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Nature Communications Aug 2022Integration-to-threshold models of two-choice perceptual decision making have guided our understanding of human and animal behavior and neural processing. Although such...
Integration-to-threshold models of two-choice perceptual decision making have guided our understanding of human and animal behavior and neural processing. Although such models seem to extend naturally to multiple-choice decision making, consensus on a normative framework has yet to emerge, and hence the implications of threshold characteristics for multiple choices have only been partially explored. Here we consider sequential Bayesian inference and a conceptualisation of decision making as a particle diffusing in n-dimensions. We show by simulation that, within a parameterised subset of time-independent boundaries, the optimal decision boundaries comprise a degenerate family of nonlinear structures that jointly depend on the state of multiple accumulators and speed-accuracy trade-offs. This degeneracy is contrary to current 2-choice results where there is a single optimal threshold. Such boundaries support both stationary and collapsing thresholds as optimal strategies for decision-making, both of which result from stationary representations of nonlinear boundaries. Our findings point towards a normative theory of multiple-choice decision making, provide a characterisation of optimal decision thresholds under this framework, and inform the debate between stationary and dynamic decision boundaries for optimal decision making.
Topics: Animals; Bayes Theorem; Decision Making; Diffusion; Humans
PubMed: 36038538
DOI: 10.1038/s41467-022-32741-y -
The Journal of General Physiology Oct 2023Osmosis is an important force in all living organisms, yet the molecular basis of osmosis is widely misunderstood as arising from diffusion of water across a membrane...
Osmosis is an important force in all living organisms, yet the molecular basis of osmosis is widely misunderstood as arising from diffusion of water across a membrane separating solutions of differing osmolarities, and hence different water concentrations. In 1923, Peter Debye proposed a physical model for a semipermeable membrane emphasizing the repulsive forces between solute molecules and membrane that prevent the solute from entering the membrane. His work was hardly noticed at the time and slipped out of view. We show that Debye's analysis of van 't Hoff's law for osmotic equilibrium also provides a consistent and plausible mechanism for osmotic flow. A difference in osmolyte concentrations in solutions separated by a semipermeable membrane leads to different pressures at the two water-membrane interfaces because the total repulsive force between solute molecules and the membrane is different at the two interfaces. Water is therefore driven through the membrane for exactly the same reason that pure water flows in response to an imposed hydrostatic pressure difference. In this paper, we present the Debye model in both equilibrium and flow conditions. We point out its applicability regardless of the nature of the membrane with examples ranging from the predominantly convective flow of water through synthetic membranes and capillary walls to the purely diffusive flow of independent water molecules through a lipid bilayer and the flow of a single-file column of water molecules in narrow protein channels.
Topics: Diffusion; Lipid Bilayers; Osmosis; Pressure; Water
PubMed: 37624228
DOI: 10.1085/jgp.202313332 -
Acta Crystallographica. Section F,... Feb 2016Mass transport takes place within the mesoscopic to macroscopic scale range and plays a key role in crystal growth that may affect the result of the crystallization... (Review)
Review
Mass transport takes place within the mesoscopic to macroscopic scale range and plays a key role in crystal growth that may affect the result of the crystallization experiment. The influence of mass transport is different depending on the crystallization technique employed, essentially because each technique reaches supersaturation in its own unique way. In the case of batch experiments, there are some complex phenomena that take place at the interface between solutions upon mixing. These transport instabilities may drastically affect the reproducibility of crystallization experiments, and different outcomes may be obtained depending on whether or not the drop is homogenized. In diffusion experiments with aqueous solutions, evaporation leads to fascinating transport phenomena. When a drop starts to evaporate, there is an increase in concentration near the interface between the drop and the air until a nucleation event eventually takes place. Upon growth, the weight of the floating crystal overcomes the surface tension and the crystal falls to the bottom of the drop. The very growth of the crystal then triggers convective flow and inhomogeneities in supersaturation values in the drop owing to buoyancy of the lighter concentration-depleted solution surrounding the crystal. Finally, the counter-diffusion technique works if, and only if, diffusive mass transport is assured. The technique relies on the propagation of a supersaturation wave that moves across the elongated protein chamber and is the result of the coupling of reaction (crystallization) and diffusion. The goal of this review is to convince protein crystal growers that in spite of the small volume of the typical protein crystallization setup, transport plays a key role in the crystal quality, size and phase in both screening and optimization experiments.
Topics: Crystallization; Crystallography, X-Ray; Diffusion; Humans; Protein Conformation; Protein Stability; Proteins
PubMed: 26841759
DOI: 10.1107/S2053230X16000030 -
Journal of Mathematical Biology Nov 2023Malignant gliomas are notoriously invasive, a major impediment against their successful treatment. This invasive growth has motivated the use of predictive partial...
Malignant gliomas are notoriously invasive, a major impediment against their successful treatment. This invasive growth has motivated the use of predictive partial differential equation models, formulated at varying levels of detail, and including (i) "proliferation-infiltration" models, (ii) "go-or-grow" models, and (iii) anisotropic diffusion models. Often, these models use macroscopic observations of a diffuse tumour interface to motivate a phenomenological description of invasion, rather than performing a detailed and mechanistic modelling of glioma cell invasion processes. Here we close this gap. Based on experiments that support an important role played by long cellular protrusions, termed tumour microtubes, we formulate a new model for microtube-driven glioma invasion. In particular, we model a population of tumour cells that extend tissue-infiltrating microtubes. Mitosis leads to new nuclei that migrate along the microtubes and settle elsewhere. A combination of steady state analysis and numerical simulation is employed to show that the model can predict an expanding tumour, with travelling wave solutions led by microtube dynamics. A sequence of scaling arguments allows us reduce the detailed model into simpler formulations, including models falling into each of the general classes (i), (ii), and (iii) above. This analysis allows us to clearly identify the assumptions under which these various models can be a posteriori justified in the context of microtube-driven glioma invasion. Numerical simulations are used to compare the various model classes and we discuss their advantages and disadvantages.
Topics: Humans; Glioma; Anisotropy; Computer Simulation; Diffusion; Travel
PubMed: 38015257
DOI: 10.1007/s00285-023-02025-0 -
Biochimica Et Biophysica Acta Oct 2016The dynamics of constituents and the surface response of cellular membranes-also in connection to the binding of various particles and macromolecules to the membrane-are... (Review)
Review
The dynamics of constituents and the surface response of cellular membranes-also in connection to the binding of various particles and macromolecules to the membrane-are still a matter of controversy in the membrane biophysics community, particularly with respect to crowded membranes of living biological cells. We here put into perspective recent single particle tracking experiments in the plasma membranes of living cells and supercomputing studies of lipid bilayer model membranes with and without protein crowding. Special emphasis is put on the observation of anomalous, non-Brownian diffusion of both lipid molecules and proteins embedded in the lipid bilayer. While single component, pure lipid bilayers in simulations exhibit only transient anomalous diffusion of lipid molecules on nanosecond time scales, the persistence of anomalous diffusion becomes significantly longer ranged on the addition of disorder-through the addition of cholesterol or proteins-and on passing of the membrane lipids to the gel phase. Concurrently, experiments demonstrate the anomalous diffusion of membrane embedded proteins up to macroscopic time scales in the minute time range. Particular emphasis will be put on the physical character of the anomalous diffusion, in particular, the occurrence of ageing observed in the experiments-the effective diffusivity of the measured particles is a decreasing function of time. Moreover, we present results for the time dependent local scaling exponent of the mean squared displacement of the monitored particles. Recent results finding deviations from the commonly assumed Gaussian diffusion patterns in protein crowded membranes are reported. The properties of the displacement autocorrelation function of the lipid molecules are discussed in the light of their appropriate physical anomalous diffusion models, both for non-crowded and crowded membranes. In the last part of this review we address the upcoming field of membrane distortion by elongated membrane-binding particles. We discuss how membrane compartmentalisation and the particle-membrane binding energy may impact the dynamics and response of lipid membranes. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.
Topics: Diffusion; Gels; Lipid Bilayers; Membrane Lipids; Membrane Proteins; Molecular Dynamics Simulation; Static Electricity
PubMed: 26826272
DOI: 10.1016/j.bbamem.2016.01.022 -
Magnetic Resonance in Medicine Jun 2020To demonstrate how triple diffusion encoding (TDE) MRI can be applied to separately estimate the intra-axonal and extra-axonal diffusion tensors in white matter (WM).
PURPOSE
To demonstrate how triple diffusion encoding (TDE) MRI can be applied to separately estimate the intra-axonal and extra-axonal diffusion tensors in white matter (WM).
METHODS
Using a TDE pulse sequence with an axially symmetric b-matrix, diffusion MRI data were acquired at 3T for 3 healthy adults with an axial b-value of 4000 s/mm , a radial b-value of 307 s/mm , and 64 diffusion encoding directions. This acquisition was then repeated with the radial b-value set to 0. A previously proposed theory was applied to these data in order to estimate the intra-axonal diffusivity and axonal water fraction for each WM voxel. Conventional single diffusion encoding data were also obtained with b-values of 1000 and 2000 s/mm , which provided additional information sufficient for determining both the intra-axonal and extra-axonal diffusion tensors.
RESULTS
From the TDE data, the average intra-axonal diffusivity in WM was found to be 2.24 ± 0.18 µm /ms, and the average axonal water fraction was found to be 0.60 ± 0.11. From the 2 diffusion tensors, average WM values were estimated for several compartment-specific diffusion parameters. In particular, the extra-axonal mean diffusivity was 1.09 ± 0.19 µm /ms, the intra-axonal fractional anisotropy was 0.50 ± 0.14, and the extra-axonal fractional anisotropy was 0.23 ± 0.13.
CONCLUSION
By using a simple TDE pulse sequence with an axially symmetric b-matrix, the diffusion tensors for the intra-axonal and extra-axonal spaces can be separately estimated in adult WM. This allows one to determine compartment-specific diffusion properties for these 2 water pools.
Topics: Adult; Anisotropy; Axons; Diffusion; Diffusion Magnetic Resonance Imaging; Diffusion Tensor Imaging; Humans; White Matter
PubMed: 31763730
DOI: 10.1002/mrm.28084 -
The Journal of Physiology Mar 2021Timely delivery of oxygen (O ) to tissue mitochondria is so essential that elaborate circulatory systems have evolved to minimize diffusion distances within tissue. Yet,... (Review)
Review
Timely delivery of oxygen (O ) to tissue mitochondria is so essential that elaborate circulatory systems have evolved to minimize diffusion distances within tissue. Yet, knowledge is surprisingly limited regarding the diffusion pathway between blood capillaries and tissue mitochondria. An established and growing body of work examines the influence cellular and extracellular structures may have on subcellular oxygen availability. This brief review discusses the physiological and pathophysiological significance of oxygen availability, highlights recent computer modelling studies of transport at the cell-membrane level, and considers alternative diffusion pathways within tissue. Experimental and computer modelling studies suggest that oxygen diffusion may be accelerated by cellular lipids, relative to cytosolic and interstitial fluids. Such acceleration, or 'channelling', would occur due to greatly enhanced oxygen solubility in lipids, especially near the midplane of lipid bilayers. Rapid long-range movement would be promoted by anisotropically enhanced lateral diffusion of oxygen along the midplane and by junctions holding lipid structures in close proximity to one another throughout the tissue. Clarifying the biophysical mechanism of oxygen transport within tissue will shed light on limitations and opportunities in tumour radiotherapy and tissue engineering.
Topics: Capillaries; Cell Membrane Permeability; Diffusion; Mitochondria; Oxygen; Oxygen Consumption
PubMed: 33215707
DOI: 10.1113/JP278815 -
International Journal of Molecular... Nov 2023Using the framework of a continuous diffusion model based on the Smoluchowski equation, we analyze particle dynamics in the confinement of a transmembrane nanopore. We... (Review)
Review
Using the framework of a continuous diffusion model based on the Smoluchowski equation, we analyze particle dynamics in the confinement of a transmembrane nanopore. We briefly review existing analytical results to highlight consequences of interactions between the channel nanopore and the translocating particles. These interactions are described within a minimalistic approach by lumping together multiple physical forces acting on the particle in the pore into a one-dimensional potential of mean force. Such radical simplification allows us to obtain transparent analytical results, often in a simple algebraic form. While most of our findings are quite intuitive, some of them may seem unexpected and even surprising at first glance. The focus is on five examples: (i) attractive interactions between the particles and the nanopore create a potential well and thus cause the particles to spend more time in the pore but, nevertheless, increase their net flux; (ii) if the potential well-describing particle-pore interaction occupies only a part of the pore length, the mean translocation time is a non-monotonic function of the well length, first increasing and then decreasing with the length; (iii) when a rectangular potential well occupies the entire nanopore, the mean particle residence time in the pore is independent of the particle diffusivity inside the pore and depends only on its diffusivity in the bulk; (iv) although in the presence of a potential bias applied to the nanopore the "downhill" particle flux is higher than the "uphill" one, the mean translocation times and their distributions are identical, i.e., independent of the translocation direction; and (v) fast spontaneous gating affects nanopore selectivity when its characteristic time is comparable to that of the particle transport through the pore.
Topics: Nanopores; Diffusion
PubMed: 37958906
DOI: 10.3390/ijms242115923 -
PloS One 2023The diffusion phenomena taking place in complex networks are usually modelled as diffusion process, such as the diffusion of diseases, rumors and viruses. Identification...
The diffusion phenomena taking place in complex networks are usually modelled as diffusion process, such as the diffusion of diseases, rumors and viruses. Identification of diffusion source is crucial for developing strategies to control these harmful diffusion processes. At present, accurately identifying the diffusion source is still an opening challenge. In this paper, we define a kind of diffusion characteristics that is composed of the diffusion direction and time information of observers, and propose a neural networks based diffusion characteristics classification framework (NN-DCCF) to identify the source. The NN-DCCF contains three stages. First, the diffusion characteristics are utilized to construct network snapshot feature. Then, a graph LSTM auto-encoder is proposed to convert the network snapshot feature into low-dimension representation vectors. Further, a source classification neural network is proposed to identify the diffusion source by classifying the representation vectors. With NN-DCCF, the identification of diffusion source is converted into a classification problem. Experiments are performed on a series of synthetic and real networks. The results show that the NN-DCCF is feasible and effective in accurately identifying the diffusion source.
Topics: Neural Networks, Computer; Diffusion
PubMed: 37186596
DOI: 10.1371/journal.pone.0285563 -
ACS Nano Nov 2020Collective decision making by living cells is facilitated by exchange of diffusible signals where sender cells release a chemical signal that is interpreted by receiver...
Collective decision making by living cells is facilitated by exchange of diffusible signals where sender cells release a chemical signal that is interpreted by receiver cells. A variety of nonliving artificial cell models have been developed in recent years that mimic various aspects of diffusion-based intercellular communication. However, localized secretion of diffusive signals from individual protocells, which is critical for mimicking biological sender-receiver systems, has remained challenging to control precisely. Here, we engineer light-responsive, DNA-encoded sender-receiver architectures, where protein-polymer microcapsules act as cell mimics and molecular communication occurs through diffusive DNA signals. We prepare spatial distributions of sender and receiver protocells using a microfluidic trapping array and set up a signaling gradient from a single sender cell using light, which activates surrounding receivers through DNA strand displacement. Our systematic analysis reveals how the effective signal range of a single sender is determined by various factors including the density and permeability of receivers, extracellular signal degradation, signal consumption, and catalytic regeneration. In addition, we construct a three-population configuration where two sender cells are embedded in a dense array of receivers that implement Boolean logic and investigate spatial integration of nonidentical input cues. The results offer a means for studying diffusion-based sender-receiver topologies and present a strategy to achieve the congruence of reaction-diffusion and positional information in chemical communication systems that have the potential to reconstitute collective cellular patterns.
Topics: Artificial Cells; Cell Communication; DNA; Diffusion; Signal Transduction
PubMed: 33078948
DOI: 10.1021/acsnano.0c07537