experiments on diffusion and osmosis

5 Engaging Ways to Teach Osmosis and Diffusion Without Lecturing

Life, at its most basic, is a series of complex chemical and physical exchanges, all harmoniously synchronized to ensure the seamless operation of biological systems. Osmosis and diffusion are central to these exchanges, representing two of nature’s most gracefully orchestrated principles.

Diffusion is like a dance of particles that move from a crowded place to a less crowded place until there’s balance. Osmosis is a special dance for water that goes through a thin barrier. These moves help keep us alive and let plants absorb water from the ground.

However, these fluid-movement processes can be hard to teach due to their abstract and intangible nature. Sometimes, the textbooks make them look boring too. That’s where this article helps. We will present five creative ways to teach osmosis and diffusion, making learning fun and memorable.

1. Engage Students With Interactive Models 

Teaching osmosis and diffusion can be a challenge, primarily because these processes are invisible to the naked eye. The chance to observe these phenomena directly can significantly enhance students’ understanding.

Interactive models provide an excellent solution. They offer students a visual journey into the minuscule world of particles, allowing them to witness these exchanges in real-life scenarios. This dynamic learning approach elevates the educational experience.

One such valuable resource is the virtual labs offered by Labster. For example, the Osmosis and Diffusion Lab simulation immerses students in a virtual environment where they can observe osmosis occurring in cell membranes. They can conduct experiments with various samples, studying these processes firsthand.

Discover Labster's Osmosis and Diffusion virtual lab today!

This engaging, virtual approach allows students to apply theoretical classroom knowledge in real-time, making the learning experience more impactful. 

2. Inject Fun With Games and Activities

Adding games and activities to the teaching process not only makes learning fun but also enhances understanding and retention of complex concepts.

Here are a few interesting activities for teaching osmosis and diffusion:

• Osmosis Egg-experiment: An engaging experiment where a de-shelled egg is placed in different solutions. Students can predict and see what the weight changes over time due to osmosis.
• Kahoot Quiz Game: Develop quizzes about osmosis and diffusion using Kahoot . This interactive game format will allow students to test their knowledge and compete with their peers.
• Role-Playing Game: Divide students among groups and have them play roles as molecules to demonstrate osmosis and diffusion physically. This can help to understand these processes in a fun and interactive way.

3. Infuse Technology into Lessons

In the digital era, technology is a powerful tool to transform teaching and learning. Especially when it comes to teaching osmosis and diffusion, infusing technology into lessons can create a more engaging, interactive, and immersive learning experience.

Using technology, educators can bring to life the otherwise invisible processes of osmosis and diffusion, fostering deeper understanding. For example, with multiple simulations and animated videos, you can take students on a microscopic journey into a cell to see how molecules move, bringing abstract concepts to life.

Online virtual simulations, like Labster's Osmosis and Diffusion simulation , allow students to experiment right from their tech gadgets. They closely observe these chemical exchange processes, which provides them with deeper insights into the subject. 

4. Inspire Students Through Career Exploration

When educators mention how abstract concepts will help them in the real professions in the future, it boosts their interest and curiosity. They begin to see the relevance and realize the importance of the concepts they are being taught. 

You can quote how multiple medical professions heavily rely on the understanding of osmosis and diffusion. Doctors need to understand these principles when administering intravenous fluids to balance electrolytes in a patient's body. Biomedical engineers apply these concepts in designing artificial organs or drug-delivery systems

By exploring careers related to osmosis and diffusion, students can see the practical and professional implications of these concepts. This sparks their interest and motivates them to explore it further.

5. Connect Topic to Real-World Applications

Beyond career references, you can extend the relevance to real-world applications. This allows students to understand these concepts are not just textbook theories, but vital processes that impact our everyday lives.

A classic example of osmosis in the real world is the process of water absorption by plant roots from the soil. Diffusion, on the other hand, is illustrated every time we spray perfume, and its scent spreads across the room.

Furthermore, osmosis knowledge is also crucial when designing saline solutions for IV drips - too much or too little salt can cause harmful fluid shifts in the body. 

Incorporating these real-world applications into lessons brings science to life, making it more relatable and meaningful for students. 

Final Thoughts

Although teaching osmosis and diffusion can be a challenging task, it can be transformed into an exciting and memorable journey with the right tools and approaches. Through virtual lab simulations, fun games, and real-world applications, educators can make these abstract concepts tangible and engaging for students.

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Simple Candy Osmosis Experiment

Demonstrate Osmosis Using Gummy Bears

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Osmosis is the diffusion of water across a semipermeable membrane. The water moves from an area of higher to lower solvent concentration (an area of lower to higher solute concentration). It's an important passive transport process in living organisms, with applications to chemistry and other sciences. You don't need fancy lab equipment to observe osmosis. You can experiment with the phenomenon using gummy bears and water. Here's what you do:

Osmosis Experiment Materials

Basically, all you need for this chemistry project are colored candies and water:

• Gummy bear candies (or other gummy candy)
• Plate or shallow bowl

The gelatin of the gummy candies acts as a semipermeable membrane . Water can enter the candy, but it's much harder for sugar and coloring to leave exit it.

What You Do

It's easy! Simply place one or more of the candies in the dish and pour in some water. Over time, water will enter the candies, swelling them. Compare the size and "squishiness" of these candies with how they looked before. Notice the colors of the gummy bears starts to appear lighter. This is because the pigment molecules (solute molecules) are being diluted by the water (solvent molecules) as the process progresses.

What do you think would happen if you used a different solvent, such as milk or honey, that already contains some solute molecules? Make a prediction, then try it and see.

How do you think osmosis in a gelatin dessert compares with osmosis in candy? Again, make a prediction and then test it!

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Optional Lab Activities

Osmosis and diffusion, lab objectives.

At the conclusion of the lab, the student should be able to:

• define the following terms: diffusion, osmosis, equilibrium, tonicity, turgor pressure, plasmolysis
• describe what drives simple diffusion (why do the molecules move?)
• list the factors that may affect the speed of simple diffusion
• list which molecules, in general, can freely diffuse across the plasma membrane of a cell
• describe what drives osmosis (why do water molecules move?)
• explain why water moves out of a cell when the cell is placed in a hypertonic solution
• explain why water moves into a cell when the cell is placed in a hypotonic solution
• describe what physically happens to a cell if water leaves the cell
• describe what physically happens to a cell if water enters the cell

Introduction

Understanding the concepts of diffusion and osmosis is critical for conceptualizing how substances move across cell membranes. Diffusion can occur across a semipermeable membrane; however diffusion also occurs where no barrier (or membrane) is present. A number of factors can affect the rate of diffusion, including temperature, molecular weight, concentration gradient, electrical charge, and distance. Water can also move by the same mechanism. This diffusion of water is called osmosis .

In this lab you will explore the processes of diffusion and osmosis. We will examine the effects of movement across membranes in dialysis tubing, by definition, a semi-permeable membrane made of cellulose. We will also examine these principles in living plant cells.

Part 1. Diffusion Across a Semi-Permeable Membrane: Dialysis

• Cut a piece of dialysis tubing, approximately 10 cm.
• Soak the dialysis tubing for about 5 minutes prior to using.
• Tie off one end of the tubing with dental floss.
• Use a pipette and fill the bag with a 1% starch solution leaving enough room to tie the other end of the tubing.
• Tie the other end of the tubing closed with dental floss.
• Fill a 250 mL beaker with distilled water.
• Add Lugol’s iodine to the distilled water in the beaker until the water is a uniform pale yellow color.
• Place the dialysis tubing bag in the beaker.
• The movement of starch
• The movement of iodine
• The color of the solution in the bag after 30 minutes
• The color of the solution in the beaker after 30 minutes
• Add the dialysis bag to the beaker and allow the experiment to run for 30 minutes. Record the colors of both the dialysis bag and the beaker.

Lab Questions

• Is there evidence of the diffusion of starch molecules? If so, in which direction did starch molecules diffuse?
• Is there evidence of the diffusion of iodine molecules? If so, in which direction did iodine molecules diffuse.
• What can you say about the permeability of the dialysis membrane? (What particles could move through and what particles could not?)
• What is the difference between a semi-permeable and a selectively permeable membrane

Part 2. Plasmolysis—Observing Osmosis in a Living System, Elodea

If a plant cell is immersed in a solution that has a higher solute concentration than that of the cell, water will leave/enter (circle one) the cell. The loss of water from the cell will cause the cell to lose the pressure exerted by the fluid in the plant cell’s vacuole, which is called turgor pressure. Macroscopically, you can see the effects of loss of turgor in wilted houseplants or limp lettuce. Microscopically, increased loss of water and loss of turgor become visible as a withdrawal of the protoplast from the cell wall (plasmolysis) and as a decrease in the size of the vacuole (Figure 1).

• Obtain a leaf from the tip of an Elodea Place it in a drop of water on a slide, cover it with a coverslip, and examine the material first at scanning, then low power objective and then at high power objective.
• Locate a region of health. Note the location of the chloroplasts.  Sketch a few cells. For the next step, DO NOT move the slide .
• While touching one corner of the coverslip with a piece of Kimwipe to draw off the water, add a drop of 40% salt solution to the opposite corner of the coverslip. Do this simultaneously.  Be sure that the salt solution moves under the coverslip. Wait about 5 minutes, then examine as before. Sketch these cells next to your sketch of cells in step two, note the location of the chloroplasts. Label it 40% salt solution .
• What happened to the cells in the salt solution?
• Assuming that the cells have not been killed, what should happen if the salt solution were to be replaced by water?
• Are plant cells normally hypertonic, hypotonic, or isotonic to their environment? Why?
• Can plant cells burst? Explain.

Overall Conclusions

• Review your hypothesis for each experiment. Was your original hypothesis supported or rejected for each experiment. Explain why or why not. This should be based on the best information collected from the experiment. Explain how you arrived at this conclusion.
• If it was incorrect, give the correct answer, again based on the best information collected from the experiment.

Sources of Error

• Identify and explain two things that people may have done incorrectly that would have caused them to get different answers from the rest of the class. Be  specific .
• Biology 101 Labs. Authored by : Lynette Hauser. Provided by : Tidewater Community College. Located at : http://www.tcc.edu/ . License : CC BY: Attribution
• BIOL 211 - Majors Cellular [or Animal or Plant]. Authored by : Carey Schroyer and Diane Forson. Provided by : Open Course Library. Located at : http://opencourselibrary.org/biol-211-majors-cellular-or-animal-or-plant/ . License : CC BY: Attribution

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Osmosis vs Diffusion – Definition and Examples

Osmosis and diffusion are two important types of mass transport. Here are the definitions of osmosis and diffusion, examples of each process, and a look at the differences between them.

Osmosis and Diffusion Definitions

Osmosis – Osmosis is the movement of solvent particles (usually water) across a semipermeable membrane from a dilute solution to a concentrated solution. The solvent dilutes the concentrated solution until concentration is equalized on both sides of the membrane.

Diffusion – Diffusion is the movement of solvent and solute particles from an area of higher concentration to lower concentration. At equilibrium, the net effect is a homogeneous concentration throughout the medium.

Osmosis and Diffusion Examples

Osmosis Examples : Soaking gummy bear candies is an easy osmosis demonstration. The gelatin in the candies acts as a semipermeable membrane. A good biology example is the swelling of red blood cells when they are placed in fresh water and their shrinkage (crenation) when they are placed in salt water. Plant root hairs uptaking water is another example of osmosis.

Diffusion Examples : A good example of diffusion is the way perfume fills an entire room. Another example is the movement of small molecules and ions across the cell membrane. Dropping food coloring into water is an example of diffusion. Other processes occur, but diffusion is the main transport method.

Comparing Similarities

There are similarities between osmosis and diffusion:

• Both osmosis and diffusion are passive transport processes. In other words, they are spontaneous and there is no energy required for them to occur.
• Both processes equalize the concentration of the solution.

Osmosis vs Diffusion

There are key differences between osmosis and diffusion:

• Osmosis only occurs across a semipermeable membrane, while diffusion can occur in any mixture (including across a semipermeable membrane).
• In biology, osmosis only refers to the movement of water. In chemistry, solvents other than water may move. Diffusion has the same meaning in both disciplines.
• In osmosis, only the solvent is free to move across the membrane. In diffusion, both solvent and solute particles are free to move.

• Both osmosis and diffusion are passive transport processes that equalize concentration. In other words, no energy needs to be supplied to the system for them to occur.
• In diffusion, particles move from higher concentration to lower concentration until equilibrium is reached.
• In osmosis, there is a semipermeable membrane that only allows the solvent particles to move. Solvent (usually water) moves until equilibrium is reached.
• Don’t be confused by concentration in osmosis. Remember, the only way to equalize concentration on both sides of the barrier is for water to move. The solvent molecules move from lower solvent concentration to higher solvent concentration, but they move from higher solute concentration to lower solute concentration. The concentration of the solution is what’s important.
• Osmosis may be considered a special case of diffusion involving a semipermeable membrane where which only the solvent moves.

Other Types of Transport Processes

There are different types of diffusion. The type of diffusion contrasted with osmosis is simple diffusion. Active diffusion and facilitated transport are other mass transport processes.

• Simple diffusion – Particles move from higher to lower concentration until concentration is homogeneous.
• Active transport – Solute particles move from lower to higher concentration. In biology, enzymes (proteins) carry solutes across a membrane and energy (ATP) is required.
• Facilitated transport – Solutes move from higher to lower concentration across a membrane, assisted by transmembrane proteins. This is a way for large molecules to cross a semipermeable membrane. It is a passive transport process, like simple diffusion.

There are also different types of osmosis, all involving a semipermeable membrane:

• Regular osmosis – Solvent particles move from higher to lower concentration (low to high solute concentration) until equilibrium is reached.
• Reverse osmosis (RO ) – In a solution of solutes and water, hydraulic pressure forces water across the semipermeable membrane. The result increases solute concentration on one side of the membrane, while adding purified water to the other side. Because solvent moves against the concentration gradient, energy (pressure) is required.
• Forward osmosis (FO) – Osmotic pressure draws water across a semipermeable membrane, separating it from solutes. Both reverse osmosis and forward osmosis require energy (pressure), but reverses osmosis pushes water, while forward osmosis draws or “pulls” it. Also, reverse osmosis can generate fresh drinking water, while the product of forward osmosis contains solute particles. For example, sugar and salt can be used to draw water from impure water, producing an emergency drink.

Diffusion vs Effusion

Effusion is a type of mass transport process seen in gases. Diffusion allows gas particles to freely disperse through their container. Effusion is transport of gas molecules through pores that are smaller than their average mean free path (distance between particle collisions). Effusion occurs more slowly than diffusion. The rate of effusion is inversely proportional to the square root of the mass of the particles, according to Graham’s law.

• Glater, J. (1998). “The early history of reverse osmosis membrane development.” Desalination . 117 (1–3): 297–309. doi: 10.1016/S0011-9164(98)00122-2
• Haynie, Donald T. (2001). Biological Thermodynamics . Cambridge: Cambridge University Press. pp. 130–136. ISBN 978-0-521-79549-4.
• Kramer, Eric; David Myers (2012). “Five popular misconceptions of osmosis.” American Journal of Physics . 80 (694): 694–699. doi: 10.1119/1.4722325
• Landau, L.D.; Lifshitz, E.M. (1980). Statistical Physics (3rd ed). Vol. 5. Butterworth-Heinemann. ISBN 978-0-7506-3372-7.
• Muir, D. C. F. (1966). “Bulk flow and diffusion in the airways of the lung.” British Journal of Diseases of the Chest . 60 (4): 169–176. doi: 10.1016/S0007-0971(66)80044-X

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Welcome to the Visible Body Blog!

Free lesson plan: diffusion and osmosis with visible biology.

Posted on 1/21/22 by Sarah Boudreau

Diffusion and osmosis are concepts that are important in understanding how cells—and organisms at large—function. Rather than let students “learn through osmosis,” we here at Visible Body have put together a lesson plan that uses visuals to illustrate how diffusion works.

By the end of this lesson, students will learn… 

• The factors that influence the rate of diffusion 
• The difference between diffusion and osmosis
• How a  selectively permeable membrane works
• The following vocabulary: 
• Active transport
• Passive transport
• Concentration gradient
• Selectively permeable membrane
• Isotonic, hypotonic, and hypertonic 
• Osmotic pressure

In addition to VB Suite access, this lesson will require the following: 

• A Ziploc bag
• Three beakers or glasses
• Food coloring
• Hot and cold water

Step 1: Overview

At the beginning of the lesson, prepare the iodine example for step 3 in front of the students: 

• Place a teaspoon of starch into the plastic bag. 
• Fill a glass halfway with water and add ten drops of iodine. 
• Place the bag of starch into the solution. 

At this point in the course, students are aware of the parts of the cell and the basics of what cells need to function. To begin this lesson, we’ll take what they know (parts of the cell) and use it as an entry point to understand diffusion. 

Introduce the idea that there are two ways for molecules to move into the cell: active transport and passive transport (plus phagocytosis and pinocytosis).

Active transport uses energy, passive transport does not. We will focus on passive transport today, examining diffusion and a type of diffusion called osmosis .

Introduce the term concentration gradient and explain how this concept is central to understanding diffusion.

Start by illustrating a gradient using colors. Pull up one of the cell models in Visible Biology. Next to the cell, use the drawing tool to draw a color gradient as illustrated in the image below. The transparency tools will help you transition from saturated color to blank space. Point out to the students how one side is more weighed down with color than the other, making things uneven.

Using the same color and a semitransparent brush, draw a rectangular block of diluted color to represent equilibrium. Compare the color gradient to the equalized block of color.  

Next, explain how this same idea applies to molecules on either side of a cell membrane. Particles in a fluid move around randomly; this is known as Brownian motion. The higher the concentration of particles, the more likely molecules are to bump into other molecules  and gain enough energy to bounce away. In lower concentrations, that happens less often. Diffusion happens when particles move “down” a concentration gradient from an area of higher concentration to an area of lower concentration. When there is no more gradient, there is no more energy difference between areas and so movement in all directions becomes equal. 

Using the drawing tool again, draw a sequence of oxygen molecules in a gradient moving into the cell.

A concentration gradient using the drawing tools and animal cell model in VB Suite .

If you're looking for more resources, this video from our Visible Biology YouTube series provides a fun, easy-to-understand overview of diffusion: 

Lesson on diffusion from the Visible Biology YouTube series with Dr. Cindy Harley.

Review questions for students:

• Describe the difference(s) between active and passive transport.
• What is a concentration gradient?

Step 2: Diffusion Rates

Next, show the students diffusion in action and explore the factors that influence the rate at which diffusion takes place. 

Take two beakers and pour hot water in one and cold water in the other. Drop 3-4 droplets of food coloring into each of the beakers and ask students to note how quickly the food coloring diffuses in the different beakers.

Ask the students why the hot water beaker and the cold water beaker might have different diffusion rates. 

Next, walk the students through the factors that influence diffusion rates. This table is adapted from Biology LibreText , an open-source textbook: 

Note that concentration gradients can act in opposite directions. For example, Na+ may move in one direction and K+ in the opposite direction. Unless they are charged, crowded, etc., diffusing molecules are not affected by other concentration gradients. 

• Why did the beakers of hot and cold water have different diffusion rates?
• What other factors influence diffusion?

Step 3: Osmosis and Selectively Permeable Membranes

Unlike the food coloring example in step 2, where the food coloring and the water have no barrier between them, cells have membranes that hold organelles in and keep other things out. Describe how when diffusion of water occurs across a membrane, it’s known as osmosis. 

To illustrate osmosis, return to the starch and iodine example you prepared earlier. Explain that iodine changes its color when it comes into contact with starch. By now, the starch in the baggie will have turned purple because the plastic bag is permeable to iodine; the iodine has moved across the “membrane.”

In a cell, molecules need to move in and out of the cell, but how does the cell membrane let only certain molecules pass through? 

To help students understand selective permeability, watch the cell transport animation in Visible Biology. Discuss how two sheets of phospholipids create a selectively permeable membrane that lets only small molecules through.

Return to the VB Suite cell model and the drawing tool. Using the drawing tool, draw many other molecules outside of the cell and a few on the inside and use arrows to illustrate the movement of molecules from one side of the concentration gradient to the other.

Introduce the concept of osmotic pressure . 

Next, introduce the different terms that describe relationships between sides of the membrane. The definitions below are from Biology Online .

• What is a selectively permeable membrane?
•  What is the difference between the terms hypotonic, hypertonic, and isotonic?

Step 4: The Big Picture

Finally, briefly connect osmosis and diffusion to the big picture: how does diffusion affect other processes?

Here are some ideas for “big picture” connections:

• During cellular respiration, diffusion occurs when oxygen moves into the cell and when carbon dioxide moves out.
• Oxygen moves into the lungs via diffusion .
• Check out this webinar on comparative physiology of the heart by Dr. Cindy Harley that discusses diffusion and hearts. 

NGSS Standards

The above lesson plan fits these Next Generation Science Standards (NGSS):

HS-LS1 From Molecules to Organisms: Structures and Processes. Students who demonstrate understanding can: 

• Develop and use a model to illustrate the hierarchical organization of interacting systems that provide specific functions within multicellular organisms. (HS-LS1-2)

Did you know that the Visible Body Education Team has created a library of lesson plans and lab activities? Here's where you can find these resources , complete with NGSS standards.

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Home » Articles » STEM » STEM Science » How to Demonstrate Diffusion with Hot and Cold Water

How to Demonstrate Diffusion with Hot and Cold Water

We all need some space sometimes, right that’s true down to a molecular level. molecules don’t like to stay too close together and will try to move to less crowded areas. that process is called diffusion and we will explore all about it in this simple but revealing experiment., article contents.

What is Diffusion?

Have you ever smelled your neighbor’s lunch on your way home? Or smelled someone’s perfume minutes after that person was gone? You experienced the diffusion!

Diffusion is a movement of particles from the area of high concentration to an area of low concentration. It usually occurs in liquids and gases.

Let’s get some complex-sounding terminology out of the way. When talking about diffusion, we often hear something about the concentration gradient (or electrical gradient if looking at electrons). Gradient just means a change in the quantity of a variable over some distance. In the case of concentration gradient, a variable that changes is the concentration of a substance. So we can define the concentration gradient as space over which the concentration of our substance changes.

For example, think of the situation when we spray the air freshener in the room. There is one spot where the concentration of our substance is very high (where we sprayed it initially) and in the rest of the room it is very low (nothing initially). Slowly concentration gradient is diffusing – our freshener is moving through the air. When the concentration gradient is diffused, we reach equilibrium – the state at which a substance is equally distributed throughout a space.

It’s important to note that particles never stop moving , even after the equilibrium is reached. Imagine two parts of the room divided by a line. It may seem like nothing is happening, but particles from both sides are moving back and forth. It’s just that it is an equal probability of them moving from left to right as it’s from right to left. So we can’t notice any net change.

Diffusion is a type of passive transport . That means it doesn’t require energy to start. It happens naturally, without any shaking or stirring.

There is also a facilitated diffusion which happens in the cell membranes when molecules are transported with the help of the proteins.

You may remember hearing about Osmosis and think about how is this different from it. It is actually a very similar concept. Osmosis is just a diffusion through the partially permeable membrane. We talked about it more in our Gummy Bear Osmosis Experiment so definitely check it out.

What causes Diffusion?

Do particles really want to move somewhere less crowded? Well, no, not in the way we would think of it. There is no planning around, just the probability.

All fluids are bound to the same physical laws – studied by Fluid mechanics , part of the physics. We usually think of fluids as liquids, but in fact, air and other types of gas are also fluids ! By definition , fluid is a substance that has no fixed shape and yields easily to external pressure.

Another property of the fluids is that they flow or move around. Molecules in fluids move around randomly and that causes collisions between them and makes them bounce off in different directions.

This random motion of particles in a fluid is called Brownian motion . It was named by the biologist Robert Brown who observed and described the phenomenon in 1827. While doing some experiments with pollen under the microscope, he noticed it wiggles in the water. He concluded that pollen must be alive. Even though his theory was far off, his observation was important in proving the existence of atoms and molecules.

Factors that influence Diffusion

There are several factors that influence the speed of diffusion. The first is the extent of the concentration gradient . The bigger the difference in concentration over the gradient, the faster diffusion occurs.

Another important factor is the distance over which our particles are moving. We can look at it as the size of a container. As you may imagine, with the bigger distance, diffusion is slower, since particles need to move further.

Then we have characteristics of the solvent and substance. The most notable is the mass of the substance and density of the solvent . Heavier molecules move more slowly; therefore, they diffuse more slowly. And it’s a similar case with the density of the solvent. As density increases, the rate of diffusion decreases. It’s harder to move through the denser solvent, therefore our molecules slow down.

And the last factor we will discuss is the temperature . Both heating and cooling change the kinetic energy of the particles in our substance. In the case of heating, we are increasing the kinetic energy of our particles and that makes them move a lot quicker. So the higher the temperature, the higher the diffusion rate.

We will demonstrate the diffusion of food coloring in water and observe how it’s affected by the difference in temperature. Onwards to the experiment!

Materials needed for demonstrating Diffusion

• 2 transparent glasses – Common clear glasses will do the trick. You probably have more than needed around the house. We need one for warm water and one for cold water so we can observe the difference in diffusion.
• Hot and cold water – The bigger the difference in temperature in two glasses, the bigger difference in diffusion will be observed. You can heat the water to near boiling or boiling state and use it as hot water. Use regular water from the pipe as “cold water”. That is enough difference to observe the effects of temperature on diffusion.
• Food coloring – Regular food coloring or some other colors like tempera (poster paint) will do the trick. Color is required to observe the diffusion in our solvent (water). To make it more fun, you can use 2 different colors. Like red for hot and blue for cold.

Instructions for demonstrating diffusion

We have a video on how to demonstrate diffusion at the start of the article so you can check it out if you prefer a video guide more. Or continue reading instructions below if you prefer step by step text guide.

• Take 2 transparent glasses and fill them with the water . In one glass, pour the cold water and in the other hot water. As we mentioned, near-boiling water for hot and regular temperature water from the pipe will be good to demonstrate the diffusion.
• Drop a few drops of food coloring in each cup . 3-4 drops are enough and you should not put too much food color. If you put too much, the concentration of food color will be too large and it will defuse too fast in both glasses. 
• Watch closely how the color spreads . You will notice how color diffuses faster in hot water. It will take longer to diffuse if there is more water, less food color and if the water is cooler.

What will you develop and learn

• What is diffusion and how it relates to osmosis
• Factors that influence diffusion
• What is Brownian motion
• How to conduct a science experiment
• That science is fun! 😊

If you liked this activity and are interested in more simple fun experiments, we recommend exploring all about the heat conduction . For more cool visuals made by chemistry, check out Lava lamp and Milk polarity experiment . And if you, like us, find the water fascinating, definitely read our article about many interesting properties of water .

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Very Simple Diffusion and Osmosis Experiment

5 comments:

Good blog. Very easy to understand the point of each piece of text.

How do you make your starch solution and glucose solution?

Since no quantitative data is being collected, there is no need to make solutions of a specific concentration. I put some corn starch in a beaker of water and boil it until it clears up a bit. I put several teaspoons of Karo syrup in a beaker of water and stir until throughly mixed.

where can i find these dialysis tubing??

We order them with our lab supplies. You can also use a plastic sandwich bag.

The Kitchen Pantry Scientist

Simple recipes for real science, diffusion and osmosis experiments.

Think about the way pollutants move from one place to another through air, water and even soil. Or consider how bacteria are able to take up the substances they need to thrive. Your body has to transfer oxygen, carbon dioxide and water by processes involving diffusion as well.

Lots of things can affect how fast molecules diffuse, including temperature.  When molecules are heated up, they vibrate faster and move around faster, which helps them achieve equilibrium more quickly than they would if it were cold.

Diffusion takes place in gases (like air), liquids (like food coloring moving through water,) and even solids (semiconductors for computers are made by diffusing elements into one another.)

Every so often, measure the circle of food coloring as it diffuses into the jello around it.  How many cm per hour is it diffusing?  If you put one plate in the refrigerator and an identical one at room temperature, do they diffuse at the same rate?  Why do you think you see more than one color for certain shades of food coloring? What else could you try?

Here’s a post on how to use this experiment to make sticky window decorations:   https://kitchenpantryscientist.com/?p=4489

We made plates and did the same experiment using 2 cups of red cabbage juice , 2 cups of water and 4 packs of gelatin to see how fast a few drops of vinegar or baking soda solution would diffuse (a pigment in red cabbage turns pink when exposed to acid, and blue/green when exposed to a base!)

It’s also fun to experiment with the diffusion of substances across a membrane, like a paper towel.  This is called osmosis. Membranes like the ones around your cells are selectively permeable and let water and oxygen in and out, but keep other, larger molecules from freely entering and exiting your cells.

For this experiment, you’ll need a jar (or two), paper towels, rubber bands and food coloring.  Fill a jar with water and secure a paper towel in the jar’s mouth (with a rubber band) so that it hangs down into the water, making a water-filled chamber that you can add food coloring to.  Put a few drops of food coloring into the chamber and see what happens.

top “chambers” for food coloring

Are the food coloring molecules small enough to pass through the paper towel “membrane?”  What happens if you put something bigger, like popcorn kernels in the chamber? Can they pass through the small pores in the paper towel?

Do the same experiment in side-by-side jars, but fill one with ice water and the other with hot  water.  Does this affect the rate of osmosis or how fast the food coloring molecules diffuse throughout the water?

Think about helium balloons.  If you take identical balloons and fill one with helium and the other with air, the helium balloon will shrink much faster as the smaller helium atoms diffuse out more quickly than the larger oxygen molecules.

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Top 6 Experiments on Osmosis (With Diagram)

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The following points highlight the top six experiments on osmosis in plants. Some of the experiments are: 1. Demonstration of the Phenomenon of Osmosis 2. Demonstration of Osmosis by Osmoscopes 3. Demonstration of Plasmolysis and Determination of Isotonic Conc. of the Cell Sap 4. Determination of Osmotic Pressure of Integrated Plant Tissues and Others.

Experiment # 1

Demonstration of the phenomenon of osmosis:.

Experiment:

A small funnel is taken and its broad mouth is closed with a piece of parchment or egg membrane. It is then completely filled with 1 ml glucose solution (180 06gm/litre). The nose of a 10 ml pipette is fitted with the stem of the funnel with the help of rubber tubing.

The level of the sugar solution is brought to a visible mark by adding more sugar solution drop by drop through open end of the pipette. The appara­tus is then placed over a beaker containing pure water and clamped pro­perly. The increase in the level of sugar solution is noted at definite inter­vals.

Observation:

The level of sugar solution increases in the pipette gradually. The rate of this increase declines with time. A positive test for glucose (a brick red ppt.) is obtained when an aliquot of water from the beaker is tested with Fehling solution (Mix Fehling A containing 35gm GUSO 4 plus 500 ml water, and Fehling B containing 50gm NaOH plus 173gm Rochelle salt plus 500 ml water, in equal proportions, add the test solution to it and heat strongly).

The following inferences can be drawn from this experi­ment:

(a) The sugar solution rises in the pipette because of accumulation of water molecules which pass through the semipermeable membrane due to endosmosis.

(b) The accumulation of water dilutes the osmotic cone, of sugar solution. Hence the rate of increase of the level of sugar solution inside the pipette decreases with time.

(c) The positive reaction of sugar in the water of the beaker indicates that some sugar molecules have also come out through the membrane by exosmosis as the membrane is not truly semipermeable but differentially permeable.

Experiment # 2

Demonstration of osmosis by osmoscopes:.

A. Egg osmoscope:

The inner contents of an egg are taken out through a small hole made at one end of it. Tb obtain the semipermeable membrane, about one-third of the shell is immersed in conc. HCL very carefully.

The acid dissolves the shell (made up of CaCO 2 ) exposing the inner mem­brane of the egg. It is then washed well with water without damaging the semipermeable membrane. The nose of a one milliliter pipette is inserted through the hole of the shell up to some distance avoiding contact with the membrane, and sealed with sealing wax or lacre.

The egg is filled with a strong solution of 1 M sucrose (342.30gm/litre) through the open end of the pipette and the level is brought to a visible mark on the pipette which is noted. Now, the egg membrane of the setup is immersed in a beaker of pure water and clamped verti­cally (Figure 3).

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Open Access

Peer-reviewed

Research Article

ECD-CDGI: An efficient energy-constrained diffusion model for cancer driver gene identification

Roles Data curation, Methodology, Writing – original draft

Affiliation School of Data Science and Artificial Intelligence, Wenzhou University of Technology, Wenzhou, China

Roles Methodology, Supervision, Writing – review & editing

* E-mail: [email protected] (LZ); [email protected] (XF); [email protected] (QZ)

Roles Investigation

Affiliation College of Computer Science and Electronic Engineering, Hunan University, Changsha, China

Roles Supervision, Writing – review & editing

Roles Supervision

Affiliation Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, China

• Tao Wang, 
• Linlin Zhuo, 
• Yifan Chen, 
• Xiangzheng Fu, 
• Xiangxiang Zeng, 

• Published: August 30, 2024
• https://doi.org/10.1371/journal.pcbi.1012400
• Reader Comments

This is an uncorrected proof.

The identification of cancer driver genes (CDGs) poses challenges due to the intricate interdependencies among genes and the influence of measurement errors and noise. We propose a novel energy-constrained diffusion (ECD)-based model for identifying CDGs, termed ECD-CDGI. This model is the first to design an ECD-Attention encoder by combining the ECD technique with an attention mechanism. ECD-Attention encoder excels at generating robust gene representations that reveal the complex interdependencies among genes while reducing the impact of data noise. We concatenate topological embedding extracted from gene-gene networks through graph transformers to these gene representations. We conduct extensive experiments across three testing scenarios. Extensive experiments show that the ECD-CDGI model possesses the ability to not only be proficient in identifying known CDGs but also efficiently uncover unknown potential CDGs. Furthermore, compared to the GNN-based approach, the ECD-CDGI model exhibits fewer constraints by existing gene-gene networks, thereby enhancing its capability to identify CDGs. Additionally, ECD-CDGI is open-source and freely available. We have also launched the model as a complimentary online tool specifically crafted to expedite research efforts focused on CDGs identification.

Author summary

Cancer has become a major disease threatening human life and health. Cancer usually originates from abnormal gene activities, such as mutations and copy number variations. Mutations in cancer driver genes are crucial for the selective growth of tumor cells. Identifying cancer driver genes is crucial in cancer-related research and treatment strategies, as it helps understand cancer occurrence and development. However, the complex gene-gene interactions, measurement errors, and the prevalence of unlabeled data significantly complicate the identification of these driver genes. We developed a new method that integrates an energy-constrained diffusion mechanism with an attention mechanism to uncover implicit gene dependencies in biomolecular networks and generate robust gene representations. Extensive experiments demonstrated that our model accurately identifies known cancer driver genes and effectively discovers potential ones. Furthermore, we analyzed and predicted patient-specific mutated genes, enhancing our understanding of their pathogenesis and advancing precision medicine. In summary, our method offers a promising tool for advancing the identification of cancer driver genes.

Citation: Wang T, Zhuo L, Chen Y, Fu X, Zeng X, Zou Q (2024) ECD-CDGI: An efficient energy-constrained diffusion model for cancer driver gene identification. PLoS Comput Biol 20(8): e1012400. https://doi.org/10.1371/journal.pcbi.1012400

Editor: Jinyan Li, Chinese Academy of Sciences Shenzhen Institutes of Advanced Technology, CHINA

Received: October 25, 2023; Accepted: August 10, 2024; Published: August 30, 2024

Copyright: © 2024 Wang et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: Our code and data are publicly available in the GitHub repository: https://github.com/taowang11/ECD-CDGI .

Funding: This work received partial support from the Natural Science Foundation of China under Grant No. 62302339, to L.Z. Additionally, this work was partially funded by the Natural Science Foundation of China under Grant No. 62372158 to X.F. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

Introduction

Cancer is typically driven by the accumulation of genetic variations, including single nucleotide variations, small insertions or deletions, and copy number variations [ 1 , 2 ]. Gene mutations can lead to activation or inactivation, promoting cancer occurrence and metastasis. Cancer driver genes(CDGs) mutations enable tumor cells to gain selective growth advantages in evading immune cell clearance and drug treatment [ 3 , 4 ]. Therefore, developing methods to identify CDGs is of great significance for cancer pathologic research, as well as the development of cancer diagnosis, treatment, and targeted drugs [ 5 ]. The recent advancements in next-generation sequencing technology have helped researchers facilitate the generation of a vast amount of cancer genomic data and classify somatic mutations in common and rare cancer types [ 6 ]. Systematically identifying CDGs from large-scale human cancer genomic data remains a significant challenge [ 7 , 8 ].

Many computational methods and tools have been developed to address this challenging issue in the past few years. Traditional computational methods for identifying CDGs can be divided into two main categories: mutation frequency-based and network-based. The mutation frequency-based methods generally assume that mutations in driver genes have a higher probability of being recurrent across samples compared to non-driver genes, thus identifying significantly mutated genes as CDGs [ 9 , 10 ]. The network-based methods consider cancer to result from mutations in multiple genes that collectively play essential roles in cancer-related biological pathways [ 11 , 12 ]. Despite the remarkable achievements of these methods in studying gene variations, there are still some limitations. For example, mutation frequency-based methods often fail to detect driver genes with low mutation frequencies due to the lack of reliable background mutation frequencies. Additionally, when biological networks lack numerous associative relationships or are inundated with a large amount of noise data, this type of method can lead to poor accuracy in identifying driver genes.

Recently, machine learning(ML) techniques, particularly deep learning methods, have achieved tremendous success in identifying CDGs [ 13 – 15 ]. ML-based approaches framethe prediction of driver genes as a classification task, leveraging available data and knowledge to identify driver genes or driver mutations. Typically, these methods utilize a low-dimensional representation of genes’ multi-omic feature vectors, subsequently employing classifiers to identify CDGs. For instance, Parvandeh et al. utilized cancer gene network data to calculate the differences between nodes using the Minkowski distance [ 16 ]. They integrated the nearest neighbor algorithm and evolutionary scoring calculation to potential CDGs. Similarly, Han et al. trained an ensemble of models on various types of gene mutations and then applied Poisson’s distribution coupled with Monte Carlo simulations to discover low-background mutation rate CDGs [ 17 ]. In another study, Habibi et al. combined mutation data, protein-protein interaction (PPI), and biological process networks. They calculated the score of gene features, engineered a gene-gene network significantly linked to cancer, and performed cluster analysis to study CDGs [ 18 ]. However, these traditional machine learning approaches face limitations due to their neglect of complex interactions inherent in gene-gene networks. GNNs offer a promising solution to this constraint. By employing an iterative message passing and aggregation mechanism, GNNs are capable of learning low-dimensional embeddings that capture the complex relationships among genes, based on their interactions within the network [ 19 ].

Consequently, GNNs have been instrumental in enhancing the accuracy of CDGs identification [ 20 – 22 ]. For example, the EMOGI model incorporates diverse multi-omics data, including copy number variation, methylation and PPI network to identify CDGs using graph convolutional neural networks (GCNs) [ 23 ]. The EMOGI model primarily focuses on a subset of genes in the PPI network, conducting training and evaluation solely at the node level. Building upon this, MTGCN integrates both CDG identification and interaction prediction tasks into a collaborative training framework, thereby improving the precision of CDG prediction [ 24 ]. These approaches utilize Chebyshev polynomials within the convolutional layers and separate the embeddings from their neighboring nodes during the aggregation process, which can effectively address the issue of "over-smoothing" often encountered with multiple iterative convolution operations. As a result, these models demonstrate superior performance compared to traditional GCNs [ 25 ] and Graph Attention Networks (GATs) [ 26 ]. However, these models do have their limitations. Specifically, biomolecular networks are typically highly heterogeneous, a condition primarily attributed to the diversity of genomic data, including gene expression, protein interactions, and metabolite profiles. To our knowledge, the message propagation in most GNN models is often influenced by nodes with high degrees. Consequently, this can lead to the masking or domination of gene features by heterogeneous, highly connected neighbors, which impedes the accurate representation of gene features. To overcome this limitation, Zhang et al. introduced the HGDC model based on graph diffusion models [ 27 ]. Initially, HGDC creates an auxiliary graph employing graph diffusion and random walk techniques and jointly trains it alongside the original graph to enhance node representation. Subsequently, it refines the propagation and aggregation mechanisms inherent in GCNs, making the model more suitable for heterogeneous biomolecular networks. Finally, it deploys a multi-layer attention classifier to accurately identify CDGs.

While existing models demonstrate strong performance in identifying CDGs, they have limitations. Most notably, these models often focus solely on the immediate neighborhood of nodes, overlooking potentially complex interdependencies between any two genes. Additionally, data noise introduced by errors in the collection process can further compromise performance. To address these challenges, we propose the ECD-CDGI model, which joins the diffusion process with an attention mechanism to unveil hidden relationships between any two genes and enhance CDG Identification. In summary, the main contributions of this paper are described as follows:

• ECD-CDGI considers gene interactions as a diffusion process to maintain gene expression globally consistent in terms of the underlying structure while mitigating the effects of noisy data, and for the first time, realizes the combination of energy-constrained diffusion and attention mechanisms to identify CDGs.
• We design an ECD-Attention encoder based on diffusion processes and attention mechanisms to capture implicit dependencies between genes in biomolecular networks. This approach generates robust gene representations, which are further enhanced by integrating topological information.
• We introduce a hierarchical attention module to aggregate the output results across each layer during the information propagation process. By augmenting the diversity of node representations, this strategy subsequently improves the predictive accuracy of the ECD-CDGI model.
• Extensive experiments indicate that the ECD-CDGI model possesses the ability to not only identify known CDGs but also efficiently uncover potential cancer genes. Moreover, compared to the GNN-based approach, the ECD-CDGI model exhibits lower constraints from gene-gene networks, which enhances its ability to identify potential cancer genes.

Materials and methods

The task of identifying CDGs generally draws upon multi-omics data sources including genomics, transcriptomics, proteomics, and metabolomics. The primary workflow entails applying dimensionality reduction techniques to these multi-omics datasets, effectively extracting the low-dimensional representations of genes in the biomolecular network in a reduced dimensional space. Subsequently, the representations of these genes are compared to the representations of known CDGs, enabling the prediction of CDGs. For the scope of this experiment, we utilize a gene set within a 58-dimensional feature space, as cited in the referenced work [ 27 ].

The efficacy of the proposed ECD-CDGI model in predicting CDGs was evaluates across three distinct biomolecular network datasets: PathNet [ 28 ], GGNet [ 29 ], and PPNet [ 30 ]. Specifically, the PathNet dataset comprises a network of interlinked biochemical pathways within cells or organisms, incorporating data from both KEGG and Reactome pathways. GGNet is constructed from RNA interaction data, forming a gene-gene network. Meanwhile, PPNet is extracted from the STRING database. Each of these datasets offers a unique perspective, contributing to a comprehensive evaluation of the model’s performance.

In this study, the term "cancer driver genes" refers to genes that are clearly identified and widely recognized for their crucial roles in the initiation and progression of tumors. These genes are categorized as positive samples. Specifically, 711 well-established driver genes were sourced from the NCG database [ 31 ], and an additional 85 high-confidence driver genes were identified using the DigSEE tool [ 32 ], totaling 796 genes. The positive samples across PPNet, GGNet, and PathNet networks, are derived from these genes. Additionally, drawing on prior findings [ 23 ], negative samples were selected based on the following criteria: Exclude genes 1) listed in the NCG database [ 31 ], 2) linked to "cancer pathways" from the KEGG database [ 33 ], 3) listed in the OMIM disease database [ 34 ], 4) predicted by MutSigdb [ 9 ] to be cancer-related, 5) with expression patterns similar to known cancer genes. Generally, negative samples comprise genes that are unlikely to be related to cancer. The data used in this study is presented in Table 1 .

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https://doi.org/10.1371/journal.pcbi.1012400.t001

Problem formulation

The proposed ECD-CDGI model leverages an encoder grounded in both energy-constrained diffusion processes and attention mechanisms. To facilitate a comprehensive understanding of this model and its architecture, we will delineate the foundational principles and associated technologies underpinning the model in the section.

Energy-constrained diffusion process

In this way, the diffusivity serves as a measure of the influence between any two nodes and can also be interpreted as attention of each node-node pair. This insight informs the architecture of encoders built on energy-constrained diffusion processes and attention mechanisms.

Model architecture

Fig 1 illustrates the architecture of the ECD-CDGI model, comprising primarily three modules: the Data Module, the Encoder Module (including ECD-Attention encoder, GNN encoder and Residual connection), and the Multi-layer Attention Module. To enrich the datasets, both the initial feature vectors of gene nodes in the biomolecular network and the network’s topological structure were extracted, as detailed in the materials section. To address the challenges posed by noisy observational data and latent dependencies among nodes within biomolecular networks, we design a novel encoder, termed ECD-Attention. This encoder is ground in energy-constrained diffusion processes and attention mechanisms. Fig 1(D) illustrates the energy-constrained diffusion process, wherein the energy (information) from each node is distributed to all other nodes in the network, ensuring that the state of each node is influenced by that of every other node. Simultaneously, a GNN encoder is used to mine the topological structure of the biomolecular network, thereby augmenting gene representations. Employing a multi-layer attention mechanism, the proposed model assimilates information across multiple scales to efficiently identify CDGs.

The ECD-CDGI model employs a automatic approach to identify CDGs, including several key stages: Initially, the multi-omics data information of genes within the biomolecular network is fed into the ECD-Attention encoder, while concurrently, the topological information is input into the GNN encoder. The features extracted from both encoders are then concatenated, followed by residual connections and layer normalization operations. Subsequently, leveraging the message propagation mechanism, the encoding process undergoes multiple iterations, generating multiple sets of gene representations. Ultimately, the multi-layered data is fused utilizing the hierarchical attention module, resulting in the final node representations. These comprehensive representations are then employed to predict CDGs.

The architecture of the ECD-CDGI model mainly includes three principal modules: (A) Data Module, (B) Encoder Module, and (C) Multi-layer Attention Module. (A) The Data Module primarily contains the initial feature vectors and topological architecture of gene nodes within the biomolecular network. (B) The Encoder Module is consisting of three key components: a newly-conceived ECD-Attention encoder based on energy-constrained diffusion process (D) , a GNN encoder, and a residual connection. (C) Employing a hierarchical structure, the Multi-layer Attention Module integrates data across various layers to formulate a comprehensive node representation, which is then used to identify CDGs effectively. (D) The energy-constrained diffusion process.

https://doi.org/10.1371/journal.pcbi.1012400.g001

ECD-Attention encoder.

Building on the insights gained from the Preliminary Section, the diffusion process is governed by energy constraints, which aim to reduce the overall system energy during diffusion, thereby stabilizing the system. And inspired by previous work [ 38 ], we introduce an ECD-Attention encoder that incorporates both energy-constrained diffusion and attention mechanisms. This encoder is crafted to ensure the local consistency of each gene node’s current state during the information propagation process that is similar to the diffusion process, while also preserving global consistency with other gene nodes in the biomolecular network. Notably, the encoder effectively dampens the impact of data noise and reveal latent interdependencies between genes. The following is a detailed presentation of the relevant principles and steps.

Leveraging the energy-constrained diffusion and attention mechanisms, the diffusivity matrix in the diffusion process can be reinterpreted as an attention matrix for gene-gene pairs. Echoing the principles outlined in the Preliminary Section, a straightforward dot-product method is employed to quantify the similarity between any two genes. Furthermore, within the energy-constrained diffusion process, the node state update rule considers the state of all nodes, meaning each node’s state is influenced by every other node. Node state updates are executed by integrating the complete node-node similarity matrix with the value vector. Clearly, this approach is well-suited for the Transformer architecture. In the Transformer architecture, node-node attentions resemble the signal propagation rate S observed in energy-constrained diffusion processes. This process normalizes the similarity between nodes using dot product and sigmoid operations.

GNN encoder

Residual connection

Multi-layer attention

To evaluate the efficacy of the ECD-CDGI model, we execute multiple sets of experiments using publicly available datasets. Initially, we engage in comparative analyses against state-of-the-art methods for CDG identification to validate the model’s superior capabilities. Subsequently, we design a series of ablation experiments to evaluate the individual contributions of various modules within the ECD-CDGI architecture. In the final phase, we delve into specific case studies and explore the scalability prospects of our proposed model.

Implementation detail

This study was conducted using the Python and Pytorch frameworks, focusing on parameters associated with the ECD-Attention encoder, GCN encoder, and multi-layer attention module, along with various hyperparameters. Genomic data served as the initial input for the model, with its dimensionality set at 58. In the ECD-Attention encoder, the transformation weight matrices are preset to a dimension of 100. The multi-layer attention module is configured with four layers by default, with each layer’s initial weight preset at 0.5. Both the ECD-Attention and GCN encoders are integrated across 4 layers. Other hyperparameters include a hidden layer dimension of 100, 100 training rounds, a default learning rate of 0.001, and Adam as the optimizer.

Comparison experiment

We designed a series of benchmarking experiments across three publicly accessible datasets GGNet, PathNet, and PPNet, to compare the performance of our ECD-CDGI model with six other methods. These comprise three advanced CDG prediction models EMOGI [ 23 ], MTGCN [ 24 ], and HGDC [ 27 ], as well as three conventional GNN models GCN [ 25 ], GAT [ 26 ], and ChebNet [ 40 ]. To ensure a level playing field, each method was fed the same feature matrix corresponding to biomolecular networks. We carried out ten times of 5-fold cross-validation for each model. The final performance metrics, represented by the average AUC and AUPR scores, are presented in Table 2 .

https://doi.org/10.1371/journal.pcbi.1012400.t002

As reflected in Table 2 , EMOGI, MTGCN, HGDC, ChebNet, and our proposed ECD-CDGI model all demonstrated commendable performance in the task of identifying CDGs. The GCN and GAT models lagged behind in terms of effectiveness. Notably, the EMOGI, MTGCN, HGDC, and ChebNet algorithms all employ Chebyshev polynomials to perform convolution operations. During the message propagation and aggregation phases, these models differentiate between neighboring nodes and the nodes themselves, thereby mitigating the performance degradation typically induced by over-smoothing. Building upon this, the HGDC model incorporates an auxiliary network crafted using graph diffusion technology and aims to enhance predictive accuracy through joint training with the original network. However, it’s noteworthy that HGDC’s performance remains on par with, or even slightly underperforms, the original ChebNet model. This suggests that the auxiliary network generated through graph diffusion techniques may introduce an element of unpredictable noise.

It’s important to highlight that our proposed ECD-CDGI model outperformed all competitors across all datasets. It led the second-best performing model by margins of 1.30%, 1.24%, and 2.13% in the AUC index, and by 1.57%, 2.02%, and 2.76% in the AUPR index. These results underscore the efficacy of the ECD-Attention encoder, which is grounded in energy-constrained diffusion and attention mechanisms. This encoder is adept at unveiling the complex interdependencies among genes. When combined with the GCN encoder to harness the topological information of the gene-gene network, it substantially enhances the quality of node representation. As illustrated in Fig 2 , we plotted the ROC and PR curves for each model on three datasets. The curves for ECD-CDGI model consistently outpace other models and demonstrate remarkable stability. This provides additional validation that the ECD-CDGI model is both efficient and reliable in identifying CDGs.

ROC curves for multiple models on (a) PPNet, (b) PathNet, and (c) GGNet datasets; PR curves for (d) PPNet, (e) PathNet, and (f) GGNet datasets.

https://doi.org/10.1371/journal.pcbi.1012400.g002

Ablation experiment

This section aimed to evaluate the individual contributions of four key modules within the ECD-CDGI model: the ECD-Attention encoder, the GCN encoder, the residual connection, and the multi-layer attention mechanism. To facilitate this, we conduct ablation experiments across three datasets GGNet, PathNet, and PPNet, while holding other variables constant. The term ’w/o ECD-Att’ denotes a model configuration that removes the ECD-Attention encoder, relying solely on the GCN encoder. Conversely, ’w/o GCN’ signifies a setup where the GCN encoder is excluded, with only the ECD-Attention encoder in place. And ’w/o Residual’ means that the residual connection module has been removed, while ’w/o multi-Att’ implies that the model delete the multi-layer attention mechanism and employs only the encoder’s final layer output for both training and prediction.

We performed ten times of 5-fold cross-validation experiments for each model configuration across three datasets. The results are summarized as average values for the AUC and AUPR metrics, as detailed in Table 3 . Generally speaking, any version of the ECD-CDGI model that omits one of its key components, whether it’s the ECD-Attention encoder, GCN encoder, residual connection, or multi-layer attention mechanism, experiences a decline in performance. The ECD-Attention encoder captures global information, revealing potential dependencies between indirectly connected genes. The GCN encoder receives information from neighboring nodes and effectively propagates messages based on gene interactions. Residual connections maximize the retention of original features during iterations, preventing the loss of information from nodes in previous layers. The multi-layer attention mechanism automatically learns weights and integrates node representations across weighted iterations, enhancing model performance.

https://doi.org/10.1371/journal.pcbi.1012400.t003

Diving into details, the model’s performance declines slightly on the GGNet dataset when the GCN encoder is omitted, whereas a more substantial decrease is observed on both the PathNet and PPNet datasets. Intriguingly, this pattern is reversed when the ECD-Attention encoder is omitted. This suggests that the high heterogeneity and complex topological structure of the GGNet dataset may make it difficult for GCNs to effectively capture the intricate relationships and dependencies within the data. The finding also highlights the ECD-Attention encoder’s ability to uncover latent interdependencies among genes, thus boosting the model’s overall performance. Most notably, the model experiences its poorest performance when the Residual module is omitted, indicating its critical role in mitigating the over-smoothing arising during information propagation. It is noteworthy that the Residual module serves as a pivotal element within the ECD-Attention encoder, supplying essential information about the node’s current state during the energy-constrained diffusion process.

Skewed distribution and enrichment analysis

We conducted extensive experiments and analyses across the GGNet, PPNet, and PathNet datasets to evaluate the capability of our proposed ECD-CDGI model to identify previously unknown CDGs. To mitigate the influence of random variables, we ran the ECD-CDGI model through 100 iterations on each of these datasets, thereafter analyzing the predicted gene scores.

As illustrated in Fig 3 , the gene scores predicted by the ECD-CDGI model across all datasets exhibit a positive skewness. A scant number of genes gain conspicuously high scores, deviating from the central cluster of the data, while the majority of gene scores hover between -2 and 0. This is likely attributable to the fact that the overwhelming majority of genes are not CDGs, resulting in only subtle variations in their scores. In contrast, the outliers in the dataset suggest a small subset of genes with markedly higher scores, pointing to a heightened likelihood of them being CDGs. Overall, the ECD-CDGI model demonstrates a robust ability to differentiate these CDGs from other non-CDGs.

https://doi.org/10.1371/journal.pcbi.1012400.g003

We selected and merged the top 100 genes with the highest scores from three networks, resulting in a total of 178 unique genes. This was done to assess the ECD-CDGI model’s ability to recognize these genes. With reference to the DisGeNET database [ 41 ], these highly scored genes were further enriched. In Fig 4(A) each bar on the left represents a different cancer category; the length of the bar indicates the statistical significance of the gene set linked to that disease. A higher -log10(P) value correlates with a lower p-value, suggesting a stronger association between the gene set and the disease. These results suggest that these high-scoring genes are significantly associated with various diseases, predominantly cancers, particularly pancreatic tumors. To further investigate these genes, we conducted pathway and process enrichment analyses using KEGG pathways, GO biological processes, and other resources, categorizing the genes into clusters based on similarities. In Fig 4(B) , on the right, genes are depicted as nodes in different colors, each color representing a distinct enriched pathway. The size of each node correlates with the level of gene enrichment in the corresponding pathway. Purple lines between nodes indicate interactions among genes or the biological processes in which they participate. Of these, 44 genes (24.72%) showed significant enrichment in the "Cancer Pathway" (KEGG Pathway). These genes are likely pivotal in the genesis and progression of tumors. This underscores the capacity of the ECD-CDGI model to identify CDGs accurately, thereby aiding in the elucidation of cancer initiation and progression mechanisms as well as informing relevant treatment strategies.

(a) Results of gene enrichment analysis for various cancers using the ECD-CDGI model; (b) Enrichment analysis leveraging KEGG pathways and GO biological processes.

https://doi.org/10.1371/journal.pcbi.1012400.g004

Identifying new cancer genes

To validate the efficacy of the ECD-CDGI model in identifying novel cancer genes, we conducted targeted experiments. Specifically, we computed the average prediction probabilities for four categories of genes: known CDGs, non-CDGs, a set of potential cancer genes from the ncg7.1 database, and other genes across the GGNet, PathNet, and PPNet datasets. The results detailed in Fig 5 reveal that known CDGs garnered the highest average predicted probabilities, while non-CDGs received the lowest. This underscores the ECD-CDGI model’s capability to accurately differentiate between CDGs and non-CDGs. Intriguingly, the average predicted probability for potential cancer genes was also markedly higher than that for non-CDGs and other genes. This suggests that the ECD-CDGI model is not only proficient in identifying known CDGs but is also adept at uncovering potential cancer genes.

https://doi.org/10.1371/journal.pcbi.1012400.g005

Case analysis

We undertook a comprehensive comparative analysis to evaluate the adaptability of the ECD-CDGI model across diverse datasets. Specifically, we selected the top 50 genes with predictive scores from the GGNet, PPNet, and PathNet datasets, and then quantified the number and percentage of CDGs involved. These findings are visually represented in Fig 6(A) through a Venn diagram. Interestingly, the likelihood of identifying a CDG that is unique to a single dataset is notably lower than discovering one that appears across multiple datasets. This observation indicates that genes scoring highly across various datasets are more likely to be CDGs. It’s important to acknowledge that due to inherent constraints in each dataset, such as the presence of noisy data, the complexity of multi-omics data, and variations in gene topological networks, predictive inaccuracies may occur within the ECD-CDGI model. To mitigate these limitations, a cross-dataset analysis can be performed to enhance the precision in identifying CDGs.

(a)Venn diagram illustrating the quantity and proportion of CDGs identified by ECD-CDGI model across three datasets. (b)Pie chart showing the proportion of known CDGs, cancer-related genes, and other genes identified as CDGs by the ECD-CDGI model on three datasets.

https://doi.org/10.1371/journal.pcbi.1012400.g006

Additionally, we delved into the analysis of CDGs that were consistently identified across all three datasets. As depicted in Fig 6(B) , out of the 26 genes analyzed, 19 were classified as CDGs, making up 73.08% of the total. Three genes, although not defined as CDGs, were listed as cancer-related in the ncg7.1 database, and constituted 11.54% of the sample. Four other genes TTN, PCLO, LRP2, and RYR2, accounted for the remaining 15.38%. While these genes are not cataloged in the ncg7.1 database, existing literature [ 42 – 44 ] suggests their significant relevance to cancer.

To investigate patient-specific CDGs, we gathered and assessed patient-specific data using the ECD-CDGI model. Mutant genes with higher prediction scores are more likely to be specific driver genes, potentially accelerating cancer progression. Specifically, we utilized the Xena tool [ 45 ] to collect somatic mutation data from 5776 patients across 14 cancer types in the TCGA database [ 45 ]. Initially, we screened and retained genes present in the GGNet, PathNet, and PPNet networks from the patients’ mutant gene data. Building on this, we selected 5535 patients with five or more mutant genes for further analysis. We quantified the mutant genes of each patient (see Fig 7 ) and observed that some patients had fewer than five cancer driver genes, with 2.40% of patients lacking any cancer driver genes in their mutations. Prior studies suggest that having five or more cancer driver genes may correlate with individual cancer development [ 46 ]. Therefore, identifying patients’ specific CDGs is crucial for targeted treatment.

https://doi.org/10.1371/journal.pcbi.1012400.g007

In this study, we assessed the ECD-CDGI model’s efficacy in identifying patient-specific CDGs for mutant genes, alongside relevant analyses. Specifically, the model was trained using omics data from 14 cancer types on three biomolecular networks: GGNet, PathNet, and PPNet. For each type of cancer, the model generated three predictive gene ranking lists. For each patient, the Rank algorithm [ 47 ] was employed to merge the three gene rankings into a consolidated final list. Subsequently, the top five mutant genes from the final ranking were selected as the specific CDGs for each patient. As illustrated in Fig 8 , within the PPNet network, the shortest distances between the identified driver genes were notably shorter than those between the mutant genes prior to screening. This suggests that the identified CDGs are closely interconnected, likely cooperating within shared biological pathways or functional modules. This tight linkage intensifies their impact on tumor formation, potentially accelerating tumor progression and malignancy.

https://doi.org/10.1371/journal.pcbi.1012400.g008

In subsequent analyses, we focused on the top 500 genes with the highest prediction scores across the GGNet, PPNet, and PathNet datasets. After removing well-established CDGs, we consider the remaining genes as potential cancer genes. We then probed whether a relationship exists between these potential cancer genes identified by the ECD-CDGI and their connectivity to known CDGs.

As illustrated in Fig 9(A) and 9 (B) , for the PPNet and PathNet datasets, the Spearman correlation coefficients are both below 0.1, and the p-values significantly exceed the 5% significance threshold. This indicates only a marginal correlation. Fig 9(C) reveals that in the GGNet dataset, the Spearman correlation coefficient is 0.17, with a p-value of 0.0238, falling below the 0.05 threshold, signifying a slight but statistically significant positive correlation between the two variables. These results suggest that the potential cancer genes identified by the ECD-CDGI model exhibit a lower degree of reliance on known CDGs. Importantly, this implies that the ECD-CDGI model is less constrained by existing gene-gene networks in identifying potential cancer genes. As a result, it is better suited for the discovery of novel cancer genes, a task that proves challenging for methods based on GNNs.

https://doi.org/10.1371/journal.pcbi.1012400.g009

Discussion and Conclusion

This study investigates the pivotal importance of identifying CDGs for both cancer research and clinical treatment, and evaluates various methodologies geared towards this purpose. While existing machine learning and deep learning techniques are indeed effective, they come with inherent limitations. Most notably, these methods often overlook the complex interdependencies between any two genes and may be compromised by noisy data, a byproduct of data collection oversights.

To address these shortcomings, we introduce the ECD-CDGI model, which incorporates a energy-constrained diffusion process and an attention mechanism. By combining with GNNs and multi-layer attention techniques, our model offers a robust tool for identifying CDGs. Our specially designed ECD-Attention encoder not only uncovers the complex global interrelationships between any two genes but also captures nuanced local information to individual gene nodes. Additionally, we integrate residual connections within the model’s layers to mitigate the performance degradation caused by over-smoothing during inter-layer information propagation. Employing GNN technology, the ECD-CDGI model is capable of extracting topological information from gene-gene networks and leverages a multi-layer attention mechanism for predicting CDGs. Comparison and ablation experiments conducted on public datasets confirm the model’s superior performance. We anticipate that the ECD-CDGI model will assume a significant role in cancer research and treatment protocols, offering researchers an efficient tool for understanding the mechanism of cancer development.

Despite its efficacy in CDG prediction, the ECD-CDGI model has certain limitations. Firstly, the presence of missing or erroneous links in biomolecular networks can compromise the model’s performance. Excessive errors or missing links can mislead the learning process and diminish the model’s accuracy. Secondly, while graph neural networks utilize the topological information in biomolecular networks effectively, the absence of comprehensive omics data still impacts their performance. In practical applications, critical omics data, including gene expression, protein interactions, and metabolite profiles, are often incomplete or unavailable. This lack of data can prevent the model from fully understanding gene network interactions, potentially misleading its learning process. Additionally, integrating and synergizing various types of omics data presents challenges due to differing data characteristics and noise levels, where improper handling could impair the model’s performance. To address these issues, future work will focus on mitigating the identified problems. Firstly, we plan to employ debiasing and sampling techniques to minimize the effects of erroneous or incomplete data. Additionally, we will explore multi-omics fusion techniques to fully leverage diverse datasets. Concurrently, we will assess imputation methods to further diminish the impact of data gaps in omics datasets.

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Osmosis Experiments ( CIE IGCSE Biology )

Revision note.

Biology Lead

Osmosis Experiments

Immersing plant cells in solutions of different concentrations.

• The most common osmosis practical involves cutting cylinders of root vegetables such as potato or radish and placing them into distilled water and sucrose solutions of increasing concentration
• The cylinders are weighed before placing into the solutions
• They are left in the solutions for 20 - 30 minutes and then removed, dried to remove excess liquid and reweighed

Potatoes are usually used in osmosis experiments to show how the concentration of a solution affects the movement of water, but radishes can be used too

• Water must have moved into the plant tissue from the solution surrounding it by osmosis
• The solution surrounding the tissue is more dilute than the plant tissue (which is more concentrated)
• Water must have moved out of the plant tissue into the solution surrounding it by osmosis
• The solution surrounding the tissue is more concentrated than the plant tissue (which is more dilute)
• There has been no net movement of water as the concentration in both the plant tissue and the solution surrounding it must be equal
• Remember that water will still be moving into and out of the plant tissue, but there wouldn’t be any net movement in this case

Investigating osmosis using dialysis tubing

• Dialysis tubing (sometimes referred to as visking tubing) is a non-living partially permeable membrane made from cellulose
• Pores in this membrane are small enough to prevent the passage of large molecules (such as sucrose ) but allow smaller molecules (such as glucose and water ) to pass through by diffusion  and osmosis
• Filling a section of dialysis tubing with concentrated sucrose solution
• Suspending the tubing in a boiling tube of water for a set period of time
• Water moves from a region of higher water potential (dilute solution) to a region of lower water potential (concentrated solution), through a partially permeable membrane

An example setup of a dialysis tubing experiment

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Author: Lára

Lára graduated from Oxford University in Biological Sciences and has now been a science tutor working in the UK for several years. Lára has a particular interest in the area of infectious disease and epidemiology, and enjoys creating original educational materials that develop confidence and facilitate learning.