Journal of Biological Physics

A model of competition between populations of two species, describedby a two dimensional map, is analytically and numerically studied. A rich dynamics is observed.

The low-energy orientational oscillations of the peptide groups of an α-helix are considered and the value of the frequency is estimated to be in agreement with experiments. Approximate formulae are derived for the projection of a dipole moment on the helix axis and for the helix parameters. Within the framework of a three-chain model, the asymptotics of the soliton solution is obtained using a discrete approach. The analysis of α-helix geometry exhibits two types of low-frequency oscillations of the α-helix. The first one is connected with atom movements along the helix axis with the peptide groups twisting around the helix axis. Accordingly, it changes the hydrogen bond lengths between neighbouring peptide groups. In the second case, the slopes of the peptide groups to the helix axis oscillate without the helix parameters changing. Here, the energy of interactions between peptide-group dipoles is changed and, as a result, the oscillations have an optical nature. The frequency of the optical orientational oscillations is approximately 100 cm-1.

We have used cell culture of astrocytes aligned within microchannels to investigate calcium effects on primary cilia morphology. In the absence of calcium and in the presence of flow of media (10 μL.s−1) the majority (90%) of primary cilia showed reversible bending with an average curvature of 2.1 ± 0.9 × 10−4 nm−1. When 1.0 mM calcium was present, 90% of cilia underwent bending. Forty percent of these cilia demonstrated strong irreversible bending, resulting in a final average curvature of 3.9 ± 1 × 10−4 nm−1, while 50% of cilia underwent bending similar to that observed during calcium-free flow. The average length of cilia was shifted toward shorter values (3.67 ± 0.34 μm) when exposed to excess calcium (1.0 mM), compared to media devoid of calcium (3.96 ± 0.26 μm). The number of primary cilia that became curved after calcium application was reduced when the cell culture was pre-incubated with 15 μM of the microtubule stabilizer, taxol, for 60 min prior to calcium application. Calcium caused single microtubules to curve at a concentration ≈1.0 mM in vitro, but at higher concentration (≈1.5 mM) multiple microtubule curving occurred. Additionally, calcium causes microtubule-associated protein-2 conformational changes and its dislocation from the microtubule wall at the location of microtubule curvature. A very small amount of calcium, that is 1.45 × 1011 times lower than the maximal capacity of TRPPs calcium channels, may cause gross morphological changes (curving) of primary cilia, while global cytosol calcium levels are expected to remain unchanged. These findings reflect the non-linear manner in which primary cilia may respond to calcium signaling, which in turn may influence the course of development of ciliopathies and cancer.

Non-linear localization phenomena in biological lattices have attracted a steadily growing interest and their existence has been predicted in a wide range of physical settings. We investigate the non-linear proton dynamics of a hydrogen-bonded chain in a semi-classical limit using the coherent state method combined with a Holstein–Primakoff bosonic representation. We demonstrate that even a weak inherent discreteness in the hydrogen-bonded (HB) chain may drastically modify the dynamics of the non-linear system, leading to instabilities that have no analog in the continuum limit. We suggest a possible localization mechanism of polarization oscillations of protons in a hydrogen-bonded chain through modulational instability analysis. This mechanism arises due to the neighboring proton–proton interaction and coherent tunneling of protons along hydrogen bonds and/or around heavy atoms. We present a detailed analysis of modulational instability, and highlight the role of the interaction strength of neighboring protons in the process of bioenergy localization. We perform molecular dynamics simulations and demonstrate the existence of nanoscale discrete breather (DB) modes in the hydrogen-bonded chain. These highly localized and long-lived non-linear breather modes may play a functional role in targeted energy transfer in biological systems.

Single-molecule force-quench atomic force microscopy (FQ-AFM) is used to detect folding intermediates of a simple protein by detecting changes of molecular stiffness of the protein during its folding process. Those stiffness changes are obtained from shape and peaks of an autocorrelation of fluctuations in end-to-end length of the folding molecule. The results are supported by predictions of the equipartition theorem and agree with existing Langevin dynamics simulations of a simplified model of a protein folding. In the light of the Langevin simulations the experimental data probe an ensemble of random-coiled collapsed states of the protein, which are present both in the force-quench and thermal-quench folding pathways.

Endogenous circadian rhythms allow living organisms to anticipate daily variations in their natural environment. Temperature regulation and entrainment mechanisms of circadian clocks are still poorly understood. To better understand the molecular basis of these processes, we built a mathematical model based on experimental data examining temperature regulation of the circadian RNA-binding protein CHLAMY1 from the unicellular green alga Chlamydomonas reinhardtii, simulating the effect of temperature on the rates by applying the Arrhenius equation. Using numerical simulations, we demonstrate that our model is temperature-compensated and can be entrained to temperature cycles of various length and amplitude. The range of periods that allow entrainment of the model depends on the shape of the temperature cycles and is larger for sinusoidal compared to rectangular temperature curves. We show that the response to temperature of protein (de)phosphorylation rates play a key role in facilitating temperature entrainment of the oscillator in Chlamydomonas reinhardtii. We systematically investigated the response of our model to single temperature pulses to explain experimentally observed phase response curves.

Rattlesnake venom can differ in composition and in metalloproteinase-associated activities. The molecular basis for this intra-species variation in Crotalus scutulatus scutulatus (Mojave rattlesnake) remains an enigma. To understand the molecular basis for intra-species variation of metalloproteinase-associated activities, we modeled the three-dimensional structures of four metalloproteinases based on the amino acid sequence of four variations of the proteinase domain of the C. s. scutulatus metalloproteinase gene (GP1, GP2, GP3, and GP4). For comparative purposes, we modeled the atrolysin metalloproteinases of C. atrox as well. All molecular models shared the same topology. While the atrolysin metalloproteinase molecular models contained highly conserved substrate binding sites, the Mojave rattlesnake metalloproteinases showed higher structural divergence when superimposed onto each other. The highest structural divergence among the four C. s. scutulatus molecular models was located at the northern cleft wall and the S’1-pocket of the substrate binding site, molecular regions that modulate substrate selectivity. Molecular dynamics and field potential maps for each C. s. scutulatus metalloproteinase model demonstrated that the non-hemorrhagic metalloproteinases (GP2 and GP3) contain highly basic molecular and field potential surfaces while the hemorrhagic metalloproteinases GP1 and atrolysin C showed extensive acidic field potential maps and shallow but less dynamic active site pockets. Hence, differences in the spatial arrangement of the northern cleft wall, the S’1-pocket, and the physico-chemical environment surrounding the catalytic site contribute to differences in metalloproteinase activities in the Mojave rattlesnake. Our results provide a structural basis for variation of metalloproteinase-associated activities in the rattlesnake venom of the Mojave rattlesnake.

A query learning algorithm based on hidden Markov models (HMMs) isdeveloped to design experiments for string analysis and prediction of MHCclass I binding peptides. Query learning is introduced to aim at reducingthe number of peptide binding data for training of HMMs. A multiple numberof HMMs, which will collectively serve as a committee, are trained withbinding data and used for prediction in real-number values. The universeof peptides is randomly sampled and subjected to judgement by the HMMs.Peptides whose prediction is least consistent among committee HMMs aretested by experiment. By iterating the feedback cycle of computationalanalysis and experiment the most wanted information is effectivelyextracted. After 7 rounds of active learning with 181 peptides in all,predictive performance of the algorithm surpassed the so far bestperforming matrix based prediction. Moreover, by combining the bothmethods binder peptides (log Kd < -6) could be predicted with84% accuracy. Parameter distribution of the HMMs that can be inspectedvisually after training further offers a glimpse of dynamic specificity ofthe MHC molecules.