We might imagine lipolysis as a matter of supply. Your adipocytes should be liberating fatty acids to support direct use and to support ketogenesis in ketosis, unless insulin tells them otherwise. Thinking about this in terms of how we keep the supply flowing leads one to realizing that a hypoinsulinemic state is probably required in order to be losing weight; you need at least periods of low insulin so that fat can continue to be liberated for use. This leads to thinking that you have to be ketotic to lead weight, which isn't true; fat oxidation occurs outside of ketosis, too, and use of fat for energy doesn't require conversion into ketone bodies. Ketones, perhaps, just make the fat more available to more cells. Assuming there's enough of it.
Thinking about insulin as a lever makes it seem like the system is either on or off: you're either in energy-storing mode or you're in energy-liberating mode. The wrinkles that emerge there include those of insulin sensitivity. You can have adipocytes which are locally overfat, or in a globally overfat system, which basically stop responding to the anabolic signal, and make fat available at all times. Moving from that state to ketosis, maybe even to fasting, would clearly be useful. The energy refuses to be stored, so you need to make sure it can be burned.
The body, too, has levers to make more fat available when there isn't enough. Just as glucagon can tell the liver that it should make glucose in a demand-driven way, the body has signalling molecules to make more fat flow, chiefly catecholamines. Now, I'm obviously a pretty lousy biochemist, but broadly, catecholamines are stimulating and drive adaptation to stress. That's not a bad thing, but, for instance, those who break them down slowly (slow COMT) or those who already have a background level of elevated stress hormones (chronic stress), extra catecholamines can mean moving more readily from stress to distress. In insufficiency, we are lethargic, depressed, and unable to meet the demands of living, and in excess, we might well be anxious, the bad kind of restless, and maybe even sleepless. Hypoarousal at one extreme, hyperarousal at the other.
The leaky fat cells of the overfat and insulin resistant individual don't require catecholamines to feed the fat needs of a ketogenic diet: fat is already abundant. This may be one of the reasons for the effect whereby people say that keto works "the first time" and not afterwards. Whether because of adipogenesis or because of becoming more insulin sensitive, they might have to actually get much fatter to see ketosis as easy and as deep as they do on the first go 'round.
Different individuals may have different degrees of difficulty, but we can imagine a state in which an individual's fat cells aren't really engaged in that much lipolysis, and where it takes more signalling in order to get them to give up some fatty acids to support ketosis. It's easy to imagine that state as multiply distressing. You might be hypoketotic hypoglycemic, and experiencing total energy shortage. You might find that you have to find a way to eat a lot of fat in order to support ketosis. You might end up swimming in catecholamines. Add in the rise of cortisol with the dawn effect and the concomitant rise in gluconeogenesis and insulin, and you might begin your day feeling miserable, and gradually move towards anxiety.
We aren't quite so helplessly subject to the whims of our endocrinology, we can participate in the hormonal dialogue through the foods we consume. Food is full of signalling molecules that tell our bodies about the kinds of energy available to us and how we should probably use them. This may be a time of plenty or a time of starvation. This may be a time where we need energy, or a time where we need to hibernate. We may need the capacity to eat more, or the ability to fast.
It seems like one such signal might be calcium consumption. Much as the hypothetical process by which potassium intake seems to promote satiety, calcium seems to be active in fuel partitioning and in particular in promoting lipolysis. This is, in fact, fairly settled science, and has been for a long time. That paper is from twenty years ago. Calcium activates pathways to lipolysis that do not involve the release and global effects of catecholamines. Increased lipolysis, fatty acids available for direct oxidation and for building ketones, without the body needing to signal that more fat liberation is needed in a way that might create distress for the overall organism.
A lot of folks take calcium and magnesium supplements together for the anxiolytic effects of magnesium by supporting COMT function to break down catecholamines, but especially if they're healthy (or getting healthier) on a ketogenic diet, they may also be getting an indirect effect from the calcium they consume. Intake of calcium may not directly have an anxiolytic effect, but by promoting lipolysis, it may prevent the need for the body to swim in catecholamines like norepinephrine due to inadequate fatty acid availability, particularly in fasted states.
The potato diet gestures towards the potential utility of potassium as a tool to support weight loss, and these mechanistic insights suggest that calcium may also have an important place. Particularly in people who are doing a ketogenic diet whose fat cells aren't dysregulated, it may be important to be able to support access to fatty acids without stress and distress. It's ironic that dairy is such a barrier to weight loss for so many, and yet dairy is balanced in both elements supporting anabolism (particularly the carbohydrate-like insulinotropic effects of whey protein) and catabolism (with saturated fats and calcium.) For as much as it is hyperphagic, cheese might actually be a useful source of catabolic signals through the removal of whey, although it seems likely that direct calcium supplementation could be even more effective.
While the mechanisms and effects of calcium influencing lipolysis from adipocytes are well known, there are a lot of potential links, from hypoketotic states to anxiety during weight loss on ketogenic diets, which seem currently to be under-explored.
(Could this mean high-calcium dairy is a more helpful addition to the potato diet than low-calcium dairy? How much does vitamin D deficiency play into the broad impacts of calcium flux here? Indeed, high vitamin D in the presence of inadequate calcium can be anxiogenic itself as the need for calcium is signalled, which also seems to inhibit lipolysis in adipocytes. Will the body ever drive the parathyroid to liberate calcium from bones to support lipolysis? That would be pretty extreme. It seems worth noting that some who shun dairy also extol bone broth, which if cooked for sufficiently long, also could be a valuable calcium source.
Note, too, that there are drugs which specifically target beta-3 adrenergic receptors and seem to promote lipolysis in a similar way, while also exhibiting anxiolytic effects. Mirabegron, for instance, can be used in combination with metformin (which promotes fat oxidation) to drive weight loss. Amibegron is sometimes prescribed as an anxiolytic. Are the levers we can pull to promote lipolysis without catecholamines themselves anxiolytic, or is it just preventing the anxiogenesis of catecholamines used to signal the need for lipolysis?)