Salt bridges in proteins are bonds between oppositely charged residues that are sufficiently close to each other to experience electrostatic attraction. They contribute to protein structure and to the specificity of interaction of proteins with other biomolecules, but in doing so they need not necessarily increase a protein's free energy of unfolding. The net electrostatic free energy of a salt bridge can be partitioned into three components: charge-charge interactions, interactions of charges with permanent dipoles, and desolvation of charges. Energetically favorable Coulombic charge-charge interaction is opposed by often unfavorable desolvation of interacting charges. As a consequence, salt bridges may destabilize the structure of the folded protein. There are two ways to estimate the free energy contribution of salt bridges by experiment: the pK(a) approach and the mutation approach. In the pK(a) approach, the contribution of charges to the free energy of unfolding of a protein is obtained from the change of pK(a) of ionizable groups caused by altered electrostatic interactions upon folding of the protein. The pK(a) approach provides the relative free energy gained or lost when ionizable groups are being charged. In the mutation approach, the coupling free energy between interacting charges is obtained from a double mutant cycle. The coupling free energy is an indirect and approximate measure of the free energy of charge-charge interaction. Neither the pK(a) approach nor the mutation approach can provide the net free energy of a salt bridge. Currently, this is obtained only by computational methods which, however, are often prone to large uncertainties due to simplifying assumptions and insufficient structural information on which calculations are based. This state of affairs makes the precise thermodynamic quantification of salt bridge energies very difficult. This review is focused on concepts and on the assessment of experimental methods and does not cover the vast literature.
Recently we have identified angiostatin, an endogenous angiogenesis inhibitor of 38 kDa which specifically blocks the growth of endothelial cells (O'Reilly, M. S., Holmgren, L., Shing, Y., Chen, C., Rosenthal, R. A., Moses, M., Lane, W. S., Cao, Y., Sage, E. H., and Folkman, J. (1994) Cell 79, 315-328; Folkman, J. (1995) Nat. Med. 1, 27-31). Angiostatin was shown to represent an internal fragment of plasminogen containing the first four kringle structures. We now report on the inhibitory effects of individual or combined kringle structures of angiostatin on capillary endothelial cell proliferation. Recombinant kringle 1 and kringle 3 exhibit potent inhibitory activity with half-maximal concentrations (ED 50 ) of 320 nM and 460 nM, respectively. Also, recombinant kringle 2 displays a significant inhibition, although decreased compared with both kringle 1 and kringle 3. In contrast, kringle 4 is an ineffective inhibitor of basic fibroblast growth factor-stimulated endothelial cell proliferation. Among the tandem kringle arrays, the recombinant kringle 2-3 fragment exerts inhibitory activity similar to kringle 2 alone. However, relative to kringle 2-3, a marked enhancement in inhibition is observed when individual kringle 2 and kringle 3 are added together to endothelial cells. This implies that it is necessary to open the cystine bridge between kringle 2 and kringle 3 to obtain the maximal inhibitory effect of kringle 2-3. An increased (<2-fold) inhibitory activity is observed for the kringle 1-3 fragment (ED 50 ؍ 70 nM) compared with kringle 1-4 (ED 50 ؍ 135 nM). These data indicate that the anti-proliferative activity of angiostatin on endothelial cells is shared by kringle 1, kringle 2, and kringle 3, but probably not by kringle 4 and that more potent inhibition results when kringle 4 is removed from angiostatin. Thus, in view of the variable lysine affinity of the homologous domains, it would appear that lysine binding capability does not correlate with the relative inhibitory effects of the kringle-containing constructs. However, as we also demonstrate, appropriate folding of kringle structures is essential for angiostatin to maintain its full anti-endothelial activity.
Networks of randomly connected neurons are among the most popular models in theoretical neuroscience. The connectivity between neurons in the cortex is however not fully random, the simplest and most prominent deviation from randomness found in experimental data being the overrepresentation of bidirectional connections among pyramidal cells. Using numerical and analytical methods, we investigate the effects of partially symmetric connectivity on the dynamics in networks of rate units. We consider the two dynamical regimes exhibited by random neural networks: the weak-coupling regime, where the firing activity decays to a single fixed point unless the network is stimulated, and the strong-coupling or chaotic regime, characterized by internally generated fluctuating firing rates. In the weak-coupling regime, we compute analytically, for an arbitrary degree of symmetry, the autocorrelation of network activity in the presence of external noise. In the chaotic regime, we perform simulations to determine the timescale of the intrinsic fluctuations. In both cases, symmetry increases the characteristic asymptotic decay time of the autocorrelation function and therefore slows down the dynamics in the network.
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