Range of Relevant Forces in Biology tte native conformation of a protein represents a minimum of its free energy. Nevertheless the stability of proteins is very marginal as their free energies of un folding range from 5 to 15 kcal moh1 (8-25 k^T), a minute amount of energy that results from subtracting the two large quantities that represent the energy of the native and unfolded states (Fersht 1999). tte native conformation is mainly stabilized by weak localized interactions (electrostatic interactions, van der Waals forces, hydrogen bonds, and the hydrophobic effect), ttese are the same forces that stabilize intermolecular bonds in protein pairs, tterefore, it is not surprising that, as we will see later (Sect. 8.3.3), the process of forced unfolding of proteins has been modeled in close analogy with that of the force dissociation ofbonded pairs.

What then is the magnitude of the biologically relevant forces that affect proteins? Given that changes in protein conformation are measured in the angstrom to nanometer range and the energies involved range from 1 to 25 k%T, the relevant biological forces are expected to be in the piconewton range, tte ranges of the diverse biological forces known are summarized in Fig. 8.1b. Because proteins are subject to the ubiquitous thermal forces, the number of possible configurations (entropy) is at its maximum when a protein forms a random coil or is denatured, ttis entropy becomes progressively reduced with the formation of secondary and tertiary structures. Stretching these structures in the low-force regime, to overcome "entro-pic forces," has been achieved experimentally and requires the application of forces on the order of a few piconewtons (Sect. 8.2.5). Several molecular motors such as myosin, kinesin, and RNA/DNA polymerases also generate forces in the same range, from a few piconewtons to tens of piconewtons. Indeed, the strongest molecular motors known to date are the portal protein of the $29 bacteriophage (Smith et al. 2001) and the pilus motor of bacteria (Maier et al. 2002), which are capable of generating forces of up to approximately 60 and 110 pN, respectively, tte next force magnitude group, the "enthalpic force" regime, includes the forces needed to unfold folded domains of proteins (intramolecular interactions) as well as those required to overcome specific intermolecular interactions such as ligand/receptor or antigen/ antibody, ttese forces are typically in the range 100-300 pN, when measured at a high loading rate (this parameter is discussed in Sect. 8.3.3). However, since the typical loading rates in vivo may be much lower in some cases, the corresponding forces may also be lower as shall be seen later (Sect. 8.3.3). Finally, the forces needed to break apart covalent bonds are almost 2 orders of magnitude larger, in the range of a few nanonewtons (reviewed by Zlatanova and Leuba 2003). tte kinetic range covered by the different nanomanipulation techniques and the typical velocities of some biological processes are shown in Fig. 8.1d.

Mechanical Proteins and Mechanical Nanomachines

Some proteins in the cell have a defined "mechanical function" related to their molecular elasticity and/or plasticity, ttese proteins can be classified into two groups: the so-called elastomeric proteins, which present entropic elasticity (e.g., elastin, PEVK, and N2B regions of titin) (Sect. 8.3.3), and the "enthalpic proteins," which show also an enthalpic component in their elasticity, tte "mechanical stability," i.e., resistance to unfolding in response to an applied mechanical force, of this latter group is a parameter of physiological importance (Sect. 8.3.3). ttese a)

Elastic fiber

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