Triosephosphate isomerase (TIM) catalyzes the reaction to convert dihydroxyacetone phosphate into glyceraldehyde 3-phosphate, and vice versa. In most organisms, its functional oligomeric state is a homodimer; however, tetramer formation in hyperthermophiles is required for functional activity. The tetrameric TIM structure also provides added stability to the structure, enabling it to function at more extreme temperatures. We apply Principal Component Analysis to find that the TIM structure space is clearly divided into two groups-the open and the closed TIM structures. The distribution of the structures in the open set is much sparser than that in the closed set, showing a greater conformational diversity of the open structures. We also apply the Elastic Network Model to four different TIM structures-an engineered monomeric structure, a dimeric structure from a mesophile-Trypanosoma brucei, and two tetrameric structures from hyperthermophiles Thermotoga maritima and Pyrococcus woesei. We find that dimerization not only stabilizes the structures, it also enhances their functional dynamics. Moreover, tetramerization of the hyperthermophilic structures increases their functional loop dynamics, enabling them to function in the destabilizing environment of extreme temperatures. Computations also show that the functional loop motions, especially loops 6 and 7, are highly coordinated. In summary, our computations reveal the underlying mechanism of the allosteric regulation of the functional loops of the TIM structures, and show that tetramerization of the structure as found in the hyperthermophilic organisms is required to maintain the coordination of the functional loops at a level similar to that in the dimeric mesophilic structure.

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The spatial organization of nucleosomes in 30-nm fibers remains unknown in detail. To tackle this problem, we analyzed all stereochemically possible configurations of two-start chromatin fibers with DNA linkers L = 10–70 bp (nucleosome repeat length NRL = 157–217 bp). In our model, the energy of a fiber is a sum of the elastic energy of the linker DNA, steric repulsion, electrostatics, and the H4 tail-acidic patch interaction between two stacked nucleosomes. We found two families of energetically feasible conformations of the fibers—one observed earlier, and the other novel. The fibers from the two families are characterized by different DNA linking numbers—that is, they are topologically different. Remarkably, the optimal geometry of a fiber and its topology depend on the linker length: the fibers with linkers L = 10n and 10n + 5 bp have DNA linking numbers per nucleosome ΔLk ≈ −1.5 and −1.0, respectively. In other words, the level of DNA supercoiling is directly related to the length of the inter-nucleosome linker in the chromatin fiber (and therefore, to NRL). We hypothesize that this topological polymorphism of chromatin fibers may play a role in the process of transcription, which is known to generate different levels of DNA supercoiling upstream and downstream from RNA polymerase. A genome-wide analysis of the NRL distribution in active and silent yeast genes yielded results consistent with this assumption.

Loops in proteins connect secondary structures such as alpha-helix and beta-sheet, are often on the surface, and may play a critical role in some functions of a protein. The mobility of loops is central for the motional freedom and flexibility requirements of active-site loops and may play a critical role for some functions. The structures and behaviors of loops have not been much studied in the context of the whole structure and its overall motions, and especially how these might be coupled. Here we investigate loop motions by using coarse-grained structures (Cα atoms only) to solve for the motions of the system by applying Lagrange equations with elastic network models to learn about which loops move in an independent fashion and which move in coordination with domain motions, faster and slower, respectively. The normal modes of the system are calculated using eigen-decomposition of the stiffness matrix. The contribution of individual modes and groups of modes are investigated for their effects on all residues in each loop by using Fourier analyses. Our results indicate overall that the motions of functional sets of loops behave in similar ways as the whole structure. But, overall only a relatively few loops move in coordination with the dominant slow modes of motion, and that these are often closely related to function.

A core gene regulatory circuit encodes irreversible cell cycle state transitions Statistical analysis on randomly generated ODE models elucidates circuit dynamics Steady states specify cell cycle phases, and oscillatory states, their transitions State transition patterns inferred by delayed correlation and parameter perturbation