Two ways (assuming Adapter templateset, but it's similar with SelfServicing):
A. The LEFT function using DBFuncionCall:
EntityField2 leftPart = new EntityField2("LeftExp",
new DBFunctionCall("LEFT", new object[] { MyEntityFields.SomeColumn, 1}) );
// here filter is a relationPredicateBucket
filter.PredicateExpression.Add(leftPart == "1");
B. Like predicate should work for the example you posted:
// here filter is a relationPredicateBucket
filter.Add(MyEntityFields.SomeColumn % "1%");