Surveying determinants of protein structure designability across different energy models and amino-acid alphabets: A consensus

A variety of analytical and computational models have been proposed to answer the question of why some protein structures are more “designable” (i.e., have more sequences folding into them) than others. One class of analytical and statistical-mechanical models has approached the designability problem from a thermodynamic viewpoint. These models highlighted specific structural features important for increased designability. Furthermore, designability was shown to be inherently related to thermodynamically relevant energetic measures of protein folding, such as the foldability F and energy gap Δ10.Δ10. However, many of these models have been done within a very narrow focus: Namely, pair–contact interactions and two-letter amino-acid alphabets. Recently, two-letter amino-acid alphabets for pair–contact models have been shown to contain designability artifacts which disappear for larger-letter amino-acid alphabets. In addition, a solvation model was demonstrated to give identical designability results to previous two-letter amino-acid alphabet pair–contact models. In light of these discordant results, this report synthesizes a broad consensus regarding the relationship between specific structural features, foldability F, energy gap Δ10,Δ10, and structure designability for different energy models (pair–contact vs solvation) across a wide range of amino-acid alphabets. We also propose a novel measure ZdkZdk which is shown to be well correlated to designability. Finally, we conclusively demonstrate that two-letter amino-acid alphabets for pair–contact models appear to be solvation models in disguise. © 2000 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69591/2/JCPSA6-112-5-2533-1.pd

Universal correlation between energy gap and foldability for the random energy model and lattice proteins

The random energy model, originally used to analyze the physics of spin glasses, has been employed to explore what makes a protein a good folder versus a bad folder. In earlier work, the ratio of the folding temperature over the glass–transition temperature was related to a statistical measure of protein energy landscapes denoted as the foldability F. It was posited and subsequently established by simulation that good folders had larger foldabilities, on average, than bad folders. An alternative hypothesis, equally verified by protein folding simulations, was that it is the energy gap Δ between the native state and the next highest energy that distinguishes good folders from bad folders. This duality of measures has led to some controversy and confusion with little done to reconcile the two. In this paper, we revisit the random energy model to derive the statistical distributions of the various energy gaps and foldability. The resulting joint distribution allows us to explicitly demonstrate the positive correlation between foldability and energy gap. In addition, we compare the results of this analytical theory with a variety of lattice models. Our simulations indicate that both the individual distributions and the joint distribution of foldability and energy gap agree qualitatively well with the random energy model. It is argued that the universal distribution of and the positive correlation between foldability and energy gap, both in lattice proteins and the random energy model, is simply a stochastic consequence of the “thermodynamic hypothesis.” © 1999 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70084/2/JCPSA6-111-14-6599-1.pd

Conservation and divergence of C-terminal domain structure in the retinoblastoma protein family.

The retinoblastoma protein (Rb) and the homologous pocket proteins p107 and p130 negatively regulate cell proliferation by binding and inhibiting members of the E2F transcription factor family. The structural features that distinguish Rb from other pocket proteins have been unclear but are critical for understanding their functional diversity and determining why Rb has unique tumor suppressor activities. We describe here important differences in how the Rb and p107 C-terminal domains (CTDs) associate with the coiled-coil and marked-box domains (CMs) of E2Fs. We find that although CTD-CM binding is conserved across protein families, Rb and p107 CTDs show clear preferences for different E2Fs. A crystal structure of the p107 CTD bound to E2F5 and its dimer partner DP1 reveals the molecular basis for pocket protein-E2F binding specificity and how cyclin-dependent kinases differentially regulate pocket proteins through CTD phosphorylation. Our structural and biochemical data together with phylogenetic analyses of Rb and E2F proteins support the conclusion that Rb evolved specific structural motifs that confer its unique capacity to bind with high affinity those E2Fs that are the most potent activators of the cell cycle

Protein sequestration generates a flexible ultrasensitive response in a genetic network

Ultrasensitive responses are crucial for cellular regulation. Protein sequestration, where an active protein is bound in an inactive complex by an inhibitor, can potentially generate ultrasensitivity. Here, in a synthetic genetic circuit in budding yeast, we show that sequestration of a basic leucine zipper transcription factor by a dominant-negative inhibitor converts a graded transcriptional response into a sharply ultrasensitive response, with apparent Hill coefficients up to 12. A simple quantitative model for this genetic network shows that both the threshold and the degree of ultrasensitivity depend upon the abundance of the inhibitor, exactly as we observed experimentally. The abundance of the inhibitor can be altered by simple mutation; thus, ultrasensitive responses mediated by protein sequestration are easily tuneable. Gene duplication of regulatory homodimers and loss-of-function mutations can create dominant negatives that sequester and inactivate the original regulator. The generation of flexible ultrasensitive responses is an unappreciated adaptive advantage that could explain the frequent evolutionary emergence of dominant negatives

Designing sequential transcription logic: a simple genetic circuit for conditional memory

The ability to learn and respond to recurrent events depends on the capacity to remember transient biological signals received in the past. Moreover, it may be desirable to remember or ignore these transient signals conditioned upon other signals that are active at specific points in time or in unique environments. Here, we propose a simple genetic circuit in bacteria that is capable of conditionally memorizing a signal in the form of a transcription factor concentration. The circuit behaves similarly to a "data latch" in an electronic circuit, i.e. it reads and stores an input signal only when conditioned to do so by a "read command". Our circuit is of the same size as the well-known genetic toggle switch (an unconditional latch) which consists of two mutually repressing genes, but is complemented with a "regulatory front end" involving protein heterodimerization as a simple way to implement conditional control. Deterministic and stochastic analysis of the circuit dynamics indicate that an experimental implementation is feasible based on well-characterized genes and proteins. It is not known, to which extent molecular networks are able to conditionally store information in natural contexts for bacteria. However, our results suggest that such sequential logic elements may be readily implemented by cells through the combination of existing protein-protein interactions and simple transcriptional regulation.Comment: 20 pages, 5 figures; supplementary material available upon request from the author