Dynamic

and

static

calcium

gradients

inside

large

snail

-LRB-

Helix

aspersa

-RRB-

neurones

detected

with

calcium-sensitive

microelectrodes

We

have

used

quartz

sensitive

microelectrodes

-LRB-

CASMs

-RRB-

in

large

voltage-clamped

snail

neurones

to

investigate

the

inward

spread

of

after

a

brief

depolarisation

Both

steady

state

and

-LSB-

-RSB-

i

transients

changed

with

depth

of

penetration

When

the

CASM

tip

was

within

μm

of

the

far

side

of

the

cell

the

-LSB-

-RSB-

i

transient

time

to

peak

was

s

rising

to

s

at

a

distance

of

μm

We

estimate

that

the

transients

travelled

centripetally

at

an

average

speed

of

s

and

decreased

in

size

by

half

over

a

distance

of

about

μm

Cyclopiazonic

acid

had

little

effect

on

the

size

and

time

to

peak

of

transients

but

slowed

their

recovery

significantly

This

suggests

that

the

endoplasmic

reticulum

curtails

rather

than

reinforces

the

transients

Injecting

the

calcium

buffer

BAPTA

made

the

transients

more

uniform

in

size

and

increased

their

times

to

peak

and

rates

of

recovery

near

the

membrane

We

have

developed

a

computational

model

for

the

transients

which

includes

diffusion

uptake

and

extrusion

Good

fits

were

obtained

with

a

rather

large

apparent

diffusion

coefficient

of

about

s

This

may

assist

fast

recovery

by

extrusion

Introduction

Changes

in

free

intracellular

calcium

-LRB-

-LSB-

-RSB-

i

-RRB-

play

a

vital

role

in

intracellular

signalling

notably

in

coupling

electrical

excitation

to

secretion

contraction

and

other

activation

processes

-LSB-

-RSB-

Many

of

the

processes

activated

by

a

rise

in

-LSB-

-RSB-

i

are

believed

to

occur

in

the

nucleus

-LSB-

-RSB-

which

in

large

neurones

may

be

far

from

the

cell

membrane

It

is

well-established

that

a

brief

depolarization

of

most

nerve

cells

causes

an

influx

of

ions

across

the

plasma

membrane

and

thus

a

local

rise

in

-LSB-

-RSB-

i

The

spatiotemporal

characteristics

of

this

rise

in

calcium

are

defined

by

the

interactions

between

ions

and

the

cytoplasmic

milieu

Calcium-induced

calcium

release

-LRB-

CICR

-RRB-

processes

via

either

or

ryanodine

receptors

can

facilitate

the

regenerative

spread

of

the

calcium

signal

throughout

the

cell

whilst

immobile

calcium

buffers

will

slow

and

attenuate

the

signal

If

the

increase

in

sub-membrane

-LSB-

-RSB-

i

is

to

act

as

a

signal

at

a

distance

the

speed

at

which

the

ions

travel

from

the

cell

membrane

to

their

target

depends

critically

on

the

rate

of

diffusion

of

ions

in

the

cytoplasm

Most

studies

of

calcium

homeostasis

and

signalling

in

nerve

and

muscle

cells

have

been

made

using

optical

methods

to

measure

-LSB-

-RSB-

i

via

the

binding

of

ions

by

fluorescent

or

other

indicators

-LSB-

-RSB-

Such

indicators

tend

to

increase

intracellular

buffering

and

mobility

-LSB-

-RSB-

Many

authors

-LRB-

for

example

-LSB-

-RSB-

-RRB-

have

modelled

the

effect

of

mobile

indicators

on

transients

but

very

few

have

produced

data

on

intracellular

movement

from

the

periphery

towards

the

centre

inside

real

neurones

in

the

absence

of

such

alien

additives

We

now

present

such

data

obtained

with

sensitive

microelectrodes

-LRB-

CASMs

-RRB-

for

the

first

time

CASMs

offer

an

alternative

but

rarely-used

method

for

measuring

-LSB-

-RSB-

i

They

have

the

advantage

of

measuring

-LSB-

-RSB-

i

in

a

small

volume

without

adding

any

extraneous

compounds

which

might

interact

with

throughout

the

cell

But

they

are

rather

slow

to

respond

and

only

a

realistic

choice

for

large

cells

since

they

tend

to

create

a

leak

at

the

site

of

penetration

-LSB-

-RSB-

In

previous

work

with

CASMs

made

from

aluminosilicate

glass

the

CASMs

were

rarely

moved

once

a

stable

potential

had

been

obtained

from

deep

inside

the

neurone

-LSB-

e.g.

-RSB-

Recently

a

modified

electrode

construction

technique

has

allowed

us

to

use

CASMs

with

very

slender

tips

and

longer

lives

made

from

thin-walled

quartz

glass

We

have

also

found

it

possible

with

a

motorized

micromanipulator

to

move

the

CASMs

in

repeatable

steps

up

and

down

usually

without

apparently

causing

damage

to

the

cell

We

have

sought

to

record

transients

at

different

distances

from

the

inside

of

the

membrane

at

the

far

side

of

the

penetrated

cell

Our

recordings

at

different

depths

were

quite

repeatable

and

enabled

us

to

reconstruct

the

radial

inward

movement

of

the

entering

towards

the

centre

of

the

cell

We

have

done

this

in

large

neurones

with

initially

no

added

indicator

or

buffer

Although

our

method

does

tend

to

induce

a

leak

of

ions

at

the

penetration

site

we

believe

that

the

leak

simply

increases

the

steady

state

level

without

apparently

influencing

the

kinetics

of

the

transients

We

investigated

the

role

of

the

endoplasmic

reticulum

by

blocking

its

uptake

pump

with

cyclopiazonic

acid

We

also

injected

the

mobile

buffer

BAPTA

which

has

very

similar

Ca-buffering

properties

to

many

fluorescent

indicators

to

measure

its

effects

on

diffusion

We

have

modelled

the

increases

mathematically

and

have

been

able

to

model

the

transients

closely

by

assuming

that

calcium

signalling

in

these

cells

can

be

described

by

influx

diffusion

extrusion

sequestration

and

buffering

Good

fits

were

obtained

with

a

diffusion

coefficient

of

about

s

which

is

higher

than

reported

in

other

cell

types

Materials

and

methods

General

All

experiments

were

done

on

large

-LRB-

μm

diameter

-RRB-

snail

neurones

in

isolated

sub-oesophageal

ganglia

-LSB-

-RSB-

Cells

were

voltage-clamped

using

two

microelectrodes

to

mV

and

depolarized

at

intervals

by

or

mV

to

generate

an

influx

of

ions

The

resulting

changes

in

-LSB-

-RSB-

i

were

measured

using

CASMs

The

main

differences

from

previous

methods

were

that

we

made

the

CASMs

with

quartz

rather

than

aluminosilicate

glass

and

used

a

motorized

micromanipulator

-LRB-

Luigs

Neumann

Ratingen

Germany

-RRB-

to

move

the

CASM

up

and

down

in

reproducible

steps

Rotating

the

Z-control

wheel

by

moved

the

CASM

up

or

down

by

μm

thus

for

a

μm

step

we

rotated

it

manually

by

Preparation

An

aestivating

snail

Helix

aspersa

was

killed

humanely

by

rapid

removal

of

the

circumoesophageal

ring

of

ganglia

These

ganglia

were

mounted

dorsal

side

uppermost

on

a

plastic

bath

insert

The

thick

connective

tissue

covering

the

back

of

the

visceral

and

right

and

left

pallial

ganglia

was

then

removed

and

the

bath

insert

with

ganglia

was

mounted

in

the

experimental

chamber

at

an

angle

of

to

the

vertical

Once

covered

with

snail

Ringer

-LRB-

flow

rate

ml

min

bath

volume

ml

-RRB-

the

inner

connective

tissue

was

torn

with

a

fine

tungsten

hook

to

expose

some

of

the

neurones

All

experiments

were

carried

out

at

room

temperature

°C

starting

at

least

an

hour

after

the

dissection

Solutions

The

normal

snail

Ringer

contained

-LRB-

mM

-RRB-

NaCl

KCl

HEPES

titrated

with

NaOH

to

pH

Nominally

Ca-free

Ringers

had

the

same

composition

but

with

no

and

mM

The

EGTA

Ca-free

solution

had

an

additional

mM

EGTA

The

Ringer

was

the

same

as

normal

Ringer

except

that

it

had

mM

instead

of

HEPES

was

bubbled

with

in

air

and

contained

mM

The

high

K

low

Ca

solution

for

BAPTA

iontophoresis

calibration

contained

KCl

NaCl

and

mM

HEPES

The

pH

was

adjusted

to

with

KOH

Cyclopiazonic

acid

-LRB-

CPA

-RRB-

was

kept

frozen

as

a

mM

stock

solution

in

dimethyl

sulphoxide

and

diluted

in

snail

Ringer

on

the

day

of

use

All

these

chemicals

were

from

Sigma

Microelectrodes

Conventional

micropipettes

were

pulled

from

mm

filamented

borosilicate

glass

tubing

and

backfilled

with

either

M

CsCl

-LRB-

for

passing

current

-RRB-

or

M

KCl

-LRB-

for

recording

membrane

potential

-RRB-

Tips

were

broken

if

necessary

by

touching

a

pin

in

the

bath

to

give

resistances

between

and

MΩ

BAPTA

was

iontophoresed

from

similar

micropipettes

filled

with

mM

BAPTA

-LRB-

K

salt

-RRB-

CASMs

were

made

by

a

method

refined

from

those

described

previously

-LSB-

-RSB-

Every

few

days

we

pulled

long

sharp

micropipettes

from

unfilamented

quartz

tubing

-LRB-

mm

o.d.

mm

i.d.

-RRB-

using

a

Sutter

puller

-LRB-

Sutter

Instrument

Co

Novato

Cal

-RRB-

We

then

broke

the

tips

on

a

glass

rod

to

o.d.

μm

We

then

left

the

micropipettes

in

air

for

h

before

silanizing

them

with

bis

-LRB-

dimethylamino

-RRB-

dimethylsilane

-LRB-

Fluka

-RRB-

as

described

before

-LSB-

-RSB-

Individual

CASMs

were

prepared

as

follows

on

the

day

of

the

experiment

First

we

backfilled

or

silanized

micropipettes

with

mM

-LRB-

instead

of

the

mM

KCl

mM

used

before

which

we

realised

shortened

the

CASM

's

useful

life

-RRB-

using

a

ml

syringe

connected

to

the

back

of

each

micropipette

via

a

silicone

rubber

tube

to

force

air

out

of

the

tips

We

then

sucked

a

column

-LRB-

μm

-RRB-

of

sensor

cocktail

into

the

tip

of

each

micropipette

taking

care

to

avoid

any

air

gap

between

cocktail

and

backfill

The

cocktail

composition

was

-LRB-

mg/g

-RRB-

Ca

ionophore

ETH

-LRB-

Fluka

-RRB-

tetrakis

-LSB-

-LRB-

trifluoromethyl

-RRB-

phenyl

-RSB-

borate

high

molecular

weight

PVC

and

tetrahydrofuran

-LRB-

all

from

Fluka

-RRB-

Filled

microelectrodes

were

left

in

air

to

allow

the

tetrahydrofuran

to

evaporate

for

at

least

h

before

use

and

had

useful

lives

of

days

During

the

experiment

we

applied

kPa

of

air

pressure

to

the

back

of

the

CASM

since

this

maximizes

its

response

-LSB-

-RSB-

Before

use

each

microelectrode

was

tested

in

the

experimental

bath

initially

perfused

with

normal

snail

Ringer

Once

the

potential

had

stabilised

the

perfusate

was

switched

to

Ca-free

-LRB-

EGTA

-RRB-

Ringer

's

solution

Any

electrode

showing

a

potential

change

of

less

than

mV

was

discarded

The

potentials

recorded

from

the

CASMs

during

the

experiments

were

displayed

as

VCa

-LRB-

Vm

being

automatically

subtracted

when

both

electrodes

were

in

the

same

cell

-RRB-

and

we

have

not

converted

them

either

to

pCa

or

nM

free

-LSB-

-RSB-

i

except

for

modelling

purposes

Calibration

of

CASMs

is

difficult

because

in

our

hands

their

responses

tend

to

change

when

they

are

withdrawn

from

a

cell

at

the

end

of

an

experiment

Previous

work

-LSB-

-RSB-

suggests

that

their

responses

are

essentially

linear

with

pCa

between

and

-LRB-

mM

nM

-RRB-

with

a

potential

change

of

mV

per

decade

Half-response

times

ranged

from

to

s

but

were

not

routinely

measured

Results

were

discarded

if

on

withdrawal

the

electrode

potentials

had

changed

by

more

than

mV

Estimating

the

BAPTA

intophoresis

transport

number

We

first

used

CASMs

to

measure

how

much

BAPTA

was

required

to

change

the

VCa

of

ml

of

the

high

K

low

Ca

solution

from

to

mV

-LRB-

CASM

zeroed

in

normal

snail

Ringer

-RRB-

The

BAPTA

was

injected

into

the

ml

aliquots

using

an

oocyte

microinjector

The

average

quantity

of

BAPTA

needed

was

nmol

We

then

made

droplets

-LRB-

volumes

nl

-RRB-

of

the

same

solution

under

oil

measured

VCa

as

with

a

snail

neurone

and

injected

BAPTA

iontophoretically

We

found

that

to

achieve

the

equivalent

VCa

change

as

in

the

ml

samples

we

had

to

inject

an

average

μC

nl

giving

a

transport

number

of

Data

collection

and

analysis

Potentials

from

the

microelectrodes

were

led

via

Ag/AgCl

wires

to

preamplifiers

in

the

cage

Outputs

from

these

and

the

clamp

amplifier

were

filtered

-LRB-

Bessel

-RRB-

and

recorded

at

Hz

on

a

PC

via

a

CED

micro

interface

and

Spike

data

collection

program

-LRB-

Cambridge

Electronic

Design

UK

-RRB-

The

CASM

potential

was

differentially

recorded

with

the

Vm

microelectrode

potential

as

reference

Figures

were

prepared

from

the

CED

data

after

loading

into

Microsoft

EXCEL

Large

spikes

in

the

VCa

records

generated

by

electronic

pickup

were

erased

and

the

clamp

current

records

were

restricted

in

range

For

more

details

of

most

of

the

apparatus

see

-LSB-

-RSB-

Data

are

presented

as

means

S.E.M.

of

n

observations

The

statistical

significance

of

observed

shifts

in

means

was

determined

by

a

one-tailed

Wilcoxon

rank

sum

test

The

difference

between

means

was

considered

significant

when

the

p-value

was

higher

than

For

baseline

adjustment

selecting

transients

time

to

peak

and

exponential

fitting

a

home

made

Matlab

script

with

a

graphical

user

interface

was

used

Computational

modelling

There

is

an

extensive

body

of

literature

on

the

modelling

of

signalling

in

a

wide

variety

of

cell

types

for

example

-LSB-

-RSB-

In

this

study

we

set

out

to

develop

a

minimal

computational

model

of

signalling

in

snail

neurones

We

used

the

model

to

validate

and

explain

the

results

obtained

from

the

experiments

Furthermore

we

used

the

model

to

estimate

the

mobility

of

in

these

large

neuronal

cell

bodies

which

have

not

been

exposed

to

mobile

indicators

The

model

includes

the

following

dynamic

processes

diffusion

influx

extrusion

sequestration

and

buffering

We

assume

that

influx

and

extrusion

mechanisms

at

the

plasma

membrane

are

uniformly

distributed

over

the

cell

's

surface

The

CASM

and

the

axon

attached

to

the

soma

only

represent

a

small

fraction

of

the

cell

's

volume

-LRB-

-RRB-

and

surface

area

-LRB-

-RRB-

furthermore

transients

were

measured

near

the

far

side

of

the

cell

opposite

to

the

site

of

penetration

Since

we

could

not

detect

any

major

deformation

of

the

cell

looking

through

the

microscope

we

assume

that

the

transients

measured

close

to

the

membrane

can

be

modelled

with

spherical

symmetry

Using

these

assumptions

we

can

reduce

the

three-dimensional

diffusion

problem

to

a

one-dimensional

radial

diffusion

equation

in

a

sphere

Similar

computational

models

for

diffusion

in

a

spherical

cell

can

be

found

elsewhere

-LSB-

-RSB-

The

removal

of

after

a

brief

influx

is

relatively

slow

with

time

constants

ranging

from

to

s

while

buffering

occurs

on

the

micro

and

millisecond

time

scale

We

therefore

can

separate

these

different

processes

kinetically

and

remove

the

explicit

buffering

terms

from

the

transport

equation

-LSB-

-RSB-

In

so

doing

we

have

to

replace

the

diffusion

coefficient

DCa

-LRB-

s

-RRB-

with

an

apparent

diffusion

coefficient

Dapp

Here

we

used

the

notation

from

-LSB-

-RSB-

κe

andκb

denote

the

endogenous

and

exogenous

binding

ratio

respectively

the

associated

diffusion

coefficients

are

De

and

Db

The

diffusion

coefficient

of

free

cytoplasmic

is

denoted

by

DCa

and

was

assumed

to

be

s

-LSB-

-RSB-

Furthermore

all

other

transport

processes

have

to

be

scaled

down

by

the

total

binding

ratio

κtot

κe

κb

The

total

binding

ratio

κtot

depends

on

the

concentration

however

when

the

concentration

is

much

lower

than

the

dissociation

constant

it

may

be

approximated

to

be

constant

Moreover

although

some

data

are

available

on

buffering

in

snail

neurones

-LSB-

-RSB-

precise

measurements

that

separate

the

buffering

and

sequestration

processes

are

not

We

have

therefore

worked

with

apparent

fluxes

and

apparent

parameters

in

most

cases

Multiplication

of

these

apparent

parameters

with

the

total

buffering

power

should

yield

the

real

parameters

The

general

transport

equation

that

describes

the

calcium

dynamics

in

the

cell

taking

into

account

the

different

aforementioned

considerations

then

becomes

The

first

term

on

the

right

hand

side

represents

the

radial

diffusional

process

that

is

driven

by

the

concentration

gradient

in

the

cell

The

transmembrane

fluxes

jin

app

and

jout

app

describe

the

apparent

influx

of

calcium

through

channels

and

apparent

efflux

of

calcium

by

the

pump

respectively

Jseq

app

denotes

the

apparent

calcium

flux

associated

with

sequestration

to

stores

and

mitochondria

in

the

cell

's

cytoplasm

and

finally

jbasal

app

represents

the

basal

influx

of

at

rest

The

surface-to-volume

ratio

rsv

-LRB-

m

-RRB-

is

necessary

to

convert

the

flux

density

j

-LRB-

mol

m

s

-RRB-

into

a

concentration

flux

J

-LRB-

mM

s

-RRB-

The

concentration

-LSB-

-RSB-

i

and

all

fluxes

are

functions

of

position

r

-LRB-

m

-RRB-

and

time

t

-LRB-

s

-RRB-

however

for

readability

we

do

not

write

this

explicitly

There

are

few

precise

quantitative

data

available

about

the

different

transport

processes

involved

To

prevent

the

introduction

of

many

unknown

parameters

we

therefore

kept

the

mechanistic

complexity

to

a

bare

minimum

Consequently

we

modelled

the

influx

as

a

square

pulse

with

the

same

duration

as

the

depolarisation

where

the

apparent

current

denoted

by

ICa

app

-LRB-

A

-RRB-

relates

to

the

real

current

as

follows

ICa

app

ICa/κtot

S

denotes

the

surface

area

-LRB-

-RRB-

of

the

cell

and

F

is

Faraday

's

constant

The

extrusion

of

by

the

pump

is

modelled

by

the

following

linear

equation

-LRB-

for

example

see

-LSB-

-RSB-

-RRB-

where

Pout

app

denotes

the

apparent

extrusion

permeability

-LRB-

m

s

-RRB-

and

relates

to

the

real

permeability

as

follows

Pout

app

Pout/κtot

The

flux

associated

with

sequestration

was

also

assumed

to

be

linear

where

kseq

app

denotes

the

apparent

sequestration

rate

constant

-LRB-

s

-RRB-

and

relates

to

the

real

rate

constant

as

follows

kseq

out

kseq/κtot

-LSB-

-RSB-

s

is

the

steady

state

concentration

This

approximate

model

is

also

known

as

a

pool

model

-LSB-

-RSB-

Finally

the

basal

influx

jbasal

app

was

directly

calculated

from

the

steady

state

concentration

and

the

extrusion

parameter

jbasal

app

Pout

app

-LSB-

-RSB-

s.

Microelectrode

model

In

this

study

we

used

CASMs

to

measure

the

concentration

after

short

depolarisations

If

we

assume

equal

activity

coefficients

in

the

Ringer

and

cytoplasm

the

steady

state

cytoplasmic

concentration

can

be

directly

estimated

from

the

Nernst

equation

applied

to

the

CASM

potential

where

the

steady

state

Nernst-potential

is

denoted

by

ECa

-LRB-

V

-RRB-

R

is

the

gas

constant

and

the

temperature

T

was

K

The

backfill

concentration

-LSB-

-RSB-

CASM

in

the

microelectrode

was

mM

The

reference

potential

was

manually

adjusted

prior

to

the

experiment

such

that

the

measured

potential

was

mV

in

Ringer

solution

the

Ringer

solution

contained

mM

Were

the

resistance

and

capacitance

of

the

CASMs

to

be

infinitely

small

and

VCa

to

follow

the

Nernst

equation

over

the

whole

range

it

could

be

used

directly

to

estimate

the

cytoplasmic

concentration

VCa

is

indeed

close

to

the

Nernstian

value

at

-LSB-

-RSB-

i

over

nM

-LSB-

-RSB-

Unfortunately

the

resistance

of

these

microelectrodes

is

very

high

which

will

introduce

a

delayed

microelectrode

response

To

allow

for

this

delay

we

used

a

RC

filter

to

calculate

the

model

microelectrode

potential

VCa

The

response

time

of

the

microelectrode

is

denoted

by

τCASM

-LRB-

s

-RRB-

We

assume

that

it

is

constant

and

depends

only

weakly

on

the

microelectrode

potential

and

-LSB-

-RSB-

i.

Integration

and

parameter

fitting

Assuming

a

linear

transport

equation

a

rather

complex

analytical

solution

consisting

of

an

infinite

series

of

exponentials

with

different

time

constants

can

be

obtained

using

standard

methods

-LSB-

-RSB-

The

amplitudes

An

and

the

time

constants

τn

are

The

constants

αn

are

the

positive

roots

of

the

following

equation

where

the

diffusion

time

constant

τD

-LRB-

-RRB-

and

the

extrusion

time

constant

τp

d

-LRB-

-RRB-

The

slowest

time

constant

determines

the

overall

recovery

time

When

there

is

no

sequestration

this

time

constant

depends

on

the

cell

diameter

d

the

extrusion

rate

constant

and

the

diffusion

coefficient

in

a

complex

way

However

when

diffusion

is

much

faster

than

extrusion

-LRB-

extrusion

limited

-RRB-

the

time

constant

is

simply

τ0

d

-LRB-

-RRB-

and

vica

versa

when

diffusion

is

much

slower

than

extrusion

-LRB-

diffusion

limited

-RRB-

the

time

constant

is

simply

τ0

-LRB-

-RRB-

To

compare

the

model

with

the

results

obtained

from

the

experiments

we

solved

the

transport

equation

simultaneously

with

the

differential

equation

for

the

microelectrode

potential

Although

the

analytical

solution

is

very

useful

for

theoretical

analysis

and

testing

it

requires

many

terms

to

obtain

an

accurate

solution

and

does

not

allow

for

non-linearity

Therefore

we

used

a

numerical

approach

for

solving

both

equations

allowing

more

flexibility

Time

integration

was

done

using

the

forward

Euler

scheme

and

diffusion

was

calculated

using

a

finite

volume

scheme

-LRB-

see

for

example

-LSB-

-RSB-

-RRB-

The

value

of

surface-to-volume

ratio

rsv

in

Eq

-LRB-

-RRB-

using

this

finite

volume

scheme

is

simply

the

ratio

of

the

cell

surface

S

and

the

volume

of

the

first

compartment

at

the

membrane

Both

solutions

were

calculated

using

a

Matlab

mex-routine

written

in

C++

In

a

typical

experiment

several

transients

were

measured

in

succession

at

different

depths

The

relative

distance

was

reconstructed

from

the

micromanipulator

movements

that

were

all

either

or

μm

The

diameter

of

the

cell

was

estimated

from

all

of

these

successive

steps

Unfortunately

the

absolute

position

-LRB-

offset

-RRB-

of

the

transient

measured

closest

to

the

membrane

was

not

known

exactly

We

therefore

allowed

the

depth

as

an

adjustable

parameter

within

the

limits

of

μm

The

transients

measured

closer

to

the

middle

were

therefore

more

reliable

Furthermore

the

response

time

of

the

electrode

was

estimated

to

be

about

s

and

was

allowed

to

vary

within

these

limits

The

remaining

four

unknown

parameters

in

the

transport

equation

together

with

the

response

time

were

obtained

from

an

optimal

fit

A

simplex

search

algorithm

was

used

to

find

this

least

square

fit

To

increase

reliability

of

the

parameter

estimates

several

transients

measured

at

different

depths

were

fitted

simultaneously

Also

any

slow

baseline

drift

was

removed

and

the

first

two

seconds

of

the

transients

that

show

an

electrical

artefact

were

not

used

during

the

fitting

process

Results

Changes

in

measured

calcium

with

depth

of

penetration

At

the

start

of

all

experiments

the

tip

of

a

CASM

was

placed

centrally

on

the

top

of

the

chosen

neurone

and

moved

down

in

μm

steps

until

there

was

a

sudden

fall

in

the

potential

as

shown

in

Fig.

Inside

the

cell

the

CASM

registers

both

the

membrane

potential

-LRB-

Vm

-RRB-

and

the

change

in

VCa

-LRB-

the

voltage

set

to

zero

outside

the

cell

proportional

to

pCa

-RRB-

In

this

representative

example

the

CASM

was

moved

down

in

four

steps

before

its

potential

changed

from

zero

to

about

mV

During

a

further

six

steps

downward

the

CASM

potential

gradually

became

more

negative

eventually

more

negative

than

mV

By

this

time

the

electrode

tip

was

μm

from

the

top

of

the

cell

which

had

a

diameter

of

about

μm

We

then

inserted

the

membrane

potential

microelectrode

-LRB-

the

output

of

which

was

electrically

subtracted

from

the

CASM

potential

to

give

VCa

-RRB-

and

clamp

current

microelectrode

using

manually-operated

micromanipulators

To

test

that

the

CASM

and

Vm

electrodes

were

recording

the

same

change

in

Vm

we

then

hyperpolarised

the

cell

by

mV

for

s

There

were

only

small

transient

changes

in

VCa

generated

by

electrical

pickup

and

imperfect

subtraction

of

rapid

changes

We

then

-LRB-

not

shown

in

Fig.

-RRB-

started

to

depolarize

the

cell

by

mV

for

s

repeated

every

min

to

allow

an

influx

of

ions

The

recorded

increase

in

-LSB-

-RSB-

i

was

very

small

VCa

increased

from

to

mV

and

then

recovered

After

the

first

depolarisation

we

raised

the

CASM

by

μm

and

left

it

unmoved

for

min

to

allow

recovery

from

the

initial

penetrations

As

shown

in

detail

in

Fig.

we

then

moved

the

CASM

down

every

min

between

the

and

depolarisations

in

six

steps

of

μm

and

two

steps

of

μm

-LRB-

The

third

of

these

steps

made

the

clamp

current

increase

from

to

but

this

was

not

correlated

with

any

change

in

-LSB-

-RSB-

i.

-RRB-

As

the

CASM

tip

was

moved

down

the

transient

increases

in

VCa

after

each

depolarisation

became

larger

and

the

steady-state

VCa

after

each

recovery

became

more

negative

After

the

sixth

step

VCa

had

fallen

to

mV

although

after

the

next

two

it

had

risen

slightly

to

mV

After

the

last

step

down

VCa

rose

to

mV

before

any

depolarisation

suggesting

the

CASM

had

gone

too

far

although

there

was

no

change

in

the

clamp

current

We

therefore

then

withdrew

the

CASM

in

several

steps

two

each

of

and

μm

After

the

first

μm

step

up

the

VCa

paradoxically

decreased

as

if

the

upward

movement

somehow

allowed

a

better

seal

Such

paradoxical

improvements

on

withdrawal

were

often

seen

in

the

early

part

of

an

experiment

Fig.

shows

the

VCa

responses

to

the

first

nine

depolarisations

of

Fig.

in

more

detail

As

the

CASM

tip

was

moved

closer

to

the

far

side

of

the

cell

the

responses

to

the

depolarisations

became

larger

and

faster

Presumably

this

reflects

the

fact

that

during

the

depolarisations

entered

the

cytoplasm

only

at

the

cell

membrane

Once

Vm

is

returned

to

mV

entry

ceased

and

the

both

diffused

into

the

cell

interior

and

was

pumped

out

by

the

plasma

membrane

Ca

ATPase

or

PMCA

In

some

experiments

we

were

able

to

make

several

different

sequences

of

downward

and

upward

movements

in

the

same

cell

to

a

depth

at

which

as

shown

in

Fig.

the

apparent

-LSB-

-RSB-

i

rose

rapidly

This

experiment

was

done

on

a

cell

of

diameter

about

μm

and

the

depths

at

which

the

apparent

-LSB-

-RSB-

i

began

to

increase

were

respectively

and

μm

In

other

words

it

appears

that

when

the

CASM

tip

reached

the

far

side

of

the

cell

it

suffered

a

loss

of

sensitivity

or

caused

a

local

leak

We

could

see

no

change

in

the

clamp

current

associated

with

the

sudden

increases

in

VCa

In

many

other

cells

once

the

CASM

created

a

sudden

rise

in

-LSB-

-RSB-

i

it

took

many

minutes

to

recover

if

at

all

The

simplest

explanation

of

the

decreases

in

apparent

-LSB-

-RSB-

i

as

the

CASM

was

advanced

deeper

and

deeper

into

a

cell

is

that

the

electrode

insertion

induced

a

leak

at

the

site

of

penetration

As

the

CASM

was

pushed

in

its

tip

moved

further

away

from

the

leak

which

itself

may

be

reduced

by

better

sealing

During

long

experiments

as

shown

below

CASM

movement

had

less

dramatic

effects

on

steady-state

levels

suggesting

that

the

leak

declined

with

time

In

Fig.

we

show

mean

steady-state

VCa

values

against

the

estimated

distance

of

the

CASM

tip

from

the

bottom

of

the

cell

from

the

early

part

of

a

total

of

six

experiments

in

which

the

CASM

was

moved

down

in

steps

like

those

of

Figs.

and

The

bottom

of

the

cell

was

taken

as

the

point

at

which

VCa

rose

rapidly

without

a

change

in

membrane

potential

Transients

recorded

within

μm

of

this

were

plotted

as

close

to

the

membrane

The

mean

VCa

close

to

the

cell

membrane

was

mV

which

corresponds

to

a

pCa

of

similar

to

the

-LRB-

equivalent

to

a

-LSB-

-RSB-

i

of

nM

-RRB-

measured

in

snail

neurones

which

had

not

been

injected

with

buffers

-LSB-

-RSB-

The

VCa

transients

became

faster

as

the

CASM

tips

were

moved

closer

to

the

far

side

of

the

cell

Fig.

shows

the

mean

times

to

peak

of

the

VCa

increases

from

the

same

six

experiments

From

a

best-fit

line

through

the

points

we

can

calculate

that

the

mean

rate

at

which

the

VCa

peak

moved

towards

the

centre

of

the

cell

was

μm

s

We

also

show

in

Fig.

the

average

size

of

the

same

transients

in

mV

from

base

to

peak

The

distance

over

which

the

transients

decreased

to

half

their

-LRB-

extrapolated

-RRB-

initial

size

of

about

mV

was

about

μm

assuming

that

close

to

the

membrane

is

equivalent

to

about

μm

The

effect

of

removing

external

calcium

If

calcium

ions

driven

by

the

large

electrochemical

gradient

normally

leak

into

the

top

of

the

cell

around

the

tips

of

the

microelectrodes

reducing

external

calcium

should

reduce

the

apparent

-LSB-

-RSB-

i

We

have

tested

the

effect

of

a

possible

leak

by

exposing

cells

to

either

nominally

Ca-free

solutions

or

the

same

with

added

EGTA

Measured

with

a

CASM

the

-LSB-

-RSB-

of

the

nominal

solution

was

about

μM

that

of

the

EGTA

Ca-free

Ringer

less

than

nM

Fig.

shows

a

representative

experiment

in

which

the

cell

was

superfused

with

the

Ca-free

solutions

with

the

CASM

at

three

different

depths

For

the

first

two

exposures

to

Ca-free

solution

the

CASM

was

μm

deep

in

a

cell

of

diameter

about

mm

The

Ca-free

solutions

caused

VCa

to

decrease

by

mV

from

respectively

and

mV

There

was

little

difference

between

the

effect

of

the

two

Ca-free

solutions

except

that

the

EGTA

solution

almost

abolished

the

second

depolarisation-induced

rise

in

Ca

As

the

CASM

was

moved

deeper

into

the

cell

the

steady-state

VCa

fell

to

mV

and

the

reduction

seen

with

Ca-free

Ringer

decreased

to

and

mV

respectively

While

some

of

the

decreases

seen

with

the

removal

of

external

Ca

may

reflect

increased

pump

activity

it

seems

most

likely

that

the

elevated

VCa

levels

seen

near

the

middle

of

the

cell

are

due

to

leakage

round

the

microelectrodes

where

they

cross

the

cell

membrane

The

effect

of

buffering

We

have

done

most

of

our

experiments

in

HEPES-buffered

Ringer

although

it

is

known

that

solutions

greatly

increase

intracellular

pH

buffering

while

reducing

pH

buffering

power

extracellularly

-LSB-

-RSB-

It

is

possible

that

such

a

change

in

pH

buffering

might

influence

the

diffusion

of

ions

We

have

therefore

recorded

the

effects

of

changing

the

extracellular

buffer

from

HEPES

to

on

transients

recorded

at

different

depths

While

it

is

well

established

-LSB-

-RSB-

that

the

intracellular

pH

-LRB-

pHi

-RRB-

decrease

caused

by

entry

leads

to

a

decrease

in

steady-state

-LSB-

-RSB-

i

the

transients

were

little

changed

-LRB-

not

shown

-RRB-

By

min

after

changing

the

superfusate

to

the

Na-dependent

chloride/bicarbonate

exchanger

-LSB-

-RSB-

should

have

returned

pHi

to

normal

so

we

then

again

moved

the

CASM

down

in

steps

This

time

the

VCa

baseline

did

not

change

and

the

transient

times

to

peak

were

very

similar

to

those

recorded

in

HEPES

In

a

total

of

four

similar

experiments

the

average

time

to

peak

at

distances

of

μm

was

s

in

HEPES

and

s

in

The

role

of

calcium

stores

It

seems

possible

that

the

VCa

gradients

described

above

and

the

higher

steady-state

apparent

-LSB-

-RSB-

i

than

previously

reported

in

cells

which

had

added

buffer

were

partly

due

to

mechanically-induced

leakage

from

the

endoplasmic

reticulum

calcium

stores

Having

penetrated

the

cell

membrane

the

CASM

must

have

been

moved

down

through

the

endoplasmic

reticulum

and

might

have

caused

significant

injury

We

have

therefore

tested

the

effects

of

the

SERCA

pump

inhibitor

cyclopiazonic

acid

-LRB-

CPA

-RRB-

It

is

well-established

that

CPA

empties

the

stores

over

a

period

of

several

minutes

by

blocking

their

uptake

mechanism

-LSB-

-RSB-

and

emptying

the

stores

will

presumably

stop

them

leaking

Fig.

shows

one

of

four

similar

experiments

with

CPA

in

all

of

which

-LRB-

once

the

stores

were

empty

-RRB-

it

had

little

effect

on

either

the

baseline

VCa

or

the

near-membrane

VCa

changes

with

CASM

movement

The

times-to-peak

are

trending

to

be

later

in

CPA

treated

cells

although

this

was

not

very

pronounced

close

to

the

membrane

and

statistically

not

significant

-LRB-

p-value

assuming

time-to-peak

is

later

after

CPA

-LRB-

n

-RRB-

-RRB-

For

distances

of

and

μm

from

the

membrane

the

times

to

peak

were

significantly

longer

-LRB-

p-values

assuming

times-to-peak

are

later

after

CPA

-LRB-

-RRB-

-LRB-

-RRB-

and

-LRB-

-RRB-

-RRB-

The

recovery

time

after

the

transients

was

clearly

much

longer

in

CPA

treated

cells

-LRB-

p-values

assuming

recovery

times

are

longer

after

CPA

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

and

-LRB-

-RRB-

-RRB-

as

shown

in

Fig.

Interestingly

the

effect

of

CPA

on

recovery

times

was

more

pronounced

for

transients

measured

close

to

the

membrane

Furthermore

the

transient

size

showed

a

downward

trend

and

decreased

on

average

about

-LRB-

nominal

-LSB-

-RSB-

i

-RRB-

in

CPA

treated

cells

Although

this

percentage

was

statistically

not

significant

-LRB-

p-values

assuming

transients

are

smaller

after

CPA

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

and

-LRB-

-RRB-

-RRB-

it

may

suggest

that

a

small

fraction

of

the

increase

in

-LSB-

-RSB-

i

is

caused

by

release

of

The

effect

of

BAPTA

injection

Exogenous

calcium

buffers

have

been

widely

shown

to

influence

signalling

in

a

variety

of

cells

for

example

in

nerve

terminals

-LSB-

-RSB-

and

Xenopus

oocytes

-LSB-

-RSB-

The

fast

buffer

BAPTA

is

particularly

interesting

since

it

has

similar

properties

to

many

of

the

indicators

used

to

study

signalling

We

have

therefore

examined

the

effects

of

BAPTA

injected

iontophoretically

on

both

the

steady-state

VCa

and

the

transients

induced

by

depolarisations

Fig.

shows

a

representative

part

of

one

of

four

similar

experiments

Before

the

BAPTA

injection

we

recorded

VCa

transients

at

several

different

CASM

depths

At

the

closest

approach

to

the

membrane

the

time

to

peak

was

s

and

VCa

reached

a

peak

of

mV

The

first

two

BAPTA

injections

loaded

the

cell

to

give

an

estimated

BAPTA

concentration

of

μM

At

the

closest

approach

to

the

membrane

the

VCa

transient

then

had

a

time

to

peak

of

s

After

two

more

BAPTA

injections

giving

an

estimated

final

concentration

of

μm

the

transient

time

to

peak

at

the

closest

point

was

again

slower

at

s

In

three

of

the

experiments

we

were

able

to

measure

times

to

peak

and

the

size

of

the

VCa

transients

at

three

different

depths

before

and

after

injecting

BAPTA

to

a

final

concentration

of

μm

The

collected

data

are

plotted

in

Fig.

and

C

This

shows

that

BAPTA

tended

to

make

the

transients

more

uniform

throughout

the

cell

both

in

times

to

peak

and

overall

sizes

Although

the

first

two

BAPTA

injections

had

little

effect

on

the

steady-state

VCa

the

second

two

lowered

VCa

from

to

mV

In

a

total

of

four

similar

experiments

large

BAPTA

injections

-LRB-

raising

the

BAPTA

concentration

by

over

μM

-RRB-

also

lowered

the

steady

state

VCa

by

an

average

mV

This

effect

of

BAPTA

is

similar

to

that

reported

before

in

snail

neurones

-LSB-

-RSB-

in

which

intracellular

CASM

responses

were

calibrated

by

pressure-injecting

BAPTA

calibration

solutions

Computational

modelling

of

transients

in

large

snail

neurones

In

this

section

we

present

a

minimal

computational

model

that

agrees

fairly

well

with

our

experimental

results

In

the

model

we

assume

that

during

a

s

current

pulse

-LRB-

ICa

app

-RRB-

enters

the

cell

at

the

plasma

membrane

whence

it

diffuses

into

the

interior

with

an

apparent

diffusion

coefficient

Dapp

Furthermore

is

removed

at

the

plasma

membrane

by

a

pump

with

extrusion

permeability

Pout

app

we

also

allow

for

sequestration

everywhere

in

the

cell

with

rate

kseq

app

Further

mathematical

details

can

be

found

in

Section

In

modelling

transients

at

different

depths

we

overcame

our

imprecise

knowledge

of

the

different

parameters

by

estimating

them

using

a

least

square

fit

Fig.

shows

eight

simultaneously

fitted

transients

that

were

measured

in

the

middle

of

a

long

experiment

at

various

depths

ranging

form

close

to

the

membrane

at

about

μm

to

about

μm

away

from

the

membrane

The

depths

estimated

from

micrometer

movements

are

the

lower

values

shown

above

the

peaks

To

fit

the

data

these

positions

were

allowed

to

vary

within

the

limits

of

half

a

CASM

step

The

depths

obtained

from

the

fit

-LRB-

upper

values

-RRB-

are

reasonably

close

to

the

micrometer

positions

Interestingly

modelled

positions

near

the

membrane

are

slightly

shifted

towards

the

centre

of

the

cell

which

might

indicate

lower

mobility

close

to

the

membrane

The

optimal

fit

yielded

an

apparent

diffusion

coefficient

of

Dapp

s

Furthermore

the

fit

required

an

apparent

sequestration

rate

constant

of

kseq

app

s

which

corresponds

to

a

time

constant

of

s.

Attempts

to

fit

the

transients

without

sequestration

failed

The

extrusion

permeability

was

Pout

app

μm

s

which

corresponds

to

a

time

constant

of

about

s

much

shorter

than

the

diffusional

time

constant

of

s

-LRB-

see

Section

-RRB-

This

suggests

that

clearance

is

limited

by

diffusion

rather

than

by

the

pump

rate

In

most

cells

we

observed

that

after

influx

a

rather

steep

gradient

develops

in

the

direction

of

the

membrane

which

fits

the

diffusion-limited

case

The

response

time

was

estimated

to

be

τCASM

s

which

was

slower

than

the

s

that

was

measured

in

μM

Ringer

In

most

experiments

the

times-to-peak

very

close

to

the

membrane

ranged

from

to

s.

Because

the

time-to-peak

near

the

membrane

should

equal

the

duration

of

the

influx

the

response

time

of

the

electrode

in

cytoplasm

is

about

s

The

estimated

apparent

diffusion

coefficient

for

the

recordings

shown

in

Fig.

of

Dapp

s

is

higher

than

reported

in

other

studies

s

in

frog

muscle

-LSB-

-RSB-

s

in

cytoplasmic

extracts

of

Xenopus

oocytes

-LSB-

-RSB-

s

in

the

axoplasm

of

metacerebral

cells

of

Aplysia

californica

-LSB-

-RSB-

and

s

in

rod

photoreceptor

outer

segments

-LSB-

-RSB-

A

diffusion

coefficient

of

s

has

been

reported

in

intact

Myxicola

axoplasm

-LSB-

-RSB-

but

much

higher

values

were

seen

in

ATP-depleted

axoplasm

and

with

high

-LSB-

-RSB-

i

In

most

of

these

studies

the

diffusion

coefficient

was

estimated

using

a

simple

model

with

only

a

few

parameters

Our

model

contained

more

parameters

that

we

varied

to

obtain

a

good

fit

The

parameters

for

influx

extrusion

and

sequestration

and

to

some

extent

the

positions

and

the

response

time

may

compromise

the

estimate

of

Dapp

We

therefore

calculated

the

mean

error

variance

as

a

function

of

the

apparent

diffusion

coefficient

of

four

fits

obtained

from

four

different

cells

While

fixing

the

apparent

diffusion

coefficient

all

other

parameters

were

allowed

to

vary

in

order

to

obtain

an

optimal

fit

In

each

cell

we

fitted

at

least

three

transients

measured

at

distances

and

μm

and

calculated

the

mean

error

variance

as

a

function

of

Dapp

All

cells

gave

a

reasonable

fit

with

a

minimum

error

at

s

-LRB-

Fig.

-RRB-

Since

we

allow

all

other

parameters

to

compensate

for

an

incorrect

diffusion

coefficient

this

value

should

be

a

conservative

estimate

Attempts

to

fit

the

transients

with

Dapp

values

smaller

than

s

failed

Some

cells

fitted

better

than

others

since

the

expected

transient

size

did

not

always

match

perfectly

when

multiple

transients

were

used

However

perfect

fits

could

be

obtained

with

any

individual

transient

Close

inspection

of

the

traces

revealed

that

baseline

variations

could

affect

the

transient

size

Possibly

the

influx

is

reduced

or

removal

mechanisms

are

enhanced

at

higher

basal

-LSB-

-RSB-

i

levels

We

still

conclude

that

the

diffusion

coefficient

is

considerably

higher

-LRB-

five

to

seven

times

-RRB-

than

reported

for

other

cell

types

A

large

fraction

of

the

cytoplasmic

is

bound

to

buffers

The

properties

and

distribution

of

these

buffers

are

therefore

critical

for

mobility

in

the

cytoplasm

Analysis

of

transients

under

differing

free

concentrations

and

exogenous

buffering

in

snail

neurones

indeed

showed

that

is

quite

well

buffered

in

snail

neurones

-LSB-

-RSB-

To

explain

the

high

diffusion

coefficient

a

large

fraction

of

the

buffers

must

be

mobile

When

we

injected

the

cells

with

BAPTA

it

clearly

changed

the

VCa

transients

considerably

promoting

spatially

uniform

global

signals

as

described

in

Xenopus

oocytes

-LSB-

-RSB-

These

were

loaded

with

μm

Oregon

Green

to

record

-LSB-

-RSB-

i

which

may

itself

have

influenced

movement

Our

Fig.

shows

three

transients

measured

at

μm

from

the

membrane

with

different

BAPTA

concentrations

the

nominal

concentrations

were

and

μM

BAPTA

slightly

increased

the

times

to

peak

-LRB-

and

s

-RRB-

reduced

the

size

of

the

transients

and

slowed

the

recovery

time

significantly

-LRB-

and

s

-RRB-

These

values

are

consistent

with

a

reduced

clearance

rate

Typically

if

the

mobility

is

not

changed

reduction

of

the

clearance

rate

slows

the

recovery

time

but

also

increases

the

time-to-peak

After

normalisation

of

the

times

to

peak

we

could

only

detect

a

slight

reduction

in

the

latency

-LRB-

s

-RRB-

between

and

μM

BAPTA

suggesting

that

the

mobility

of

BAPTA

is

comparable

to

that

of

the

endogenous

buffers

We

fitted

the

three

transients

simultaneously

to

the

model

allowing

a

different

exogenous

binding

ratio

for

each

transient

The

model

gives

a

reasonable

fit

with

an

endogenous

buffer

diffusion

coefficient

of

De

s

and

binding

ratio

of

κe

This

suggests

that

the

endogenous

buffers

have

a

comparable

binding

ratio

to

that

in

Aplysia

axons

-LSB-

-RSB-

but

appear

to

be

much

more

mobile

The

apparent

diffusion

coefficients

for

at

the

different

BAPTA

concentrations

are

Dapp

s

-LRB-

μM

BAPTA

-RRB-

Dapp

s

-LRB-

μM

BAPTA

-RRB-

and

Dapp

s

-LRB-

μM

BAPTA

-RRB-

The

estimated

diffusion

coefficient

of

BAPTA

was

Db

s

which

slightly

increases

the

mobility

of

at

higher

BAPTA

concentrations

Similar

values

for

the

BAPTA

diffusion

coefficient

were

reported

by

others

-LSB-

-RSB-

Discussion

We

have

shown

that

with

CASMs

it

is

possible

to

record

steady-state

calcium

levels

and

depolarisation-induced

transients

at

different

depths

in

large

snail

neurones

The

decrease

in

calcium

levels

as

the

CASM

was

pushed

deeper

was

probably

due

to

increasing

the

distance

from

a

site

of

leakage

around

the

CASM

and

other

microelectrode

insertions

at

the

top

of

the

cell

We

found

that

the

sizes

and

kinetics

of

the

transients

measured

after

brief

-LRB-

s

-RRB-

depolarisations

to

zero

or

mV

varied

systematically

and

repeatably

with

distance

from

the

plasma

membrane

at

the

bottom

of

the

cell

Blocking

the

endoplasmic

reticulum

SERCA

pump

with

CPA

had

little

effect

on

the

transient

sizes

and

times

to

peak

but

significantly

slowed

subsequent

recovery

times

Injecting

BAPTA

both

reduced

and

slowed

the

transients

close

to

the

membrane

while

magnifying

them

deep

inside

the

cell

By

fitting

our

results

to

a

mathematical

model

we

calculate

that

the

apparent

diffusion

coefficient

is

about

s

The

problem

of

leakage

Ion-sensitive

and

other

non-patch

microelectrodes

inevitably

make

a

hole

in

the

cell

membrane

which

allows

leakage

in

or

out

of

the

cell

Given

the

gradients

the

ions

whose

leakage

is

most

likely

to

distort

the

measured

intracellular

level

are

and

Thus

Vaughan-Jones

-LSB-

-RSB-

recorded

-LSB-

-RSB-

i

in

crab

muscle

with

a

sensitive

microelectrode

-LRB-

NASM

-RRB-

inserted

radially

-LRB-

perpendicular

to

the

long

axis

-RRB-

and

found

that

low

external

caused

a

surprisingly

rapid

fall

in

-LSB-

-RSB-

i

He

considered

that

this

might

have

been

caused

by

the

low

external

reducing

a

leak

This

was

later

confirmed

by

experiments

in

which

it

was

shown

that

NASMs

inserted

along

the

long

axis

into

a

cannulated

fibre

recorded

only

small

changes

in

-LSB-

-RSB-

i

when

external

was

reduced

but

when

inserted

radially

the

recorded

-LSB-

-RSB-

i

was

at

first

high

but

fell

as

the

NASM

was

pushed

deeper

-LSB-

-RSB-

Perhaps

because

the

gradient

is

small

and

pHi

very

well

buffered

no

one

has

considered

that

pH-sensitive

microelectrode

measurements

have

been

contaminated

by

leakage

On

the

other

hand

-LSB-

-RSB-

i

is

very

low

and

only

moderately

buffered

In

our

hands

CASMs

unfortunately

do

not

perform

well

unless

their

tips

are

at

least

μm

in

diameter

-LSB-

-RSB-

Furthermore

only

after

much

manipulation

did

CASMs

record

a

low

-LSB-

-RSB-

i

which

increased

on

depolarization

The

initially

high

levels

were

recorded

even

in

cells

loaded

with

whose

fluorescence

indicated

a

normal

low

-LSB-

-RSB-

i.

Experiments

in

which

CASMs

were

calibrated

while

inside

neurones

by

injecting

buffers

led

to

the

conclusion

that

the

true

-LSB-

-RSB-

i

in

quiescent

voltage

clamped

snail

neurones

with

injected

buffer

was

nM

-LRB-

equivalent

to

a

CASM

VCa

of

about

mV

-RRB-

and

that

CASMs

usually

cause

a

leak

at

the

point

of

insertion

-LSB-

-RSB-

The

early

experiments

with

CASMs

were

all

done

with

a

manually-operated

micromanipulator

so

that

systematic

movements

were

not

attempted

once

a

stable

VCa

was

obtained

The

current

results

were

obtained

with

a

motor-driven

and

remote-controlled

micromanipulator

Typically

the

CASM

was

moved

down

in

several

μm

steps

before

its

potential

changed

at

all

This

shows

that

the

cell

membrane

is

very

extensible

since

the

cell

as

a

whole

did

not

visibly

move

as

the

CASM

was

inserted

For

example

in

Fig.

the

CASM

was

moved

down

by

μm

before

the

potential

first

fell

As

the

CASM

tip

was

then

moved

deeper

the

potential

became

more

and

more

negative

This

was

probably

due

to

a

combination

of

movement

away

from

the

site

of

leakage

and

a

reduction

in

the

size

of

the

leak

It

is

hard

to

distinguish

between

these

two

possibilities

but

the

reproducible

effects

of

movement

as

shown

for

example

in

Fig.

suggest

that

the

leak

was

relatively

constant

although

tending

to

reduce

with

time

In

some

experiments

the

steady-state

VCa

appeared

to

stabilize

some

distance

from

the

apparent

far

side

of

the

cell

as

shown

in

the

control

part

of

Fig

and

was

not

reduced

further

as

the

tip

approached

the

far

side

of

the

cell

Presumably

the

leakage

was

by

then

too

small

to

have

a

significant

effect

influx

rather

than

release

determines

the

increase

in

-LSB-

-RSB-

i

Our

finding

that

the

peak

of

the

VCa

transient

diffuses

away

from

the

membrane

at

a

speed

of

about

μm

s

confirms

the

long-held

view

that

signalling

which

relies

purely

on

diffusion

will

inevitably

have

a

slow

response

time

The

lack

of

effect

of

CPA

and

the

decline

of

the

signal

size

with

distance

rather

unexpectedly

both

rule

out

significant

regeneration

of

the

signal

as

it

spreads

inwards

This

is

surprising

since

snail

neurones

respond

well

to

caffeine

and

certainly

have

the

capacity

for

Ca-induced

release

-LRB-

CICR

-RRB-

-LSB-

-RSB-

For

example

the

addition

of

a

low

concentration

of

caffeine

slightly

enhanced

transients

-LSB-

-RSB-

while

the

removal

of

caffeine

temporarily

reduced

the

peak

amplitudes

suggesting

that

the

stores

were

at

least

partly

emptied

-LSB-

-RSB-

Either

the

signal

is

large

enough

without

any

store

contribution

or

something

about

our

experimental

conditions

has

inhibited

CICR

We

depolarised

the

cell

for

s

to

ensure

a

large

load

every

min

but

this

may

have

in

some

way

have

inhibited

store

release

On

the

other

hand

in

other

experiments

we

have

avoided

depolarising

the

cell

for

long

periods

and

not

found

that

the

first

subsequent

response

was

different

The

distance

over

which

the

VCa

transients

fell

to

half

their

extrapolated

initial

size

was

about

μm

similar

to

the

distance

between

the

cell

membrane

and

the

nucleus

In

normal-sized

neurones

of

course

the

nucleus

would

be

much

closer

We

conclude

that

the

main

mechanism

in

our

experiments

that

leads

to

an

increase

in

-LSB-

-RSB-

i

is

transmembrane

influx

through

voltage-gated

channels

opened

by

depolarisation

and

not

massive

release

triggered

by

a

small

influx

as

in

vertebrate

cardiac

muscle

The

only

previous

direct

measurements

of

movement

in

nerve

cells

without

added

buffers

were

described

by

Gorman

et

al.

-LSB-

-RSB-

They

were

able

to

detect

a

rise

in

-LSB-

-RSB-

i

only

within

about

μm

of

the

membrane

in

Aplysia

neurones

after

a

s

depolarisation

Their

CASMs

were

made

with

a

different

sensor

-LRB-

ETH

-RRB-

to

that

which

we

used

and

appear

to

have

been

relatively

insensitive

at

low

values

of

-LSB-

-RSB-

i.

The

transmembrane

pump

and

sequestration

by

cytoplasmic

organelles

determine

clearance

The

depolarisation-induced

influx

is

presumably

cleared

by

extrusion

across

the

cell

membrane

and

sequestration

to

cytoplasmic

organelles

The

PMCA

or

H

ATPase

in

snail

neurones

appears

to

exchange

two

extracellular

protons

for

one

intracellular

at

the

expense

of

ATP

-LSB-

-RSB-

When

it

is

blocked

by

ortho-vanadate

the

-LSB-

-RSB-

i

does

not

fully

recover

from

an

influx

but

ends

in

a

plateau

This

suggests

that

the

PMCA

is

the

essential

removal

mechanism

since

the

endoplasmic-reticulum

and

mitochondrial

uptake

mechanisms

are

not

inhibited

by

cytoplasmic

o-vanadate

-LSB-

-RSB-

Nevertheless

for

many

different

cell

types

it

has

been

shown

that

mitochondria

participate

in

clearance

when

concentrations

are

high

-LSB-

-RSB-

It

is

very

difficult

to

measure

the

action

of

mitochondria

in

snail

neurones

directly

However

an

increased

muffling

power

at

high

concentrations

-LSB-

-RSB-

suggests

that

mitochondria

may

play

a

role

close

to

the

membrane

where

high

transients

occur

Instead

of

reinforcing

the

signals

and

thereby

generating

a

fast

travelling

wave

into

the

cell

the

stores

clearly

play

a

role

in

the

recovery

of

the

transients

CPA

significantly

increased

the

clearance

time

from

to

s

these

were

measured

in

the

centre

of

the

cell

and

were

corrected

for

the

CASM

response

time

From

this

we

estimate

that

the

stores

contribute

about

to

the

clearance

This

is

lower

but

comparable

to

the

result

found

in

Purkinje

cell

somata

from

rat

cerebellar

slices

where

blocking

of

the

endoplasmic

pump

also

significantly

slowed

the

recovery

time

after

influx

-LSB-

-RSB-

Calcium

transients

change

systematically

with

depth

Although

the

steady-state

VCa

levels

were

probably

elevated

by

continuous

entry

the

recorded

transients

and

the

way

they

changed

with

depth

were

we

believe

physiologically

significant

It

seems

unlikely

that

the

kinetics

of

the

diffusion

of

from

the

far

side

of

the

cell

towards

the

centre

would

be

changed

by

a

constant

or

slowly-declining

leak

Our

average

value

for

the

speed

at

which

a

depolarisation-induced

transient

flows

from

the

periphery

to

the

centre

of

a

nerve

cell

with

no

added

mobile

buffer

was

μm

s

We

can

find

no

previous

measurements

of

this

parameter

in

excitable

cells

although

several

groups

have

modelled

the

process

-LRB-

for

example

-LSB-

-RSB-

-RRB-

The

only

real

measurement

we

have

found

was

done

with

μm

in

an

isolated

atrial

myocyte

with

inhibited

sarcoplasmic

reticulum

pumps

-LSB-

-RSB-

Our

estimate

from

their

Fig.

is

that

the

calcium

peak

moved

at

least

times

faster

than

in

our

observations

but

the

authors

model

showed

that

this

was

probably

due

to

the

Their

modelled

data

as

shown

in

their

Fig.

suggest

that

with

no

added

mobile

buffer

their

transients

might

travel

to

the

centre

of

their

model

myocyte

at

a

similar

speed

to

that

which

we

measure

although

their

time

axis

does

not

extend

far

enough

Furthermore

when

the

speed

at

which

transients

travel

depends

on

diffusion

the

velocity

is

not

constant

but

varies

with

distance

typically

velocity

first

increases

and

then

decreases

when

the

centre

of

the

cell

is

approached

In

contrast

true

waves

are

constantly

regenerated

and

tend

to

move

with

a

constant

speed

-LSB-

-RSB-

Calcium

diffusion

in

large

snail

neurones

without

added

buffer

If

recovery

from

a

brief

influx

relies

on

extrusion

at

the

plasma

membrane

diffusion

will

become

important

for

large

cells

because

has

to

diffuse

to

the

plasma

membrane

to

be

extruded

Moreover

the

fastest

possible

clearance

without

sequestration

is

the

diffusion

limit

When

the

extrusion

rate

is

much

faster

than

diffusion

the

recovery

time

constant

is

proportional

to

the

square

of

the

cell

's

diameter

and

inversely

proportional

to

the

diffusion

coefficient

-LRB-

see

Section

-RRB-

Because

large

snail

neurones

mainly

rely

on

transmembrane

extrusion

mechanisms

and

do

not

seem

to

reinforce

signals

the

diffusion

coefficient

becomes

a

critical

parameter

for

clearance

and

spatial

signalling

Fig.

shows

the

recovery

times

assuming

that

diffusion

is

the

rate-limiting

process

for

various

different

diffusion

coefficients

as

function

of

the

cell

's

diameter

The

recovery

time

of

large

snail

neurones

is

about

s

-LRB-

dashed

line

-RRB-

which

requires

a

diffusion

coefficient

between

and

s

However

most

snail

and

other

animal

nerve

cell

bodies

are

much

smaller

with

diameters

between

and

μm

The

recovery

times

of

these

cells

is

typically

in

the

order

of

seconds

-LRB-

dotted

line

-RRB-

Hence

with

diffusion

coefficients

s

the

cell

can

still

be

cleared

readily

by

the

pump

Why

is

more

mobile

in

large

snail

neurones

It

is

possible

that

large

cells

that

do

not

use

release

mechanisms

for

signalling

and

rely

on

extrusion

at

the

membrane

for

reasonably

fast

recovery

require

a

high

mobility

to

function

A

high

mobility

will

also

ensure

fast

signal

transmission

to

the

nucleus

This

is

quite

different

from

large

cells

that

use

release

mechanisms

to

trigger

rapid

on/off

responses

such

as

muscle

oocytes

and

chromaffin

cells

These

cells

typically

have

low

mobilities

and

do

not

rely

as

much

on

extrusion

but

recycle

internally

released

Small

neurones

and

axonal

regions

with

high

surface

to

volume

ratios

represent

another

class

of

geometries

which

do

not

require

high

mobility

for

fast

recovery

Because

is

well

buffered

with

an

estimated

binding

ratio

of

the

mobility

of

the

endogenous

mobile

buffers

must

be

high

to

explain

the

high

apparent

mobility

of

Possibly

the

ratio

of

mobile

buffers

to

immobile

buffers

is

higher

in

large

snail

neurones

or

the

diffusion

coefficient

of

the

mobile

buffer

fraction

is

much

higher

than

in

other

cells

This

may

be

related

to

less

cytoplasmic

crowding

for

example

by

reduced

cytoskeleton

causing

the

movement

of

proteins

to

be

less

constricted

-LSB-

-RSB-

Axonal

regions

and

muscle

cells

contain

high

concentrations

of

cytoskeletal

components

that

may

restrict

or

slow

considerably

the

movement

of

larger

calcium

binding

proteins

compared

to

large

snail

neurones

The

great

majority

of

studies

on

intracellular

signalling

have

been

done

with

indicators

such

as

Fura

which

can

be

used

on

all

sizes

and

types

of

cell

But

the

interaction

of

the

signals

with

the

indicator

may

have

subtle

effects

which

are

hard

to

predict

It

is

to

be

regretted

that

CASMs

so

far

have

such

large

tips

and

slow

responses

that

they

can

be

used

only

on

exceptionally

large

cells


Paradigm shift in hydrocephalus research in legacy of Dandy 's pioneering work : rationale for third ventriculostomy in communicating hydrocephalus Objective This study aims to question the generally accepted cerebrospinal fluid -LRB- CSF -RRB- bulk flow theory suggesting that the CSF is exclusively absorbed by the arachnoid villi and that the cause of hydrocephalus is a CSF absorption deficit . In addition , this study aims to briefly describe the new hydrodynamic concept of hydrocephalus and the rationale for endoscopic third ventriculostomy -LRB- ETV -RRB- in communicating hydrocephalus . Introduction The modern era of hydrocephalus research began with the experimental studies of Dandy and Blackfan -LSB- 3 -RSB- in 1914 , which , until today constitutes an unsurpassed contribution to this field . By plugging the aqueduct , they produced hydrocephalus in dogs . The division of hydrocephalus into the obstructive and communicating type originates from their work . The bulk flow theory and the concept of cerebrospinal fluid -LRB- CSF -RRB- malabsorption as the cause of hydrocephalus are also based on their experiment -LSB- 3 -RSB- . However , Dandy strongly opposed the view that idiopathic communicating hydrocephalus is caused by an obstruction at the arachnoid villi . Such an obstruction can not cause a higher pressure in the ventricles than in the subarachnoid space but would rather dilate the subarachnoid space . He also objected to the view that the CSF is absorbed by the arachnoid villi and instead proved that the CSF is absorbed by the capillaries -LSB- 3 , 4 -RSB- . If this is true , the modern era of CSF and hydrocephalus research started and ended with Dandy , who left the pathophysiology of idiopathic communicating hydrocephalus unexplained for future exploration . By going back to Dandy and following his lead of a capillary CSF absorption , a new understanding of hydrocephalus may be found . O'Connel -LSB- 19 -RSB- and Bering -LSB- 1 -RSB- suggested that increased pulse pressure in the ventricles is the cause of communicating hydrocephalus . In 1978 , Di Rocco and Pettorossi -LSB- 5 -RSB- verified that an intraventricular pulsating balloon causes communicating hydrocephalus in sheep . In 1993 , Greitz re-valuated the physiology of the CSF circulation and hydrocephalus by using flow sensitive magnetic resonance imaging -LRB- MRI -RRB- and radionuclide cisternography -LSB- 9 -RSB- . He suggested that the capillaries absorb the CSF and that the distending force in the production of chronic hydrocephalus is an increased systolic pulse pressure in brain tissue -LSB- 14 -RSB- . The hydrodynamic concept of hydrocephalus Classification of hydrocephalus The classification is based on capillary absorption of the CSF -LSB- 9 -- 14 -RSB- . Hydrocephalus is divided into two main groups , acute hydrocephalus and chronic hydrocephalus -LSB- 14 -RSB- . Acute hydrocephalus is caused by an intraventricular CSF obstruction in accordance with the conventional view . As opposed to that view , it is suggested that chronic hydrocephalus is caused by decreased intracranial compliance . Causes of decreased intracranial compliance Although the etiology of the decreased intracranial compliance such as CSF obstructions at the foramen magnum and adhesions in the subarachnoid space after intracranial bleedings , trauma , operations and infections is well known , the etiology remains unknown in many idiopathic and congenital cases of hydrocephalus . However , the final stage of chronic hydrocephalus , independent of its etiology , is uniform . The final stage is characterised by narrow capacitance vessels and reduced cerebral blood volume . This reduces cerebral blood flow , reduces intracranial compliance and enhances the intracerebral pulse pressure . Intracerebral pulse pressure theory of chronic hydrocephalus Chronic hydrocephalus consists of two subtypes , communicating hydrocephalus and chronic obstructive hydrocephalus -LSB- 14 -RSB- . The associated malabsorption of CSF is not involved as a causative factor in chronic hydrocephalus . The theory is based on one basic mechanism , i.e. that chronic hydrocephalus is caused by decreased intracranial compliance increasing the systolic pressure transmission into the brain parenchyma -LSB- 9 , 10 , 12 -- 14 -RSB- . The increased systolic pressure in the brain is the cause of the distension of the brain and ventricles . The systolic expansion of the brain distends the brain towards the skull and simultaneously compresses the periventricular region of the brain . The rationale result is the predominant enlargement of the ventricles and a narrowing of the subarachnoid space . Rationale for ETV in communicating hydrocephalus As described above , communicating hydrocephalus is caused by decreased compliance increasing the systolic pressure transmission into the brain . The systolic force compresses the brain including the intracranial capacitance vessels , i.e. the cerebral veins and capillaries . This results in a vicious cycle with narrow capacitance vessels and significantly reduced cerebral blood volume that causes further decrease in intracranial compliance and further increase in intra-cranial pulse pressure . It is obvious that an endoscopic third ventriculostomy -LRB- ETV -RRB- may interrupt the vicious cycle and reduce the systolic pressure in the brain simply by venting ventricular CSF through the stoma . The patent aqueduct in communicating hydrocephalus is too narrow to vent the ventricular CSF sufficiently . By reducing the pulse pressure , the ETV also reduces the compression of the capacitance vessels thereby restoring some degree of venous compliance , which in turn reduces the intracerebral pulse pressure further . ETV versus shunting The proposed concept opens a new avenue in that ETV may be an effective treatment also in communicating hydrocephalus -LSB- 8 , 16 -- 18 -RSB- . It thus constitutes an interchangeable alternative to shunting . The primary aim of the treatment of chronic hydrocephalus is to restore intracranial compliance , which is achieved by both treatments -LSB- 14 -RSB- . Effective shunting is based on a slight over-drainage of CSF that ultimately causes a direct and forced dilation of the compressed veins -LSB- 14 -RSB- . Therefore , shunting is more effective in increasing intracranial compliance than ETV where the dilating effect on the veins works indirectly by reducing the systolic compressing force on the veins . Because ETV provides a more physiological treatment and has less late complications than shunting , it may be of benefit to increase the number of patients finally treated by ETV -LSB- 2 , 6 -- 8 , 15 , 17 , 18 , 20 -RSB- . In patients shunted under 1 year of age , ETV should be considered as an alternative treatment when they grow older . However , the final answer as to which is the optimal treatment must be based on randomized clinical studies . Discussion The aim of this paper is to briefly describe the hydrodynamic concept of hydrocephalus , which is based on Dandy 's observation of capillary absorption of the CSF . Oi and Di Rocco -LSB- 20 -RSB- recently suggested that a minor CSF pathway through the brain parenchyma is the dominant CSF absorption site in the embryo , foetus and infant . The theory described here suggests that the minor pathway in the developing immature brain as well as the major pathway in adults are through the brain capillaries . It is beyond the scope of this brief communication to present the numerous physiological -LRB- and self-evident -RRB- evidences that the brain capillaries have the capacity to absorb fluids such as the CSF and its constituencies -LSB- 3 , 4 , 9 , 11 , 12 , 14 -RSB- . This contrasts to the total lack of physiological evidence that the arachnoid villi can absorb the CSF . The CSF dynamics has been described in earlier published papers -LSB- 9 , 11 , 12 , 14 -RSB- . The proposed concept indicates a paradigm shift in our view on hydrocephalus . It is suggested that chronic hydrocephalus is caused by decreased intracranial compliance rather than a CSF absorption deficit -LSB- 14 -RSB- . The associated CSF malabsorption is a secondary phenomenon to the decreased intracranial compliance . The only residue of the conventional view is acute hydrocephalus , which is caused by a CSF absorption deficit -LRB- of the periventricular capillaries -RRB- . Normal-pressure hydrocephalus , aqueductal stenosis as well as communicating hydrocephalus in infants and adults are typical manifestations within the spectrum of chronic hydrocephalus . It should be emphasised that chronic hydrocephalus is an unstable hemodynamic disorder occurring at normal or slightly increased mean intracranial pressure with superimposed vascular pressure waves that can be fatal . The theory may thus have identified decreased intra-cranial compliance as a new and potential universal cause of chronic hydrocephalus . Decreased compliance is common to all different types of chronic hydrocephalus whatever their etiology . If the theory is correct , there is hope for improved treatment of chronic hydrocephalus of unknown etiology . How come then that treatment failure rather is the rule than the exception of this devastating condition ? The reason may be that shunting and ETV essentially represents symptomatic treatments of hydrocephalus . To improve therapy , we have to find treatments that are more effective in increasing compliance in cases with unknown etiology or are directed against the cause of the decreased compliance in cases with known etiology .

O O O B O O O O O O O O O O O O O O O B O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B I O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B I O O O O O O O O O O O B O O B O O O O O O O O O O O O O O O O B O O O O O O O O B O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B I O O B I O O O B O B O O O O O O B O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B I O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B I O O B O O O O O O O O O O O O O O B O O O O O O O B I O O B O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O

cerebrospinal fluid
compliance
etv
hydrocephalus
pathophysiology
pulse pressure