private void Form1_Load(object sender, EventArgs e)
{
  _myData = new MyData();
  textBox1.DataBindings.Add("Text", _myData, "TheValue", false, DataSourceUpdateMode.OnPropertyChanged);
  textBox2.DataBindings.Add("Text", _myData, "TheValue", false, DataSourceUpdateMode.Never);
} 

public class MyData : INotifyPropertyChanged
{
  private string _theValue = string.Empty;
 
  public string TheValue
  {
    get { return _theValue; }
    set
    {
      if (string.IsNullOrEmpty(value) && value == _theValue)
        return;
 
      _theValue = value;
      NotifyPropertyChanged(() => TheValue);
    }
  }
 
  public event PropertyChangedEventHandler PropertyChanged;
 
  public void NotifyPropertyChanged<T>(Expression<Func<T>> property)
  {
    if (PropertyChanged == null)
      return;
 
    var memberExpression = property.Body as MemberExpression;
    if (memberExpression == null)
      return;
 
    PropertyChanged.Invoke(this, new PropertyChangedEventArgs(memberExpression.Member.Name));
  }
}