How do I databind a ColumnDefinition's Width or RowDefinition's Height?

Under the View-Model-ViewModel pattern for WPF, I am trying to databind the Heights and Widths of various definitions for grid controls, so I can store the values the user sets them to after using a GridSplitter. However, the normal pattern doesn't seem to work for these particular properties.

Note: I'm posting this as a reference question that I'm posting as Google failed me and I had to work this out myself. My own answer to follow.

There were a number of gotchas I discovered:

1. Although it may appear like a double in XAML, the actual value for a *Definition's Height or Width is a 'GridLength' struct.
2. All the properties of GridLength are readonly, you have to create a new one each time you change it.
3. Unlike every other property in WPF, Width and Height don't default their databinding mode to 'TwoWay', you have to manually set this.

Thusly, I used the following code:

private GridLength myHorizontalInputRegionSize = new GridLength(0, GridUnitType.Auto)
public GridLength HorizontalInputRegionSize
{
    get
    {
        // If not yet set, get the starting value from the DataModel
        if (myHorizontalInputRegionSize.IsAuto)
            myHorizontalInputRegionSize = new GridLength(ConnectionTabDefaultUIOptions.HorizontalInputRegionSize, GridUnitType.Pixel);
        return myHorizontalInputRegionSize;
    }
    set
    {
        myHorizontalInputRegionSize = value;
        if (ConnectionTabDefaultUIOptions.HorizontalInputRegionSize != myHorizontalInputRegionSize.Value)
        {
            // Set the value in the DataModel
            ConnectionTabDefaultUIOptions.HorizontalInputRegionSize = value.Value;
        }
        OnPropertyChanged("HorizontalInputRegionSize");
    }
}

And the XAML:

<Grid.RowDefinitions>
    <RowDefinition Height="*" MinHeight="100" />
    <RowDefinition Height="Auto" />
    <RowDefinition Height="{Binding Path=HorizontalInputRegionSize,Mode=TwoWay}" MinHeight="50" />
</Grid.RowDefinitions>