Model library

All the names of the models follow the rule: ‘[geometry][dimension][p]_[parameterization]_[…]_[model form]’, with the simplest case as ‘[geometry][dimension]’ (e.g., ring3D). For example, dualEllipse3D_avgR_discrete means a dual-ellipse geometry in 3D, parametrized by the average radius, in a discrete form.

Note

The individual components of the names

  • [geometry]: the geometry.

  • [dimension]: the model dimension.

  • [p]: (optional) when it is mentioned, the model is parametric, otherwise not.

  • [parameterization]: (optional) when multiple parameterizations exist, this is added to identify the specific parameterization. When the [parameterization] is not mentioned, the model is assumed to be with the default parameterization.

  • […]: (optional) if the [parameterization] itself is not sufficient to differentiate the implementations, extra labels are added here.

  • [model form]: (optional) the form of how the model is implemented. When it is not provided, the model is in the continuous form.

Arc

class models.arc2D(varargin)

Bases: @geometricModel.geometricModel

arc2D is a 2D model that describes an arc geometry.

Geometric parameters:

  • radius: (nm) the radius of the ring where the arc is derived.

  • theta: (degree) the closing anlge of the arc.

Relavent biological structure:

  • Cross-section of a clathrin coat

Preview:
_images/arc2D.png

Scale bar: 50 nm.

reference(par, dx)

For details, see reference().

class models.arc2D_arcLen(varargin)

Bases: @geometricModel.geometricModel

arc2D_arcLen is a 2D model that describes an arc geometry. It describes the same geometry as by arc2D but with a different parameterization.

Geometric parameters:

  • arcLength: (nm) the length of the arc.

  • theta: (degree) the closing anlge of the arc.

Relavent biological structure:

  • Cross-section of a clathrin coat

See also

arc2D

reference(par, dx)

For details, see reference().

Bucket

class models.bucket2D(varargin)

Bases: @geometricModel.geometricModel

bucket2D is a 2D model that describes a bucket geometry. It creates a bucket based on an arc. The bucket is created to contain the arc.

Geometric parameters:

  • radius: (nm) the radius of the ring where the arc is derived.

  • theta: (°) the closing anlge of the arc.

See also

arc2D

reference(par, dx)

For details, see reference().

getDerivedPars(pars)

For details, see getDerivedPars().

Ring

class models.ring2D(varargin)

Bases: @geometricModel.geometricModel

ring2D is a 2D model that describes a ring geometry.

Geometric parameters:

  • radius: (nm) the ring radius.

Relavent biological structure:

  • Top-view projections of the nuclear pore complex.

Preview:

Note

It will be available soon.

reference(par, dx)

For details, see reference().

class models.ellipse3D(varargin)

Bases: @geometricModel.geometricModel

ellipse3D describes a ellipse geometry in 3D.

Geometric parameters:

  • a: (nm) the axis along the x-axis.

  • b: (nm) the axis along the y-axis.

Preview:

Note

It will be available soon.

reference(par, dx)

For details, see reference().

class models.ring3D(varargin)

Bases: @geometricModel.geometricModel

The model class ring3D describes a ring geometry in 3D.

Geometric parameters:

  • radius: (nm) the ring radius.

Relavent biological structure:

  • Top-view projections of the nuclear pore complex.

Preview:

Note

It will be available soon.

reference(par, dx)

For details, see reference().

Spline

class models.cspline3D_midPoint(varargin)

Bases: @geometricModel.geometricModel

A c-spline for describing a linear structure traversing in 3D space.

Geometric parameters:

  • xMid, yMid, zMid: (nm) the xyz coordinates of the mid point.

  • dist: (nm): the distance between neighbouring control points

  • rotAzi[L/R]_n, rotEle[L/R]_n: (°) the azimuthal and elevation

angles or of the vector pointing to the [L/R]_n control point. [L/R] is either L (left) or R (right) with respect to the mid point. n indicates the order. For exmple, rotAziL1 means the azimuthal angle defining the 1st point on the left of the mid point.

Relavent biological structure:

  • Actin filaments

  • The central axes of microtubules

Preview:

Note

It will be available soon.

reference(par, dx)

For details, see reference().

getThings2Plot(par)

The user can define what should be also displayed in the plots.

Parameters

obj – a @geometricModel.geometricModel object.

Returns

items – things to be plotted.

Tube and derivitives

class models.csplineClosedTube3D_midPoint(varargin)

Bases: @geometricModel.geometricModel

A c-spline for describing a flexible tube that has its ends closed, traversing in 3D space.

Geometric parameters:

  • xMid, yMid, zMid: (nm) the xyz coordinates of the mid point.

  • r: (nm) the radius of the tube.

  • dist: (nm): the distance between neighbouring control points

  • rotAzi[L/R]_n, rotEle[L/R]_n: (°) the azimuthal and elevation angles or of the vector pointing to the [L/R]_n control point. [L/R] is either L (left) or R (right) with respect to the mid point. n indicates the order. For exmple, rotAziL1 means the azimuthal angle defining the 1st point on the left of the mid point.

Relavent biological structure:

  • outer membrane of a mitochondria

Preview:

Note

It will be available soon.

reference(par, dx)

For details, see reference().

getThings2Plot(par, varargin)

The user can define what should be also displayed in the plots.

Parameters

obj – a @geometricModel.geometricModel object.

Returns

items – things to be plotted.

getDerivedPars(pars)

Exports a empty variable when no derived parameters.

class models.csplineTube3D_midPoint(varargin)

Bases: @geometricModel.geometricModel

A c-spline for describing a flexible tube traversing in 3D space.

Geometric parameters:

  • xMid, yMid, zMid: (nm) the xyz coordinates of the mid point.

  • r: (nm) the radius of the tube.

  • dist: (nm): the distance between neighbouring control points

  • rotAzi[L/R]_n, rotEle[L/R]_n: (°) the azimuthal and elevation angles or of the vector pointing to the [L/R]_n control point. [L/R] is either L (left) or R (right) with respect to the mid point. n indicates the order. For exmple, rotAziL1 means the azimuthal angle defining the 1st point on the left of the mid point.

Relavent biological structure:

  • actin filaments

  • the central axes of microtubules

Preview:

Note

It will be available soon.

reference(par, dx)

For details, see reference().

getThings2Plot(par, varargin)

The user can define what should be also displayed in the plots.

Parameters

obj – a @geometricModel.geometricModel object.

Returns

items – things to be plotted.

getDerivedPars(pars)

Exports a empty variable when no derived parameters.

class models.csplineTube3D_xyz(varargin)

Bases: @geometricModel.geometricModel

A c-spline for describing a linear structure traversing in 3D space. It describe the same geometry as csplineTube3D_midPoint but with a different parameterization.

Geometric parameters:

  • x_n, y_n, z_n: (nm) the xyz coordinates of the nth control point.

  • r: (nm) the radius of the tube.

Relavent biological structure:

  • Actin filaments

  • The central axes of microtubules

See also

csplineTube3D_midPoint

Preview:

Note

It will be available soon.

reference(par, dx)

set additional parameters of the model

getThings2Plot(par)

The user can define what should be also displayed in the plots.

Parameters

obj – a @geometricModel.geometricModel object.

Returns

items – things to be plotted.

Dual rings and derivitives

class models.dualEllipse3D_discrete(varargin)

Bases: @geometricModel.geometricModel

dualEllipse3D_discrete describes two parallel ellipse in 3D. The ellipse have the same xy positions and short/long axes.

Geometric parameters:

  • ringDistance: (nm) the distance between the two parallel rings.

  • azimuthalShift: (°) the twist angle between the two parallel rings.

  • a: (nm) the length of the long axis.

  • ellipticity: (no unit) or e, is defined as e = 1-b/a, where a and b are the long and short axes.

  • aDir: (°) the rotational offset between the first corner and the long axis a.

  • cornerDegree: (°) the rotational offset between two copies per corner.

Relavent biological structure:

  • deformed nuclear pore complex

Preview:

Note

It will be available soon.

reference(par, dx)

For details, see reference().

class models.dualEllipse3D_avgR_discrete(varargin)

Bases: @geometricModel.geometricModel

dualEllipse3D_avgR_discrete describes two parallel ellipse in 3D. The ellipse have the same xy positions and short/long axes. It describe the same geometry as dualEllipse3D_discrete but with a different parameterization.

Geometric parameters:

  • ringDistance: (nm) the distance between the two parallel rings.

  • azimuthalShift: (°) the twist angle between the two parallel rings.

  • avgR: (nm) the average of the short and long axes.

  • ellipticity: (no unit) or e, is defined as e = 1-b/a, where a and b are the long and short axes.

  • aDir: (°) the rotational offset between the first corner and the long axis a.

  • cornerDegree: (°) the rotational offset between two copies per corner.

Relavent biological structure:

  • deformed nuclear pore complex

See also

dualEllipse3D_discrete

Preview:

Note

It will be available soon.

reference(par, dx)

For details, see reference().

class models.dualRing3D_discrete(varargin)

Bases: @geometricModel.geometricModel

dualRing3D_discrete describes two parallel rings in 3D. The rings have the same xy position and radius.

Geometric parameters:

  • ringDistance: (nm) the distance between the two parallel rings.

  • azimuthalShift: (°) the twist angle between the two parallel rings.

  • radius: (nm) the radius of the rings.

  • cornerDegree: (°) the rotational offset between two copies per corner.

Internal settings:

  • copyPerCorner: (integer values) the copy number of the protein per corner. For example, 2 (default).

  • cornerNum: (integer values) the number of corners. For example, 8 (default).

  • useSecondRing: (logical) true if the second ring is to be used in the model. For example, true (default).

Relavent biological structure:

  • the nuclear pore complex

Preview:

Note

It will be available soon.

reference(par, dx)

For details, see reference().

Sperical model and derivitives

class models.sphericalCap3D_surfaceArea(varargin)

Bases: @geometricModel.geometricModel

sphericalCap3D_surfaceArea describes the geometry of a spherical cap in 3D.

Geometric parameters:

  • surfaceArea: (104 nm2) the surface area of the spherical cap.

  • closeAngle: (°) the angle from the pole to the edge of the cap.

Relavent biological structure:

  • mammalian endocytic coat

Preview:

Note

It will be available soon.

reference(par, dx)

For details, see reference().

getDerivedPars(pars)

For details, see getDerivedPars().

class models.sphericalCap3Dp_surfaceArea(varargin)

Bases: @parametricModel.parametricModel

sphericalCap3Dp_surfaceArea describes a geometry of spherical cap in 3D. It describe the same geometry with the same parameterization as sphericalCap3D_surfaceArea but in a parametric form.

Geometric parameters:

  • surfaceArea: (104 nm2) the surface area of the spherical cap.

  • closeAngle: (°) the angle from the pole to the edge of the cap.

Relavent biological structure:

  • mammalian endocytic coat

See also

sphericalCap3D_surfaceArea

Preview:

See sphericalCap3D_surfaceArea

getDerivedPars(pars)

For details, see getDerivedPars().

class models.spheroid3Dp_surfaceArea(varargin)

Bases: models.spheroidCap3Dp_surfaceArea

spheroid3Dp_surfaceArea describes the geometry of spheroid in 3D. It is parametric. Spheroid is a sphere flattened at the poles.

Important

Here the flattening is applied along the z-axis, not the y-axis.

Geometric parameters:
  • surfaceArea: (104 nm2) the surface area of the spherical cap.

    • flattening: (no unit) or f, is defined as 1-c/a, where a and c are the two distinct axis lengths. c lines on the y-axis.

Relavent biological structure:

  • deformed vesicle

See also

spheroidCap3Dp_surfaceArea

Preview:

Note

It will be available soon.

getDerivedPars(par)

For details, see getDerivedPars().

class models.spheroidCap3Dp_surfaceArea(varargin)

Bases: @parametricModel.parametricModel

sphericalCap3Dp_surfaceArea describes the geometry of spheroid cap in 3D. It is parametric. Spheroid cap is a spherial cap flattened at the poles.

Important

Here the flattening is applied along the y-axis, not the z-axis.

Geometric parameters:

  • surfaceArea: (104 nm2) the surface area of the spherical cap.

  • closeAngle: (°) the angle from the pole to the edge of the cap.

    • flattening: (no unit) or f, is defined as 1-c/a, where a and c are the two distinct axis lengths. c lines on the y-axis.

Relavent biological structure:

  • mammalian endocytic coat

See also

spheroid3Dp_surfaceArea

Preview:

Note

It will be available soon.

getDerivedPars(pars)

For details, see getDerivedPars().

2D projection of 3D geometry

class models.hemispheroid2D(varargin)

Bases: @geometricModel.geometricModel

hemispheroid2D describes the side-view projection of a hemispheroid.

Geometric parameters:

  • a: (nm) the axis along the y-axis.

  • b: (nm) the axis along the x-axis.

  • xcenter: (nm) [obsolete] please set it to zero.

  • ycenter: (nm) [obsolete] please set it to zero.

Relavent biological structure:

  • actin network at the endocytic site

Preview:

Note

It will be available soon.

reference(par, dx)

For details, see reference().

class models.thickRing2D(varargin)

Bases: @geometricModel.geometricModel

thickRing2D describes the side-view projection of a thick ring.

Geometric parameters:

  • innerRadius: (nm) the inner radius of the ring.

  • outerRadius: (nm) the outer radius of the ring.

  • thickness: (nm) the thickness of the ring.

  • xcenter: (nm) [obsolete] please set it to zero.

  • ycenter: (nm) [obsolete] please set it to zero.

Relavent biological structure:

  • actin network at the endocytic site

Preview:

Note

It will be available soon.

reference(par, dx)

For details, see reference().

Random geometry

class models.locsBG3D(varargin)

Bases: @geometricModel.geometricModel

locsBG3D is usually used for simulations. It allows generating localizations in 3D at random positions.

Geometric parameters:

  • density: (μm-2) density of background localizations in the xy plane.

  • depth: (nm) the depth of the ROI.

class models.gaussianCluster2D(varargin)

Bases: @geometricModel.geometricModel

sphericalCap3Dp_surfaceArea describes a geometry of spherical cap in 3D. It describe the same geometry with the same parameterization as sphericalCap3D_surfaceArea but in a parametric form.

Geometric parameters:

  • x0: (nm) the x position of the cluster.

  • y0: (nm) the y position of the cluster.

Important

The parameter sigma of the gaussian cluster is determined by the extrinsic parameter variation.

Relavent biological structure:

  • a protein cluster on the plasma membrane

Preview:

Note

It will be available soon.

reference(par, dx)

For details, see reference().