Enthalpy–Entropy Compensation in the Melting of Human Hair

Sir,

A recent paper published by Kunchi et al. examines thermal properties of the human hair, such as melting enthalpy (ΔH_m) and melting temperature (T_m) by thermal scanning of hair obtained from 13 individuals.[1] According to their data, the value of ΔH_m is positive for all 13 individuals, indicating that the melting of the human hair at the melting temperature is an endergonic process. While both thermodynamic parameters, ΔH_m and T_m, provide valuable information for the thermodynamic basis for the melting phenomena exhibited by human hair, another fundamental thermodynamic parameter, entropy, is not discussed in the original paper. In this letter, we show our analysis of their results to provide melting entropy (ΔS_m) of the human hair, its correlation with ΔH_m, and a potential mechanism for the correlation between ΔH_m and ΔS_m.

As melting is a phase transition process, ΔS_m can be calculated using the following equation:

Where T_m is the melting temperature in Kelvin.[2] Numerical values of both ΔH_m and T_m for 13 individuals obtained from the original paper were used for the calculation of ΔS_m using Equation (1).

The resulting values of ΔS_m and its corresponding ΔH_m are shown in Figure 1. The plot elucidates two thermodynamic features in the melting of human hair for 13 individuals. First, the melting of human hair at the melting temperature is an entropy-driven process, that is, to say ΔS_m >0. Second, linear regression identified that there is a high correlation between ΔH_m and ΔS_m, which is known as enthalpy–entropy compensation, often observed in a weakly-coupled system.[3] The compensation means that as enthalpy increases the corresponding entropy also increases so that the resulting free energy change differences are minimized. For example, we showed in our earlier work that a large variation in ΔH associated with point mutations in peptides was compensated by its corresponding ΔS in their binding to the target proteins.[4] Figure 1 clearly indicates that the melting of human hair exhibits compensatory behavior, suggesting that the molecular components responsible for the melting in human hair may exhibit the property of a weakly-coupled system.

Figure 1.

Enthalpy–entropy compensation in the melting of human hair at T_m. Solid line is a linear fitting equation, y = 2 × 10^-3(x− 10^-2), (R²: 0.9967). Linear regression was performed using SigmaPlot (Systat Software, San Jose, CA, USA)

The major proteins responsible for the mechanical and thermodynamic features in the melting of human hair are keratin.[1] It is known that the human hair expresses at least 17 different keratin proteins.[5] Each type of keratin has a various number of natural variants [Table 1]. According to our search of a bioinformatics database, UniProt (https://www.uniprot.org/help/uniprotkb), the possible number of combinations of keratin compositions that one can have is enormous, as it is 1.76 × 10¹¹. Each combination of keratin proteins will have its own unique value of ΔH_m, and variation in ΔH_m between individuals can be significant as observed in the paper.[1] However, the variation in ΔH_m can be compensated by the corresponding ΔS_m as shown in this letter. This compensatory behavior between enthalpy and entropy could be a mechanism for the limited variation in T_m observed in the human hair.

Table 1.

Human hair keratins

Keratin	UniProt ID	Gene	Number of types*
K31	Q15323	KRT31	4
K32	Q14532	KRT32	12
K33a	O76009	KRT33A	2
K33b	Q14525	KRT33B	1
K34	O76011	KRT34	3
K35	Q92764	KRT35	4
K36	O76013	KRT36	7
K37	O76014	KRT37	10
K38	O76015	KRT38	2
K39	Q6A163	KRT39	4
K40	Q6A162	KRT40	10
K81	Q14533	KRT81	7
K82	Q9NSB4	KRT82	4
K83	P78385	KRT83	6
K84	Q9NSB2	KRT84	6
K85	P78386	KRT85	3
K86	O43790	KRT86	9

*Number of types – Number of natural variants + 1 (canonical sequence)

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.