Information Integration and Energy Expenditure in Gene Regulation.

The quantitative concepts used to reason about gene regulation largely derive from bacterial studies. We show that this bacterial paradigm cannot explain the sharp expression of a canonical developmental gene in response to a regulating transcription factor (TF). In the absence of energy expenditure, with regulatory DNA at thermodynamic equilibrium, information integration across multiple TF binding sites can generate the required sharpness, but with strong constraints on the resultant "higher-order cooperativities." Even with such integration, there is a "Hopfield barrier" to sharpness; for n TF binding sites, this barrier is represented by the Hill function with the Hill coefficient n. If, however, energy is expended to maintain regulatory DNA away from thermodynamic equilibrium, as in kinetic proofreading, this barrier can be breached and greater sharpness achieved. Our approach is grounded in fundamental physics, leads to testable experimental predictions, and suggests how a quantitative paradigm for eukaryotic gene regulation can be formulated.

The Hill function is the universal Hopfield barrier for sharpness of input-output responses.

The Hill functions, [Formula: see text], have been widely used in biology for over a century but, with the exception of [Formula: see text], they have had no justification other than as a convenient fit to empirical data. Here, we show that they are the universal limit for the sharpness of any input-output response arising from a Markov process model at thermodynamic equilibrium. Models may represent arbitrary molecular complexity, with multiple ligands, internal states, conformations, coregulators, etc, under core assumptions that are detailed in the paper. The model output may be any linear combination of steady-state probabilities, with components other than the chosen input ligand held constant. This formulation generalizes most of the responses in the literature. We use a coarse-graining method in the graph-theoretic linear framework to show that two sharpness measures for input-output responses fall within an effectively bounded region of the positive quadrant, [Formula: see text], for any equilibrium model with [Formula: see text] input binding sites. [Formula: see text] exhibits a cusp which approaches, but never exceeds, the sharpness of [Formula: see text], but the region and the cusp can be exceeded when models are taken away from thermodynamic equilibrium. Such fundamental thermodynamic limits are called Hopfield barriers, and our results provide a biophysical justification for the Hill functions as the universal Hopfield barriers for sharpness. Our results also introduce an object, [Formula: see text], whose structure may be of mathematical interest, and suggest the importance of characterizing Hopfield barriers for other forms of cellular information processing.

MSModDetector: a tool for detecting mass shifts and post-translational modifications in individual ion mass spectrometry data.

MOTIVATION: Post-translational modifications (PTMs) on proteins regulate protein structures and functions. A single protein molecule can possess multiple modification sites that can accommodate various PTM types, leading to a variety of different patterns, or combinations of PTMs, on that protein. Different PTM patterns can give rise to distinct biological functions. To facilitate the study of multiple PTMs on the same protein molecule, top-down mass spectrometry (MS) has proven to be a useful tool to measure the mass of intact proteins, thereby enabling even PTMs at distant sites to be assigned to the same protein molecule and allowing determination of how many PTMs are attached to a single protein. RESULTS: We developed a Python module called MSModDetector that studies PTM patterns from individual ion mass spectrometry (I2MS) data. I2MS is an intact protein mass spectrometry approach that generates true mass spectra without the need to infer charge states. The algorithm first detects and quantifies mass shifts for a protein of interest and subsequently infers potential PTM patterns using linear programming. The algorithm is evaluated on simulated I2MS data and experimental I2MS data for the tumor suppressor protein p53. We show that MSModDetector is a useful tool for comparing a protein's PTM pattern landscape across different conditions. An improved analysis of PTM patterns will enable a deeper understanding of PTM-regulated cellular processes. AVAILABILITY AND IMPLEMENTATION: The source code is available at https://github.com/marjanfaizi/MSModDetector.

Thermodynamic bounds on ultrasensitivity in covalent switching.

Switch-like motifs are among the basic building blocks of biochemical networks. A common motif that can serve as an ultrasensitive switch consists of two enzymes acting antagonistically on a substrate, one making and the other removing a covalent modification. To work as a switch, such covalent modification cycles must be held out of thermodynamic equilibrium by continuous expenditure of energy. Here, we exploit the linear framework for timescale separation to establish tight bounds on the performance of any covalent-modification switch in terms of the chemical potential difference driving the cycle. The bounds apply to arbitrary enzyme mechanisms, not just Michaelis-Menten, with arbitrary rate constants and thereby reflect fundamental physical constraints on covalent switching.

Robustness and parameter geography in post-translational modification systems.

Biological systems are acknowledged to be robust to perturbations but a rigorous understanding of this has been elusive. In a mathematical model, perturbations often exert their effect through parameters, so sizes and shapes of parametric regions offer an integrated global estimate of robustness. Here, we explore this "parameter geography" for bistability in post-translational modification (PTM) systems. We use the previously developed "linear framework" for timescale separation to describe the steady-states of a two-site PTM system as the solutions of two polynomial equations in two variables, with eight non-dimensional parameters. Importantly, this approach allows us to accommodate enzyme mechanisms of arbitrary complexity beyond the conventional Michaelis-Menten scheme, which unrealistically forbids product rebinding. We further use the numerical algebraic geometry tools Bertini, Paramotopy, and alphaCertified to statistically assess the solutions to these equations at ∼109 parameter points in total. Subject to sampling limitations, we find no bistability when substrate amount is below a threshold relative to enzyme amounts. As substrate increases, the bistable region acquires 8-dimensional volume which increases in an apparently monotonic and sigmoidal manner towards saturation. The region remains connected but not convex, albeit with a high visibility ratio. Surprisingly, the saturating bistable region occupies a much smaller proportion of the sampling domain under mechanistic assumptions more realistic than the Michaelis-Menten scheme. We find that bistability is compromised by product rebinding and that unrealistic assumptions on enzyme mechanisms have obscured its parametric rarity. The apparent monotonic increase in volume of the bistable region remains perplexing because the region itself does not grow monotonically: parameter points can move back and forth between monostability and bistability. We suggest mathematical conjectures and questions arising from these findings. Advances in theory and software now permit insights into parameter geography to be uncovered by high-dimensional, data-centric analysis.

Structural conditions on complex networks for the Michaelis-Menten input-output response.

The Michaelis-Menten (MM) fundamental formula describes how the rate of enzyme catalysis depends on substrate concentration. The familiar hyperbolic relationship was derived by timescale separation for a network of three reactions. The same formula has subsequently been found to describe steady-state input-output responses in many biological contexts, including single-molecule enzyme kinetics, gene regulation, transcription, translation, and force generation. Previous attempts to explain its ubiquity have been limited to networks with regular structure or simplifying parametric assumptions. Here, we exploit the graph-based linear framework for timescale separation to derive general structural conditions under which the MM formula arises. The conditions require a partition of the graph into two parts, akin to a "coarse graining" into the original MM graph, and constraints on where and how the input variable occurs. Other features of the graph, including the numerical values of parameters, can remain arbitrary, thereby explaining the formula's ubiquity. For systems at thermodynamic equilibrium, we derive a necessary and sufficient condition. For systems away from thermodynamic equilibrium, especially those with irreversible reactions, distinct structural conditions arise and a general characterization remains open. Nevertheless, our results accommodate, in much greater generality, all examples known to us in the literature.

How many human proteoforms are there?

Despite decades of accumulated knowledge about proteins and their post-translational modifications (PTMs), numerous questions remain regarding their molecular composition and biological function. One of the most fundamental queries is the extent to which the combinations of DNA-, RNA- and PTM-level variations explode the complexity of the human proteome. Here, we outline what we know from current databases and measurement strategies including mass spectrometry-based proteomics. In doing so, we examine prevailing notions about the number of modifications displayed on human proteins and how they combine to generate the protein diversity underlying health and disease. We frame central issues regarding determination of protein-level variation and PTMs, including some paradoxes present in the field today. We use this framework to assess existing data and to ask the question, "How many distinct primary structures of proteins (proteoforms) are created from the 20,300 human genes?" We also explore prospects for improving measurements to better regularize protein-level biology and efficiently associate PTMs to function and phenotype.

Lack of evidence for substrate channeling or flux between wildtype and mutant isocitrate dehydrogenase to produce the oncometabolite 2-hydroxyglutarate.

Monoallelic point mutations in the gene encoding the cytosolic, NADP+-dependent enzyme isocitrate dehydrogenase 1 (IDH1) cause increased production of the oncometabolite 2-hydroxyglutarate (2-HG) in multiple cancers. Most IDH1 mutant tumors retain one wildtype (WT) IDH1 allele. Several studies have proposed that retention of this WT allele is protumorigenic by facilitating substrate channeling through a WT-mutant IDH1 heterodimer, with the WT subunit generating a local supply of α-ketoglutarate and NADPH that is then consumed by the mutant subunit to produce 2-HG. Here, we confirmed that coexpression of WT and mutant IDH1 subunits leads to formation of WT-mutant hetero-oligomers and increases 2-HG production. An analysis of a recently reported crystal structure of the WT-R132H IDH1 heterodimer and of in vitro kinetic parameters for 2-HG production, however, indicated that substrate channeling between the subunits is biophysically implausible. We also found that putative carbon-substrate flux between WT and mutant IDH1 subunits is inconsistent with the results of isotope tracing experiments in cancer cells harboring an endogenous monoallelic IDH1 mutation. Finally, using a mathematical model of WT-mutant IDH1 heterodimers, we estimated that the NADPH:NADP+ ratio is higher in the cytosol than in the mitochondria, suggesting that NADPH is unlikely to be limiting for 2-HG production in the cytosol. These findings argue against supply of either substrate being limiting for 2-HG production by a cytosolic IDH1 mutant and suggest that the retention of a WT allele in IDH1 mutant tumors is not due to a requirement for carbon or cofactor flux between WT and mutant IDH1.

Monostationarity and Multistationarity in Tree Networks of Goldbeter-Koshland Loops.

A major challenge in systems biology is to elicit general properties in the face of molecular complexity. Here, we introduce a class of enzyme-catalysed biochemical networks and examine how the existence of a single positive steady state (monostationarity) depends on the network structure, enzyme mechanisms, kinetic rate laws and parameter values. We consider Goldbeter-Koshland (GK) covalent modification loops arranged in a tree network, so that a substrate form in one loop can be an enzyme in another loop. GK loops are a canonical motif in cell signalling and trees offer a generalisation of linear cascades which accommodate network complexity while remaining mathematically tractable. In particular, they permit a modular, recursive proof strategy which may be more widely applicable. We show that if each enzyme follows its own complex reaction mechanism under mass action kinetics, then any network is monostationary for all appropriate parameter values. If the kinetics is non-mass action with a plausible monotonicity requirement, and each enzyme follows the Michaelis-Menten mechanism, then monostationarity is preserved. Surprisingly, a single GK loop with a complex enzyme mechanism under non-mass action monotone kinetics can have more than one positive steady state (multistationarity). The broader interplay between network structure, enzyme mechanism and kinetics remains an intriguing open problem.

Estimating the Distribution of Protein Post-Translational Modification States by Mass Spectrometry.

Post-translational modifications (PTMs) of proteins play a central role in cellular information encoding, but the complexity of PTM state has been challenging to unravel. A single molecule can exhibit a "modform" or combinatorial pattern of co-occurring PTMs across multiple sites, and a molecular population can exhibit a distribution of amounts of different modforms. How can this "modform distribution" be estimated by mass spectrometry (MS)? Bottom-up MS, based on cleavage into peptides, destroys correlations between PTMs on different peptides, but it is conceivable that multiple proteases with appropriate patterns of cleavage could reconstruct the modform distribution. We introduce a mathematical language for describing MS measurements and show, on the contrary, that no matter how many distinct proteases are available, the shortfall in information required for reconstruction worsens exponentially with increasing numbers of sites. Whereas top-down MS on intact proteins can do better, current technology cannot prevent the exponential worsening. However, our analysis also shows that all forms of MS yield linear equations for modform amounts. This permits different MS protocols to be integrated and the modform distribution to be constrained within a high-dimensional "modform region", which may offer a feasible proxy for analyzing information encoding.

Characterization of Neuronal Tau Protein as a Target of Extracellular Signal-regulated Kinase.

Tau neuronal protein has a central role in neurodegeneration and is implicated in Alzheimer disease development. Abnormal phosphorylation of Tau impairs its interaction with other proteins and is associated with its dysregulation in pathological conditions. Molecular mechanisms leading to hyperphosphorylation of Tau in pathological conditions are unknown. Here, we characterize phosphorylation of Tau by extracellular-regulated kinase (ERK2), a mitogen-activated kinase (MAPK) that responds to extracellular signals. Analysis ofin vitrophosphorylated Tau by activated recombinant ERK2 with nuclear magnetic resonance spectroscopy (NMR) reveals phosphorylation of 15 Ser/Thr sites.In vitrophosphorylation of Tau using rat brain extract and subsequent NMR analysis identifies the same sites. Phosphorylation with rat brain extract is known to transform Tau into an Alzheimer disease-like state. Our results indicate that phosphorylation of Tau by ERK2 alone is sufficient to produce the same characteristics. We further investigate the mechanism of ERK2 phosphorylation of Tau. Kinases are known to recognize their protein substrates not only by their specificity for a targeted Ser or Thr phosphorylation site but also by binding to linear-peptide motifs called docking sites. We identify two main ERK2 docking sites in Tau sequence using NMR. Our results suggest that ERK2 dysregulation in Alzheimer disease could lead to abnormal phosphorylation of Tau resulting in the pathology of the disease.

Cellular Interrogation: Exploiting Cell-to-Cell Variability to Discriminate Regulatory Mechanisms in Oscillatory Signalling.

The molecular complexity within a cell may be seen as an evolutionary response to the external complexity of the cell's environment. This suggests that the external environment may be harnessed to interrogate the cell's internal molecular architecture. Cells, however, are not only nonlinear and non-stationary, but also exhibit heterogeneous responses within a clonal, isogenic population. In effect, each cell undertakes its own experiment. Here, we develop a method of cellular interrogation using programmable microfluidic devices which exploits the additional information present in cell-to-cell variation, without requiring model parameters to be fitted to data. We focussed on Ca2+ signalling in response to hormone stimulation, which exhibits oscillatory spiking in many cell types and chose eight models of Ca2+ signalling networks which exhibit similar behaviour in simulation. We developed a nonlinear frequency analysis for non-stationary responses, which could classify models into groups under parameter variation, but found that this question alone was unable to distinguish critical feedback loops. We further developed a nonlinear amplitude analysis and found that the combination of both questions ruled out six of the models as inconsistent with the experimentally-observed dynamics and heterogeneity. The two models that survived the double interrogation were mathematically different but schematically identical and yielded the same unexpected predictions that we confirmed experimentally. Further analysis showed that subtle mathematical details can markedly influence non-stationary responses under parameter variation, emphasising the difficulty of finding a "correct" model. By developing questions for the pathway being studied, and designing more versatile microfluidics, cellular interrogation holds promise as a systematic strategy that can complement direct intervention by genetics or pharmacology.

A fundamental trade-off in covalent switching and its circumvention by enzyme bifunctionality in glucose homeostasis.

Covalent modification provides a mechanism for modulating molecular state and regulating physiology. A cycle of competing enzymes that add and remove a single modification can act as a molecular switch between "on" and "off" and has been widely studied as a core motif in systems biology. Here, we exploit the recently developed "linear framework" for time scale separation to determine the general principles of such switches. These methods are not limited to Michaelis-Menten assumptions, and our conclusions hold for enzymes whose mechanisms may be arbitrarily complicated. We show that switching efficiency improves with increasing irreversibility of the enzymes and that the on/off transition occurs when the ratio of enzyme levels reaches a value that depends only on the rate constants. Fluctuations in enzyme levels, which habitually occur due to cellular heterogeneity, can cause flipping back and forth between on and off, leading to incoherent mosaic behavior in tissues, that worsens as switching becomes sharper. This trade-off can be circumvented if enzyme levels are correlated. In particular, if the competing catalytic domains are on the same protein but do not influence each other, the resulting bifunctional enzyme can switch sharply while remaining coherent. In the mammalian liver, the switch between glycolysis and gluconeogenesis is regulated by the bifunctional 6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase (PFK-2/FBPase-2). We suggest that bifunctionality of PFK-2/FBPase-2 complements the metabolic zonation of the liver by ensuring coherent switching in response to insulin and glucagon.

Unlimited multistability in multisite phosphorylation systems.

Reversible phosphorylation on serine, threonine and tyrosine is the most widely studied posttranslational modification of proteins. The number of phosphorylated sites on a protein (n) shows a significant increase from prokaryotes, with n /= 150 sites. Multisite phosphorylation has many roles and site conservation indicates that increasing numbers of sites cannot be due merely to promiscuous phosphorylation. A substrate with n sites has an exponential number (2(n)) of phospho-forms and individual phospho-forms may have distinct biological effects. The distribution of these phospho-forms and how this distribution is regulated have remained unknown. Here we show that, when kinase and phosphatase act in opposition on a multisite substrate, the system can exhibit distinct stable phospho-form distributions at steady state and that the maximum number of such distributions increases with n. Whereas some stable distributions are focused on a single phospho-form, others are more diffuse, giving the phospho-proteome the potential to behave as a fluid regulatory network able to encode information and flexibly respond to varying demands. Such plasticity may underlie complex information processing in eukaryotic cells and suggests a functional advantage in having many sites. Our results follow from the unusual geometry of the steady-state phospho-form concentrations, which we show to constitute a rational algebraic curve, irrespective of n. We thereby reduce the complexity of calculating steady states from simulating 3 x 2(n) differential equations to solving two algebraic equations, while treating parameters symbolically. We anticipate that these methods can be extended to systems with multiple substrates and multiple enzymes catalysing different modifications, as found in posttranslational modification 'codes' such as the histone code. Whereas simulations struggle with exponentially increasing molecular complexity, mathematical methods of the kind developed here can provide a new language in which to articulate the principles of cellular information processing.

Models in biology: 'accurate descriptions of our pathetic thinking'.

In this essay I will sketch some ideas for how to think about models in biology. I will begin by trying to dispel the myth that quantitative modeling is somehow foreign to biology. I will then point out the distinction between forward and reverse modeling and focus thereafter on the former. Instead of going into mathematical technicalities about different varieties of models, I will focus on their logical structure, in terms of assumptions and conclusions. A model is a logical machine for deducing the latter from the former. If the model is correct, then, if you believe its assumptions, you must, as a matter of logic, also believe its conclusions. This leads to consideration of the assumptions underlying models. If these are based on fundamental physical laws, then it may be reasonable to treat the model as 'predictive', in the sense that it is not subject to falsification and we can rely on its conclusions. However, at the molecular level, models are more often derived from phenomenology and guesswork. In this case, the model is a test of its assumptions and must be falsifiable. I will discuss three models from this perspective, each of which yields biological insights, and this will lead to some guidelines for prospective model builders.

A framework for modelling gene regulation which accommodates non-equilibrium mechanisms.

BACKGROUND: Gene regulation has, for the most part, been quantitatively analysed by assuming that regulatory mechanisms operate at thermodynamic equilibrium. This formalism was originally developed to analyse the binding and unbinding of transcription factors from naked DNA in eubacteria. Although widely used, it has made it difficult to understand the role of energy-dissipating, epigenetic mechanisms, such as DNA methylation, nucleosome remodelling and post-translational modification of histones and co-regulators, which act together with transcription factors to regulate gene expression in eukaryotes. RESULTS: Here, we introduce a graph-based framework that can accommodate non-equilibrium mechanisms. A gene-regulatory system is described as a graph, which specifies the DNA microstates (vertices), the transitions between microstates (edges) and the transition rates (edge labels). The graph yields a stochastic master equation for how microstate probabilities change over time. We show that this framework has broad scope by providing new insights into three very different ad hoc models, of steroid-hormone responsive genes, of inherently bounded chromatin domains and of the yeast PHO5 gene. We find, moreover, surprising complexity in the regulation of PHO5, which has not yet been experimentally explored, and we show that this complexity is an inherent feature of being away from equilibrium. At equilibrium, microstate probabilities do not depend on how a microstate is reached but, away from equilibrium, each path to a microstate can contribute to its steady-state probability. Systems that are far from equilibrium thereby become dependent on history and the resulting complexity is a fundamental challenge. To begin addressing this, we introduce a graph-based concept of independence, which can be applied to sub-systems that are far from equilibrium, and prove that history-dependent complexity can be circumvented when sub-systems operate independently. CONCLUSIONS: As epigenomic data become increasingly available, we anticipate that gene function will come to be represented by graphs, as gene structure has been represented by sequences, and that the methods introduced here will provide a broader foundation for understanding how genes work.

Paradoxical results in perturbation-based signaling network reconstruction.

Mathematical models are extensively employed to understand physicochemical processes in biological systems. In the absence of detailed mechanistic knowledge, models are often based on network inference methods, which in turn rely upon perturbations to nodes by biochemical means. We have discovered a potential pitfall of the approach underpinning such methods when applied to signaling networks. We first show experimentally, and then explain mathematically, how even in the simplest signaling systems, perturbation methods may lead to paradoxical conclusions: for any given pair of two components X and Y, and depending upon the specific intervention on Y, either an activation or a repression of X could be inferred. This effect is of a different nature from incomplete network identification due to underdetermined data and is a phenomenon intrinsic to perturbations. Our experiments are performed in an in vitro minimal system, thus isolating the effect and showing that it cannot be explained by feedbacks due to unknown intermediates. Moreover, our in vitro system utilizes proteins from a pathway in mammalian (and other eukaryotic) cells that play a central role in proliferation, gene expression, differentiation, mitosis, cell survival, and apoptosis. This pathway is the perturbation target of contemporary therapies for various types of cancers. The results presented here show that the simplistic view of intracellular signaling networks being made up of activation and repression links is seriously misleading, and call for a fundamental rethinking of signaling network analysis and inference methods.

Dimerization and bifunctionality confer robustness to the isocitrate dehydrogenase regulatory system in Escherichia coli.

An important goal of systems biology is to develop quantitative models that explain how specific molecular features give rise to systems-level properties. Metabolic and regulatory pathways that contain multifunctional proteins are especially interesting to study from this perspective because they have frequently been observed to exhibit robustness: the ability for a system to perform its proper function even as levels of its components change. In this study, we use extensive biochemical data and algebraic modeling to develop and analyze a model that shows how robust behavior arises in the isocitrate dehydrogenase (IDH) regulatory system of Escherichia coli, which was shown in 1985 to experimentally exhibit robustness. E. coli IDH is regulated by reversible phosphorylation catalyzed by the bifunctional isocitrate dehydrogenase kinase/phosphatase (IDHKP), and the level of IDH activity determines whether carbon flux is directed through the glyoxylate bypass (for growth on two-carbon substrates) or the full tricarboxylic acid cycle. Our model, which incorporates recent structural data on IDHKP, identifies several specific biochemical features of the system (including homodimerization of IDH and bifunctionality of IDHKP) that provide a potential explanation for robustness. Using algebraic techniques, we derive an invariant that summarizes the steady-state relationship between the phospho-forms of IDH. We use the invariant in combination with kinetic data on IDHKP to calculate IDH activity at a range of total IDH levels and find that our model predicts robustness. Our work unifies much of the known biochemistry of the IDH regulatory system into a single quantitative framework and highlights the importance of constructing biochemically realistic models in systems biology.

The Hill function is the universal Hopfield barrier for sharpness of input-output responses.

The Hill functions, ℋh(x)=xh/1+xh, have been widely used in biology for over a century but, with the exception of ℋ1, they have had no justification other than as a convenient fit to empirical data. Here, we show that they are the universal limit for the sharpness of any input-output response arising from a Markov process model at thermodynamic equilibrium. Models may represent arbitrary molecular complexity, with multiple ligands, internal states, conformations, co-regulators, etc, under core assumptions that are detailed in the paper. The model output may be any linear combination of steady-state probabilities, with components other than the chosen input ligand held constant. This formulation generalises most of the responses in the literature. We use a coarse-graining method in the graph-theoretic linear framework to show that two sharpness measures for input-output responses fall within an effectively bounded region of the positive quadrant, Ωm⊂ℝ+2, for any equilibrium model with m input binding sites. Ωm exhibits a cusp which approaches, but never exceeds, the sharpness of ℋm but the region and the cusp can be exceeded when models are taken away from thermodynamic equilibrium. Such fundamental thermodynamic limits are called Hopfield barriers and our results provide a biophysical justification for the Hill functions as the universal Hopfield barriers for sharpness. Our results also introduce an object, Ωm, whose structure may be of mathematical interest, and suggest the importance of characterising Hopfield barriers for other forms of cellular information processing.

Emergence of activation or repression in transcriptional control under a fixed molecular context.

For decades, studies have noted that transcription factors (TFs) can behave as either activators or repressors of different target genes. More recently, evidence suggests TFs can act on transcription simultaneously in positive and negative ways. Here we use biophysical models of gene regulation to define, conceptualize and explore these two aspects of TF action: "duality", where TFs can be overall both activators and repressors at the level of the transcriptional response, and "coherent and incoherent" modes of regulation, where TFs act mechanistically on a given target gene either as an activator or a repressor (coherent) or as both (incoherent). For incoherent TFs, the overall response depends on three kinds of features: the TF's mechanistic effects, the dynamics and effects of additional regulatory molecules or the transcriptional machinery, and the occupancy of the TF on DNA. Therefore, activation or repression can be tuned by just the TF-DNA binding affinity, or the number of TF binding sites, given an otherwise fixed molecular context. Moreover, incoherent TFs can cause non-monotonic transcriptional responses, increasing over a certain concentration range and decreasing outside the range, and we clarify the relationship between non-monotonicity and common assumptions of gene regulation models. Using the mammalian SP1 as a case study and well controlled, synthetically designed target sequences, we find experimental evidence for incoherent action and activation, repression or non-monotonicity tuned by affinity. Our work highlights the importance of moving from a TF-centric view to a systems view when reasoning about transcriptional control.