public class Main : MonoBehaviour {

    //some public and private variables...
    private OtherClass OtherGameLogic = new OtherClass(this);

    void Start () {
        //some initialisation happening
    }

    void Update () {
        // all complex frame to frame calculations are done here.
        // this is gpu and cpu intensive code...
    }
}

public class OtherClass
{

    private Main M;

    public OtherClass(Main m)
    {
        M = m;
    }

    private void SomeMethod()
    {
        m.SomeFunctionThatNeedsMToRun();
    }
}