Universal and Accessible Entropy Estimation Using a Compression Algorithm

Abstract

Entropy and free-energy estimation are key in thermodynamic characterization of simulated systems ranging from spin models through polymers, colloids, protein structure, and drug-design. Current techniques suffer from being model specific, requiring abundant computation resources and simulation at conditions far from the studied realization. Here, we present a universal scheme to calculate entropy using lossless compression algorithms and validate it on simulated systems of increasing complexity. Our results show accurate entropy values compared to benchmark calculations while being computationally effective. In molecular-dynamics simulations of protein folding, we exhibit unmatched detection capability of the folded states by measuring previously undetectable entropy fluctuations along the simulation timeline. Such entropy evaluation opens a new window onto the dynamics of complex systems and allows efficient free-energy calculations. I. INTRODUCTIONUtilizing the exponentially growing power of computers enables in-silico experiments of complex and dynamic systems [1]. In these systems, entropy ( ) and enthalpy ( ) should be evaluated to appraise the system thermodynamic properties. While enthalpy can be directly calculated from the interaction strength between the system's components, computing the entropy of an equilibrated canonical system essentially requires inferring the probabilities of all possible microstates (i.e., specific configurations). Nonetheless, for large interacting systems, contemporary computational capabilities do not allow to simulate all possible microstates and thus inadequately map the free-energy landscape. This fact limits current abilities to estimate thermodynamic properties of many interesting systems and phenomena including, for example, protein folding [1][2][3].Present strategies to estimate the entropy from simulations include density-or work-based methods [4]. These methods have been proven useful, though they rely on plentiful computational power, for simulations away from the designated realization [5][6][7]. Alternatively, a reduced phase space assignment can be used, as previously demonstrated in protein folding simulations [1,2,8].There, using a priori knowledge about specific states, each frame is assigned to that state (e.g., folded or unfolded protein states). A rough estimate of the system's entropy and thermodynamic properties is then attained using the respective state populations.Here, we present a framework for efficient and accurate asymptotic entropy (SA) calculation using a lossless compression algorithm. Conceptually, the amount of information stored in a recorded simulation is tightly related to the entropy of the physical system being simulated. At the foundation of our method we use a lossless compression algorithm which is optimized to remove information redundancy by locating repeated patterns within a stream of data.Thus, the ability to compress digital representations of physical systems is directly related to the level of redundancy, hence entropy, in t...

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“…Firstly in the ǫ pp range relevant for FG nups, we find that the computed film thickness (Figure 2c) shows a steep change from a swollen polymer film to a compact film. This is confirmed by other measures of film compaction, such as the mass density and file compressibility, where the file compressibility has been used to describe order in non-equilibrium and equilibrium many-body systems [42,43]. The mass density is calculated by converting the number density within the film thickness to mg/ml assuming a molecular weight of 220 Da for a polymer bead, and the file compressibility corresponds to the losslessly compressed size (in Bytes) of a file containing the MD bead coordinates divided by the losslessly compressed size for ǫ pp = 0.0 k B T (see Supplemental Material).…”

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“…We thank Ron Alfia for preliminary numerical results. We are grateful to Ram Avinery, Roy Beck, and Micha Kornreich for useful discussions and for providing their preprint on the application of data compression to study protein folding [69]. This…”

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