scholarly journals Knowing one's place: a free-energy approach to pattern regulation

2015 ◽  
Vol 12 (105) ◽  
pp. 20141383 ◽  
Author(s):  
Karl Friston ◽  
Michael Levin ◽  
Biswa Sengupta ◽  
Giovanni Pezzulo
Keyword(s):  
Free Energy ◽  
Self Assembly ◽  
Theoretical Formulation ◽  
Genetic Codes ◽  
Variational Free Energy ◽  
Action And Perception ◽  
Cell Groups ◽  
Biological Pattern Formation ◽  
Pattern Regulation ◽  
Epigenetic Processes

Understanding how organisms establish their form during embryogenesis and regeneration represents a major knowledge gap in biological pattern formation. It has been recently suggested that morphogenesis could be understood in terms of cellular information processing and the ability of cell groups to model shape. Here, we offer a proof of principle that self-assembly is an emergent property of cells that share a common (genetic and epigenetic) model of organismal form. This behaviour is formulated in terms of variational free-energy minimization—of the sort that has been used to explain action and perception in neuroscience. In brief, casting the minimization of thermodynamic free energy in terms of variational free energy allows one to interpret (the dynamics of) a system as inferring the causes of its inputs—and acting to resolve uncertainty about those causes. This novel perspective on the coordination of migration and differentiation of cells suggests an interpretation of genetic codes as parametrizing a generative model—predicting the signals sensed by cells in the target morphology—and epigenetic processes as the subsequent inversion of that model. This theoretical formulation may complement bottom-up strategies—that currently focus on molecular pathways—with (constructivist) top-down approaches that have proved themselves in neuroscience and cybernetics.

Use of Minimal Free Energy and Self-Assembly To Form Shapes

1995 ◽  
Vol 7 (6) ◽  
pp. 1257-1264 ◽  
Author(s):  
Enoch Kim ◽  
George M. Whitesides
Keyword(s):  
Free Energy ◽  
Self Assembly ◽  
Minimal Free Energy

scholarly journals Surface modification and adhesion improvement of polyester films

2013 ◽  
Vol 11 (1) ◽  
pp. 35-45 ◽  
Author(s):  
Aniello Cammarano ◽  
Giovanna Luca ◽  
Eugenio Amendola
Keyword(s):  
Free Energy ◽  
Surface Modification ◽  
Surface Free Energy ◽  
Self Assembly ◽  
Treatment Time ◽  
Solution Treatment ◽  
Film Surface ◽  
Critical Surface ◽  
Hydrolysis Time ◽  
Critical Surface Tension

AbstractFacile surface modification of polyester films was performed via chemical solutions treatment. Surface hydrolysis was carried out by means of sodium hydroxide solutions, leading to the formation of carboxylate groups. Three commercial polyester films of 100 μm in thickness were used in this work: AryLite™, Mylar™, and Teonex™, hydrolysis time being the main modification parameter. FTIR-ATR analysis, topography and contact angle (CA) measurements, surface free energy (SFE) and T-Peel adhesion tests were carried out to characterize the modified films. A quantitative estimate of the carboxylates surface coverage as a function of treatment time was obtained through a supramolecular approach, i.e. the ionic self-assembly of a tetracationic porphyrin chromophore onto the film surface. The surface free energy and critical surface tension of the hydrolyzed polyesters was evaluated by means of Zisman, Saito, Berthelot and Owens-Wendt methods. It was shown that NaOH solution treatment increases roughness, polarity and surface free energy of polymers. As a result, T-Peel strengths for modified Mylar™ and Teonex™ films were respectively 2.2 and 1.8 times higher than that for the unmodified films, whereas AryLite™ adhesion test failed.

scholarly journals Active user detection and channel estimation of uplink grant-free SCMA system based on variational free energy

2020 ◽  
Vol 50 (7) ◽  
pp. 964-970
Author(s):  
Quan YUAN ◽  
ZhenYong WANG ◽  
DeZhi LI ◽  
Qing GUO ◽  
ZhenBang WANG
Keyword(s):  
Free Energy ◽  
Channel Estimation ◽  
Variational Free Energy ◽  
Active User

scholarly journals Two-step crystallization and solid–solid transitions in binary colloidal mixtures

2020 ◽  
Vol 117 (45) ◽  
pp. 27927-27933
Author(s):  
Huang Fang ◽  
Michael F. Hagan ◽  
W. Benjamin Rogers
Keyword(s):  
Free Energy ◽  
Self Assembly ◽  
Materials Science ◽  
Protein Structures ◽  
Free Energy Barrier ◽  
Enhanced Sampling ◽  
Homogeneous Fluid ◽  
Metastable Structures ◽  
One Step ◽  
Crystal Phases

Crystallization is fundamental to materials science and is central to a variety of applications, ranging from the fabrication of silicon wafers for microelectronics to the determination of protein structures. The basic picture is that a crystal nucleates from a homogeneous fluid by a spontaneous fluctuation that kicks the system over a single free-energy barrier. However, it is becoming apparent that nucleation is often more complicated than this simple picture and, instead, can proceed via multiple transformations of metastable structures along the pathway to the thermodynamic minimum. In this article, we observe, characterize, and model crystallization pathways using DNA-coated colloids. We use optical microscopy to investigate the crystallization of a binary colloidal mixture with single-particle resolution. We observe classical one-step pathways and nonclassical two-step pathways that proceed via a solid–solid transformation of a crystal intermediate. We also use enhanced sampling to compute the free-energy landscapes corresponding to our experiments and show that both one- and two-step pathways are driven by thermodynamics alone. Specifically, the two-step solid–solid transition is governed by a competition between two different crystal phases with free energies that depend on the crystal size. These results extend our understanding of available pathways to crystallization, by showing that size-dependent thermodynamic forces can produce pathways with multiple crystal phases that interconvert without free-energy barriers and could provide approaches to controlling the self-assembly of materials made from colloids.

VARIATIONAL ELECTROSTATICS FOR CHARGE SOLVATION

2008 ◽  
Vol 07 (03) ◽  
pp. 397-419 ◽  
Author(s):  
ZHEN-GANG WANG
Keyword(s):  
Free Energy ◽  
Energy Functional ◽  
Dielectric Medium ◽  
Constitutive Relationship ◽  
Coulomb Interactions ◽  
Unified Framework ◽  
Variational Free Energy ◽  
The Poisson Equation ◽  
Charge Solvation ◽  
Electrostatic Problems

We show that the equations of continuum electrostatics can be obtained entirely and simply from a variational free energy comprising the Coulomb interactions among all charged species and a spring-like term for the polarization of the dielectric medium. In this formulation, the Poisson equation, the constitutive relationship between polarization and the electric field, as well as the boundary conditions across discontinuous dielectric boundaries, are all natural consequences of the extremization of the free energy functional. This formulation thus treats the electrostatic equations and the energetics within a single unified framework, avoiding some of the pitfalls in the study of electrostatic problems. Application of this formalism to the nonequilbrium solvation free energy in electron transfer is illustrated. Our calculation reaffirms the well-known result of Marcus. We address the recent criticisms by Li and coworkers who claim that the Marcus result is incorrect, and expose some key mistakes in their approach.

Self-assembly behavior of β-cyclodextrin and imipramine. A Free energy perturbation study

2010 ◽  
Vol 371 (1-3) ◽  
pp. 84-90 ◽  
Author(s):  
Tingting Sun ◽  
Xueguang Shao ◽  
Wensheng Cai
Keyword(s):  
Free Energy ◽  
Self Assembly ◽  
Free Energy Perturbation ◽  
Assembly Behavior ◽  
Energy Perturbation

scholarly journals Imaging Somatosensory Cortex Responses Measured by OPM-MEG: Variational Free Energy-based Spatial Smoothing Estimation Approach

iScience ◽  
2022 ◽  
pp. 103752
Author(s):  
Nan An ◽  
Fuzhi Cao ◽  
Wen Li ◽  
Wenli Wang ◽  
Weinan Xu ◽  
...  
Keyword(s):  
Free Energy ◽  
Somatosensory Cortex ◽  
Spatial Smoothing ◽  
Variational Free Energy

Densification and fine grain formation mechanisms of BaTiO3 ceramics consolidated by self-assembly sintering

2021 ◽  
Author(s):  
Quan Jin ◽  
Lili Zhao ◽  
Xiaoting Zhang ◽  
Run Zhang ◽  
Bin Cui
Keyword(s):  
Particle Size ◽  
Free Energy ◽  
Grain Growth ◽  
Surface Free Energy ◽  
Self Assembly ◽  
Formation Mechanisms ◽  
Fine Grained ◽  
Fine Grain ◽  
Angle Method ◽  
Sintering Method

Abstract In this paper, from the perspective of thermodynamics and kinetics, we have studied the mechanism of balancing the densification and grain growth via co-sintering the micron and nano powders, also known as self-assembly sintering. In the experiment, the 200 nm and 80 nm BaTiO 3 spherical powders were used as models for combination and co-sintering. In terms of thermodynamics, the contact angle method is applied to determine the free energy of the binary particle size system. The surface free energy of 200 nm and 80 nm BaTiO 3 powders are 51.66 J/mol and 203.47 J/mol, respectively. When the powder ratio is 1:1, the surface free energy of the binary particle size system is 127.56 J/mol, which is the reason for the balance between densification and grain growth. In terms of kinetics, the Arrhenius equation was utilized to calculate the apparent activation energy ( Q ) of the binary particle size system. The results show that the value of Q is 360 kJ/mol at 1000 °C. The fine-grained ceramics with high relative density obtained by this sintering method at a low sintering temperature (1000 °C) can be explained by the relative low value of Q.

scholarly journals Bioelectric gene and reaction networks: computational modelling of genetic, biochemical and bioelectrical dynamics in pattern regulation

2017 ◽  
Vol 14 (134) ◽  
pp. 20170425 ◽  
Author(s):  
Alexis Pietak ◽  
Michael Levin
Keyword(s):  
Regulatory Networks ◽  
Computational Modelling ◽  
Reaction Diffusion ◽  
Signalling Molecules ◽  
Physical Mechanisms ◽  
Biological Pattern Formation ◽  
The Stability ◽  
Key Aspects ◽  
Biochemical Signals ◽  
Pattern Regulation

Gene regulatory networks (GRNs) describe interactions between gene products and transcription factors that control gene expression. In combination with reaction–diffusion models, GRNs have enhanced comprehension of biological pattern formation. However, although it is well known that biological systems exploit an interplay of genetic and physical mechanisms, instructive factors such as transmembrane potential ( V mem ) have not been integrated into full GRN models. Here we extend regulatory networks to include bioelectric signalling, developing a novel synthesis: the bioelectricity-integrated gene and reaction (BIGR) network. Using in silico simulations, we highlight the capacity for V mem to alter steady-state concentrations of key signalling molecules inside and out of cells. We characterize fundamental feedbacks where V mem both controls, and is in turn regulated by, biochemical signals and thereby demonstrate V mem homeostatic control, V mem memory and V mem controlled state switching. BIGR networks demonstrating hysteresis are identified as a mechanisms through which more complex patterns of stable V mem spots and stripes, along with correlated concentration patterns, can spontaneously emerge. As further proof of principle, we present and analyse a BIGR network model that mechanistically explains key aspects of the remarkable regenerative powers of creatures such as planarian flatworms. The functional properties of BIGR networks generate the first testable, quantitative hypotheses for biophysical mechanisms underlying the stability and adaptive regulation of anatomical bioelectric pattern.

scholarly journals In vitro neural networks minimise variational free energy

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Takuya Isomura ◽  
Karl Friston
Keyword(s):  
Neural Networks ◽  
Free Energy ◽  
Variational Free Energy
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