How to bind a property to the property of another class (with no UI Control)?

I'm spending hours on Google researching my simple Task. I'm trying to do bind my variable TestString to TestClass.MeinString.

If I click on the button "tb_tbBinding" TestString and TestClass.MyString should stay the same value.

Relevant code:

public partial class Window_Test : Window, INotifyPropertyChanged
{
    public Window_Test()
    {
        InitializeComponent();
        DataContext = this;

        // Trying to bind TestClass.MeinString to TestString
        BindingOperations.SetBinding(TestClass, BindingTestClass.MeinStringProperty, new Binding("TestClass.MeinString") { UpdateSourceTrigger = UpdateSourceTrigger.PropertyChanged });
    }



    string _TestString = "Hello World!";
    public string TestString
    {
        get
        {
            return _TestString;
        }
        set
        {
            _TestString = value;
            OnPropertyChanged("TestString");
        }
    }

    BindingTestClass _TestClass = new BindingTestClass("Hallo Lukas!");
    public BindingTestClass TestClass
    {
        get
        {
            return _TestClass;
        }
        set
        {
            _TestClass = value;
            OnPropertyChanged("TestClass");
        }
    }

    private void btn_testclasschanger_click(object sender, RoutedEventArgs e)
    {
        TestClass.MeinString = "Changed String!";
    }

    private void btn_teststringchanger_click(object sender, RoutedEventArgs e)
    {
        TestString = "Changed Class!";
    }

}

My Custom Class:

 public class BindingTestClass : DependencyObject, INotifyPropertyChanged
    {
        public BindingTestClass(string myString)
        {
            MeinString = myString;
        }

        public string MeinString
        {
            get
            {
                return (string)GetValue(MeinStringProperty);
            }
            set
            {
                SetValue(MeinStringProperty, value);
                OnPropertyChanged("MeinString");
            }
        }

        public static readonly DependencyProperty MeinStringProperty = DependencyProperty.Register("MeinString", typeof(string), typeof(BindingTestClass), new FrameworkPropertyMetadata()
        {
            BindsTwoWayByDefault = true,
            DefaultUpdateSourceTrigger = UpdateSourceTrigger.PropertyChanged
        });

        public event PropertyChangedEventHandler PropertyChanged;
        protected void OnPropertyChanged(string name)
        {
            PropertyChangedEventHandler handler = PropertyChanged;
            if (handler != null)
            {
                handler(this, new PropertyChangedEventArgs(name));
            }
        }
}

Thank you guys!