Microcanonical thermostatistics analysis without histograms: Cumulative distribution and Bayesian approaches

Abstract

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.

Kinetics of first-order phase transitions from microcanonical thermostatistics

“…Although inferences about the kinetics of first-order phase transitions based on microcanonical free-energy profiles were suggested before in references [12,13], microcanonical thermostatistics have been used mainly to describe the equilibrium properties of molecular systems (see, e.g., references [16,[47][48][49][50][51]). In this paper I have extended the use of microcanonical thermostatistics in order to develop a rate theory which provides simple temperature-dependent expressions for all rate constants, i.e., the forward (κ − ) and the reverse (κ + ) rate constants given by equations ( 13) and ( 14), respectively, and the equilibrium constant (κ eq ), which is given by equation (16).…”

Microcanonical characterization of first-order phase transitions in a generalized model for aggregation

“…Refs. [19][20][21][22][23][24][25][26][27][28][29][30][33][34][35][36][37][38][39][40][41][43][44][45][46][47][48][49][50][51] ) to perform the microcanonical analysis directly from the conformational microcanonical ensemble, i.e., neglecting the kinetic energy contribution to E, thus performing the analysis based only on the conformational density of states Ω p (E p ). The conformational entropy of a system with fixed potential energy E p is then defined as 62 S p (E p ) = k B ln Ω p (E p ).…”

“…Examples of computational studies include not only lattice [17][18][19][20][21][22][23][24] and magnetic models 25,26 , but also more sophisticated biopolymeric systems, in particular, models for peptide aggregation [27][28][29][30][31][32][33] , protein dimerization 34 , homopolymer collapse [35][36][37] , protein folding [38][39][40][41][42][43][44][45][46][47][48] , and polymer adsorption [49][50][51] .…”

Shape-free theory for the self-assembly kinetics in macromolecular systems

“…It seemed a promising idea since microcanonical entropies and caloric curves have been already evaluated for several finite-size molecular systems which present firstorder phase transitions through advanced computational simulations techniques (e.g., multicanonical [13,14], entropic sampling [15], Wang-Landau [16], and statistical temperature [17,18]). To name a few examples we could mention polymer adsoption [19,20] and condensation [21], protein folding [22][23][24][25] and dimerization [26,27], droplet condensation-evaporation [28], and peptide aggregation [29][30][31][32][33]. However, the approach considered in ref.…”