Types of evolutionary stability and the problem of cooperation.

The evolutionary stability of cooperation is a problem of fundamental importance for the biological and social sciences. Different claims have been made about this issue: whereas Axelrod and Hamilton's [Axelrod, R. & Hamilton, W. (1981) Science 211, 1390-1398] widely recognized conclusion is that cooperative rules such as "tit for tat" are evolutionarily stable strategies in the iterated prisoner's dilemma (IPD), Boyd and Lorberbaum [Boyd, R. & Lorberbaum, J. (1987) Nature (London) 327, 58-59] have claimed that no pure strategy is evolutionarily stable in this game. Here we explain why these claims are not contradictory by showing in what sense strategies in the IPD can and cannot be stable and by creating a conceptual framework that yields the type of evolutionary stability attainable in the IPD and in repeated games in general. Having established the relevant concept of stability, we report theorems on some basic properties of strategies that are stable in this sense. We first show that the IPD has "too many" such strategies, so that being stable does not discriminate among behavioral rules. Stable strategies differ, however, on a property that is crucial for their evolutionary survival--the size of the invasion they can resist. This property can be interpreted as a strategy's evolutionary robustness. Conditionally cooperative strategies such as tit for tat are the most robust. Cooperative behavior supported by these strategies is the most robust evolutionary equilibrium: the easiest to attain, and the hardest to disrupt.

Stability and dynamics in a hyperthermophilic protein with melting temperature close to 200°C

The rubredoxin protein from the hyperthermophilic archaebacterium Pyrococcus furiosus was examined by a hydrogen exchange method. Even though the protein does not exhibit reversible thermal unfolding, one can determine its stability parameters—free energy, enthalpy, entropy, and melting temperature—and also the distribution of stability throughout the protein, by using hydrogen exchange to measure the reversible cycling of the protein between native and unfolded states that occurs even under native conditions.

Expression, stability, and membrane integration of truncation mutants of bovine rhodopsin

Premature termination of protein synthesis by nonsense mutations is at the molecular origin of a number of inherited disorders in the family of G protein-coupled seven-helix receptor proteins. To understand how such truncated polypeptides are processed by the cell, we have carried out COS-1 cell expression studies of mutants of bovine rhodopsin truncated at the first 1, 1.5, 2, 3, or 5 transmembrane segments (TMS) of the seven present in wild-type opsin. Our experiments show that successful completion of different stages in the cellular processing of the protein [membrane insertion, N-linked glycosylation, stability to proteolytic degradation, and transport from the endoplasmic reticulum (ER) membrane] requires progressively longer lengths of the polypeptide chain. Thus, none of the truncations affected the ability of the polypeptides to be integral membrane proteins. C-terminal truncations that generated polypeptides with fewer than two TMS resulted in misorientation and prevented glycosylation at the N terminus, whereas truncations that generated polypeptides with fewer than five TMS greatly destabilized the protein. However, all of the truncations prevented exit of the polypeptide from the ER. We conclude that during the biogenesis of rhodopsin, proper integration into the ER membrane occurs only after the synthesis of at least two TMS is completed. Synthesis of the next three TMS confers a gradual increase in stability, whereas the presence of more than five TMS is necessary for exit from the ER.

Transition-state structure as a unifying basis in protein-folding mechanisms: Contact order, chain topology, stability, and the extended nucleus mechanism

I attempt to reconcile apparently conflicting factors and mechanisms that have been proposed to determine the rate constant for two-state folding of small proteins, on the basis of general features of the structures of transition states. Φ-Value analysis implies a transition state for folding that resembles an expanded and distorted native structure, which is built around an extended nucleus. The nucleus is composed predominantly of elements of partly or well-formed native secondary structure that are stabilized by local and long-range tertiary interactions. These long-range interactions give rise to connecting loops, frequently containing the native loops that are poorly structured. I derive an equation that relates differences in the contact order of a protein to changes in the length of linking loops, which, in turn, is directly related to the unfavorable free energy of the loops in the transition state. Kinetic data on loop extension mutants of CI2 and α-spectrin SH3 domain fit the equation qualitatively. The rate of folding depends primarily on the interactions that directly stabilize the nucleus, especially those in native-like secondary structure and those resulting from the entropy loss from the connecting loops, which vary with contact order. This partitioning of energy accounts for the success of some algorithms that predict folding rates, because they use these principles either explicitly or implicitly. The extended nucleus model thus unifies the observations of rate depending on both stability and topology.

“Coarse” stability and bifurcation analysis using time-steppers: A reaction-diffusion example

Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099–1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective (“coarse”) bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice–Boltzmann model.

Presenilin-1 binds cytoplasmic epithelial cadherin, inhibits cadherin/p120 association, and regulates stability and function of the cadherin/catenin adhesion complex

Here we show that presenilin-1 (PS1), a protein involved in Alzheimer's disease, binds directly to epithelial cadherin (E-cadherin). This binding is mediated by the large cytoplasmic loop of PS1 and requires the membrane-proximal cytoplasmic sequence 604–615 of mature E-cadherin. This sequence is also required for E-cadherin binding of protein p120, a known regulator of cadherin-mediated cell adhesion. Using wild-type and PS1 knockout cells, we found that increasing PS1 levels suppresses p120/E-cadherin binding, and increasing p120 levels suppresses PS1/E-cadherin binding. Thus PS1 and p120 bind to and mutually compete for cellular E-cadherin. Furthermore, PS1 stimulates E-cadherin binding to β- and γ-catenin, promotes cytoskeletal association of the cadherin/catenin complexes, and increases Ca2+-dependent cell–cell aggregation. Remarkably, PS1 familial Alzheimer disease mutant ΔE9 increased neither the levels of cadherin/catenin complexes nor cell aggregation, suggesting that this familial Alzheimer disease mutation interferes with cadherin-based cell–cell adhesion. These data identify PS1 as an E-cadherin-binding protein and a regulator of E-cadherin function in vivo.

Genetic interactions between ATM and the nonhomologous end-joining factors in genomic stability and development

DNA ligase IV (Lig4) and the DNA-dependent protein kinase (DNA-PK) function in nonhomologous end joining (NHEJ). However, although Lig4 deficiency causes late embryonic lethality, deficiency in DNA-PK subunits (Ku70, Ku80, and DNA-PKcs) does not. Here we demonstrate that, similar to p53 deficiency, ataxia-telangiectasia-mutated (ATM) gene deficiency rescues the embryonic lethality and neuronal apoptosis, but not impaired lymphocyte development, associated with Lig4 deficiency. However, in contrast to p53 deficiency, ATM deficiency enhances deleterious effects of Lig4 deficiency on growth potential of embryonic fibroblasts (MEFs) and genomic instability in both MEFs and cultured progenitor lymphocytes, demonstrating significant differences in the interplay of p53 vs. ATM with respect to NHEJ. Finally, in dramatic contrast to effects on Lig4 deficiency, ATM deficiency causes early embryonic lethality in Ku- or DNA-PKcs-deficient mice, providing evidence for an NHEJ-independent role for the DNA-PK holoenzyme.

Site-specifically located 8-amino-2′-deoxyguanosine: thermodynamic stability and mutagenic properties in Escherichia coli

2-Nitropropane (2-NP), an important industrial solvent and a component of cigarette smoke, is mutagenic in bacteria and carcinogenic in rats. 8-Amino-2′-deoxyguanosine (8-amino-dG) is one of the types of DNA damage found in liver, the target organ in 2-NP-treated rats. To investigate the thermodynamic properties of 8-amino-dG opposite each of the four DNA bases, we have synthesized an 11mer, d(CCATCG*CTACC), in which G* represents the modified base. By annealing a complementary DNA strand to this modified 11mer, four sets of duplexes were generated each containing one of the four DNA bases opposite the lesion. Circular dichroism studies indicated that 8-amino-dG did not alter the global helical properties of natural right-handed B-DNA. The thermal stability of each duplex was examined by UV melting measurements and compared with its unmodified counterpart. For the unmodified 11mer, the relative stability of the complementary DNA bases opposite G was in the order C > T > G > A, as determined from their –ΔG° values. The free energy change of each modified duplex was lower than its unmodified counterpart, except for the G*:G pair that exhibited a higher melting transition and a larger –ΔG° than the G:G duplex. Nevertheless, the stability of the modified 11mer duplex also followed the order C > T > G > A when placed opposite 8-amino-dG. To explore if 8-amino-dG opposite another 8-amino-dG has any advantage in base pairing, a G*:G* duplex was evaluated, which showed that the stability of this duplex was similar to the G*:G duplex. Mutagenesis of 8-amino-dG in this sequence context was studied in Escherichia coli, which showed that the lesion is weakly mutagenic (mutation frequency ∼10–3) but still can induce a variety of targeted and semi-targeted mutations.

Symmetry, stability, and dynamics of multidomain and multicomponent protein systems

Symmetry is commonly observed in many biological systems. Here we discuss representative examples of the role of symmetry in structural molecular biology. Point group symmetries are observed in many protein oligomers whose three-dimensional atomic structures have been elucidated by x-ray crystallography. Approximate symmetry also occurs in multidomain proteins. Symmetry often confers stability on the molecular system and results in economical usage of basic components to build the macromolecular structure. Symmetry is also associated with cooperativity. Mild perturbation from perfect symmetry may be essential in some systems for dynamic functions.

Influence of cisplatin intrastrand crosslinking on the conformation, thermal stability, and energetics of a 20-mer DNA duplex.

cis-Diamminedichloroplatinum(II) (cisplatin) is a widely used anticancer drug that binds to and crosslinks DNA. The major DNA adduct of the drug results from coordination of two adjacent guanine bases to platinum to form the intrastrand crosslink cis-[Pt(NH3)2[d(GpG)-N7(1), -N7(2)]] (cis-Pt-GG). In the present study, spectroscopic and calorimetric techniques were employed to characterize the influence of this crosslink on the conformation, thermal stability, and energetics of a site-specifically platinated 20-mer DNA duplex. CD spectroscopic and thermal denaturation data revealed that the crosslink alters the structure of the host duplex, consistent with a shift from a B-like to an A-like conformation; lowers its thermal stability by approximately 9 degrees C; and reduces its thermodynamic stability by 6.3 kcal/mol at 25 degrees C, most of which is enthalpic in origin; but it does not alter the two-state melting behavior exhibited by the parent, unmodified duplex, despite the significant crosslink-induced changes noted above. The energetic consequences of the cis-Pt-GG crosslink are discussed in relation to the structural perturbations it induces in DNA and to how these crosslink-induced perturbations might modulate protein binding.

Amino-terminal alteration of the HLA-A*0201-restricted human immunodeficiency virus pol peptide increases complex stability and in vitro immunogenicity.

Initial studies suggested that major histocompatibility complex class I-restricted viral epitopes could be predicted by the presence of particular residues termed anchors. However, recent studies showed that nonanchor positions of the epitopes are also significant for class I binding and recognition by cytotoxic T lymphocytes (CTLs). We investigated if changing nonanchor amino acids could increase class I affinity, complex stability, and T-cell recognition of a natural viral epitope. This concept was tested by using the HLA-A 0201-restricted human immunodeficiency virus type 1 epitope from reverse transcriptase (pol). Position 1 (P1) amino acid substitutions were emphasized because P1 alterations may not alter the T-cell receptor interaction. The peptide with the P1 substitution of tyrosine for isoleucine (I1Y) showed a binding affinity for HLA-A 0201 similar to that of the wild-type pol peptide in a cell lysate assembly assay. Surprisingly, I1Y significantly increased the HLA-A 0201-peptide complex stability at the cell surface. I1Y sensitized HLA-A 0201-expressing target cells for wild-type pol-specific CTL lysis as well as wild-type pol. Peripheral blood lymphocytes from three HLA-A2 HIV-seropositive individuals were stimulated in vitro with I1Y and wild-type pol. I1Y stimulated a higher wild-type pol-specific CTL response than wild-type pol in all three donors. Thus, I1Y may be an "improved" epitope for use as a CTL-based human immunodeficiency virus vaccine component. The design of improved epitopes has important ramifications for prophylaxis and therapeutic vaccine development.

Mutagenesis of the putative alpha-helical domain of the Vpr protein of human immunodeficiency virus type 1: effect on stability and virion incorporation.

vpr is one of the auxiliary genes of human immunodeficiency virus type 1 (HIV-1) and is conserved in the related HIV-2/simian immunodeficiency virus lentiviruses. The unique feature of Vpr is that it is the only nonstructural protein incorporated into the virus particle. Secondary structural analysis predicted an amphipathic alpha-helical domain in the amino terminus of Vpr (residues 17-34) which contains five acidic and four leucine residues. To evaluate the role of specific residues of the helical domain for virion incorporation, mutagenesis of this domain was carried out. Substitution of proline for any of the individual acidic residues (Asp-17 and Glu-21, -24, -25, and -29) eliminated the virion incorporation of Vpr and also altered the stability of Vpr in cells. Conservative replacement of glutamic residues of the helical domain with aspartic residues resulted in Vpr characteristic of wild type both in stability and virion incorporation, as did substitution of glutamine for the acidic residues. In contrast, replacement of leucine residues of the helical domain (residues 20, 22, 23, and 26) by alanine eliminated virion incorporation function of Vpr. These data indicate that acidic and hydrophobic residues and the helical structure in this region are critical for the stability of Vpr and its efficient incorporation into virus-like particles.

Optimizing the stability of single-chain proteins by linker length and composition mutagenesis

Linker length and composition were varied in libraries of single-chain Arc repressor, resulting in proteins with effective concentrations ranging over six orders of magnitude (10 μM–10 M). Linkers of 11 residues or more were required for biological activity. Equilibrium stability varied substantially with linker length, reaching a maximum for glycine-rich linkers containing 19 residues. The effects of linker length on equilibrium stability arise from significant and sometimes opposing changes in folding and unfolding kinetics. By fixing the linker length at 19 residues and varying the ratio of Ala/Gly or Ser/Gly in a 16-residue-randomized region, the effects of linker flexibility were examined. In these libraries, composition rather than sequence appears to determine stability. Maximum stability in the Ala/Gly library was observed for a protein containing 11 alanines and five glycines in the randomized region of the linker. In the Ser/Gly library, the most stable protein had seven serines and nine glycines in this region. Analysis of folding and unfolding rates suggests that alanine acts largely by accelerating folding, whereas serine acts predominantly to slow unfolding. These results demonstrate an important role for linker design in determining the stability and folding kinetics of single-chain proteins and suggest strategies for optimizing these parameters.