Gabriel L. Salmon

Biological processes, from molecules diffusing to their regulatory destinations to whales pursuing food or mates, are widely exploratory. Such behaviors are effective when some verifiable functional state or outcome can be reached regardless of initial conditions. In these cases, systems repeatedly undergo distinct and abortive trajectories; the process only ends when the system finds “right” outcomes. This dominance of the terminal condition (and indifference to the initial state) provokes a very different perspective than the conventional “dynamical systems” framework that has been a centerpiece of the quantitative sciences for centuries. We hypothesize that many of these problems defy the initial-condition driven or gradients on landscapes so useful in problems ranging from mechanics to electrodynamics to chemical kinetics to mass and heat transport. We examine several mathematical frameworks that capture and unify key aspects of exploratory dynamics. One powerful way of thinking of such processes is the geometric distribution, where repeated failures are punctuated by a successful trajectory. We develop intuitions for how random walks with resets accelerate search processes. We highlight fresh and surprising behaviors of search under drift, cues, and checkpoints. Last, appreciating the probability of trajectories conditioned on satisfying macroscopic final outcomes reveals a language for the potency of variation sculpted by selection in their broadest forms. This can give the fictitious appearance of the future making itself known in the present, but we view this as conceptually similar to the way “fictitious forces” arise in non-inertial reference frames. These approaches stress unity, open questions, and applications across a range of biological phenomena.

Living matter produces a variety of beautiful spatiotemporal structures and patterns that are not enduringly present in their nonliving counterparts. These ordered, non-equilibrium steady states are often sustained through the consumption of energy. Here, we investigate the energetic cost of assembling an ordered aster from an initially disordered, uniform mixture of cytoskeletal microtubules and kinesin motors. Using a calibrated fluorescent ATP reporter, we measure reproducible radial ATP gradients on scales of tens of microns that establish within, and persist over, tens of minutes, alongside coupled spatial gradients in motor density. These appreciable gradients are predicted by a reaction-diffusion model that acknowledges the localization of ATP consumption to regions where both molecular motors and microtubules are sufficiently abundant to encourage consumption, as confirmed by finite element modeling. With our results, we compare the power per volume required by our cytoskeletal networks with the known power per volume expenditure in cells. Comparison of our measured results with estimates of the dissipative processes available to motor-microtubule mixtures leads to the hypothesis that maintaining spatial motor gradients dominates the energetic demand in this system. Our direct quantification of energetic fluxes across space unlocks future explorations of what steady states are accessible to cells, and how the cytoskeleton drives broad spatial organization. Significance: How much energy do organisms pay to form and maintain their organizing biochemical patterns? Existing measurements of cellular metabolism and energy expenditures largely resolve net or supply-side biochemical fluxes, without spatial information, impeding the study of this basic question. Here, we develop an experimental approach to directly measure the distributions of biochemical energy that respond to power expenditures of cytoskeletal motor-microtubule networks as they form aster structures, reminiscent of those found in the mitotic spindle. As these structures self-assemble, calibrated readouts in real molecular units register large, reproducible, and long-lived gradients of ATP. We interpret these measurements by developing theory to account for the functional destinies of energy expenditure. These advances clarify outstanding questions of energy in living matter.

Many biological processes can be thought of as the result of an underlying dynamics in which the system repeatedly undergoes distinct and abortive trajectories with the dynamical process only ending when some specific process, purpose, structure or function is achieved. A classic example is the way in which microtubules attach to kinetochores as a prerequisite for chromosome segregation and cell division. In this example, the dynamics is characterized by apparently futile time histories in which microtubules repeatedly grow and shrink without chromosomal attachment. We hypothesize that for biological processes for which it is not the initial conditions that matter, but rather the final state, this kind of exploratory dynamics is biology’s unique and necessary solution to achieving these functions with high fidelity. This kind of cause and effect relationship can be contrasted to examples from physics and chemistry where the initial conditions determine the outcome. In this paper, we examine the similarities of many biological processes that depend upon random trajectories starting from the initial state and the selection of subsets of these trajectories to achieve some desired functional final state. We begin by reviewing the long history of the principles of dynamics, first in the context of physics, and then in the context of the study of life. These ideas are then stacked up against the broad categories of biological phenomenology that exhibit exploratory dynamics. We then build on earlier work by making a quantitative examination of a succession of increasingly sophisticated models for exploratory dynamics, all of which share the common feature of being a series of repeated trials that ultimately end in a “winning” trajectory. We also explore the ways in which microscopic parameters can be tuned to alter exploratory dynamics as well as the energetic burden of performing such processes. Outlook It is a great privilege to take part in this special volume dedicated to the life and work of Prof. Erich Sackmann (1934-2024). For one of us (RP), at the time of making a switch from traditional condensed matter physics to a life engaged in the study of life, he went to a meeting near Munich which completely opened his eyes to the ways in which the approach of physics could be brought to bear on the study of the living. Sackmann’s work was an inspiring presence at that meeting. One of the hallmarks of his work was a principled approach to dissecting biological processes over a range of scales and phenomena. One common thread to much of his work was that it acknowledged the dynamical character of living organisms. The present paper attempts to follow in the tradition of Sackmann’s studies of dynamics by suggesting a new way of looking at many biological processes all through the unifying perspective of what we will call exploratory dynamics.

Many biological processes can be thought of as the result of an underlying dynamics in which the system repeatedly undergoes distinct and abortive trajectories with the dynamical process only ending when some specific process, purpose, structure or function is achieved. A classic example is the way in which microtubules attach to kinetochores as a prerequisite for chromosome segregation and cell division. In this example, the dynamics is characterized by apparently futile time histories in which microtubules repeatedly grow and shrink without chromosomal attachment. We hypothesize that for biological processes for which it is not the initial conditions that matter, but rather the final state, this kind of exploratory dynamics is biology's unique and necessary solution to achieving these functions with high fidelity. This kind of cause and effect relationship can be contrasted to examples from physics and chemistry where the initial conditions determine the outcome. In this paper, we examine the similarities of many biological processes that depend upon random trajectories starting from the initial state and the selection of subsets of these trajectories to achieve some desired functional final state. We begin by reviewing the long history of the principles of dynamics, first in the context of physics, and then in the context of the study of life. These ideas are then stacked against the broad categories of biological phenomenology that exhibit exploratory dynamics. We then build on earlier work by making a quantitative examination of a succession of increasingly sophisticated models for exploratory dynamics, all of which share the common feature of being a series of repeated trials that ultimately end in a "winning" trajectory. We also explore the ways in which microscopic parameters can be tuned to alter exploratory dynamics as well as the energetic burden of performing such processes.

Cells adapt to environments and tune gene expression by controlling the concentrations of proteins and their kinetics in regulatory networks. In both eukaryotes and prokaryotes, experiments and theory increasingly attest that these networks can and do consume biochemical energy. How does this dissipation enable cellular behaviors forbidden in equilibrium? This open question demands quantitative models that transcend thermodynamic equilibrium. Here, we study the control of simple, ubiquitous gene regulatory networks to explore the consequences of departing equilibrium in transcription. Employing graph theory to model a set of especially common regulatory motifs, we find that dissipation unlocks nonmonotonicity and enhanced sensitivity of gene expression with respect to a transcription factor’s concentration. These features allow a single transcription factor to act as both a repressor and activator at different concentrations or achieve outputs with multiple concentration regimes of locally enhanced sensitivity. We systematically dissect how energetically driving individual transitions within regulatory networks, or pairs of transitions, generates a wide range of more adjustable and sensitive phenotypic responses than in equilibrium. These results generalize to more complex regulatory scenarios, including combinatorial control by multiple transcription factors, which we relate and often find collapse to simple mathematical behaviors. Our findings quantify necessary conditions and detectable consequences of energy expenditure. These richer mathematical behaviors—feasibly accessed using biological energy budgets and rates—may empower cells to accomplish sophisticated regulation with simpler architectures than those required at equilibrium.

Cells adapt to environments and tune gene expression by controlling the concentrations of proteins and their kinetics in regulatory networks. In both eukaryotes and prokaryotes, experiments and theory increasingly attest that these networks can and do consume bio-chemical energy. How does this dissipation enable cellular behaviors unobtainable in equilibrium? This open question demands quantitative models that transcend thermodynamic equilibrium. Here we study the control of a simple, ubiquitous gene regulatory motif to explore the consequences of departing equilibrium in kinetic cycles. Employing graph theory, we find that dissipation unlocks nonmonotonicity and enhanced sensitivity of gene expression with respect to a transcription factor’s concentration. These features allow a single transcription factor to act as both a repressor and activator at different levels or achieve outputs with multiple concentration regions of locally-enhanced sensitivity. We systematically dissect how energetically-driving individual transitions within regulatory networks, or pairs of transitions, generates more adjustable and sensitive phenotypic responses. Our findings quantify necessary conditions and detectable consequences of energy expenditure. These richer mathematical behaviors—feasibly accessed using biological energy budgets and rates—may empower cells to accomplish sophisticated regulation with simpler architectures than those required at equilibrium. Significance Statement: Growing theoretical and experimental evidence demonstrates that cells can (and do) spend biochemical energy while regulating their genes. Here we explore the impact of departing from equilibrium in simple regulatory cycles, and learn that beyond increasing sensitivity, dissipation can unlock more flexible input-output behaviors that are otherwise forbidden without spending energy. These more complex behaviors could enable cells to perform more sophisticated functions using simpler systems than those needed at equilibrium.

Two biological activities of butyrate in the colon (suppression of proliferation of colonic epithelial stem cells and inflammation) correlate with inhibition of the activity of histone deacetylases. Cellular and biochemical studies of molecules similar in structure to butyrate, but different in molecular details (functional groups, chain-length, deuteration, oxidation level, fluorination, or degree of unsaturation), demonstrated that these activities were sensitive to molecular structure, and were compatible with the hypothesis that butyrate acts by binding to the Zn²⁺ in the catalytic site of histone deacetylases. Structure–activity relationships drawn from a set of 36 compounds offer a starting point for the design of new compounds targeting the inhibition of histone deacetylases. The observation that butyrate was more potent than other short-chain fatty acids is compatible with the hypothesis that crypts evolved (at least in part), to separate stem cells at the base of crypts from butyrate produced by commensal bacteria.

Separation of nucleic acids has long served as a central goal of analytical research. Innovations in this field may soon enable the development of rapid, on-site sequencing devices that significantly improve both the availability and accuracy of detailed bioinformatics. However, achieving efficient continuous-flow operation and size-based fractionation of DNA still presents considerable challenges. Current methods have not yet satisfied the need for rapid fractionation of size-heterogeneous nucleic acid samples into specific and narrow size distributions. Dielectrophoretic (DEP) mechanisms integrated in microfluidic devices offer unique advantages for such applications, including short processing times, microscale reaction volumes, and the potential for low cost and portability. To facilitate such developments, we have adapted a microfluidic constriction sorter device to separate a wide range of nucleic acid analytes into distinct microchannel outlets. This work demonstrates selective and tunable deflection of DNA using alternating current (AC) insulator-based dielectrophoresis. We report conditions for size-based DEP sorting of 1.0, 10.2, 19.5, and 48.5 kbp dsDNA analytes, including both plasmid and genomic DNA. Applied potentials range from 200 to 2400 V_pp with frequencies ranging from 50 Hz to 20 kHz. These conditions result in sorting efficiencies up to 92% with a strong dependence on applied potentials and frequencies. In low-frequency AC fields, long DNA molecules form macro-ion clusters. This behavior is associated with an apparent shift from positive to negative DEP sorting behavior. Using a finite element model, we characterize the dynamics of sorting in the microdevice and link differential sorting to differences in dielectrophoretic mobility. We propose the use of a continuous-flow sorting strategy to facilitate future coupling to next generation sequencing approaches.