Biophysics – Chapter 2: Molecular Transport in Living Cells This chapter explores the fundamental principles of molecular transport within living cells, a key concept in biophysics. It covers both passive and active transport mechanisms, including diffusion, osmosis, facilitated diffusion, active transport, endocytosis, and exocytosis. Key concepts include: Transport across cell membranes Role of membrane proteins and ion channels Energy requirements and ATP involvement Real-life examples from human physiology Diagrams and simplified explanations for better understanding

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Molecular Transport in Living Cells
Molecular Transport
The transport of substances across the cellular membrane can take place by several mechanisms.
According to energy needs, the transport of substances can be divided into tag transport mechanisms:
• Active Transport
• Passive Transport
Passive Transport
Passive transport of substances follows the concentration gradient without energy consumption in the
form of ATP. These include:
1. Filtration
2. Simple diffusion
3. Facilitated diffusion
4. Diffusion through protein channels
5. Osmosis
Filtration
The separation of insoluble solids from liquids or gases using a filter medium (e.g., a biological
membrane) is based on different particle sizes, different electric charges, or type of molecule. Transport is
driven by a pressure gradient e.g., hydrostatic pressure on a filtration paper (PH=ρ.g.h, i.e. density, gravity,
vertical distance).
Another example is glomerular filtration which takes place in kidneys where nephrons constantly filter the
blood across capillary walls and Bowman's capsule. This filtration is driven by blood pressure.
Small particles, which can pass through the filtration membrane, become filtrate. In contrast, large
particles remain feed. Filtration is based on pressure gradient.
Filtration depends on:
• The size of the particles (microfiltration, ultrafiltration, nanofiltration)
• The size and number of pores in the filtration layer (membrane)
• The surface charge on the filter layer (positive + or negative - )
2. Simple Diffusion
Simple diffusion is a spontaneous movement of the particles following the direction of the concentration
gradient, without binding to membrane proteins and without consumption of energy in the form of ATP.
Fat-soluble substances (e.g., hormones, ethanol, glycerol, and urea), neutral molecules of H₂O, O2 and
CO₂ penetrate the cell membrane through the simple diffusion. Diffusion stops when equal
concentrations are reached. Diffusion is not associated with any changes in the volumes.

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Fick's Law of Diffusion
Fick's Law describes how particles (atoms, molecules, etc.) move from areas of higher concentration to
areas of lower concentration, a process known as diffusion.
Formula: 𝐽 = −𝐷
𝑑𝑐
𝑑𝑥
, 𝐽 = −𝐷. 𝑆
𝑑𝑐
𝑑𝑥
, 𝐽 = −𝐷. 𝐴
𝑑𝑐
𝑑𝑥
Where:
J = Diffusion flux density (amount of substance flowing per unit area per unit time). typically measured in
mol/(m²-s).
D = Diffusion coefficient (m²/s), a constant that depends on the substance and medium (e.g., water, air).
dc/dx = Concentration gradient (change in
concentration per unit distance) along the direction of diffusion.
The negative sign indicates that diffusion occurs from high to low concentration (from positive to negative
concentration gradient)
Fick's Law suggests that temperature directly impacts diffusion. The diffusion coefficient D typically
increases with temperature, meaning diffusion occurs more rapidly as the system gets warmer. This is
because heat gives particles more kinetic energy, making them move faster and spread out more quickly.
For example:
• In cold water, diffusion happens slower.
• In hot water, diffusion happens faster.
Diffusion depends on:
• The viscosity of a solvent and particle size of the solute
Diffusion flux density, often referred
to as the diffusion flux, quantifies the
rate at which a substance diffuses
through a given area per unit time.
This is a material property that characterizes how easily
a substance diffuses through a given medium.
The unit of diffusion flux density in the SI system is usually moles
per square meter per second (mol·m⁻²·s⁻¹)
Derivatives are taken to understand how a function changes as its input changes, essentially
measuring the instantaneous rate of change. Derivatives quantify how much a function's
output changes for a tiny change in its input. Derivatives can help predict how a function will
behave in the future, as they reveal the direction and magnitude of change. If y=f(x), the
derivative with respect to x may be written as f′(x),y′,dydx,or dfdx.
The dy/dx is the derivative of y with respect to x, and y is considered to be a function. If y = x,
dy/dx = 1. dy/dx is a function itself, not an operator on a function.

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• Temperature (the higher the temperature of the solution, the faster the diffusion)
• Size of diffusion area S (area through which the particles pass during diffusion)
• Concentration
• Distances (diffusion flux decreases with increasing distance).
3. Diffusion Through A Protein Channel
Protein channels are specialized membrane proteins that allow substances to pass through the
membrane. These channels can be either pores (permanently open) or gated channels (which can open or
close depending on external factors).
Pores:
These channels are always open, providing a
continuous pathway for substances to pass through.
Example: Aquaporins, which are channels that allow
water molecules to pass through the membrane.
Gated Channels:
These channels can be opened or closed in response to
specific signals. such as electrical or chemical
changes.
Example: Ion channels, which can open in response to
voltage changes across the membrane (voltage-gated
channels) or the binding of a molecule (ligand-gated channels).
Selective Permeability:
The selective permeability of protein channels means that only certain ions or molecules are allowed to
pass through. This selectivity depends on several factors:
Size: Channels may only allow molecules or fons of a certain size to pass through For example, ion
channels are often specific to a particular ion (e.g., sodium, potassium, chloride) based on the size of the
ion.
Shape: The shape of the channel and its pore will also determine which substances can pass through. For
example, some channels may have a narrow opening that only allows smaller ions or molecules to pass.
Aquaporins are transmembrane proteins
that act as water channels, facilitating
the rapid movement of water across cell
membranes. They are found in various
organisms, from bacteria to humans, and
play a crucial role in maintaining water
balance and regulating cell function. In
addition to water, some aquaporins also
transport other small molecules like
glycerol, urea, and ammonia.
Ion channels are specialized proteins
embedded in cell membranes that act
as selective pathways for the passage
of charged ions across the membrane.

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Charge: The electric charge on the surface of the channel can attract or repel ions based on their charge.
lon channels can be selective to positively charged ions (cations) or negatively charged ions (anions)
based on the electrostatic interactions.
Gating Mechanisms:
Protein channels can be gated by external signals, meaning they can open and close in response to
certain triggers:
1. Voltage-Gated Channels:
These channels open and close in response to changes in the electrical potential across the membrane.
Example: Voltage-gated sodium channels in neurons open when the membrane potential becomes more
positive, allowing Na ions to flow in, which is critical for action potentials.
2. Ligand-Gated Channels:
These channels open when a specific molecule (ligand) binds to the channel protein.
Example: Acetylcholine receptors in muscle cells open when acetylcholine binds to the receptor,
allowing Na ions to flow into the cell and triggering muscle contraction.
3. Mechanically-Gated Channels:
These channels open in response to mechanical forces, such as pressure or stretch.
Example: Stretch-activated ion channels in sensory cells respond to mechanical deformation (e.g.,
sound waves in the ear).
Facilitated Diffusion
Facilitated diffusion allows the transport of the substances across membranes, which would not get
through by simple diffusion, or only to a very limited extent. Facilitated diffusion across membranes is
mediated by the binding of passing molecules to the protein transporters, which are formed by specifically
structured integral proteins.
Osmosis And Osmotic Pressure
Osmosis is a type of passive transport where water moves from an area with solutes across a semi-
permeable membrane. It's like water "trying" to dilute the more concentrated solution.
Size: Smaller molecules can fit through the gaps and spaces in the lipid bilayer or interact
more readily with the hydrophobic core of the membrane. Larger molecules, on the other
hand, may be too large to pass through the membrane without specialized transport proteins.
Shape: The shape of a molecule can also affect its permeability. Globular or elongated
molecules may have different ease of passage than flat or irregularly shaped molecules.
Charge: Charged molecules are repelled by the hydrophobic core of the lipid bilayer and
require the assistance of specialized transport proteins to cross the membrane. Uncharged or
neutral molecules can dissolve in the hydrophobic core and pass through more readily.

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Osmosis continues until the concentrations on both sides of the membrane are equal, or until pressure
prevents further movement, or there's no more solvent (like water evaporating).
Osmotic pressure is the pressure needed to stop osmosis and equalize the concentration It's calculated
using Van't Hoff's law:
π = R .T.c.i
where:
π is osmotic pressure
R is the gas constant
T is temperature (Kelvin)
c is solute concentration
i is the dissociation factor (for salts that split into ions).
Osmolarity refers to the concentration of all osmotically active particles in a solution. Osmolality is the
concentration of these particles in 1 kg of solvent When comparing solutions to blood plasma:
Isotonic: Same osmolarity as plasma
Hypertonic: Higher osmolarity than plasma.
Hypotonic: Lower osmolarity than plasma.
An osmole is 1 mole of any fully dissociated substance
dissolved in water.
Molarity is moles of solute per liter of solution moles/L (mol/L) ,
while molality is moles of solute per kilogram of solvent
moles/kg (mol/kg).
The MOLE (mol) amount of a pure
substance containing the same number of
chemical units as there are atoms in exactly
12 grams of carbon-12 (i.e., 6.022 X 1023
)

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An isotonic solution (like saline) has the same osmolarity as blood plasma, which is useful for medical
treatments like injections and wound rinsing, as it doesn't harm tissues.
Active Transport
Active transport is a movement of substances against the concentration gradient or the electrochemical
gradient that requires the supply of free energy in the form of ATP (Adenosine triphosphate hydrolysis).
There are two major types of active transport:
• Primary transport
• Secondary transport
Primary Transport
The energy released when ATP is broken down is mainly
used for moving ions (charged particles) across cell
membranes. Here are some key examples of ion pumps
that use this energy:
1. Sodium-Potassium Pump (Na*-K* ATPase):
• Found in the cell membrane.
• It uses ATP to move sodium (Na) out of the cell and potassium (K) into the cell
• This pump usually moves 3 sodium ions out for every 2 potassium ions in
• This helps maintain important functions like nerve signals and cell balance
2. Proton Pump (H", K-ATPase):
Found in the stomach lining (gastric mucosa).
It uses ATP to move hydrogen ions (H+
) into the stomach to make hydrochloric acid (HCI).
In exchange, it moves potassium ions (K) into the cell.
This is an antiport pump (two substances are moved in opposite directions)
3. Calcium Pump (Ca³-ATPase):
Found in the endoplasmic reticulum (ER) and cell membranes, especially in muscle and intestinal cells.
Primary active transport directly uses
ATP to move molecules against their
concentration gradient, while
secondary active transport utilizes the
energy stored in an electrochemical
gradient established by primary active
transport.

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It uses ATP to pump calcium ions (Ca²*) out of the cell or into the ER.
This is a uniport pump (only one substance is moved in one direction).
These pumps are essential for processes like muscle contraction, digestion, and maintaining the right
balance of ions inside and outside the cell.
2. Secondary Transport
These transport system includes the (Cotransport Systems) where the energy needed to move one
molecule comes from the concentration gradient of another molecule. The gradient is usually set up by
primary active transport. In this process:
Example: Glucose is transported across the membrane by binding with sodium ions (Na). The Na gradient,
created by the sodium-potassium pump, powers the active transport of glucose and sodium together. This
is called Na-glucose cotransport.
Types of Transport:
1:Uniport: A type of transport where one substance is moved in one direction. Glucose transporters
(GLUT1) in red blood cell membranes.
2:Symport A type of cotransport where two substances are moved in the same direction at the same time
The sodium-glucose symporter in the lining of the small intestine, which transports sodium ions and
glucose into the cell together.
3:Antiport A type of cotransport where two substances are moved in opposite directions at the same
time. The sodium-calcium exchanger (NCX) in cardiac muscle cells, which moves three sodium ions into
the cell and one calcium ion out.
Other Types of Active Transport: .
Exocytosis ("cell vomiting"):
The process where the cell secretes larger particles by wrapping them in a vesicle that fuses with the
membrane and releases its contents outside the cell. Example: neurotransmitter release in nerve cells.
Endocytosis ("cell eating").
The process where the cell takes in larger particles by engulfing them with its membrane, forming a vesicle
that brings them inside Example: white blood cells engulfing bacteria (phagocytosis).
These processes help the cell move important molecules and particles across its membrane in a
controlled way.
Pinocytosis (“pino” means “to drink”)
Is a process by which the cell takes in the fluids along with dissolved small molecules. In this process, the
cell membrane folds and creates small pockets and captures the cellular fluid and dissolved substances.

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Membrane Potential
The membrane potential is the electrical charge difference across a cell's membrane, measured in
millivolts (mV). This value shows the difference in charge between the inside and outside of the cell, with
the outside of the cell being considered zero. In most cells, including neurons and muscle cells, the inside
and outside are overall neutral, but there's a tiny difference in charge near the membrane's surface. This
small charge difference is crucial for the cell's ability to send electrical signals, such as action potentials
(electrical impulses in nerves and muscles)
Ion Distribution:
• There is much more sodium (Na") outside the cell than inside
• There is much more potassium (K*) inside the cell than outside.
• Anions (negative ions like proteins and phosphate) are concentrated inside the cell.
1. Resting Membrane Potential:
• The resting membrane potential is the difference in charge across the membrane when the cell is not
sending a signal.
• A typical resting membrane potential is -70 mV, meaning the inside of the cell is 70 mV more negative
than the outside.
• Without certain membrane proteins, the voltage could be even lower
2. Role of lon Channels and Pumps:
Leak channels allow Na to slowly enter the cell and K to slowly exit. The Na+/K+ pump uses energy (ATP) to
actively move Na out and K in, helping to maintain the ion concentration gradients that keep the resting
membrane potential stable.
Even though it takes energy, these processes are essential for maintaining the cell's electrical potential
and enabling it to function properly, especially for signaling.
The Action Potential
The resting membrane potential is the steady state of a cell, where there is a balance between ions moving
down their concentration gradients and being pumped back against those gradients. At rest, the inside of
the cell is negatively charged compared to the outside (about-70 mV).
An action potential is a rapid change in
electrical potential across a cell
membrane, primarily occurring in nerve
and muscle cells. It's a fundamental
mechanism for transmitting signals in the
nervous system and causing muscle
contractions.
Threshold a level, point, or value above
which something is true or will take place
and below which it is not or will not.

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Initiating an Action Potential
To send an electrical signal, the membrane potential must become more positive:
1. Depolarization: When a signal arrives, voltage-gated Na+ channels open, allowing sodium ions (Na+) to
rush into the cell. This is because Na+ is much more concentrated outside the cell. As Na+ enters, the
inside of the cell becomes less negative (closer to 0 mV).
2. As Na+ continues to flow in, the membrane potential can briefly become positive (around +30 mV).
Repolarization and Hyperpolarization
3. Once the membrane potential reaches +30 mV, voltage-gated K+ channels open, allowing potassium
ions (K+) to exit the cell. Since K+ carries a positive charge, this causes the membrane potential to
become more negative again (repolarization). eventually returning to the resting-70 mV.
4. However, K+ channels are slow to close, so the membrane potential briefly becomes even more
negative than the resting potential, a state called hyperpolarization.
The Action Potential Process.
The action potential (signal) travels along the neuron, changing the voltage by about 100 mV (from-70 mV
to +30 mV).
Voltage-gated Na+ channels have two gates:
• Activation gate opens at -55 mV, allowing Na+ to flood in. 0 Inactivation gate closes shortly after,
stopping Na+ flow during repolarization.
• Voltage-gated K+ channels have one gate that opens when the membrane reaches about -50 mV,
allowing K+ to leave the cell. These channels close after repolarization, but not before
hyperpolarization occurs
Refractory Periods.
The absolute refractory period is when the Na+ inactivation gate is closed, so no new action potential can
be started. The relative refractory period occurs during hyperpolarization. A stronger-than- usual stimulus
is required to trigger a new action potential during this phase.