diff --git a/docs/tutorial.rst b/docs/tutorial.rst
index 0bcb45a5c4..4f6e96b64f 100644
--- a/docs/tutorial.rst
+++ b/docs/tutorial.rst
@@ -802,7 +802,7 @@ Here is an example using S3Map to read an array created previously::
     array([b'H', b'e', b'l', b'l', b'o', b' ', b'f', b'r', b'o', b'm', b' ',
            b't', b'h', b'e', b' ', b'c', b'l', b'o', b'u', b'd', b'!'],
           dtype='|S1')
-    >>> z[:].tostring()
+    >>> z[:].tobytes()
     b'Hello from the cloud!'
 
 Zarr now also has a builtin storage backend for Azure Blob Storage.
@@ -841,11 +841,11 @@ store. E.g.::
     >>> z = root['foo/bar/baz']
     >>> from timeit import timeit
     >>> # first data access is relatively slow, retrieved from store
-    ... timeit('print(z[:].tostring())', number=1, globals=globals())  # doctest: +SKIP
+    ... timeit('print(z[:].tobytes())', number=1, globals=globals())  # doctest: +SKIP
     b'Hello from the cloud!'
     0.1081731989979744
     >>> # second data access is faster, uses cache
-    ... timeit('print(z[:].tostring())', number=1, globals=globals())  # doctest: +SKIP
+    ... timeit('print(z[:].tobytes())', number=1, globals=globals())  # doctest: +SKIP
     b'Hello from the cloud!'
     0.0009490990014455747
 
diff --git a/zarr/core.py b/zarr/core.py
index f8e5834070..e69895cc8d 100644
--- a/zarr/core.py
+++ b/zarr/core.py
@@ -5,6 +5,7 @@
 import operator
 import re
 from functools import reduce
+from collections.abc import MutableMapping
 
 import numpy as np
 from numcodecs.compat import ensure_bytes, ensure_ndarray
@@ -1955,7 +1956,7 @@ def _encode_chunk(self, chunk):
             cdata = chunk
 
         # ensure in-memory data is immutable and easy to compare
-        if isinstance(self.chunk_store, dict):
+        if isinstance(self.chunk_store, MutableMapping):
             cdata = ensure_bytes(cdata)
 
         return cdata
diff --git a/zarr/storage.py b/zarr/storage.py
index 19949cd8a5..6b5b486836 100644
--- a/zarr/storage.py
+++ b/zarr/storage.py
@@ -1973,11 +1973,11 @@ class LRUStoreCache(MutableMapping):
         >>> z = root['foo/bar/baz']  # doctest: +REMOTE_DATA
         >>> from timeit import timeit
         >>> # first data access is relatively slow, retrieved from store
-        ... timeit('print(z[:].tostring())', number=1, globals=globals())  # doctest: +SKIP
+        ... timeit('print(z[:].tobytes())', number=1, globals=globals())  # doctest: +SKIP
         b'Hello from the cloud!'
         0.1081731989979744
         >>> # second data access is faster, uses cache
-        ... timeit('print(z[:].tostring())', number=1, globals=globals())  # doctest: +SKIP
+        ... timeit('print(z[:].tobytes())', number=1, globals=globals())  # doctest: +SKIP
         b'Hello from the cloud!'
         0.0009490990014455747