^{1/2}{h}}

Examination of the β term shows exponential dependency on the mass of the particle. As a result, tunneling is much more likely for a lighter particle such as hydrogen. Simply doubling the mass of a tunneling proton by replacing it with its deuterium isotope drastically reduces the rate of such reactions. As a result, very large kinetic isotope effects are observed that can not be accounted for by differences in zero point energies.

Also for reactions where isotopes include H, D and T, a criterion of tunneling is the Swain-Schaad relations which compare the rate constants of the reactions when H,D or T are the protons: k_H/k_T=(k_D/k_T)^X and k_H/k_T=(k_H/k_D)^Y
Experimental values of X exceeding 3.26 and Y exceeding 1.44 are evidence of a certain amount of contribution from tunneling.

(From original Wiki page) In organic reactions, this proton tunneling effect has been observed in such reactions as the deprotonation and iodination of nitropropane with hindered pyridine base with a reported KIE of 25 at 25 °C:

and in a 1,5-sigmatropic hydrogen shift although it is observed that it is difficult to extrapolate experimental values obtained at elevated temperatures to lower temperatures:

(End of original Wiki page)

There has long been speculation that high efficiency of enzyme catalysis in proton or hydride ion transfer reactions could be due partly to the quantum mechanical tunneling effect. Environment at the active site of an enzyme positions the donor and acceptor atom close to the optimal tunneling distance. It is also possible that the enzyme provides tunneling-promoting vibration.
Studies on ketosteroid isomerase have provided experimental evidence that the enzyme actually enhances the coupled motion/hydrogen tunneling by comparing primary and secondary kinetic isotope effects of the reaction under enzyme catalyzed and non-enzyme catalyzed conditions.
There are many examples of proton tunneling in enzyme catalyzed reactions that were discovered by KIE. Some well studied examples are alcohol dehydrogenase and glucose oxidase. (Truhlar et al, Acc Chem. Res. 2002, 35, 341-349; Kohen et al, Acc. Chem. Res. 1998, 37, 397-404).