Provided herein are molecular analog gene circuits that exploit positive and negative feedback to implement logarithmically linear sensing, addition, subtraction, and scaling thus enabling multiplicative, ratiometric, and power-law computations. The circuits exhibit Weber's Law behavior as in natural biological systems, operate over a wide dynamic range of up to four orders of magnitude, and can be architected to have tunable transfer functions. The molecular circuits described herein can be composed together to implement higher-order functions that are well-described by both intricate biochemical models and by simple mathematical functions. The molecular circuits described herein enable logarithmically linear analog computation within in-vitro and in-vivo systems with a broad class of molecules, all of which obey the Boltzmann exponential equations of thermodynamics that govern molecular association, attenuation, transformation, and degradation.
Please help me write a proper abstract based on the patent claims. CLAIM: 2. A graded positive-feedback molecular circuit comprising a. an input association block comprising molecular species Min, and Mout′ as inputs and that outputs molecular species C, wherein the input association block may have an adjustable input association strength; and b. a control block comprising one or more of an association, attenuation, transformation, or degradation block, wherein the output C of the input block is converted to a molecular species C′ as an output, wherein the association, attenuation, transformation and degradation strengths of the respective association, attenuation, transformation or degradation blocks may have adjustable strengths; and c. an output transformation block comprising molecular species C′ of the control block as an input that is converted to Mout as an output, wherein the output transformation strength may be adjusted; and d. a feedback block comprising one or more of an association, attenuation, transformation, or degradation block, wherein the molecular species Mout of the output transformation block is converted to Mout′ as an output, and wherein the association, attenuation, transformation, and degradation strengths of the respective association, attenuation, transformation, and degradation blocks may be adjusted; and wherein signs of the functional derivatives of the blocks in the feedback circuit are configured such that small changes in at least one molecular species in the feedback loop, for example, C, return as further changes in C that increase the initial change in C, thus creating a positive-feedback loop. 3-23. (canceled)