Side-chain dynamics and protein folding

The processes by which protein side chains reach equilibrium during a folding reaction are investigated using both lattice and all-atom simulations. We find that rates of side-chain relaxation exhibit a distribution over the protein structure, with the fastest relaxing side chains located in positions kinetically important for folding. Traversal of the major folding transition state corresponds to the freezing of a small number of side chains, belonging to the folding nucleus, whereas the rest of the protein proceeds toward equilibrium via backbone fluctuations around the native fold. The postnucleation processes by which side chains relax are characterized by very slow dynamics and many barrier crossings, and thus resemble the behavior of a glass.     

The Goldbeter-Koshland switch in the first-order region and its response to dynamic disorder

In their classical work (Proc. Natl. Acad. Sci. USA, 1981, 78:6840-6844), Goldbeter and Koshland mathematically analyzed a reversible covalent modification system which is highly sensitive to the concentration of effectors. Its signal-response curve appears sigmoidal, constituting a biochemical switch. However, the switch behavior only emerges in the 'zero-order region', i.e. when the signal molecule concentration is much lower than that of the substrate it modifies. In this work we showed that the switching behavior can also occur under comparable concentrations of signals and substrates, provided that the signal molecules catalyze the modification reaction in cooperation. We also studied the effect of dynamic disorders on the proposed biochemical switch, in which the enzymatic reaction rates, instead of constant, appear as stochastic functions of time. We showed that the system is robust to dynamic disorder at bulk concentration. But if the dynamic disorder is quasi-static, large fluctuations of the switch response behavior may be observed at low concentrations. Such fluctuation is relevant to many biological functions. It can be reduced by either increasing the conformation interconversion rate of the protein, or correlating the enzymatic reaction rates in the network.     

Characterization of the distribution of internal motions in the basic pancreatic trypsin inhibitor using a large number of internal NMR probes

The experimental observations described in this article indicated that a distribution of many different fluctuations is present in a globular protein. These fluctuations were characterized by observation of many natural internal probes such as the labile peptide protons and the aromatic side chains. The conditions which are necessary to get reactions of the internal probes have been discussed in detail. The structural interpretation of the data was facilitated by the development and the use of new NMR techniques which provided the identification of the resonances of all the labile peptide protons. With NOE measurements a distinction between correlated and uncorrelated exchange events was obtained. This enabled us to elucidate the exchange mechanism over a wide range of p2H and temperature and to classify different subsets of fluctuations with respect to their lifetimes. It was further demonstrated that a change of external conditions such as temperature, p2H or pressure can change the distribution of fluctuations in the protein. The mechanisms responsible for rotation of internal aromatic side chains were also found to change with temperature, and mechanistic aspects of these fluctuations were discussed. This demonstration of a manifold of spatial fluctuations in a small protein provides an impression on the kind of fluctuations which have to be expected for larger proteins. When studying protein reactions one should therefore consider the presence of a large number of different, transiently formed, spatial structures available for the partner in the reaction, which may pick out only that structure which will optimally perform a particular reaction with the highest efficiency.     

Allee effect in exotic and introduced blowflies

We combined two models to investigate the theoretical dynamics of five exotic and native blowfly species in response to the Allee effect by using demographic parameters estimated from experimental populations. Most of the results suggest stabilization of dynamic behavior in response to the Allee effect. However, the results depended on the magnitude of the demographic parameters of each species, and also indicated chaotic fluctuations and limit cycles. The results are discussed in the context of larval aggregation, an important biological process for blowflies, which naturally incorporates the Allee effect.     

Temporally Resolved Fluctuation Analysis of Sleep ECG

The correlation behavior in the heart beat rate significantly differs with respect to light sleep, deep sleep, and REM sleep. We investigate whether fluctuations of the heart beat rhythm may serve as a surrogate parameter for rapidly changing sleep phenomena, and if these changes are accessible by progressive beat-by-beat analysis of the sleep electrocardiogram (ECG).     

Role of Relaxation Time Scale in Noisy Signal Transduction

Intra-cellular fluctuations, mainly triggered by gene expression, are an inevitable phenomenon observed in living cells. It influences generation of phenotypic diversity in genetically identical cells. Such variation of cellular components is beneficial in some contexts but detrimental in others. To quantify the fluctuations in a gene product, we undertake an analytical scheme for studying few naturally abundant linear as well as branched chain network motifs. We solve the Langevin equations associated with each motif under the purview of linear noise approximation and derive the expressions for Fano factor and mutual information in close analytical form. Both quantifiable expressions exclusively depend on the relaxation time (decay rate constant) and steady state population of the network components. We investigate the effect of relaxation time constraints on Fano factor and mutual information to indentify a time scale domain where a network can recognize the fluctuations associated with the input signal more reliably. We also show how input population affects both quantities. We extend our calculation to long chain linear motif and show that with increasing chain length, the Fano factor value increases but the mutual information processing capability decreases. In this type of motif, the intermediate components act as a noise filter that tune up input fluctuations and maintain optimum fluctuations in the output. For branched chain motifs, both quantities vary within a large scale due to their network architecture and facilitate survival of living system in diverse environmental conditions.     

Population models in a periodically fluctuating environment

Summary We investigate the behavior of population models in the presence of a periodically fluctuating environment. We consider in particular single-species models and models of interspecific competition. It is shown that the fluctuations cause constant equilibrium states to be replaced by periodic equilibrium states, with a shift in the mean value relative to the constant-environment state. It is shown also that the locations of points of exchange of stability may be changed as a result of the fluctuations.     

Dehydrating phospholipid vesicles measured in real-time using ATR Fourier transform infrared spectroscopy

According to the water replacement hypothesis, trehalose stabilizes dry membranes by preventing the decrease in spacing between adjacent phopspholipid headgroups during dehydration. Alternatively, the water-entrapment hypothesis postulates that in the dried state sugars trap residual water at the biomolecule sugar interface. In this study, Fourier transform infrared spectroscopy with an attenuated total reflection accessory was used to investigate the influence of trehalose on the dehydration kinetics and residual water content of egg phosphatidylcholine liposomes in real time under controlled relative humidity conditions. In the absence of trehalose, the lipids displayed a transition to a more ordered gel phase upon drying. The membrane conformational disorder in the dried state was found to decrease with decreasing relative humidity. Even at a relative humidity as high as 94% the conformational disorder of the lipid acyl chains decreased after evaporation of the bulk water. The presence of trehalose affects the rate of water removal from the system and the lipid phase behavior. The rate of water removal is decreased and the residual water content is higher, as compared to drying in the absence of trehalose. During drying, the level of hydrogen bonding to the head groups remains constant. In addition, the conformational disorder of the lipid acyl chains in the dried state more closely resembles that of the lipids in the fully hydrated state. We conclude that water entrapment rather than water replacement explains the effect of trehalose on lipid phase behavior of phosphatidylcholine lipid bilayers during the initial phase of drying.     

Modelling contact spread of infection in host-parasitoid systems: Vertical transmission of pathogens can cause chaos

All animals and plants are, to some extent, susceptible to disease caused by varying combinations of parasites, viruses and bacteria. In this paper, we develop a mathematical model of contact spread infection to investigate the effect of introducing a parasitoid-vectored infection into a one-host-two-parasitoid competition model. We use a system of ordinary differential equations to investigate the separate influences of horizontal and vertical pathogen transmission on a model system appropriate for a variety of competitive situations. Computational simulations and steady-state analysis show that the transient and long-term dynamics exhibited under contact spread infection are highly complex. Horizontal pathogen transmission has a stabilising effect on the system whilst vertical transmission can destabilise it to the point of chaotic fluctuations in population levels. This has implications when considering the introduction of host pathogens for the control of insect vectored diseases such as bovine tuberculosis or yellow fever.     

Moment expansions in spatial ecological models and moment closure through Gaussian approximation

We describe the dynamics of competing species in terms of interactions between spatial moments. We close the moment hierarchy by employing a Gaussian approximation which assumes that fluctuations are independent and distributed normally about the mean values. The Gaussian approximation provides the lowest-order systematic correction to the mean-field approximation by incorporating the effect of fluctuations. When there are no fluctuations in the system, the mean equations agree with the Gaussian approximation as the fluctuations are weak. As the fluctuations gain strength, they influence the mean quantities and hence the Gaussian approximation departs from the mean-field approximation. At large fluctuation levels, the Gaussian approximation breaks down, as may be explained by the bimodality and skewness of the fluctuation distribution of the partial differential equation.     

Mechanically probing the folding pathway of single RNA molecules

We study theoretically the denaturation of single RNA molecules by mechanical stretching, focusing on signatures of the (un)folding pathway in molecular fluctuations. Our model describes the interactions between nucleotides by incorporating the experimentally determined free energy rules for RNA secondary structure, whereas exterior single-stranded regions are modeled as freely jointed chains. For exemplary RNA sequences (hairpins and the Tetrahymena thermophila group I intron), we compute the quasiequilibrium fluctuations in the end-to-end distance as the molecule is unfolded by pulling on opposite ends. Unlike the average quasiequilibrium force-extension curves, these fluctuations reveal clear signatures from the unfolding of individual structural elements. We find that the resolution of these signatures depends on the spring constant of the force-measuring device, with an optimal value intermediate between very rigid and very soft. We compare and relate our results to recent experiments by Liphardt et al. (2001).     

Probing the Conformational Distributions of Subpersistence Length DNA

We have measured the bending elasticity of short double-stranded DNA (dsDNA) chains through small-angle x-ray scattering from solutions of dsDNA-linked dimers of gold nanoparticles. This method, which does not require exertion of external forces or binding to a substrate, reports on the equilibrium distribution of bending fluctuations, not just an average value (as in ensemble fluorescence resonance energy transfer) or an extreme value (as in cyclization), and in principle provides a more robust data set for assessing the suitability of theoretical models. Our experimental results for dsDNA comprising 42-94 basepairs are consistent with a simple wormlike chain model of dsDNA elasticity, whose behavior we have determined from Monte Carlo simulations that explicitly represent nanoparticles and their alkane tethers. A persistence length of 50 nm (150 basepairs) gave a favorable comparison, consistent with the results of single-molecule force-extension experiments on much longer dsDNA chains, but in contrast to recent suggestions of enhanced flexibility at these length scales.     

Compartment volume influences microtubule dynamic instability: a model study

Microtubules (MTs) are cytoskeletal polymers that exhibit dynamic instability, the random alternation between growth and shrinkage. MT dynamic instability plays an essential role in cell development, division, and motility. To investigate dynamic instability, simulation models have been widely used. However, conditions under which the concentration of free tubulin fluctuates as a result of growing or shrinking MTs have not been studied before. Such conditions can arise, for example, in small compartments, such as neuronal growth cones. Here we investigate by means of computational modeling how concentration fluctuations caused by growing and shrinking MTs affect dynamic instability. We show that these fluctuations shorten MT growth and shrinkage times and change their distributions from exponential to non-exponential, gamma-like. Gamma-like distributions of MT growth and shrinkage times, which allow optimal stochastic searching by MTs, have been observed in various cell types and are believed to require structural changes in the MT during growth or shrinkage. Our results, however, show that these distributions can already arise as a result of fluctuations in the concentration of free tubulin due to growing and shrinking MTs. Such fluctuations are possible not only in small compartments but also when tubulin diffusion is slow or when many MTs (de)polymerize synchronously. Volume and all other factors that influence these fluctuations can affect MT dynamic instability and, consequently, the processes that depend on it, such as neuronal growth cone behavior and cell motility in general.