If you are using a `<script>` block to work with Alpine.js and want to trigger a re-render or respond to changes in reactive data, there are a couple of methods you can employ. The approach you choose depends on how you're structuring your Alpine.js components and what exactly you're trying to achieve.

1. **Modifying Reactive Data from Script Block:** If you're manipulating the reactive data of an Alpine.js component from a separate `<script>` block, you can directly modify the data properties. This will automatically trigger a re-render of the relevant parts of the component.

   ```html
   <div x-data="{ message: 'Hello' }" id="myComponent">
       <span x-text="message"></span>
   </div>

   <script>
       function updateMessage(newMessage) {
           let component = document.querySelector('#myComponent').__x.$data;
           component.message = newMessage; // This will trigger Alpine to re-render
       }
   </script>
   ```

2. **Using Alpine.store():** Alpine.js provides a global state management solution through `Alpine.store()`. You can define a global store and then react to changes in this store within your components. Changes to the store's properties will automatically trigger updates in components that use them.

   ```html
   <script>
       Alpine.store('myStore', {
           message: 'Hello'
       });

       function updateGlobalMessage(newMessage) {
           Alpine.store('myStore').message = newMessage;
       }
   </script>

   <div x-data>
       <span x-text="$store.myStore.message"></span>
   </div>
   ```

3. **Using Custom Events:** If you prefer an event-driven approach, you can dispatch custom events from your script block and listen for these events in your Alpine components.

   ```html
   <div x-data="{ message: 'Hello' }" @custom-event.window="message = $event.detail">
       <span x-text="message"></span>
   </div>

   <script>
       function triggerCustomEvent(newMessage) {
           window.dispatchEvent(new CustomEvent('custom-event', { detail: newMessage }));
       }
   </script>
   ```

4. **Alpine.js Global API:** If you need to access or modify the state of a component from outside, you can use Alpine's global API to directly interact with the component's state.

   ```javascript
   let componentState = document.querySelector('#myComponent').__x.$data;
   // Now you can read or modify the state
   ```

Each of these methods allows you to interact with and trigger updates in your Alpine.js components from a `<script>` block. Choose the method that best fits the structure and requirements of your application.