Serialization Deserialization Control property

Serialization / DeSerialization Question

Experts,

Why can`t I serialize, Something like this? What's the work around?

public string TBoxStr
{
     get
          {
              return textbox1.text;
          }
      set
         {
            textbox1.text = value;
         }
}

I tried something like this too, and it doesn`t work.

private string tboxstr;
public string TBoxStr
{
     get
          {
             tboxstr = textbox1.text;
              return tboxstr;
          }
      set
         {
            tboxstr = value
            textbox1.text = tboxstr;
         }
}

I have no problem Serializing and Deserializing something like this -
private string property;
public string Property
{
     get
          {
              return property;
          }
      set
         {
            property = value
         }
}

I was hoping I could Serialize TBoxStr. What am I missing here?