2001 LECTURE SERIES

Making Connections: Memory in the Brain and Spinal Cord

Dr. Oswald Steward
Reeve-Irvine Research Center
University of California, Irvine
May 23, 2001

The question of how function can be restored after brain or spinal cord injury is the subject of intense research and great public interest. The key lies in understanding nerve cell "memory"--the vital connections that are formed during nervous system development and modified by experience. Dr. Steward, who holds the Reeve-Irvine Chair in Spinal Cord Injury Research at UCI, is internationally recognized for his research on the cellular and molecular basis of nerve cell growth.

Well, thank you very much for a very kind introduction. It is indeed an honor and a privilege to be here. It's especially an honor, with my position here as director of the Reeve Irvine Research Center, but another very important part of my activities here is as a fellow of the Center for the Neurobiology of Learning and Memory and I'm very proud of that. And I'm especially proud to be asked to deliver this lecture tonight. It really is a tremendous honor, as all of you know.

So the theme of the talk tonight is connections, making connections. And those of you who think a lot about memory may ask, what really does a spinal cord injury have to do with memory? And really, the common thread here is exactly that, connections. It's the making of a connection that makes nerve cells fire and makes nerve cells work. And as I'll try to show you in this talk, understanding the things that go wrong in a spinal cord injury and that we hope to set right really leads us down the very same path as understanding the cellular and molecular basis of memory.

So the Reeve Irvine Research Center is actually almost four years old now. Many of you may know that it was founded by a contribution from Joan Irvine Smith, put together with a number of other contributions, and through the very strong support of Christopher Reeve, who visits our campus regularly. Our job is to try to understand what happens with injuries to the spinal cord in order that we might fix them and really restore functions that have been lost. So what I'll be talking to you about tonight is some of the basic cellular machinery that underlies both spinal cord injury and in fact, forming connections in the brain, and that really forms the basis with which neurons communicate with each other. So if you'll bear with me, I always hesitate in launching into things about cells. When my children used to ask me questions and I would start to answer them and we were 20 minutes into the answer and they said oh, no, he's going to the cellular level. I always think and take a very deep breath before I start one of these. But in the context of this wonderful seminar series here, I think that you are used enough to thinking about basic mechanisms that it really is a pleasure to talk to a group such as you. So what I'll do for the next few minutes is tell you a little bit about sort of the basics of the brain, the wiring that makes the brain work the way it does. And we'll just start with sort of the gross overview.

So your brain looks something like this. It's not actually blue, nor is it all these different colors. But these different colors do help us to sort of understand what is going on in the brain, and here is a representation of the organization that exists in all of your brains. So enormous accomplishments have been made over the last century in understanding the workings of the brain and we now know, for example, that different parts of the brain are specialized for different functions. This red part here is specialized for the control of movement, this related part for the planning of movements. This part of the brain for touch. Here for spatial sense, what we really mean here is knowing where your body is, reaching into your pocket and being able to find a quarter, reaching into that deep purse that you carry with you and trying to find whatever it is that you're identifying by touch. That's this part of your brain right here. Sometimes it works and sometimes it doesn't. Hearing of course is here. But I really want to focus on that part of the brain that controls our movement, because that's really the most obvious thing that's missing in a patient with a spinal cord injury. I need to tell you a little bit about the building blocks of the brain in order for you to understand really what goes wrong.

And so going now to the cellular level, the brain is made up of nerve cells called neurons and supporting cells that we call glia. This is actually a picture of just exactly what nerve cells look like in your brain, in your cerebral cortex. And the cerebral cortex is just this part of your brain that forms the mantel. There are tons of other areas that are very deep here. So this area that we're looking at might just be a tiny, little piece right here. And in that little piece then we see these very long nerve cells with their cell bodies. Just to give you a sense of how big they are, so neurons have, first of all, these cell bodies and then long appendages that are called dendrites and axons and they extend from the nerve cell body, much like the arms of an octopus. They can extend for literally 10, 20, 30 times beyond the diameter of the cell body. So here for example, here is a very fine needle that's sticking down here that's actually sitting next to this nerve. And in terms of thinking about their size, so that needle then is positioned right next to a nerve cell and you can see perhaps that it is about as big as one of these arms, if you will. Another way to think about it, if you like to think about how many nerve cells could dance on the head of a pin? Well, the answer is several hundred, maybe close to one thousand. So they're both small and large. And really, the most important thing is that the connections that they form can extend over relatively vast distances. So nerve cells in your cortex, in your brain here, actually send a connection down into your spinal cord. So depending on whether you're a basketball player or someone more my size, these things can be two to three feet long, and these single projections are actually the wires then that carry this information from our brain and actually makes our brain capable of controlling our body.

Now, I'm going to move to sort of more diagrammatic things and just tell you a little bit about sort of the micro-workings. And again, the theme {is} connection. So how is it that these connections actually enable nerve cells to communicate with one another? And here I have to introduce a new term. And the term is the synapse here. And this is actually the connection that a nerve makes between itself and the next member in a series. So this is actually a cartoon illustration of a synapse. This one might be the synapse that this nerve cell makes in the spinal cord or the synapse that some other nerve cell has made here that would actually communicate with this nerve cell in your cortex. The synapse communicates with the next cell in line by releasing different kinds of chemicals, and we call these chemicals neurotransmitters. So imagine if you will that these little balls here are filled with these chemicals. We're going to draw some of these over here. What happens is that when the nerve discharges, when it fires, when it activates, these chemicals are released and actually then interact with the next cell in line and work through something we call the neurotransmitter receptor. And these receptors are what it is that really translates this chemical activity into the electrical activity that then propagates on down into the nerve connection and onto the next cell. So you might imagine that the cell in your cortex and your brain sends this electrical impulse down. The electrical impulse causes the release of the neurotransmitter that activates now a cell in your spinal cord, that in turn controls your muscle. And that really is the fundamentals of how the brain controls your movement.

So what is it that actually happens with a spinal cord injury? And here we have to talk just for a few minutes about how it is that the brain actually controls our movements. So we'll go back here to the drawing of the brain and inside your body and overlay then, this diagrammatic illustration here of the red neuron that sends along axonal projection down into the spinal cord. Here at synapses now, we use that term as a verb on the next neuron in line here. This one happens to control the arms and also on this neuron down here in your spinal cord that controls the leg. So these long distance connections are what it is that control our movements. What happens with a spinal cord injury is that these connections are cut. So for example, for someone like Christopher Reeve, he injured his neck. The nerve connections between the brain and the spinal cord were cut. Now, the important thing here is that the injury is actually very tiny. It actually is only in this little part of the spinal cord shown here in red. And in fact, everything below that injury is fine. All his nerve cells are intact. His spinal cord is intact. It's just a tiny little disconnection here that's like putting a 20-foot wide hole in the freeway that connects Orange County with San Diego. Your cars can't travel, but the hole that actually disrupts things is actually rather small in terms of the entire communication. So what that means is that really it is the level then of the injury that determines what kinds of functional loss there is. Some of you may know people who were paralyzed in their legs after a spinal cord injury. In this case what's happened is that the injury is actually occurring lower in the back here. So these connections from the brain to the arms are still in place. The connections are interrupted here. Again, the rest of the spinal cord is okay. It's just disconnected. It just isn't hearing anything from the brain. And in this case, the patient's legs are paralyzed. So what do we need to do to repair this? What do we need to do to restore function? And there are really several different major problems. But the key is that we somehow need to be able to find a way to stimulate these nerves to grow back to their normal targets from where they're interrupted here down to these targets, into the spinal cord. Probably one important step is to actually find a way to fill this little hole that's left at the injury site. It turns out that an injury to your spinal cord often results in, literally a hole. And the reason is that there is actually a process of tissue destruction that takes place after an injury that makes this hole. So one of the important things is somehow filling that hole and restoring just the tissue for these nerve fibers to be able to grow through. And the things that we hear quite a lot about these days, one certainly major possibility is that stem cells that can differentiate into all kinds of different cells of the body, may be able to actually work here at the injury site to recreate some sort of a tissue environment that is supportive for regeneration. The second thing that we need to be able to do is actually somehow trigger the growth of these nerve connections that have been cut. This is actually a photograph here of an injured spinal cord. This is an injured spinal cord in an experimental animal and here are several nerve fibers that are actually growing up, just stopping at the edge of this injury. And what we need to be able to do is somehow re-awaken these. These actually persist at an injury for years afterwards. And so we are all trying very hard to understand what could be done to actually induce these nerve endings that have been cut to grow back. And I'll just show you this slide, so watch carefully here, this is what we hope will happen. These are actually growing down and as they grow, re-establishing connections with the cells that control the arms and the legs. And that of course, at this point, sorry for the sound effects, but it's the best the computer had. That is what we really hope will happen when we are able to re-induce this growth.

One important thing, if we succeed, it will probably be necessary to actually re-learn how to use these restored connections. We won't know until we succeed. But there's at least a good possibility that the connections that form will be limited, maybe different than what exists in the normal state, and that patients will actually have to re-learn how to use connections that are a bit unusual. That isn't something that is out of line or at all impossible in our conception. We, after all, learn to drive cars in ways that obviously our ancient ancestors didn't. So we're capable of doing things in ways that are uncommon. And so even if the connections that are made are unusual, I think there's very good reason to think that they will in fact be able to restore function. So where do we stand on this? Well, we're close to being able to stimulate regeneration in experimental animals. And I say close in that you will see, we see every year new reports of studies that show limited axonal, this long distance regeneration. But it is very limited. And frankly, it's not reproducible in a way that would allow us to begin to adapt these strategies to humans. It is a situation right now where several clinical trials are in progress and really almost anytime, important new developments could be forthcoming. But I can't tell you right now that we're there. And so, what we really now need to do is to think about this growth of connections and how it works. And this really then is the segue, if you will, between spinal cord injury and studies of memory. And again, you might say well, how can that be? And the answer is that the understanding of how nerve cells grow has benefited tremendously, because we now believe that the formation of memories actually does involve growth. And in fact, especially the formation of long term memories here involves modifying connections between nerve cells in your brain and involves the actual growth of connections on at least a very limited scale. And so, for the rest of the time I'll talk a little bit about that, about what we know about that and about how it can hopefully impact our understanding of this regeneration problem.

So again, I'll introduce topics here that you've all heard before and talk a little bit about different types of memory. But this time, I'm going to focus on the things that these different types of memory have in common. And the bottom line is that they have in common connections and the cellular mechanisms that modify these connections. So in thinking about types of memory, I'd like to sort of introduce, first of all, the concept of associations. And this really is the theme of connections. Connections enable associations. So in thinking about memory, one type of memory that might be very important for you right now is where did I park the car tonight? Of course, only those of you who actually drove will remember that. The way that you do that is the same way that rats remember locations of things in a maze. And actually there are two ways that we think animals might be able to do this. One is the formation of sort of a spatial kind of gestalt of where things are, an understanding of where things exist in your environment, and kind of one of these little you are here signs. But the other way is forming relationships. And this is really the way that we think forms the basis for most of these kinds of memories and in fact, forms the real basis for this kind of memory that allows you to understand your location here in space. So in thinking about how that works, you already know this when you just even think about how you will find your car. And the important point is that this form of memory involves associations. You associate things, objects or events, in order to help you recall. So for example, tonight when I came to the memory lecture, I parked in the parking structure out there, or I guess it's out there, I'm already in trouble. And I parked on the fourth level, opposite the stairs. And I parked next to the large pole. And if you think about where you parked, you'll actually be able to form a map in your mind. In fact, you are probably even doing that as I talk. And you'll see where it is. But you'll see it on the basis of associations. So think of your kitchen sink, actually I showed my wife, Kathy, the slide before the talk and she said immediately, it's got dirty dishes in it. Not really. But the point is that when you see that and you start thinking about your kitchen sink, you don't just think about the sink. You think about the things that are associated with it, so maybe dirty dishes, but probably you're actually visualizing the sink within the context of the entire kitchen. So here is the countertop and over here the refrigerator and perhaps back over here is the stove. You map that sink in the environment. You associate it with other things. And so that is one form of associative memory, where things are brought together in your memory based on a single thing. The point is that the memory of one thing triggers the memory of other things that are associated. And really, this is not the only kind of memory in which this kind of association takes place. So think for example, about the finger movements that a skilled pianist uses to play a concerto. Each of these finger movements is not just a single thing. You're not saying move my finger over to "A" here. What this whole process is is an elaborate coordinated process that really involves movements of the fingers, again, the word in association with others. And learning this kind of skill requires, of course, constant and total repetition, and it is through these repetitions that these, in this case motor associations are developed. And of course, the same is true of other highly developed skills.

Now, when we think about memories there are obviously large differences between the kind of memory that I talked about first, where is my car, and the kind of memory that we're talking about here. The memory of where is my car is one that you learn once and you don't need again. So you do need, and it's very important in fact, that you remember where your car is when you leave tonight. But you won't remember where you parked your car when you went to the store last week. That memory is no longer necessary. So it's sort of a throwaway memory, even though it's very important at the time. It takes once to establish and then you're done with it once you've in fact, found your car. You will, I promise. This form of memory, this motor form of memory obviously is very different, it requires extensive practice, thousands, and thousands, and thousands of repetitions to establish. But the key thing is it's mediated by connections and these connections mediate associations between things. In the one case, elements in the environment that allow you to find your car, in the other movements that allow you to move your fingers in that beautiful way that allows you to play that concerto. Given that, it's not surprising that these different types of memory actually involve similar cellular mechanisms. And this is true even though these different types of memory may involve different parts of the brain. And I know that many of you who come to these lectures routinely have heard many other speakers talk about this, different parts of your brain are important for different things. So what do we know then about these basic cellular mechanisms that mediate memory storage? And the key thing I'd like you to go home with is this, learning involves the growth of new connections, the formation of new connections between nerve cells. And of course, here is the relationship, the connection if you will, between studies of memory and studies of spinal cord injury. And over the next couple of slides here, I'll try to give you some sense of what we believe is actually going on.

So here again is a nerve cell in the cerebral cortex or some part of your brain that happens to be involved in the formation of the memory of your parking place tonight. These are the connections that existed before. Something happens, there is a training event. There is a pattern of activity that's set up and magic happens, and the magic is something we don't understand entirely, but the connections that exist here change. And so for example, here you might see the growth of three new connections. Now, it's important to emphasize that this growth actually is very, very small in terms of its distance, so we're not talking about the ability to re-grow a connection all the way from an injury in the neck, down to the base of the spinal cord. Here, what we're talking about is very, very local kinds of things. So this again is a nerve cell in your cortex. This is a real one. This is the cartoon version of that same nerve cell. So this little paramital or we call it paramital, this little sort of diamond shape here is represented here. And perhaps you can imagine some of these little black lines coming through here are actually synaptic connections from other spots so they're on there and so this growth process that we see here is happening just in this tiny area right here. And it involves maybe, oh, one one-hundredth, or one one-thousandth of the total connections that this neuron actually receives. So that's one thing that happens. The other thing that happens is that connections that exist are actually removed. So here for example, this connection that was present beforehand is actually pared down through some process. And the resulting re-wired nervous system here then is what mediates the associations. So how do we think it works? Well, first of all, the process involves a re-sculpting of neuro-circuitry and then this re-wiring causes neurons to respond in different ways to the same input. So now when you say where's my car? Well, the memory is evoked that your car is in the parking structure. Or when you say I would like to play this concerto, an entire program of activity runs out. And without going into too much detail, I'll try to at least give you a cartoon version of what we think happens here. So thinking about the way associations might be formed, this is a cartoon version of what might exist as a circuit in your brain, just a wiring diagram. So here's little circles that represent nerve cells. These arrows represent the connections that are formed on these nerve cells, and each arrow represents a synapse. Remember what I told you about synapses at the first. So what happens then after they, one input, sorry, again, it's the only sounds the computer has. Let's do that again. There it is, sight and sound. So if you could see that, that actually happened right here. And what that did then was to activate this particular set of connections so that these two nerve cells down the line were set up to discharge. When new or different connections form, shown here, then that same activation generates a totally different output. New things are coming online. So this is the group of two cells, nerve cells that were activated before the growth, and here are the two new nerve cells that are activated afterwards. And through these sorts of re-wirings then, new things can come to be represented in your brain as this very local and very rapid growth process occurs.

How do we know that this happens? You might ask me well, this must be taking place on a very local level. There's actually two ways. One is that we look before and after a training event. But that's really not very satisfactory, because you really would like to see this growth. And I'd just like to show you one slide that illustrates one of the ways that this has been done. So to actually visualize the growth process as it happens, we actually grow neurons in a dish and we stimulate them with patterns of activity that are similar to the patterns that are induced during the formation of a memory trace. Here is one of these dendrites of a nerve cell growing in a dish before a stimulus. Here's the stimulus. And within a few minutes afterwards, you can see now a totally new configuration to the synaptic connections on these neurons. So each one of these arrows points to something…this is the same process of this cell, but isn't here before the period of activation. So there's really a tremendous remodeling going on within a period of just a few minutes as the cell receives a stimulus that in many ways, we believe at least, maps the kind of events that are taking place during the formation of a memory trace.

So what are the key events that mediate this growth? And here I just need to tell you a little bit about molecular events and particular genes. Most of us think about genes that determine our eye color, or hair color, or how tall we are. The genes that I'm talking about are ones that play less of a role in determining those things. They don't make you smart or make you un-smart. These are genes that get turned on in particular situations. And actually get turned on in your brain, hopefully even now genes are being turned on. And over the next few minutes, I'll just tell you a little bit about what these genes do, that they're important for the function, and in particular that learning, as well as other brain activities, are actually the key stimulants that turn on these genes. So just to again give you a little bit of sort of basic biology here. This is actually a drawing of a nerve cell blown up now from one of the ones that I showed you earlier. So of course, genes exist in the nucleus and they work by making what are called messenger RNA molecules, these messenger RNA molecules encode for particular protein products, particular molecules that make your nerve cells work. These molecules are transported out of the nucleus and into the cytoplasm of the neuron and there, proteins are synthesized. And it's this entire process of turning on genes, transport of this messenger RNA molecule out into the cytoplasm, and the making of these key proteins that is responsible, we believe, for modifying synaptic connections during the formation of a memory trace. Experience triggers gene expression and we know this now from a variety of studies, by actually measuring different products of genes after activity in the brain or after a particular learning experience. A number of investigators have been able to describe dramatic changes in the patterns of gene expression. And I'm not going to give you the list of them. There are hundreds of genes that are turned on massively every time you learn something, every time you experience something. And these include genes that we call neurotrophins. So I need to just do a little bit of a digression here, because it really is this part of the whole gene expression profile that makes this whole process not only important for you in terms of forming memories, but important for you for maintaining the health of your brain. So these neurotrophins that are amongst the genes that are turned on play a key role in early brain development. They're the ones that make your nerves grow in the first place, that keep your nerve cells alive. And you might think of them sort of as the fertilizer for the brain. When they're there, neurons are happy and healthy and growing. And when they're not, then neurons actually get sick. And in fact, low levels of these neurotrophins may be responsible for some of the neurodegenerative diseases that cause the death of nerve cells, including Alzheimer's disease. So these then are amongst the genes that are actually turned on by a particular experience. How do we actually see this and exactly how is it represented in your brain? So we've known for decades really that experience plays a key role in early brain development. If you don't allow an animal or a human being to have a normal experience, their brain is actually smaller and certainly their repertoire of behavior is much more primitive and poor than someone who, or an animal who, has experienced a wide variety of stimuli. But the new information is that the same basic event also happens in the mature brain. And so just to give you one example of now a host of studies, this is actually a part of your brain that is involved in memory storage, it's part of the hippocampus. And here it's been found that in one structure of the hippocampus there is a continual production of new nerve cells throughout your life. These nerve cells grow, here it's just sort of cartooning the way they might divide here, just like cells in early development they migrate to new positions and then they begin to grow these long axons and dendrites and make connections. And the remarkable thing is that this process, this growth process, is greatly enhanced by even a single learning experience. Now, a variety of learning experiences have been used. But just allowing an animal to come from its home cage, which is a fairly primitive environment, and explore a novel environment that's filled with toys for as little as an hour, is enough to actually trigger the generation of a whole new population of brain cells that then grow, and differentiate, and reconnect. And it is in this way then that the structure is actually renewed and maintained throughout the life of the organism. How do we turn on the genes that are important here for neuron health? And really the answer is simple as you might guess -- use your brains.

This is something that really is actually simple, important, fun, and fairly obvious. And it's been known really for quite a long time that different kinds of exercise, for example, are important not just for your body, but also turn on the expression of these neurotrophins. But really it doesn't take going out and running a road race. You can turn on your brain just by thinking about it. And I'll give you just a couple of, sort of fun examples that have come from the literature recently. So here is an experiment that involves imaging movement in a video environment. It's kind of a Mario Brothers for adults, I guess. So what is going on here is that subjects, human subjects are shown these kinds of video images that map a street scene and really these street scenes change and you can move from one place to another, and find your way from one location to another. And that's their job. So at the same time that they're doing this, their brains are being imaged by PET, P-E-T, positron emission tomography. And this is just a technique, a very fancy technique for actually imaging brain activity that's based on the patterns of activity that your nerve cells are showing at a particular time. So patients that do this, that navigate successfully through these video games and find their way from place "A" to place "B", exhibit very dramatic increases in activity in particular brain regions. And importantly, in a structure here called the hippocampus, which we believe is very important for mapping these kinds of spatial memories. And these are exactly the same kinds of activity that other investigators have shown turn on gene expression in these same structures. So for example, here in fact, both our laboratory and Dr. McGaugh's laboratory studied animals in which the gene expression patterns have been evaluated after an experience like this, well, an animal's experience like this. And this pattern of brain activation that can be generated by an experience is actually recreated in an experimental animal by asking them to navigate in a maze, or even just to play in this toy filled environment that I was telling you about. So just doing it, just using your brain turns on activity and turns it on in a way that turns on the expression of these key growth related genes. And it's interesting, this kind of use when done repetitively actually not only may generate new neurons, but may make parts of your brain bigger.

So the same group that did the study that I just showed you on activating the hippocampus did this study. Here they looked at London cab drivers and actually measured the size of their hippocampus and they found that there were quite large differences in the size of the hippocampus in cab drivers and that the size differences were greatest for those who had been driving longer. So these patterns of activity may not only make new nerve cells and new nerve connections, but might actually cause measurable structural changes in your brain. Not to worry, your brains will not grow out your ears if you try to learn too much. Remember that I did tell you that these growth events are also balanced by a sculpting down of connections that aren't used. So we need to think about this as making and breaking connections on a continuous basis. And the bottom line is that it involves the same genes that are important for neuronal health and neuronal growth. Laughing is good for your brain, too. This actually is a study that just came out in one of the major neuroscience journals. And the important finding here is that different kinds of humor activate different parts of your brain. So I'm sorry, I'm going to quote from them now. I, believe me, these are not my jokes, but, so. For example, what do scientists use for birth control? Their personalities. This is a kind of semantic joke and as we'll see, it activates one part of your brain. We just did that. The other kind of joke, for example, that they looked at was a pun, so oh, this one I even hate to share the answer. Why did the golfer wear two sets of pants? You got to know, right? Terrible. Oh, I know. So, just to show you what parts of your brain have lit up, or at least what parts lit up in those of you who thought those were funny. The semantic jokes, the scientists' method of birth control lit up this part of your brain. So this is your whole brain and again, is a PET scan. And this is actually a part of your temporal lobe. And the puns lit up a frontal area in your cortex. Probably puns take more thought, maybe, but anyway. So the bottom line is that not only memory, but also things that are quite enjoyable turn on patterns of activity in your neurons. We haven't really been able to ask in experimental animals whether or not these activities turn on gene expression. They don't get the jokes.

So I'd just like to end with this and it really I think is the most important thing for you to know. Your brains right now are continually growing dynamic structures. When I was a young person, my mother used to tell me that. She used to say I know people who have kept healthy and happy throughout their lives and the reason is that they use their brains. They do things that are important. And my mother is 84 years old and every morning gets up and plays the piano and does a crossword puzzle and is in the audience tonight. So thanks, Mom, for everything. Stand up. Where are you? Where are you? Yeah. Sorry the brainwork didn't get you to grow any taller. I couldn't tell you were standing. So she was right. And so these basic understandings are really quite important. And so the bottom line then is really exercise your brain, your nerve cells will continue to grow and be healthy throughout your life. And in fact, for those of you who have come tonight, I hope that what you've learned over the past hour has been good for you and that it's generated a few new nerve cells. So in closing, I'd like to give thanks to a few people. To Mara Hoffstetter for help in preparing the presentation, she was responsible for the animation, not the sound. That was my choice. To all of the staff at the Reeve Irvine Center for the wonderful work that they're doing. I'd like to thank Jim McGaugh for this wonderful lecture series. I won't mention, but I'll, I didn't list here, but I will thank the NBA for not scheduling a playoff game tonight. And NBC for ending West Wing last week. And finally, I'd like to thank all of you for coming to this lecture and for stimulating your brains. Thanks very much.