How I fell down a murine rabbit hole

This post is about animal models and postprandial elephants.

Personal update

Before I get started on today's topic, I wanted to introduce my latest experiment. Although butter had a temporary beneficial effect on my cholesterol levels, the benefit did not persist. In fact, towards the end of last year, while my HDL levels remained quite high, the non-HDL crept up into territory I was not comfortable with. I can't say if this was due to the butter, a year of relatively high egg consumption (3/day), a longer term effect of high red meat consumption, or the consequence of several years on a low carbohydrate diet. Whatever the cause, I decided, since I've never done it before, to try out an actual high carbohydrate diet that is low in fat and cholesterol. At least at the end of this experiment I'll be able to speak about high carbohydrate diets from a position of personal experience.

I ramped up my carbohydrate consumption gradually over a couple of weeks, and then abruptly switched out all the butter, eggs and red meat for about a pound each of white rice, bananas, fish, and the occasional mound of white potatoes. I sprinkle in a sprinkling of almonds, salad greens, carrots, spinach, shellfish, yogurt, and whatever else I feel like eating to round out my micronutrient requirements, which I roughly confirm from the USDA data. Wheat is still out, as are the vegetable oils and all processed foods.

It is too early to report much in the way of results, but in the first two weeks my HDL has dropped a little, my fasting triglycerides stayed under 70, and my non-HDL has dropped about 120 points. What is also a bit of a surprise is that my blood sugar has been quite consistent and low, almost always peaking below 125 even following heroic quantities of white rice. One benefit of rice in regard to blood sugar is that I find it difficult to eat it quickly (compared to, say, a banana or sugar water). Anyway the new diet seems to agree with me so far at this very preliminary stage. In a few weeks I will feel more qualified to comment on high carbohydrate diets, having actually tried it for the first time in my life.

"Totally Misleading"

Now on to the meat of this post. Episode 52 of "This Week in Microbiology" featured a conversation with clinical microbiologist Ellen Jo Baron. Although it is not the focus of the episode, she briefly told the story of how difficult it was to publish her PHD thesis on salmonella. She says:

"What we did was compared in vitro neutrophil activity of mouse neutrophils against the mouse typhoid organism salmonella typhimurium, and then human neutrophil activity against the human typhoid agent salmonella typhi, and my work showed that they were radically different early responses, and nobody wanted to buy that because many of the premier researchers in the field had been using the mouse model of typhoid looking at vaccines et. cetera and I was showing them that it was an inappropriate model."

In other words, the mouse immune system behaved differently from the human immune system in what was supposed to be an animal model of a human condition. Established scientists did not like the finding and resisted its publication. However, This took place in the depths of time (the 1970s), so perhaps we can forgive our primitive forbears for their unfounded prejudices.

Or maybe not? Recently in the New York Times, Gina Kolata describes a similar episode in the life of a paper published by Seok et. al. this February in the Proceedings of the National Academy of Sciences.

Like Baron, Seok et. al. were studying the behavior of immune cells under an assortment of inflammatory conditions (namely sepsis, burns and blunt trauma). The new paper recorded patterns of gene expression in human white blood cells taken from real patients. According to the the Times, the researchers ran into trouble getting their results published because they had not demonstrated that their results were consistent with the established animal models for these conditions. So they ran the experiments again with mouse cells, and, lo, they did not match at all. This, apparently, did not comfort the paper's critics. Only by submitting to PNAS (along with a recommendation that specific reviewers be consulted) was the team able to win publication.

So back to the results: after an infection, burn, or getting traumatized by a blunt instrument, a wide range of changes occur over time in gene expression in white blood cells, as they participate in the immune/healing response. Expression of some genes will increase while expression of others will decrease. As between human cells and the corresponding mouse model, correlations (r-squared) max out at 8% in the directionality of gene expression. In other words, if a gene was upregulated in humans, it was essentially random whether it would be unregulated or downregulated in the corresponding mouse model. Just about half the time, the same gene, coding the same protein, under what is supposed to be the same stimulus, does the opposite thing.

Interestingly, while gene expression patterns in the three human conditions were quite similar to one another, the three mouse models were very different not only from the human conditions but also from each other. So the human inflammatory response is a maze of twisty passages, all alike, while the mouse inflammatory response is a maze of twisty passages, all different (and all different from the human twisty passages). In addition to the directional differences in gene expression, the researchers also observed enormous differences in timing. For example, a response that lasted 4 days in the mouse might persist for 6 months in people. Yikes!

These results led Gina Kolata of the Times to say that the mouse models for these conditions were "totally misleading." Seok et al, introduce their paper by pointing out that "there have been nearly 150 clinical trials testing candidate agents intended to block the inflammatory response in critically ill patients, and every one of these trials failed" (Seok page 1). (these words were too strong even for the Times -- they changed "every one" to "most"). This paper is very clearly written and I can't really sum it up better than they do:

"here, we show that, although acute inflammatory stresses from different etiologies result in highly similar genomic responses in humans, the responses in corresponding mouse models correlate poorly with the human conditions and also, one another. Among genes changed significantly in humans, the murine orthologs are close to random in matching their human counterparts."

So another strike against the mouse as being the perfect biochemical equivalent to a human.

Meanwhile it has been known for many years that mice respond very differently than humans to bacterial lipopolysaccharide (LPS). Also known as endotoxin, LPS has made a number of prior appearances on this blog. The hapless human is about 100,000 times more sensitive to LPS than the mouse. In 2010, Robert Munford published "Murine response to endotoxin: another dirty little secret?", citing work by H. Shaw Warren, the second author on the Seok et. al. paper. So the new gene expression results add to an existing body of evidence casting doubt on the presumed similarities of human and murine immune systems.

I guess, after all, rodents and humans are not so much alike. For reference, here's a recent mammalian family tree showing the distance between humans and rodents. (McCormack et al Genome Research 2012).

J. Craig Venter gets to appear personally on phylogenetic trees like this one.

The differences in gene expression between animals and humans in response to lipopolysaccharide and inflammation in general, from the 10^6 difference in sensitivity, time course differences of several orders of magnitude, and essentially zero correlation even in directionality, cast significant doubt on my earlier thoughts about lipopolysaccharide and postprandial triglycerides. As I read studies on this topic, I am constantly finding myself disappointed to pull up references only to find animal research. This is not always disclosed in the title of the paper, or even in the abstract! In my darkest hours I sometimes find myself pointing this out to people on twitter (by the way, if I can fit "in mice" in a 140 character tweet, you can fit it in the title of your peer-reviewed research paper).

Digression on (Mathematical) Models

Recently I picked up a very nice little text book by Hugo van den Berg on mathematical modeling of biological systems.  It covers some of the basic stuff that I think someone doing mathematical modeling should be expected to know. Since I have been spending more time reading a book and less time on the Internet, Google has backed down on sending me ads for modeling agencies. And all of the modeling agencies that twitter-followed me have since un-followed me.

Some readers may not know that the field of computational biology was founded by Alan Turing, the father of computer science himself. His landmark 1953 paper on morphogenesis is available online.

xkcd #793.

If you precisely define the characteristics of an imaginary object, and then investigate the consequences of your definition, you are doing mathematics. If your imaginary object is a scientific hypothesis, say, about the interactions of an organism with its environment, then mathematics can help you to understand the consequences of your hypothesis. Given a rigorous definition, the mathematical analysis of a scientific hypothesis can help you decide whether its predictions match reality. If not, then you have made a mistake, either in your hypothesis, or in its rigorous definition. In other words, mathematics makes predictions precise and therefore testable. A mathematical hypothesis cannot make hand-wary excuses or appeals to authority to justify why the experiments are giving inconsistent results. It has no choice but to slink away, refuted (and nobody wants to associate with a refuted hypothesis, right?)

Lets say, for sake of a straw-man, that your hypothesis is that carbohydrate drives insulin, and insulin drives fat storage. Your model might look something like this: the amount of carbohydrate in the diet (in grams) is proportional to the daily average insulin level. And the daily average insulin level is proportional, on average, to the net amount of fat stored per day. You can test that model against real data and see that it is wrong. So you can then make adjustments until you get a fit, or abandon the hypothesis if it turns out to be unworkable.

A celestial example

Mathematics is also useful when systems become too complex for intuitive reasoning. Systems with interacting parts reach that level of complexity much more quickly than most people would guess. Take one example from physics. Assume two stars are approaching each other in space. They are interacting gravitationally, but are far enough away from other masses that they can be approximated as an isolated system. There are three possible outcomes: (i) the stars collide, (ii) the stars approach each other and then drift apart, or (iii) the stars settle into stable elliptical orbits. No matter how you set things off, you will never observe anything else. Newton solved this problem in the 17th century and, with a bit of adjustment from Einstein's relativity, the answer is close enough that our most precise observations cannot detect any deviation.

What might the stable orbits look like with three stars instead of two, and how would we need to set things off in order to end up in a stable orbit? You might expect that the solution would look like a slightly more complex version of the solutions to the two star problem. In fact the addition of the third star renders the mathematics so complex that a general solution is still not known. In fact, the vast majority of initial conditions do not result in stable orbits at all. Newton presented this problem in its modern form in 1687. New solutions are still being discovered in 2013.

One solution, discovered numerically by Chris Moore in 1993, has three equal masses orbiting each other in a figure eight configuration. It has been estimated that the probability of this configuration arising in the real world is between one per galaxy and one per universe (see Montgomery 2001 citing calculations by Douglas Heggie). This might explain why nobody has yet observed stars doing this in the wild, but doesn't quite rule out such a discovery in the future. Not very intuitive in my opinion.

A stable orbit with 9 masses. From Montgomery 2001.

Update on the Postprandial Elephant

Actually this all relates to the stuff I talked about in my last post. I made four main points, albeit in my long-winded and incomprehensible fashion.

1. Eating fat makes triglycerides show up in the blood.
2. Very low carbohydrate diets reduce the increase in postprandial triglycerides after a meal.
3. The shape and height of the postprandial triglyceride curve, as well as the time at which the peak occurs, reflect metabolic function and possibly inflammation.
4. Therefore: measuring triglycerides after meals may be useful while eating a low carb diet.

Point 3 is conjecture at this point: what is the shape of the triglyceride curve really telling us? Could a mathematical model help us distinguish among different theories, in order to determine which is most plausible? One theory was that lipopolysaccharide (LPS), also known as endotoxin, enters the blood stream along with fat in the meal, causing an acute inflammatory response that shows up on my test strips as elevated postprandial triglycerides.

The Core Triglyceride Model

In the process of looking into triglyceride metabolism, I constructed a very simple mathematical model in an attempt to simulate what might happen when lipids absorb from an idealized gut into an idealized bloodstream, and then further clear out into an idealized human body. The model is depicted below. The parameters (p and c) are not directly related to any specific biological function, so for now the model will be useful primarily for making qualitative and not quantitative assessments.

Simplified diffusion model of postprandial triglyceride metabolism.

In addition, as the model is concerned with postprandial dynamics, I subtracted out the steady-state term that would establish a fasting triglyceride level. Below I consider a few different adjustments to the model that could get it closer to matching real data. I will be qualitatively comparing the curves produced by the model against data from Sharman et. al., as I did in my last post. Here are those curves to refresh your memory.

Data from Sharman et. al. 2004. Postprandial triglycerides following oral fat tolerance test. Subjects consumed the baseline diet identified in the legend. 

Hypothesis: Altered Absorption/Clearance Rate

My mathematical model as presented in The Postprandial Elephant is a diffusion model. It considers two membranes (the gut and the vascular endothelium), and models the transport of lipids across those membranes by a simplified diffusion process. This means that the rate of transport of lipids across a membrane is proportional to the concentration on the "source" side of the membrane. (For more accuracy you would use the difference between the concentrations on the two sides of the membrane, but I believe this simplification is justified.)

I made one other assumption last time in order to make the math easier. That assumption, which I did not explain in my previous post, was that the absorption rate across the gut matched the clearance rate of lipids out of circulation (i.e. p=c in the model equations shown in the diagram above). Lets explore what happens when we eliminate this simplification and vary the two parameters against each other.

In order to get a higher peak triglyceride level, as observed in metabolically unhealthy individuals, we could raise the absorption factor p (think of this as a "leaky gut"). Or we could reduce the clearance rate c (e.g. via "insulin resistance"). So lets see what happens, using jSim to produce numerical solutions. (FYI I am now using jSim for this stuff, which I find works much better than the OpenCell software I was using before).

Simplified triglyceride model with balanced absorption and clearance (black), fast absorption (red) and slow clearance (blue). Numerical simulations with jSim. Plot made with R.

Note first of all that the fast absorption curve shows an earlier peak, as well as a steeper initial rise. This is not consistent with the abnormal metabolism cases, which show a delayed peak. In fact, the delayed peak, in my view, appears to be one of the hallmarks of impaired metabolic function. While it is still possible that accelerated fat absorption has some relevance to abnormal metabolism, we need to reject the hypothesis that it is the primarily driver for the observed impairments.

The slow clearance theory looks better. The peak is both higher and later in time, as you might expect for a circumstance where lipids are being digested at the normal rate, but cleared more slowly than they should. However: note two attributes of the curve do not seem to match the data. First, the initial rise in triglycerides (the slope in the 0-2 hour range) is steeper than the baseline curve. The data appears to show a slower initial rise. Slower clearance, holding absorption rate constant, will always result in a steeper initial slope.

Second, look at what happens off to the right hand side. We see in this simulation, representing a clearance rate of 1/2 the balanced case, the triglyceride levels remain significantly elevated all the way out to the right hand side of the graph, more than 10 hours after the meal. The real curves look much more symmetrical. In fact, again you can see how lowering the clearance rate while holding absorption rate constant will always result in a right-hand slope that is less steep than the left hand slope. So I think it seems fair to reject this model as well, at least as a primary driver of the phenomenon.

Now I believe it has been shown that impaired metabolic states are associated with decreased triglyceride clearance. This may also be part of the explanation for why fasting triglycerides are elevated in those states. However, I think, based on the above, that there is more to the picture.

Hypothesis: Enzyme Limiting

Apparently (per Hugo van den Berg), a common trick in modeling biological systems is to assume that one process or another may be limited by the availability of a necessary enzyme.

For this next experiment, we will assume that the rate at which fat is absorbed from the gut remains constant, but that clearance of triglycerides out of circulation is limited by an enzyme. It doesn't matter which enzyme. The key here is that enzyme limited processes produce curves with a certain characteristic shape, where a linear enzyme-limited regime gives way more or less quickly to an exponential decay at lower levels of the state variable. This exponential regime will look just like the simplified diffusion model discussed above.

If you are a biochem fan, then you can pretend, for example, that triglyceride clearance is mediated by targeted cell surface receptors that recognize apo-lipoproteins on chylomicrons, VLDLs etc, and that the availability of these enzymes and/or the appropriate apolipoproteins themselves is a limiting factor in the rate of triglyceride clearance. Or that the availability of lipoprotein lipase is a rate-limiting step. Either way, from a statistical mechanics perspective, the absorption rate will be proportional not only to the density of triglycerides in circulation, but also to the probability of a triglyceride or lipoprotein randomly bumping into the appropriate enzyme. Hugo van den Berg goes through the derivation, and you end up with an equation of this form:

State equation for an enzyme limited process.

Since we now have an enzyme limited process that depends on the concentration of fat in circulation, we ought to add a constant "source" term representing the body's own production of triglycerides in the fasted state. The source term will determine fasting triglyceride levels in this model. Then we add our original absorption term accounting for the lipids coming in to circulation from the gut, at a rate proportional to the intestinal fat concentration L. This gives us the following full state equation for triglycerides in circulation:

Fat clearance with a constant source term, gut absorption by diffusion, and enzyme limited clearance.

As you can see from the figure below, in the simplest enzyme limiting case, we have a steeper initial rise, and a less steep right-hand curve. The linear character of enzyme-limited triglyceride clearance is clearly visible on the right hand side of the curve, as the drop-off in the 6+ hour range looks like a straight line. Enzyme limiting is strong enough with these parameter values that we don't even see the exponential transition. The "balanced" base case without enzyme limiting is also shown, for comparison. Enzyme limited processes will in general show a much longer decay time than simple diffusion models, which exhibit only exponential decay. That said, the curve does show a higher and later peak. Working against this hypothesis is the accelerated initial rise compared to the base case, which is possibly inconsistent with the real data.

Numerical simulations with jSim. Plot made with R.

If you futz around with the parameters of the model, you can get much closer to real-looking curves (see the figure below). I haven't thoroughly investigated what the biological significance of these parameter values may be, but it is intriguing. You can still observe the linear decay characteristics, but right-hand the slope is steeper here and more consistent with the data from Sharman et. al. The initial rise is now slower than the base case. This suggests that, with these parameter values, absorption is faster in the exponential regime (at low triglyceride levels), but slower in the linear regime at high triglyceride levels. It is not clear to me biologically why the characteristic clearance rates in the two regimes would move in opposite directions, but this is something that may be observable in experiments that were carefully designed for that purpose. The mathematical modeling process could therefore inspire targeted experiments that may otherwise not seem useful, sort of like the way theory in physics inspires experiments in that field. Sadly I will probably not be the one to do those experiments.

Numerical simulations with jSim. Plot made with R.

Note that all of these "enzyme limited" curves reflect the same rate of digestion/absorption out of the gut. No gut barriers were harmed in this virtual experiment.

All told, this is a pretty decent looking curve, even if I don't understand its biological significance.
In the enzyme limiting case, it is clear that the baseline (fasting) triglyceride level is relevant to postprandial behavior. One might expect the enzyme production to adjust in compensation to chronically elevated fasting triglycerides. In addition, the fasting triglycerides could now be elevated for one of three reasons: increased endogenous production, decreased passive clearance or limited enzyme availability. Ultimately, of course, if you add enough knobs and switches to the model and you can obtain any result you want. Further refinements could be motivated by more detailed biochemical understanding (preferably with biochemistry that is relevant to humans, not just animal models).

Hypothesis: Acute Inflammation

My original hunch was that inflammation had something to do with the sustained elevation in triglycerides observed in abnormal metabolic states. Under this hypothesis, the meal triggers an inflammatory response and, given a standardized type and amount of fat in the test meal, the changes in the height and timing of the peak triglyceride reading will vary because of differences in postprandial inflammation. That inflammation may be due to the introduction of LPS and other microbial components into circulation in the course of digestion and absorption of the meal.

The purpose of the innate immune system is to recognize conserved molecular patterns associated with microbes (in contrast the adaptive immune system is the part that engineers targeted antibodies when a novel threat is detected). LPS is the most widely studied example of an inflammatory microbial product. It is not a single entity, however, but a family of molecules that vary widely in biological activity. Different arrangements of LPS can elicit different immune responses. Some microbes change their LPS based on their growth environment (e.g. Salmonella LPS changes as a function of temperature. Other pathogens have found a way to modify their LPS to bypass the innate immune response, which helps them kill their hosts before the adaptive immune system can figure out how to make antibodies. So it's complicated.

I played around with a mathematical model of endotoxemia, courtesy of a very nice paper by Day et. al. published in 2006 in the Journal of Theoretical Biology ("A reduced mathematical model of the acute inflammatory response II. Capturing scenarios of repeated endotoxin administration"). I implemented the model in jSim. The Day et. al. model shows clearly how multiple doses of LPS may have non-intuitive effects: an initial dose sometimes sensitizes the virtual patient to a later dose, which produces a heightened, and sometimes lethal response to an amount that would ordinarily be tolerable. In other scenarios, an initial dose has a de-sensitizing effect. These sorts of complex interactions appear in real patients (and animal models) and can arise from the interactions between the inflammatory and anti-inflammatory components of the model.

Given that these researchers are seeking to model life-threatening conditions, the model does not seem to be suitable for my purposes where very low levels of LPS are of interest. Still I think the time spent fiddling around with the model was worthwhile.

By the way, it is worth noting that the behavior of this model relies on choosing appropriate values for 15 different parameters. There is a great deal of potential variability arising from what parameter values you choose. I'll look at those parameters again below.

By the way, Judy Day is a mathematician, and some of her subsequent work has looked into what general characteristics need to be present in a system of differential equations in order to give rise to the tolerance phenomena such as those observed in the biology of endotoxin exposure. So immunology is inspiring novel work in pure mathematics. Cool!

Inspiration for the acute inflammation theory

This idea that fat ingestion can cause an excessive increase in triglycerides via an acute inflammatory response to LPS was inspired in part by the so-called "lipemia of sepsis," which is the observation that individuals with systemic bacterial infections show elevations in their triglyceride levels. Sepsis is a chronic, long term condition, though, and not an acute one.

Sepsis with gram negative bacteria is of course associated with systemic elevations in LPS, since gram negative bacteria shed LPS when they divide. The body detects LPS via targeted receptors and responds with a cascade of inflammatory cytokines such as IL-1, TNF-alpha, and ifKB. Later, a counter-regulatory response is seen, characterized by elevated levels of cortisol and other anti-inflammatory molecules. A lot of complex biochemistry happens. Since LPS has a lipid end that is fat soluble, and since LPS is naturally present in high quantities in the gut, it is absorbed into the body whenever we eat fat. Therefore I thought something similar to the "lipemia of sepsis" might occur on a smaller/gentler scale after meals. For this to be so, the LPS introduced with a meal would have to cause an inflammatory response on the time scale necessary to induce elevated triglycerides in the 4-6 hour window.

First, lets look at a couple of studies supporting the notion that inflammation might cause postprandial increases in triglycerides.

An old-ish paper by Feingold and Grunfeld ("Role of Cytokines in Inducing Hyperlipidemia," Diabetes 1992) discusses the relationships between the various cytokines and lipid metabolism. They reference studies showing that "acute-phase [inflammatory] proteins are increased in the circulation of individuals with diabetes in a manner similar to that seen during infections or inflammatory illnesses." However: "the doses of TNF and IL-1 that stimulate hepatic fatty acid synthesis are similar to those that produce fever" so they are likely higher than the levels that are induced after meals.

Another Feingold and Grunfeld paper from 1992 (this one with lots of other authors) ("Endotoxin rapidly induces changes in lipid metabolism that produce hypertriglyceridemia", Journal of Lipid Research) found that low doses of LPS stimulate triglyceride production by the liver, while high doses inhibit clearance of triglycerides from circulation. So this suggests that it is not only the fat being absorbed that is relevant. We need to consider triglycerides produced and/or released into circulation by the body. The authors do point out, however, that "lipoprotein metabolism differs markedly in humans compared to rodents and whether the changes observed in lipid metabolism after infections or LPS in experimental animals also occur in humans is unknown." Fair enough. Surely someone has done that in the last 21 years?

A bit earlier, back in 1990, Harris (of "Barcia and Harris" fame, see below) teamed up with Feingold and Grunfeld and another guy named Rapp. The title pretty much sums it up: "Human Very Low Density Lipoproteins and Chylomicrons Can Protect against Endotoxin-induced Death in Mice." There are those words "in mice" again. It's human VLDL, but it protects mice from the effects of LPS. So it makes sense that the body might make VLDLs (which show up in the blood as triglycerides) in response to LPS, as a protective measure.

Last time, I mentioned in passing the 2005 paper by Barcia and Harris called "Triglyceride-rich lipoproteins as agents of innate immunity" (Clinical Infectious Diseases 2005). The authors make the case that lipoproteins, including the VLDLs that show up when you measure triglycerides, play a role in innate immunity. They argue that LPS in circulation will dissolve into the circulating lipoprotein particles and, therefore, an elevation in triglycerides will actually attenuate the immune response to LPS, staving off the life-threatening consequences of an overreaction by the innate immune system. If lipoproteins (including VLDLs) are protective against LPS, then, again, you might expect the liver to produce extra ones in response to LPS exposure.

Ultimately Barcia and Harris admit that "most of the evidence supporting a protective role for lipoproteins against LPS has understandably been generated with animal models of infection" and that "existing [human] data are contradictory and thus inconclusive." Okay.

Last on this list is a paper titled "Metabolic Endotoxemia Initiates Obesity and Insulin Resistance" (Cani et. al. 2007, Diabetes). Allow me, if I may, to add the words "in Mice" to the title. These mostly French researchers found that a high fat diet increased circulating LPS in mice. In a separate experiment, LPS infusion induced insulin resistance, fatty liver, weight gain, and chronic inflammation. In mice. Finally, transgenic mice deficient in LPS receptors (CD14 to be precise) were immune to most of the harmful effects of LPS infusion and the obesity-inducing high fat diet. Very interesting! For mice.

What do the human studies show?

First, I'm going to briefly go over Timlin and Parks ("Temporal pattern of de novo lipogenesis in the postprandial state in healthy men" AJCN 2005), which I mentioned in my last post.
The human liver can make fat from scratch, and does so in certain circumstances to a greater or lesser extent depending on the individual. This process, known as de novo lipogenesis (DNL), is a potential factor in elevated triglycerides. Timlin and Parks notes that studies have shown chronic consumption of high carbohydrate diets (>50% from mono- and disaccharides) is associated with increased DNL. This makes sense, in the same way that your body makes more glucose when you are eating a low carbohydrate diet. Timlin and Parks hypothesized that an acute increase in DNL would be seen after food consumption, but the magnitude was unknown (it is very nice to see the scientists admit in the paper what their original hypothesis was!). Their experiment was to feed liquid meals high in sugar to human subjects and measure DNL postprandially. They excluded individuals with diabetes or other metabolic diseases, those taking drugs that affect lipids or metabolism, and smokers. Subjects were normal to slightly overweight. The liquid test meal roughly matched the macronutrient composition of the 3-day pre-study diet, which was about 51% carbs, 34% fat, and 14% protein.

Results: triglycerides peaked after the meals, with higher peaks after the second meal. What interested me in this paper originally is it showed that DNL peaks at the same time (around 4-5 hours) as the peak triglyceride levels observed in other studies of abnormal triglyceride metabolism. Some of the new fatty acids manufactured by the liver at this time could show up in circulation as VLDL particles.

Timlin and Parks showed that the magnitude of DNL was very different for different people. One person's DNL peaked at 3.9% (compared to total VLDL), another's was 29.9%. This maximum value is not very high compared to the wide divergence between the peak triglycerides seen in healthy vs. unhealthy humans. I played around with the data a bit and I don't think these levels of DNL would be sufficient to explain the differences in postprandial triglycerides seen between individuals (as observed, e.g., by Sharman et. al.). It is possible that other studies on DNL might show wider divergence, for example in individuals with metabolic syndrome or diabetes, who were excluded by Timlin and Parks. I would also love to see a comparison between individuals eating a low fat vs. a very low carbohydrate diet, but I do not believe that has been done yet. Note that Timlin and Parks did not measure LPS and it is unclear what accounts for the wide divergence in DNL seen between the different study subjects.

A digression on postprandial NEFAs

In my last post I said I would look more closely to what happens to non-esterified fatty acids ("NEFA") after meals. I suspected based on a mouse study that NEFA would behave in basically the same way as triglycerides: peaking after a meal and then returning to baseline. Below is a chart showing NEFA values after a meal from a human study and a mouse study. I think the data speaks for itself: no, they are not very much alike. In every human study I have seen, NEFAs drop after meals in humans, but increase after meals in mice.

The mouse data is for olive oil alone and the human data is for a "mixed meal" that includes a very small rice cake and a 10 gram piece of cheese. It is known that insulin strongly suppresses NEFA release from adipose tissue, The rice cake should have contained about 7 grams of carbohydrates. Add in probably less than 3 grams of protein for the cheese and we're not talking about a serious insulin spike here. Perhaps this is enough, or perhaps there is more to the story than insulin.

This was the lowest carbohydrate content in any human study of this kind that I could find that measured postprandial NEFA. Not sure why there do not seem to be any directly comparable studies between humans and animals (e.g. a pure fat meal in humans, or a mixed meal in mice), but if you know of one, let me know!

Postprandial NEFA levels. Data from Agren et. al. 1998 (human: blue line) and Murray et. al. 1999 (mouse: red line). I can't be the first person to notice this, but they are not very much alike. Plot made with R.

Omega 3s and Postprandial Triglycerides

Way back in 1988, William Harris et. al. ran an interesting experiment on the effects of various background diets on postprandial triglycerides ("Reduction of postprandial triglyceridemia in humans by dietary n-3 fatty acids", Journal of Lipid Research 1988). They varied the predominant fat in the diet and then ran oral fat tolerance tests. The diets were varied by incorporating one of three fats predominant fat types: saturated fat, vegetable oil, or fish oil. (Note by the way that the saturated fat diet contained a mixture of peanut oil and cocoa butter, so I don't think it is at all representative of what would be in a healthy low carbohydrate diet. The authors meant it as a simulation of the fatty acids in a standard American diet.)

This paper is great because it shows such a large effect. The intervention was quite extreme in that the fish oil diet had 24-28 grams of omega 3 fatty acids per day. This is the sort of extreme intervention you might do in a self experiment, where, lacking entirely in statistical power, you can't waste your time trying to detect a small effect.

Results? The diet high in n-3 fats substantially reduced postprandial triglycerides, regardless of the composition of the test meal. Since they are hypothesized to lower inflammation, this lends some support to my inflammation theory.

Postprandial triglycerides after a test meal predominantly composed of
the same fat as the background diet. From Harris et. al. 1988.

Postprandial triglycerides after test meals containing primarily
saturated fat (A) and fish oil (B). From Harris et. al. 1988.

It is interesting to note in passing that the vegetable oil diet (comprised of a mixture of safflower oil and corn oil) is the worst of the three diets. As I mentioned, the amount of fish oil provided was extremely high -- 24-28g per day of omega-3s. With about a pound of wild salmon per day in my current diet, I'm now eating a bit more than this, so it is a reasonable amount for a diet where protein is primarily from marine sources. We are not talking about an arctic, whale-blubber diet. By the way, this paper is the reason I do not count marine fats when considering the fat content of my high-carbohydrate diet. Right now, my experimental diet contains less than 10% non-marine fat.

In 2003, Yongsoon Park and William Harris published a study (in the Journal of Lipid Research) demonstrating that n-3 fatty acid supplementation lowers triglycerides by accelerating their clearance from circulation, using an injected radio-labeled lipid emulsion to track clearance in the fasting and postprandial state. However, the study notes that fish oil supplements are also known to inhibit hepatic production of VLDL in the fasted state. I'm not sure if they inhibit DNL, or otherwise slow the release of VLDLs from the liver in the postprandial state.

Lipopolysaccharide and Postprandial Triglycerides

So enough about NEFA and inflammation in general. Lets look for some human LPS papers. There are a number of studies since 2007 showing that fat consumption and digestion allows LPS to absorb into circulation from the gut. I believe the first was by Clett Erridge et. al. ("A high fat meal induces low-grade endotoxemia: evidence of a novel mechanism of postprandial inflammation"). The peak circulating levels of LPS occurred very soon after the meal (approximately 30 mins) and the LPS was cleared very quickly thereafter, consistent with other studies showing the circulating half-life of LPS to be on the order of 5 minutes. The Erridge et. al. hypothesized that this short exposure was of a sufficient magnitude to induce an inflammatory response, which would evolve over the next few hours. They noted that baseline levels of the inflammatory cytokine TNF-a correlates with postprandial lipemia. In other words, background chronic inflammation was associated with a greater increase in triglycerides after meals. That said, these researchers did not observe an increase in TNF-a associated with the spike in LPS following the high-fat test meal. This is a bit anomalous as an LPS infusion would normally cause a rise in TNF-a. So it does not all quite hold together. Perhaps the time scale involved in the LPS-induced rise in TNF-a is too long and is more of a chronic, not postprandial, phenomenon. Erridge et. al. did not measure postprandial triglycerides, so we have to make inferences from these intermediate variables.

What happens if you just measure triglycerides after an LPS infusion?

I have only found one study measuring triglycerides after an LPS infusion in humans. It is 18 years old and has racked up a grand total of 7 citations (van der Poll et. al., Effect of hypertriglyceridemia on endotoxin responsiveness in humans, Infection and Immunity 1995). Not one of those studies was an attempt at replication. According to this study, an LPS infusion in humans resulted in no change in triglycerides at 2, 6 and 24 hours post-infusion. Meanwhile, the study participants experienced the clinical symptoms of endotoxemia, which is to say, fever and other generalized flu-like symptoms. Interestingly, the study also showed that, in contrast to its effects in animals, high triglycerides (induced by a lipid infusion) did not reduce a human's inflammatory response to LPS. Once again, humans and animals: different.

Based on this study, I do not think it is plausible that the LPS introduced into circulation by a single high-fat meal could affect the postprandial triglyceride response to that same meal. At least until someone tries to replicate van der Poll's experiment and gets a different answer.

So what about those seven studies that cited van der Poll et. al.? Two were animal studies. One was a letter to a different journal by Stephen Lowry, the senior author on van der Poll et. al. Another was a follow-up study by van der Poll that measured cytokines but not triglycerides following LPS infusion. One (Copeland et. al. 2005) exposed both mice and humans to endotoxin and measured a variety of things other than triglycerides. One (Amersfoort et. al. 2003) was a very good review of the biochemistry of sepsis and septic shock. And the last one was a not-as-thorough review published in a dentistry journal.

The two papers linked above (Amersfoort and Copeland) are worth briefly discussing. Amersfoort is a very extensive review with 620 references. The van der Poll study is among the references though it is not actually cited by the text. Amersfoort says that a number of experiments have shown that infusions of lipid emulsions or lipoproteins can reduce the effects of endotoxin, but cites 5 animal studies in support. Remember van der Poll showed that this does not happen in humans. The only findings cited that are of interest to humans in this regard are two studies by Pajkrt et. al. showing that infusions of high-density lipoproteins actually do reduce endotoxin response in humans. Very interesting, but not directly relevant to postprandial triglycerides. However, perhaps this can help explain why high HDL levels are associated with lower inflammation. High HDL is also associated with lower triglycerides, so perhaps it is chronic, as opposed to acute, response to low levels of LPS that raises triglycerides. That is, hypothetically, high HDL, lowering response to endotoxin, could possibly improve triglyceride clearance on a chronic bases.

Copeland is, in a way, a bit of a precursor to the paper that started the meat of this post (Seok et. al.), and not only because it shares several authors in common (H. Shaw Warren and Steve E. Calvano, plus the same Stephen Lowry who was senior author on van der Poll et. al. back in 1995). Copeland et. al. first calibrated a dose of endotoxin in humans in order to produce a similar response as a corresponding dose in mice. They did this by matching the levels of an anti-inflammatory cytokine, IL-6, which is released after the initial inflammatory response to endotoxin. Next, they gave this matched dose to a group of humans and a group of mice and measured a variety of physiological and biochemical phenomena. Turns out the biochemical phenomena (cytokine levels) matched extremely well. The physiological parameters (blood pressure, heart rate and body temperature) were completely different. At this point, should we be surprised?

So remember the Day endotoxemia model and its 15 parameters? 8 are estimated by the authors without reference to any studies. 4 are based on animal research only, and 3 are based, at least in part, on experimental data from humans. Now I don't mean to denigrate this work at all, but I think it is important to point out (in my lengthy fashion) how uncertain our biological understanding is.

To sum up

All of the work by Harris and others on omega-3 supplementation strongly supports the idea that inflammation is a factor in postprandial triglyceride abnormalities. That work does not distinguish between chronic and acute inflammation. Chronic inflammation could explain the phenomena via alterations in passive (diffusion) and enzyme-mediated triglyceride clearance rates. Acute inflammation could play a role, possibly via postprandial de-novo lipogenesis, which is elevated postprandially (see Timlin and Parks).

What about the higher levels of circulating LPS seen in metabolic disease? The half-life of circulating LPS is on the order of 5 minutes. Therefore, it does not seem plausible that increased absorption following meals can explain a chronic elevation in LPS, as those differences would disappear within minutes of each meal. Therefore, the elevation seems more likely to be the result of changes to the systems that regulate LPS levels. These systems are complex, as discussed by JC Marshall in his excellent paper hypothesizing that LPS may be better thought of as an exogenous hormone ("Lipopolysaccharide: An endotoxin or an exogenous hormone?", Clinical Infectious Diseases 2005). If, for example, elevated cortisol (which can be a counter-regulatory response to prolonged chronic inflammation) suppresses the immune functions that clear LPS, then we would see elevated LPS wherever we see elevated cortisol. This does not point to LPS or the microbiome as the "cause" of the chronic inflammation we observe.

So long and thanks for all the biochemistry.

So what happened to all of that wonderful biochemistry? If you throw away the stuff based on animal studies, my original LPS-mediated acute inflammation hypothesis pretty much falls to pieces. Now it is still possible that other acute inflammatory pathways not involving LPS could explain the increase in postprandial triglycerides, but at this point that seems no more likely than the other, more straightforward, hypotheses I outlined above. I'm guessing a combination of impaired clearance with an enzyme-limiting term can account for the bulk of the observations. This could be the result of chronic low-level inflammation. That said, it looks to me as if the basic science is not really there (in humans) for me to productively make headway on the problem.

So what now? I'm going to see in a couple of weeks what the high carbohydrate diet is doing to me when I get some detailed blood work. I'm also going to look askance at animal-based biochemistry studies, and the gurus who depend too heavily on them as the basis for their health and nutrition arguments.