public class Patient
{
    public int Id { get; set; }
    public string Name { get; set; }
    public string Email ( get; set; }
    public virtual Nutritionist Nutritionist { get; set; }
}

public class Nutritionist
{
    public int Id { get; set; }
    public string Name { get; set; }
    public virtual List<Patient> Patients { get; set; }
}

[TestMethod]
    public void Changing_Nutritionist_In_Disconnected_Context_Works()
    {
        Patient p;
        Nutritionist n;
        using (var c = new Context())
        {
            // Get a patient where I know p.Nutritionist.Id == 1 in database.
            p = c.Patients.Find(1);

            // Get some other nutritionist
            n = c.Nutritionists.Find(3);
        }
        using (var c = new Context())
        {
            //change patient's email and nutritionist
            p.Email = "patient@domain.com";
            p.Nutritionist = n;

            c.Patients.Attach(p);
            c.Entry(p).State = EntityState.Modified;
            c.SaveChanges();
        }
        using (var c = new Context())
        {
            Assert.AreEqual(3,c.Patients.Find(1).Nutritionist.Id);
        }
    }

exec sp_executesql N'UPDATE [dbo].[Patients]
SET [Name] = @0, [Email] = @1
WHERE ([Id] = @2)
',N'@0 nvarchar(max) ,@1 nvarchar(max) ,@2 int',@0=N'some name',@1=N'patient@domain.com',@2=1
go

cn.Patients.Attach(p);
cn.Nutritionists.Attach(n);
cn.Entry(p).Reference(x => x.Nutritionist).Load();
p.Nutritionist = n;
cn.Entry(p).State = EntityState.Modified;
cn.SaveChanges();