Minimum Free Energy Research Articles

RocMLMs: Predicting Rock Properties Through Machine Learning Models

AbstractMineral phase transformations significantly alter the bulk density and elastic properties of mantle rocks and consequently have profound effects on mantle dynamics and seismic wave propagation. These changes in the physical properties of mantle rocks result from evolution in the equilibrium mineralogical composition, which can be predicted by the minimization of the Gibbs Free Energy with respect to pressure (P), temperature (T), and chemical composition (X). Thus, numerical models that simulate mantle convection and/or probe the elastic structure of the Earth's mantle must account for varying mineralogical compositions to be self‐consistent. Yet coupling Gibbs Free Energy minimization (GFEM) approaches with numerical geodynamic models is currently intractable for high‐resolution simulations because prediction speeds of widely‐used GFEM programs (100–102 ms) are impractical in many cases. As an alternative, this study introduces machine learning models (RocMLMs) that have been trained to predict thermodynamically self‐consistent rock properties at arbitrary PTX conditions between 1–28 GPa and 773–2,273 K, and dry mantle compositions ranging from fertile (lherzolitic) to refractory (harzburgitic) end‐members define9d with a large data set of published mantle compositions. RocMLMs are 101–103 times faster than GFEM calculations or GFEM‐based look‐up table approaches with equivalent accuracy. Depth profiles of RocMLMs predictions are nearly indistinguishable from reference models PREM and STW105, demonstrating good agreement between thermodynamic‐based predictions of density, Vp, and Vs and geophysical observations. RocMLMs are therefore capable, for the first time, of emulating dynamic evolution of density, Vp, and Vs due to partial melting and refertilization of dry mantle rocks in high‐resolution numerical geodynamic models.

GraphPPL.jl: A Probabilistic Programming Language for Graphical Models

This paper presents GraphPPL.jl, a novel probabilistic programming language designed for graphical models. GraphPPL.jl uniquely represents probabilistic models as factor graphs. A notable feature of GraphPPL.jl is its model nesting capability, which facilitates the creation of modular graphical models and significantly simplifies the development of large (hierarchical) graphical models. Furthermore, GraphPPL.jl offers a plugin system to incorporate inference-specific information into the graph, allowing integration with various well-known inference engines. To demonstrate this, GraphPPL.jl includes a flexible plugin to define a Constrained Bethe Free Energy minimization process, also known as variational inference. In particular, the Constrained Bethe Free Energy defined by GraphPPL.jl serves as a potential inference framework for numerous well-known inference backends, making it a versatile tool for diverse applications. This paper details the design and implementation of GraphPPL.jl, highlighting its power, expressiveness, and user-friendliness. It also emphasizes the clear separation between model definition and inference while providing developers with extensibility and customization options. This establishes GraphPPL.jl as a high-level user interface language that allows users to create complex graphical models without being burdened with the complexity of inference while allowing backend developers to easily adopt GraphPPL.jl as their frontend language.

Cortical development in the structural model and free energy minimization.

A model of neocortical development invoking Friston's Free Energy Principle is applied within the Structural Model of Barbas etal. and the associated functional interpretation advanced by Tucker and Luu. Evolution of a neural field with Hebbian and anti-Hebbian plasticity, maximizing synchrony and minimizing axonal length by apoptotic selection, leads to paired connection systems with mirror symmetry, interacting via Markov blankets along their line of reflection. Applied to development along the radial lines of development in the Structural Model, a primary Markov blanket emerges between the centrifugal synaptic flux in layers 2,3 and 5,6, versus the centripetal flow in layer 4, and axonal orientations in layer 4 give rise to the differing shape and movement sensitivities characteristic of neurons of dorsal and ventral neocortex. Prediction error minimization along the primary blanket integrates limbic and subcortical networks with the neocortex. Synaptic flux bypassing the blanket triggers the arousal response to surprising stimuli, enabling subsequent adaptation. As development progresses ubiquitous mirror systems separated by Markov blankets and enclosed blankets-within-blankets arise throughout neocortex, creating the typical order and response characteristics of columnar and noncolumnar cortex.

Predicting p53-dependent cell transitions from thermodynamic models.

A cell's fate involves transitions among its various states, each defined by a distinct gene expression profile governed by the topology of gene regulatory networks, which are affected by 3D genome organization. Here, we develop thermodynamic models to determine the fate of a malignant cell as governed by the tumor suppressor p53 signaling network, taking into account long-range chromatin interactions in the mean-field approximation. The tumor suppressor p53 responds to stress by selectively triggering one of the potential transcription programs that influence many layers of cell signaling. These range from p53 phosphorylation to modulation of its DNA binding affinity, phase separation phenomena, and internal connectivity among cell fate genes. We use the minimum free energy of the system as a fundamental property of biological networks that influences the connection between the gene network topology and the state of the cell. We constructed models based on network topology and equilibrium thermodynamics. Our modeling shows that the binding of phosphorylated p53 to promoters of target genes can have properties of a first order phase transition. We apply our model to cancer cell lines ranging from breast cancer (MCF-7), colon cancer (HCT116), and leukemia (K562), with each one characterized by a specific network topology that determines the cell fate. Our results clarify the biological relevance of these mechanisms and suggest that they represent flexible network designs for switching between developmental decisions.

Theoretical Analysis of Self-Shrinkage Spheroidization of Irregular Degradable Polymer Powder under Thermodynamic Nonequilibrium State

Laser three-dimensional (3D) printing offers significant advantages in integrating the shape and function of regenerative tissues through biomimetic manufacturing. However, its effectiveness is limited by the lack of specialized biopolymer powders—while solvent methods that use residual solvents produce powders with poor biocompatibility, mechanical methods result in irregularly shaped crystals. In this study, a biopolymer powder spheroidization and shaping technology, which utilizes the evolution of irregular powders into spheres with minimal surface free energy in the molten state, is proposed based on the thermodynamic principle of minimum energy. Initially, the motion trajectory and temperature field of the poly(L-lactic acid) (PLLA) powder during spheroidization were quantitatively assessed and optimized using Stokes’ law and Fourier's principle. Subsequently, the cohesive forces and aggregation kinetics of the polymer chains were calculated using molecular dynamics. Finally, based on these calculations, a phase-field model was constructed to simulate the evolution of the spheroidization rate and deduce the optimal parameters for the process. This precise approach enhances PLLA spheroidization control for laser 3D printing, improves part densification and surface quality, and offers a clean and efficient path for preparing high-quality PLLA spheroidized powder for laser 3D printing.

Slow but flexible or fast but rigid? Discrete and continuous processes compared

A tradeoff exists when dealing with complex tasks composed of multiple steps. High-level cognitive processes can find the best sequence of actions to achieve a goal in uncertain environments, but they are slow and require significant computational demand. In contrast, lower-level processing allows reacting to environmental stimuli rapidly, but with limited capacity to determine optimal actions or to replan when expectations are not met. Through reiteration of the same task, biological organisms find the optimal tradeoff: from action primitives, composite trajectories gradually emerge by creating task-specific neural structures. The two frameworks of active inference – a recent brain paradigm that views action and perception as subject to the same free energy minimization imperative – well capture high-level and low-level processes of human behavior, but how task specialization occurs in these terms is still unclear. In this study, we compare two strategies on a dynamic pick-and-place task: a hybrid (discrete-continuous) model with planning capabilities and a continuous-only model with fixed transitions. Both models rely on a hierarchical (intrinsic and extrinsic) structure, well suited for defining reaching and grasping movements, respectively. Our results show that continuous-only models perform better and with minimal resource expenditure but at the cost of less flexibility. Finally, we propose how discrete actions might lead to continuous attractors and compare the two frameworks with different motor learning phases, laying the foundations for further studies on bio-inspired task adaptation.

Role of Solvent and Noncovalent Interactions in Alkaline Reactivity of Strained and Strain-Free Macrocyclic Disulfides.

This study employs ab initiomolecular dynamics simulations to investigate the impact of solvent and non-bonded interactions on the structure-reactivity relationship of both strain-free and strained macrocyclic disulfides. Our findings reveal that interactions with water as a solvent significantly influence the minimum energy geometry structures of both conformers of the studied macrocycle. In particular, our simulations identify short contacts, specifically S···π-aromatic interactions, which suppress reactivity for the strained isomer by obstructing the reaction cone at the minimum free energy. Surprisingly, the free energy barriers for the disulfide reaction with a simple nucleophile (OH-anion) remain very similar, despite one conformer having a markedly more strained disulfide bond than the other. Enhanced molecular dynamics simulations in explicit solution elucidate this apparent contradiction by revealing different solvent exposures of the two sulfur atoms in the macrocycles.

Fracture as an Emergent Phenomenon

The mechanics of fracture propagation provides essential knowledge for the risk tolerance design of devices, structures, and vehicles. Techniques of free energy minimization provide guidance, but have limited applicability to material systems evolving away from equilibrium. Experimental evidence shows that the material response depends on driving forces arising from mechanical fields. Recent years have witnessed the development of new methods for modeling complex dynamic and quasistatic fracture. New approaches may differ remarkably from previous ones, as they involve implicit coupling between damaged and undamaged states, allowing fracture to be modeled as emergent phenomena.The focus of this workshop is on the most advanced techniques for modeling fracture, represented by eigenerosion methods, variational approaches, phase field fracture models, and non-local approaches. Technical progress is contingent on the further development of the mathematical framework underlying these techniques. This is necessary for accurate and reliable computational modeling of fracture for multiple freely propagating cracks. The objective of this workshop is to mathematically identify and discuss open issues related to fracture modeling and to highlight recent advances. Addressing fundamental issues will foster exchange between the different communities, essential for advancing the field.

Wfold: A new method for predicting RNA secondary structure with deep learning

Precise estimations of RNA secondary structures have the potential to reveal the various roles that non-coding RNAs play in regulating cellular activity. However, the mainstay of traditional RNA secondary structure prediction methods relies on thermos-dynamic models via free energy minimization, a laborious process that requires a lot of prior knowledge. Here, RNA secondary structure prediction using Wfold, an end-to-end deep learning-based approach, is suggested. Wfold is trained directly on annotated data and base-pairing criteria. It makes use of an image-like representation of RNA sequences, which an enhanced U-net incorporated with a transformer encoder can process effectively. Wfold eventually increases the accuracy of RNA secondary structure prediction by combining the benefits of self-attention mechanism's mining of long-range information with U-net's ability to gather local information. We compare Wfold's performance using RNA datasets that are within and across families. When trained and evaluated on different RNA families, it achieves a similar performance as the traditional methods, but dramatically outperforms the state-of-the-art methods on within-family datasets. Moreover, Wfold can also reliably forecast pseudoknots. The findings imply that Wfold may be useful for improving sequence alignment, functional annotations, and RNA structure modeling.

Mechanism of Dual-Site Recognition in a Classic DNA Aptamer.

Nucleic acid aptamers possess unique advantages in specific recognition. However, the lack of in-depth investigation into their dynamic recognition mechanisms has restricted their rational design and potential applications in fields such as biosensing and targeted therapy. We herein utilized enhanced sampling molecular dynamics to address affinities of adenosine monophosphate (AMP) to the dual binding sites in the DNA aptamer, focusing on the dynamic recognition mechanism and pathways. The present results indicate that in addition to the widely known intermolecular interactions, inequivalence of chemical environments of the two binding sites leads to slightly higher stability of AMP binding to the site proximal to the aptamer terminus. In the presence of two AMPs captured by the two sites, each binding free energy is enhanced. In particular, an additional hydrogen bond of AMP to A10 is introduced in the dual-site binding complex, which increases the binding energy from -4.25 ± 0.47 to -9.48 ± 0.33 kcal mol-1 in the site close to the loop. For the dual-site recognition process, the free energy landscape and minimum free energy pathway calculations elucidate the crucial role of electrostatic interactions between the AMP phosphate groups and Na+ ions in positively cooperative binding mechanisms.

Associative Learning and Active Inference.

Associative learning is a behavioral phenomenon in which individuals develop connections between stimuli or events based on their co-occurrence. Initially studied by Pavlov in his conditioning experiments, the fundamental principles of learning have been expanded on through the discovery of a wide range of learning phenomena. Computational models have been developed based on the concept of minimizing reward prediction errors. The Rescorla-Wagner model, in particular, is a well-known model that has greatly influenced the field of reinforcement learning. However, the simplicity of these models restricts their ability to fully explain the diverse range of behavioral phenomena associated with learning. In this study, we adopt the free energy principle, which suggests that living systems strive to minimize surprise or uncertainty under their internal models of the world. We consider the learning process as the minimization of free energy and investigate its relationship with the Rescorla-Wagner model, focusing on the informational aspects of learning, different types of surprise, and prediction errors based on beliefs and values. Furthermore, we explore how well-known behavioral phenomena such as blocking, overshadowing, and latent inhibition can be modeled within the active inference framework. We accomplish this by using the informational and novelty aspects of attention, which share similar ideas proposed by seemingly contradictory models such as Mackintosh and Pearce-Hall models. Thus, we demonstrate that the free energy principle, as a theoretical framework derived from first principles, can integrate the ideas and models of associative learning proposed based on empirical experiments and serve as a framework for a better understanding of the computational processes behind associative learning in the brain.

Thermodynamic investigation of biomass-steam gasification in converter vaporisation flue for synthesis gas production

Biomass gasification for hydrogen production is a highly promising technology for energy conversion and utilisation. This paper proposed a novel technology for the injection of biomass and steam into the flue of a converter vaporisation to produce hydrogen-rich syngas. The feasibility of hydrogen generation through gasification between biomass, steam, and carbon dioxide in the high-temperature flue gas was investigated based on the thermodynamic principle of Gibbs free energy minimisation. The influence of gasification parameters on the composition of syngas was also explored. The results indicate that in the gasification process, biomass and steam injected into the converter vaporisation flue can effectively inhibit the generation of by-products such as tar. As the steam volume increases, the volume fraction of hydrogen in the product also increases, while the concentration of carbon monoxide decreases. By adjusting the steam-to-biomass ratio, syngas with a hydrogen content exceeding 20% can be produced. At a reaction temperature of 1200 °C, with a steam addition of 5%, a biomass addition of 8 g/L, and a [Formula: see text] ratio of 3, the gas products are composed of 25% hydrogen and 67% carbon dioxide. The process has the potential to achieve a hydrogen yield of up to 90%, a syngas yield of 94%, and a CO2 conversion rate of 70%. Additionally, the lower heating value of the syngas is measured at 11.24 MJ/Nm3. The research results have confirmed the viability of the new technology, thus establishing a theoretical foundation for the industrial implementation of injecting biomass and steam into the converter vaporisation flue to produce hydrogen-rich syngas.

How preferences enslave attention: calling into question the endogenous/exogenous dichotomy from an active inference perspective

AbstractIt is easy to think of attention as a purely sensorimotor, exogenous mechanism divorced from the influence of an agent’s preferences and needs. However, according to the active inference framework, such a strict reduction cannot be straightforwardly invoked, since all cognitive and behavioural processes can at least be described as maximising the evidence for a generative model entailed by the ongoing existence of that agent; that is, the minimisation of variational free energy. As such, active inference models could cast an (embodied) cognitive mechanism like attention, described in this paper as a relevance filter, as constrained (or enslaved) by these prior preferences for which an agent must seek evidence, whether or not such priors are having direct, real-time neurocognitive effects on the sensorimotor loops that couple the attending agent and her surrounding environment. This duality with respect to the role of priors corresponds to a wider, ongoing debate in the active inference community regarding the framework’s explanatory power. More specifically, the debate centres on whether the notion of a generative model and the priors embedded ubiqitously therein act as a purely useful instrumental tool for scientists aiming to model the behaviours of self-organising entities, or, rather, the brain (and body) is genuinely constituted by a predictive hierarchy within which higher-order dynamics constrain and contextualise activity unfolding at lower levels. With a focus on the second (ontologically realist) construal of active inference presented here, this paper argues that in cognitive systems endowed with attentional schema, higher-order preferences do, indeed, impose a demonstrable and powerful modulating effect on the way attention unfolds. Furthermore, these preferences in question transcend the contingent, task-relevant goals that have already been shown to bias attention. Rather, attention is powerfully tuned by the most-deep rooted priors the agent possesses, such that, when sensory evidence against these priors is observed and free energy spikes, the agent attentionally prioritises the homeostatic restoration of these preferred states over their shorter-term desires. This suggests that, at its core, attention is a goal-driven process, which calls into question the putative dichotomy that exists between endogenous (goal-directed) attention and exogenous (stimulus-driven) attention. What emerges in its place is a symbiotic relationship between attention and preferences, whereby the fulfilment of the latter rests on successful application of the former, and the former derives its function from the organismic need to find evidence for the latter.

Efficient acceleration of the convergence of the minimum free energy path via a path-planning generated initial guess.

We demonstrate that combining a shifted clustering algorithm with a fast-marching-based algorithm can generate accurate approximations of the minimum energy path (MEP) given a free energy landscape (FEL). Using this approximation as the initial guess for the MEP, followed by further refinement with the string method (referred to as the fast marching tree (FMT)-string combined approach), significantly reduces the number of iterations required for MEP convergence. This approach saves substantial time compared to using linear interpolation (LI) for the initial guess. Our method offers a viable solution for obtaining an effective initial guess of the MEP when an approximate or converged FEL is available. This work highlights the potential of applying FMT-based approaches to extract the MEP in chemical reactions.

From computational prediction to experimental validation: Hesperidin's anti-Urolithiatic activity in sodium oxalate-induced urolithiasis models in fruit flies and mice

Kidney stones have been a long-standing health issue, contributing to renal failure, especially in co-morbid patients. There is an increasing interest in exploring natural compounds with anti-urolithiatic properties. Our study utilized in-silico techniques followed by in vivo experiments to evaluate the anti-urolithiatic potential of selected phytoconstituents. Molecular docking studies were conducted on 11 different targets, including inhibitors of kidney stone formation, antioxidant enzymes, and biomarkers of kidney injury, to explore the potential of anti-urolithiatic effects of 38 phytoconstituents from medicinal plants possessing diuretic activity. Further, the anti-urolithiatic activity of the phytoconstituent was evaluated using a sodium oxalate-induced urolithiatic fruit fly and mouse model. Hesperidin emerged as a promising candidate, exhibiting binding interactions with a specific set of 11 target proteins involved in crystal formation with minimal free energy. Hesperidin demonstrated promising anti-urolithiatic potential in mitigating urolithiasis as evidenced by reduced crystal covered area of Malpighian tubules of fruit fly and reduced blood urea nitrogen (BUN), serum creatinine and serum sodium, potassium levels in mice. Moreover, it increased urine volume, preventing crystal deposition, and reduced urine urea nitrogen, creatinine, sodium, and potassium levels, enhancing urine flow and preventing crystal accumulation. Histopathological analysis further supported its efficacy by showing minimal crystal deposition and reduced kidney damage. Hesperidin exhibited superior effectiveness in reducing various serum and urine parameters, making it promising alternatives for urolithiasis management warranting further investigation to determine its safety and optimal dosages in human.

Topologically frustrated structures in inkjet printed chiral nematic liquid crystal droplets - experiments and simulations.

Director field alignment in inkjet printed droplets of chiral nematic liquid crystalline materials is investigated using both experiments and numerical simulations. Experimental investigations are performed by depositing droplets of varying sizes and pitches on homeotropic alignment layers. The competition between the bulk behaviour of the chiral nematic liquid crystal and the boundary conditions imposed by the droplet surface leads to the formation of a range of possible internal director configurations. Numerical investigations are performed using a free energy minimisation approach, and the resultant simulated polarising optical microscope images are found to agree well with experimental observations.

Unraveling the mechanism of carbonic anhydrase IX inhibition by alkaloids from Ruta chalepensis: A synergistic analysis of in vitro and in silico data

Due to the pivotal role of carbonic anhydrase IX (CA IX) in pathological conditions, there's a pressing need for novel inhibitors to improve patient outcomes and clinical management. Herein, we investigated the inhibitory efficacy of six alkaloids from Ruta chalepensis against CA IX through in vitro inhibition assay and computational modeling. Skimmianine and maculosidine displayed significant inhibitory activity in vitro, with low IC50 values of 105.2 ± 3.2 and 295.7 ± 14.1 nM, respectively. Enzyme kinetics analyses revealed that skimmianine exhibited a mixed inhibition mode, contrasting with the noncompetitive inhibition mechanism observed for the reference drug (acetazolamide), as indicated by intersecting lines in the Lineweaver-Burk plots. The findings of docking calculations revealed that skimmianine and maculosidine exhibited extensive polar interactions with the enzyme. These alkaloids demonstrate substantial binding interactions and occupy identical binding site as acetazolamide, thereby enhancing their efficacy as inhibitors of CA IX. Utilizing a 100 ns molecular dynamics (MD) simulation, the dynamic interactions between isolated alkaloids and CA IX were intensively assessed. Analysis of diverse MD parameters revealed that skimmianine and maculosidine displayed consistent trajectories and notable energy stabilization during their interaction with CA IX. The findings of MM/PBSA analysis depicted the minimum binding free energy for skimmianine and maculosidine. In addition, the Potential Energy Landscape (PEL) analysis revealed distinct and stable conformational states for the CA IX-ligand complexes, with Skimmianine showing the most stable and lowest energy configuration. These computational findings align with experimental results, emphasizing the potential efficacy of skimmianine and maculosidine as inhibitors of CA IX.

Feasibility of a Personal Neuromorphic Emulation.

The representation of intelligence is achieved by patterns of connections among neurons in brains and machines. Brains grow continuously, such that their patterns of connections develop through activity-dependent specification, with the continuing ontogenesis of individual experience. The theory of active inference proposes that the developmental organization of sentient systems reflects general processes of informatic self-evidencing, through the minimization of free energy. We interpret this theory to imply that the mind may be described in information terms that are not dependent on a specific physical substrate. At a certain level of complexity, self-evidencing of living (self-organizing) information systems becomes hierarchical and reentrant, such that effective consciousness emerges as the consequence of a good regulator. We propose that these principles imply that an adequate reconstruction of the computational dynamics of an individual human brain/mind is possible with sufficient neuromorphic computational emulation.

AlphaFold2 Predicts Alternative Conformation Populations in Green Fluorescent Protein Variants.

Artificial intelligence-based protein structure prediction methods such as AlphaFold2 have emerged as powerful tools for characterizing proteins sequence-structure relationship offering unprecedented opportunities for the molecular interpretation of biological and biochemical phenomena. While initially confined to providing a static representation of proteins through their global free-energy minimum, AlphaFold2 has demonstrated the ability to partially sample conformational landscapes, providing insights into protein dynamics, which is fundamental for interpreting and potentially tuning the function of natural and artificial proteins. In this study, we show that targeted column masking of AlphaFold2's multiple sequence alignment enables the characterization and estimation of the population ratio of the two main conformations of engineered green fluorescent proteins with alternative β-strands. The possibility of quickly estimating relative populations through AlphaFold2 predictions is expected to speed-up the computational design of related systems for sensing applications.

Condensate formation in a chiral lattice gas

Abstract We investigate the formation of condensates in a binary lattice gas in the presence of chiral interactions. These interactions differ between a given microscopic configuration and its mirror image. We consider a two dimensional lattice gas with nearest-neighbour interactions to which we add interactions involving favoured local structures that are chiral. We focus on favoured local structures that have the shape of the letter L and explore condensate formation through simulations and analytical calculations. At low temperature, this model can exhibit four different phases that are characterised by different periodic tiling patterns, depending on the strength of interactions and the chemical potential. When particle numbers are conserved, some of these phases can coexist. We analyse the structure and surface tension of interfaces between coexisting phases and determine the shapes of minimal free energy of crystalline condensates. We show that these shapes can be quadrilaterals or octagons of different orientation and symmetry.