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Register a new userImpulse-Response Approach to Elastobaric Model for Proteins
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Robert D. Young
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A novel energy landscape model, ELM, for proteins recently explained a collection of incoherent, elastic neutron scattering data from proteins. The ELM of proteins considers the elastic response of the proton and its environment to the energy and momentum exchanged with the neutron. In the ELM, the elastic potential energy is expressed as a sum of a temperature dependent term resulting from equipartition of potential energy among the active degrees of freedom and a wave vector transfer dependent term resulting from the elastic energy stored by the protein during the neutron scattering event. The elastic potential energy involves a new elastobaric coefficient that is proportional to the product of two factors: one factor depends on universal constants and the other on the incident neutron wave vector per degree of freedom. The ELM was tested for dry protein samples with an elastobaric coefficient corresponding to 3 degrees of freedom. A discussion of the data requirements for additional tests of ELM is presented resulting in a call for published data that have not been preprocessed by temperature and wave-vector dependent normalizations.
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Radiotherapy can effectively kill malignant cells, but the doses required to cure cancer patients may inflict severe collateral damage to adjacent healthy tissues. Hyperthermia (HT) is a promising option to improve the outcome of radiation treatment (RT) and is increasingly applied in hospital. However, the synergistic effect of simultaneous thermoradiotherapy is not well understood yet, while its mathematical modelling is essential for treatment planning. To better understand this synergy, we propose a theoretical model in which the thermal enhancement ratio (TER) is explained by the fraction of cells being radiosensitised by the infliction of sublethal damage through mild HT. Further damage finally kills the cell or inhibits its proliferation in a non-reversible process. We suggest the TER to be proportional to the energy invested in the sensitisation, which is modelled as a simple rate process. Assuming protein denaturation as the main driver of HT-induced sublethal damage and considering the temperature dependence of the heat capacity of cellular proteins, the sensitisation rates were found to depend exponentially on temperature; in agreement with previous empirical observations. Our predictions well reproduce experimental data from in-vitro and in-vivo studies, explaining the thermal modulation of cellular radioresponse for simultaneous thermoradiotherapy.
We study the space of all compact structures on a two-dimensional square lattice of size $N=6times6$. Each structure is mapped onto a vector in $N$-dimensions according to a hydrophobic model. Previous work has shown that the designabilities of structures are closely related to the distribution of the structure vectors in the $N$-dimensional space, with highly designable structures predominantly found in low density regions. We use principal component analysis to probe and characterize the distribution of structure vectors, and find a non-uniform density with a single peak. Interestingly, the principal axes of this peak are almost aligned with Fourier eigenvectors, and the corresponding Fourier eigenvalues go to zero continuously at the wave-number for alternating patterns ($q=pi$). These observations provide a stepping stone for an analytic description of the distribution of structural points, and open the possibility of estimating designabilities of realistic structures by simply Fourier transforming the hydrophobicities of the corresponding sequences.
In biophysics, the search for analytical solutions of stochastic models of cellular processes is often a challenging task. In recent work on models of gene expression, it was shown that a mapping based on partitioning of Poisson arrivals (PPA-mapping) can lead to exact solutions for previously unsolved problems. While the approach can be used in general when the model involves Poisson processes corresponding to creation or degradation, current applications of the method and new results derived using it have been limited to date. In this paper, we present the exact solution of a variation of the two-stage model of gene expression (with time dependent transition rates) describing the arbitrary partitioning of proteins. The methodology proposed makes full use of the the PPA-mapping by transforming the original problem into a new process describing the evolution of three biological switches. Based on a succession of transformations, the method leads to a hierarchy of reduced models. We give an integral expression of the time dependent generating function as well as explicit results for the mean, variance, and correlation function. Finally, we discuss how results for time dependent parameters can be extended to the three-stage model and used to make inferences about models with parameter fluctuations induced by hidden stochastic variables.
In this paper, we study linear filters to process signals defined on simplicial complexes, i.e., signals defined on nodes, edges, triangles, etc. of a simplicial complex, thereby generalizing filtering operations for graph signals. We propose a finite impulse response filter based on the Hodge Laplacian, and demonstrate how this filter can be designed to amplify or attenuate certain spectral components of simplicial signals. Specifically, we discuss how, unlike in the case of node signals, the Fourier transform in the context of edge signals can be understood in terms of two orthogonal subspaces corresponding to the gradient-flow signals and curl-flow signals arising from the Hodge decomposition. By assigning different filter coefficients to the associated terms of the Hodge Laplacian, we develop a subspace-varying filter which enables more nuanced control over these signal types. Numerical experiments are conducted to show the potential of simplicial filters for sub-component extraction, denoising and model approximation.
We introduce a formulation for normal mode analyses of globular proteins that significantly improves on an earlier, 1-parameter formulation (M. Tirion, PRL 77, 1905 (1996)) that characterized the slow modes associated with protein data bank structures. Here we develop that empirical potential function which is minimized at the outset to include two features essential to reproduce the eigenspectra and associated density of states over all frequencies, not merely the slow ones. First, introduction of preferred dihedral-angle configurations via use of torsional stiffness constants eliminates anomalous dispersion characteristics due to insufficiently bound surface sidechains. Second, we take into account the atomic identities and the distance of separation of all pairwise interactions. With these modifications we obtain stable, reliable eigenmodes over a wide range of frequencies.
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