Material-UI Left Drawer in App Bar won't close on overlay click or menu item click in React

I am having an issue I can't seem to pin down where my LeftDrawer for my App Bar isn't closing if I click a menu item or the overlay (Not sure if this is an option, or possible with react components). Ideally, I would like both options to close the Drawer. Thank you in advance for taking your time to look at this!

This is my Navbar class I am using to toggle open the LeftDrawer:

// Dependencies
import React from 'react';

//Comonents
import LeftDrawer from './left-drawer.jsx';

// Styles
import './nav-bar.scss';
import AppBar from 'material-ui/AppBar';

class NavBar extends React.Component {
  constructor(props){
    super(props);

    this.state = {
      open: false
    };
  }

  toggleDrawer(){
    this.setState({
      open: !this.state.open
    });
  }

  render(){
    return (
      <div className='nav-bar'>
        <AppBar title='My App' onLeftIconButtonTouchTap={() => this.toggleDrawer()}/>
        <LeftDrawer open={this.state.open} onToggleDrawer={this.toggleDrawer.bind(this)} />
      </div>
    );
  }
}

export default NavBar;

This is the LeftDrawer class with the MenuItems:

// Dependencies
import React from 'react';
import { Link } from 'react-router-dom';

// Styles
import Drawer from 'material-ui/Drawer';
import MenuItem from 'material-ui/MenuItem';

export default class LeftDrawer extends React.Component {
constructor(props) {
    super(props);
    this.state = {open: false};
}

handleToggle() {
    this.setState({open: !this.state.open});
}

handleClose() {
    this.setState({open: false});
}

render() {
    return (
        <div>
            <Drawer
                docked={false}
                width={200}
                open={this.props.open}
                onRequestChange={(open) => this.setState({open})}
            >
                <Link to="/home"><MenuItem onTouchTap={this.handleClose.bind(this)}>Home</MenuItem></Link>
                <Link to="/topics"><MenuItem onTouchTap={this.handleClose.bind(this)}>404</MenuItem></Link>
            </Drawer>
        </div>
        );
    }
}