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Distribution and Dispersion00:54

Distribution and Dispersion

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To understand intra-specific interactions in populations, scientists measure the spatial arrangement of species individuals. This geographic arrangement is known as the species distribution or dispersion. Highly territorial species exhibit a uniform distribution pattern, in which individuals are spaced at relatively equal distances from one another. Species that are highly tied to particular resources, such as food or shelter, tend to concentrate around those resources, and thus exhibit a...
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The Colloidal State01:29

The Colloidal State

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The formation of a colloidal system is exemplified by an aqueous solution containing Cl− ions is introduced to another containing Ag+ ions, resulting in the precipitation of solid AgCl as extremely tiny crystals. Instead of settling out as a filterable precipitate, these crystals remain suspended in the liquid, showcasing a colloidal system.A colloidal system involves colloidal particles within the approximate range of 1 to 1000 nm in at least one dimension, dispersed in a medium called...
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Protein Diffusion in the Membrane01:24

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Proteins show rotational as well as lateral diffusion across the membrane. The lateral diffusion of proteins was confirmed through the cell fusion experiment where mouse and human cells were fused, resulting in hybrid cells. When the human and mouse cells fused, the specific membrane proteins on human and mouse cells were marked with the red and green-fluorescent markers, respectively. Initially, the red and green fluorescence was located on the respective hemisphere of the cell. As time...
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The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a...
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Polymers: Molecular Weight Distribution01:10

Polymers: Molecular Weight Distribution

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For any given polymer, the weight average molecular weight (Mw) is higher than, if not equal to, the number average molecular weight (Mn). The only situation in which the weight average molecular weight and the number average molecular weight are equal is when a polymer consists only of chains with equal molecular weight. However, this never happens in a synthetic polymer, since it is difficult to control the polymerization process up to a molecular level with accuracy to a hundred percent.
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Updated: Mar 6, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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    Area of Science:

    • Systems Biology
    • Biophysics
    • Computational Biology

    Background:

    • Intracellular biomolecular circuits often display multimodal stationary distributions due to intrinsic noise.
    • Dispersion around distribution peaks influences phenotypic robustness and adaptability.
    • Tuning dispersion typically alters peak positions or modality, complicating system design.

    Purpose of the Study:

    • To derive conditions for controlling peak shape without shifting peak positions in biomolecular circuits.
    • To develop a method for tuning dispersion while preserving modality and peak locations.
    • To provide design rules for engineering stochastic phenotypes.

    Main Methods:

    • Utilized the Chemical Fokker-Planck Equation to analyze system dynamics.
    • Formalized peak sharpness using local probability ratios.
    • Employed Monte Carlo simulations for validation.

    Main Results:

    • Established conditions for invariant peak and valley positions during parameter variation.
    • Demonstrated monotonic variation of sharpness with a control parameter, preserving modality.
    • Validated dispersion tuning without peak shifts in gene expression and Schlögl systems.
    • Showed preliminary evidence of sharpness control in a multivariate Genetic Toggle Switch model.

    Conclusions:

    • Developed a method to independently control peak sharpness and position in biomolecular circuits.
    • Validated the approach in unimodal and bimodal systems, offering a pathway for phenotype engineering.
    • Provided foundational insights for designing robust and adaptable stochastic cellular phenotypes.