Microcanonical thermostatistics analysis has become an important tool to reveal essential aspects of phase transitions in complex systems. An efficient way to estimate the microcanonical inverse temperature β(E) and the microcanonical entropy S (E) is achieved with the statistical temperature weighted histogram analysis method (ST-WHAM). The strength of this method lies on its flexibility, as it can be used to analyse data produced by algorithms with generalised sampling weights. However, for any sampling weight, ST-WHAM requires the calculation of derivatives of energy histograms H(E), which leads to non-trivial and tedious binning tasks for models with continuous energy spectrum such as those for biomolecular and colloidal systems. Here, we discuss two alternative methods that avoid the need for such energy binning to obtain continuous estimates for H(E) in order to evaluate β(E) by using ST-WHAM: (i) a series expansion to estimate probability densities from the empirical cumulative distribution function (CDF), and (ii) a Bayesian approach to model this CDF. Comparison with a simple linear regression method is also carried out. The performance of these approaches is evaluated considering coarse-grained protein models for folding and peptide aggregation.

BackgroundThe Bacillus subtilis endo-β-1,4-glucanase (BsCel5A) hydrolyzes β-1,3-1,4-linked glucan, and the enzyme includes a family 3 carbohydrate-binding module (CBM3) that binds β-1,4-linked glucan.MethodsHere we investigate the BsCel5A β-1,3-1,4 glucanase activity after exchanging the CBM3 domain for the family 11 CBM from Ruminiclostridium thermocellum celH (RtCBM11) having β-1,3-1,4 glucan affinity.ResultsThe BsCel5A-RtCBM11 presents a 50.4% increase in Vmax, a 10% reduction in K0.5, and a 2.1-fold increase in catalytic efficiency. Enzyme mobility and binding to barley β-1,3-1,4 glucan and pre-treated sugarcane bagasse were investigated using Electron Paramagnetic Resonance (EPR) with Site-Directed Spin Labeling (SDSL) of the binding site regions of the CBM3 and RtCBM11 domains in the BsCel5A-CBM3 and BsCel5A-RtCBM11, respectively. Although higher mobility than the RtCBM11 was shown, no interaction of the spin-labeled CBM3 with β-1,3-1,4 glucan was observed. In contrast, a Ka value of 0.22 mg/mL was estimated from titration of the BsCel5A-RtCBM11 with β-1,3-1,4 glucan. Enzyme binding as inferred from altered EPR spectra of the BsCel5A-RtCBM11 was observed only after xylan or lignin extraction from sugarcane bagasse. Binding to xylan- or lignin-free lignocellulose was correlated with a 4.5- to 5-fold increase in total reducing sugar release as compared to the milled intact sugarcane bagasse, suggesting that xylan impedes enzyme access to the β-1,3-1,4 glucan. ConclusionsThese results show that the non-specific binding of the BsCel5A-RtCBM11 to the lignin component of the cell wall is minimal, and represent the first reported use of EPR to directly study the interaction of glycoside hydrolyse enzymes with natural insoluble substrates.Electronic supplementary materialThe online version of this article (10.1186/s13068-017-0964-0) contains supplementary material, which is available to authorized users.

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