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With adequ. protein and nutrients "crash"- beats "low and steady" -dieting. In the obese that's almost certain, in athletes more experimental evidence are needed.

You will have heard and read that rapid weight loss will make you lose muscle and set you up for weight regain aka the "Yo-Yo effect". As a waredownloadsoft reader, you know that things are not as simple as that. While some studies appear to support this urban myth others suggest that the exact opposite may be the case.

A 2014 study by Purcell, Sumithran, and Prendergast that was published in the venerable scientific journal The Lancet for example, showed that rapid weight loss on a very low calorie diet leads to better long-term outcomes than gradual weight loss on a much less restricted diet.
That's a results of which I feel that it is important enough to re-address ii in its own waredownloadsoft article. After all, the "slow and steady" advise is still ubiquitous, both in the mainstream and in the health and fitness community. In said study, Purcell et al.

"aimed to investigate whether the rate of weight loss affects the rate of regain, and whether weight lossinduced changes in circulating appetite-mediating hormones and subjective appetite are affected by the rate of weight loss" (Purcell. 2012).

To this end, the researchers from the University of Melbourne conducted a two-phase, non-masked, randomized controlled trial. The study participants were recruited through radio and newspaper advertisements and word of mouth in Melbourne, Australia.

• Inclusion criteria were healthy men and women aged between 18–70 years who were weight stable for 3 months and had a BMI between 30.0–45.0kg/m². 
• Exclusion criteria included use of a very low energy diet or weight loss drugs in the previous 3 months, contraceptive use, pregnancy or lactation, smoking, current use of drugs known to affect body weight, previous weight loss surgery, and the presence of clinically significant disease (including diabetes).

Eligible participants were randomized into 2 different weight loss programs — a 12-week rapid program or a 36-week gradual program —using a computer-generated randomization sequence with a block design to account for the potential confounding factors of age, sex, and body mass index (BMI). Investigators and laboratory staff were blind to the group assignments.

Figure 1: Overview of the study design (Purcell. 2014)

Both, the subjects on the rapid and the gradual weight loss program had the same simple goal: "Reduce your body weight by at least 12.5%." The way the subjects were supposed to achieve this weight loss was yet completely different. For phase 1 of the study (until 12.5% weight loss), the following interventions were prescribed:

• Better ZERO than Some Food? Study Suggest Just That! Learn more.

  Rapid weight loss: Participants in the rapid weight loss group replaced 3 meals a day with a commercially available meal replacement (Optifast, Nestlé Nutrition) over a period of 12 weeks (450–800 kcal/day). 
• Gradual weight loss: Participants in the gradual group replaced 1 to 2 meals daily with the same supplements and followed a diet program based on recommendations from the Australian Guide to Healthy Eating for the other meals over a period of 36 weeks (400–500 kcal deficit per day).

Both groups were given comparable dietary education materials and had appointments every 2 weeks with the same dietician. Participants who achieved 12.5% or greater weight loss were eligible for phase 2. In phase 2, participants met with their same dietician at weeks 4 and 12, and then every 12 weeks until week 144. During appointments, the dietician assessed adherence based on participants' self-reported food intake, and participants were encouraged to partake in 30 minutes of physical activity of mild to moderate intensity. Participants who gained weight were told to reduce their energy intake by 400–500 kcal in order to get back on the weight loss track.
To assess the success of the diets, the scientists used the mean weight loss that was maintained at week 144 of phase 2 (primary outcome), the mean difference in fasting ghrelin and leptin concentrations measured at baseline, end of phase 1 (week 12 for rapid and week 36 for gradual), and at weeks 48 and 144 of phase 2, as well as the overall changes in weight, BMI, waist and hip circumferences, fat mass, fat free mass, ghrelin, leptin, and physical activity (secondary outcomes).

Figure 2: Percent of participants achieving the weight loss target in phase 1 completers (left) and all subjects including the losers who didn't complete the full study - that the right figure shows even greater differences actually supports the superiority of the rapid vs. gradual weight loss regimen (p = 0.0001 | Purcell. 2015)

The overall message of the results was clear, the "rate of weight loss does not affect the proportion of weight regained within 144 weeks" (Purcell. 2014). The same goes for the implication that "[t]hese findings are not consistent with present dietary guidelines which recommend gradual over rapid weight loss, based on the belief that rapid weight loss is more quickly regained" (ibid).

Figure 3: Relative changes in measures body composition (left) and activity from pre- to follow up (Purcell. 2015).

But this wouldn't be the waredownloadsoft if we didn't go beyond the mere averages for the main study outcomes. So, let's take a look at the actual changes from the pretest to the follow up in Figure 3. What do you see? Yes, the rapid weight loss group had better (albeit not significantly better) results in everything and that despite the fact that they didn't increase their physical activity (see Figure 2, right). So let's not forget that this information that's missing from the abstract, when we're discussing the "bottom line" to this article in the following paragraphs.
References:

• Bistrian, B. R., and Mindy Sherman. "Results of the treatment of obesity with a protein-sparing modified fast." International journal of obesity 2.2 (1977): 143-148.
• Garthe, Ina, et al. "Effect of two different weight-loss rates on body composition and strength and power-related performance in elite athletes." International journal of sport nutrition and exercise metabolism 21 (2011): 97-104.
• Iselin, Hans U., and Peter Burckhardt. "Balanced hypocaloric diet versus protein-sparing modified fast in the treatment of obesity: a comparative study." International journal of obesity (1982).
• Martin, Corby K., et al. "Empirical evaluation of the ability to learn a calorie counting system and estimate portion size and food intake." British Journal of Nutrition 98.2 (2007): 439-444.
• Martin, Corby K., and Kishore M. Gadde. "Weight loss: slow and steady does not win the race." The Lancet Diabetes & Endocrinology 2.12 (2014): 927-928.
• Mero, Antti A., et al. "Moderate energy restriction with high protein diet results in healthier outcome in women." J Int Soc Sports Nutr 7.4 (2010): 1-11.
• Nackers, Lisa M., Kathryn M. Ross, and Michael G. Perri. "The association between rate of initial weight loss and long-term success in obesity treatment: does slow and steady win the race?." International journal of behavioral medicine 17.3 (2010): 161-167.
• Purcell, Katrina, et al. "The effect of rate of weight loss on long-term weight management: a randomised controlled trial." The Lancet Diabetes & Endocrinology 2.12 (2014): 954-962.
• Rolls, Barbara J., P. M. Van Duijvenvoorde, and Edmund T. Rolls. "Pleasantness changes and food intake in a varied four-course meal." Appetite 5.4 (1984): 337-348.

You don't need supplemental K, well... unless you are on a protein modified fast without fruits and veggies ;-)

The 1984 study by Norbiato et al. is not a very recent, but it's probably a very important study which was set up to investigate "the role of potassium deficiency in the development of glucose intolerance during caloric deprivation" (Norbiato. 1984).

Or, put simly, the scientists wanted to know if a low potassium level may promote insulin resistance and modify or is modified in response to dieting (in this case protein-modified fasting). In the study, two groups of subjects were studied. The "normal" group consisted of ten subjects, who were 27-45 years old and whose body weights ranged from 89 to 115% of the "ideal body weight". The "obese" group group consisted of twenty subjects aged 21-48 years who were 70%-131% overweight.
Before the obese subjects were put on a protein modified fast (PMF) all subjects, lean or obese, received a "weight-maintaining diet" with 200g/day carbohydrates for 8 days.

Figure 1: Macronutrient composition of the ~380kcal PMF diet (Norbiato. 1984).

"The diets were calculated according to individual tastes, employing varying proportions of egg white, beef tenderloin, skim-milk cheese and water-packed canned tuna. For the PMF, total calories varied from a mean of 350-399 in individual subjects, with a mean of 378+/-36 (SD) 

[...] Calculated protein intakes, according to standard tables, were 70.8+/-7.6 g/day (about 79% of calories). Calculated fat intake was 5.7+/-3.5 g /day (19% of calories). Carbohydrate contributed 3.2+/-1.3 g/day, 2% of caloric input" (Norbiato. 1984).

As far as its potassium content is concerned the PMF diet was (as probably most diets that are almost exclusively protein) on the skinny side (15 +/- 3.9 mmol of potassium/day | adult men and women should get 100mmol/day and 72mmol/day, that's 3,800mg and 2,800mg/day or 8-9 bananas if you want to "go bananas" instead of leafy greens ;-). Nevertheless, only 10 out of 20 of the obese subjects received an oral potassium chloride (64 mmol/day) supplement (KC1-retard, Zyma, Italy). The other ten patients received identical placebo tablets.
Interestingly, the potassium levels dropped in both groups during fasting. More importantly, though, the decrease in potassium was associated with a sign. reduction in peripheral levels of insulin along with an increase in insulin receptors and a striking reduction of peripheral glucose utilization in the obese subjects on their protein modified fast.

Figure 2: Mean integrated area under the glucose tolerance test curve in obese subjects submitted to protein-modified fast (PMF) with or without oral KCl supplementation (K): studies were performed in the control period after a 14-day fast and after after 10 days of refeeding with a diet containing 700 kcal (45% carbohydrate) per day (Norbiato. 1984).

Increase in insulin receptor binding and impaired glucose management? How does this go together? Well, if the receptor does not respond, it is no wonder that the researchers found that their subjects ability to handle glucose was significantly impaired in the euglycaemic clamp study.
References:

• Norbiato, Guido, et al. "Effects of potassium supplementation on insulin binding and insulin action in human obesity: protein‐modified fast and refeeding." European journal of clinical investigation 14.6 (1984): 414-419.
• Rowe, John W., et al. "Effect of experimental potassium deficiency on glucose and insulin metabolism." Metabolism 29.6 (1980): 498-502.