How Do Cells Adapt? Stories Told in Landscapes

Abstract

Cells adapt to changing environments. Perturb a cell and it returns to a point of homeostasis. Perturb a population and it evolves toward a fitness peak. We review quantitative models of the forces of adaptation and their visualizations on landscapes. While some adaptations result from single mutations or few-gene effects, others are more cooperative, more delocalized in the genome, and more universal and physical. For example, homeostasis and evolution depend on protein folding and aggregation, energy and protein production, protein diffusion, molecular motor speeds and efficiencies, and protein expression levels. Models provide a way to learn about the fitness of cells and cell populations by making and testing hypotheses.

Keywords: adaptation; evolution; fitness; homeostasis; landscape.

Figure 1

Three ways a cell’s fitness is encoded in its proteins: (➊) its abundance in the cell, affected by messenger RNA (mRNA) levels; (➋) its efficacy of biological action, affected by mutations; and (➌) proteostasis, its folding and aggregation health, controlled by protein synthesis, degradation, and chaperoning.

Figure 2

Evolution is described as populations moving on landscapes. This is represented in two different ways, as a tendency toward either (a) maxima on a landscape of fitness or (b) minima on a landscape of fitness potential. They are just different ways to visualize the same process.

Figure 3

Homeostasis is a tendency toward the minimum of a potential function. (a, top) Homeostasis is maintained by a balance of two rates: synthesis (J_syn), supplying material and increasing the concentration x, and degradation (J_deg), decreasing x. The sum is the net rate of change, Δx/Δt. (a, bottom) The integrated net change rate is a potential ϕ(x). (b) After perturbation, x(t) relaxes to x₀ over time. (c) The noisy stochastic version of this relaxation is shown, for example, for few-particle systems.

Figure 4

Homeostasis dynamics and evolutionary dynamics often use similar math, but with different variables. (Top row) Gene module with two self-activating genes (x and y), mutually repressing each other (a and b are the strengths of self-activation and mutual repression, respectively; S is the minimal concentration needed to activate changes; and k is the degradation rate). (Bottom row) Allele frequency changes due to natural selection and random mutation (22) (w is the fitness of allele x, w₀ is the average fitness, and m is the mutation rate between alleles x and y).

Figure 5

Evolution happens over a large dynamic range of timescales, modeled with the simplest (linear) fitness potential (inset), V (m) = constant × m (63).

Figure 6

(a) Fitness-landscape pathways for how cells evolve under changing temperatures. Route ➊–➋ shows a (mesophilic) cell evolving to adapt to a warmer climate. Route ➌–➍ shows a (thermophilic) cell evolving to adapt to a colder climate. The thickness of the black arrows shows the adaptation speed computed from the thermal proteome unfolding model, which predicts that cells can adapt much faster to warmer climates than to colder ones (63). (b) Bacterial growth rates versus temperature. Panel b adapted with permission from Reference .

Figure 7

Proteins that are most abundant in the cell are slower to evolve; that is, they have a lower rate of amino acid substitutions. A cell’s fitness is more affected by mutating an abundant protein than by mutating a less abundant protein. There is a larger fitness cost to the cell for misfolding and aggregation, so the number of viable mutant sequences is smaller. The model predicts the roles of misfolding (red line) and of aggregation (blue line) for this anticorrelation between the evolution rate (given by the percentage sequence difference between orthologous proteins of related species) and abundance (measured by relative microRNA concentration) (63).

Figure 8

The hospital model of proteostasis in bacteria. (a) The gray lane represents the pathway of protein folding, misfolding, and aggregation without chaperones. The other arrows show the proteostasis trafficking through different chaperones. (b) Hospital model predictions of proteostasis flows for a class II protein (mildly misfolded) indicate that it traffics mainly through the DnaK system. Heavy arrows show the main flux. (c) Hospital model predictions of proteostasis flows for a class III protein (strongly misfolded) indicate that it traffics mainly through the GroEl system.

Figure 9

Adding external salt shrivels a cell osmotically, which increases internal protein crowding and slows protein diffusion, thus slowing cell growth. In the protein transport rate model, added salt in the surroundings (f_p; horizontal axis) reduces the cell growth rate (vertical axis) by densifying the proteins inside and slowing their diffusional transport (68).

Figure 10

Bacteria trade off producing ribosomes versus nonribosomal proteins. This trade-off maximizes energy efficiency. (a) In the ribosomal upswitch model, J_ATP is the rate of converting glucose to the nucleoside triphosphates, J_ribo is the production rate of ribosomal proteins, and J_prot is the production rate of nonribosomal proteins. These relative flows are determined by the abundance of glucose. (b) In the predicted fitness landscape, the fast-growth energy efficiency is maximized when the fraction of nonribosomal proteins is about 75% (83).

Figure 11

Fitness landscapes for (a) molecular motors and (b) ion pumps. A simple model asserts a fitness function for biomolecular machines of power output per unit energy input. Panel a shows that five different motors (red circles) appear to optimize their output work (for a given input chemical potential from ATP degradation) by how the rate barriers are distributed through the kinetic cycle. Panel b shows the same for six different ion pumps (red circles). The inset shows a diagram of the F₀F₁ ATPase motor. Figure adapted with permission from Reference .

Figure 12

Experimental cell fitness landscapes in systematically controlled environments. (a) Producing excess protein (LacZ) reduces cellular fitness. The blue dots and line represent the fitness in the absence of the inducer isopropyl β-d-1-thiogalactopyranoside (IPTG), and the purple dots and line correspond to the environment with 1 mM IPTG. The red dot is a control strain with a deleted lacY gene in the presence of IPTG (89). (b) Increasing the concentration of an antibiotic drug in the medium diminishes bacterial fitness nonlinearly. Drug-resistant cells are more tolerant, but they are also more sharply inhibited at high drug concentrations. Drug resistance is measured by the activity of the the chloramphenicol-resistance enzyme chloramphenicol acetyltransferase. Lines of different colors represent the shape of the fitness landscape at fixed values of drug resistance. Panel b adapted with permission from Reference . (c) In fluctuating environments, cells evolve across a fitness moat to reach higher fitness in those complex environments. The variable E₀ is the expression level of an operon affecting the growth rate in the absence of IPTG; the colored dots represent different stages of adaptation to reach the optimal fitness, progressing from green, to blue, to gray, to red. Panel c adapted with permission from Reference .

Figure 13

Population fitness landscape as a function of environmental factors. Each point on this landscape is the exponential growth rate of a yeast cell population for a given (antibiotic drug, drug resistance) combination. Experimentally measured values are indicated as colored dots. Abbreviations: atc, anhydrotetracycline; zeo, Zeocin.

Figure 14

The Goldilocks balance that leads to a just-right level of protein: not too much and not too little. Population fitness is the result of some microscopic factors: cellular fitness and gene expression. For a given cellular fitness landscape (colored shading), cellular gene expression (black histograms) can be either unimodal (overlaid with the green fitness landscape) or bimodal (overlaid with the blue and orange fitness landscapes). Each point on the macroscopic population fitness landscape (colored dots) results from weighted averaging of cellular fitness values over the corresponding gene expression distribution. Cellular fitness landscapes predict the evolution of gene expression changes: In constant environments, cells evolve toward unimodal gene expression located at the peak of each cellular fitness landscape. Abbreviations: dox, doxycycline; zeo, Zeocin.

Figure 15

(a) Illustrating the Red Queen idea. Predator chases prey, and neither increases its own individual fitness in the evolutionary chase. (b) Illustrating the curl-flux principle. The population flow on a landscape is not directly down the gradient of a potential function; it also swirls if the system has an out-of-equilibrium driving force.

Figure 16

The Waddington landscape and the new curl-flux-based understanding of it. The stem cell state is represented by the valley at the top of the landscape. The differentiated state is represented by the two valleys at the bottom. Metaphorically, Waddington differentiation is like a ball rolling from the top valley to the bottom ones. Two transcription factors can self-activate, other-repress, or degrade. The stem state is strong for self-activation (top right); the differentiated state is strong for repression (bottom right). What is new is our recent understanding of the curl-flux dynamics, showing how the stem cell state is also stable, why reprogramming is difficult, and how differentiation requires induction and is not just caused by spontaneous fluctuation (19). The full dynamical model shows that the stem cell state is stable, not unstable as in Waddington’s static landscape. It shows that the reprogramming path is uphill. The dynamics model shows that the reprogramming path is not identical to the differentiation path. In the static model, the stem cell state (the hill) is not stable, so a small perturbation would allow spontaneous differentiation.