C# – InvalidOperationException – A TwoWay or OneWayToSource binding cannot work on the read-only property

It's hard to guess without code, but you should be able to set the BindingMode to OneWay.

<TextBox Text="{Binding Path=MyProperty, Mode=OneWay}" />

or from code:

Binding binding = new Binding();
binding.Mode = BindingMode.OneWay;

Some research results for OneWayToSource...

Option # 1.

// Control definition
public partial class FlagThingy : UserControl
{
    public static readonly DependencyProperty IsModifiedProperty = 
            DependencyProperty.Register("IsModified", typeof(bool), typeof(FlagThingy), new PropertyMetadata());
}

<controls:FlagThingy x:Name="_flagThingy" />

// Binding Code
Binding binding = new Binding();
binding.Path = new PropertyPath("FlagIsModified");
binding.ElementName = "container";
binding.Mode = BindingMode.OneWayToSource;
_flagThingy.SetBinding(FlagThingy.IsModifiedProperty, binding);

Option # 2

// Control definition
public partial class FlagThingy : UserControl
{
    public static readonly DependencyProperty IsModifiedProperty = 
            DependencyProperty.Register("IsModified", typeof(bool), typeof(FlagThingy), new PropertyMetadata());

    public bool IsModified
    {
        get { return (bool)GetValue(IsModifiedProperty); }
        set { throw new Exception("An attempt ot modify Read-Only property"); }
    }
}

<controls:FlagThingy IsModified="{Binding Path=FlagIsModified, 
    ElementName=container, Mode=OneWayToSource}" />

Option # 3 (True read-only dependency property)

System.ArgumentException: 'IsModified' property cannot be data-bound.

// Control definition
public partial class FlagThingy : UserControl
{
    private static readonly DependencyPropertyKey IsModifiedKey =
        DependencyProperty.RegisterReadOnly("IsModified", typeof(bool), typeof(FlagThingy), new PropertyMetadata());

    public static readonly DependencyProperty IsModifiedProperty = 
        IsModifiedKey.DependencyProperty;
}

<controls:FlagThingy x:Name="_flagThingy" />

// Binding Code
Same binding code...

Reflector gives the answer:

internal static BindingExpression CreateBindingExpression(DependencyObject d, DependencyProperty dp, Binding binding, BindingExpressionBase parent)
{
    FrameworkPropertyMetadata fwMetaData = dp.GetMetadata(d.DependencyObjectType) as FrameworkPropertyMetadata;
    if (((fwMetaData != null) && !fwMetaData.IsDataBindingAllowed) || dp.ReadOnly)
    {
        throw new ArgumentException(System.Windows.SR.Get(System.Windows.SRID.PropertyNotBindable, new object[] { dp.Name }), "dp");
    }
 ....